Automotive Math and Motor Control Library Set for NXP MPC560xB devices

Automotive Math and Motor Control
Library Set for NXP MPC560xB
devices
User's Guide
Document Number: MPC560XBMCLUG
Rev. 7
Automotive Math and Motor Control Library Set for NXP MPC560xB devices, Rev. 7
2
NXP Semiconductors
Contents
Section number
Title
Page
Chapter 1
Revision History
Chapter 2
2.1
ATTACHMENT A - NXP Automotive Software License Agreement v1.3................................................................ 67
Chapter 3
Introduction
3.1
Architecture Overview..................................................................................................................................................77
3.2
General Information......................................................................................................................................................78
3.3
Multiple Implementation Support.................................................................................................................................79
3.3.1
Global Configuration Option......................................................................................................................... 80
3.3.2
Additional Parameter Option......................................................................................................................... 81
3.3.3
API Postfix Option.........................................................................................................................................81
3.4
Supported Compilers.................................................................................................................................................... 82
3.5
Matlab Integration.........................................................................................................................................................83
3.6
Installation.....................................................................................................................................................................84
3.7
Library File Structure....................................................................................................................................................87
3.8
Integration Assumption.................................................................................................................................................89
3.9
Library Integration into a Green Hills Multi Development Environment.................................................................... 89
3.10
Library Integration into a Wind River Compiler Environment.................................................................................... 93
3.11
Library Integration into a Freescale CodeWarrior Eclipse IDE................................................................................... 96
3.12
Library Integration into a S32 Design Studio for Power Architecture IDE................................................................. 99
3.13
Library Testing..............................................................................................................................................................102
3.14
3.13.1
AMMCLIB Testing based on the MATLAB Simulink Toolbox.................................................................. 103
3.13.2
AMMCLIB target-in-loop Testing based on the SFIO Toolbox................................................................... 105
Functions Precision.......................................................................................................................................................106
Chapter 4
4.1
Function Index.............................................................................................................................................................. 109
Automotive Math and Motor Control Library Set for NXP MPC560xB devices, Rev. 7
NXP Semiconductors
3
Section number
Title
Page
Chapter 5
API References
5.1
5.2
5.3
5.4
Function GDFLIB_FilterFIRInit_F32.......................................................................................................................... 117
5.1.1
Declaration..................................................................................................................................................... 117
5.1.2
Arguments...................................................................................................................................................... 117
5.1.3
Return.............................................................................................................................................................117
5.1.4
Description..................................................................................................................................................... 118
5.1.5
Re-entrancy.................................................................................................................................................... 118
5.1.6
Code Example................................................................................................................................................ 118
Function GDFLIB_FilterFIR_F32................................................................................................................................120
5.2.1
Declaration..................................................................................................................................................... 120
5.2.2
Arguments...................................................................................................................................................... 120
5.2.3
Return.............................................................................................................................................................120
5.2.4
Description..................................................................................................................................................... 121
5.2.5
Re-entrancy.................................................................................................................................................... 122
5.2.6
Code Example................................................................................................................................................ 122
Function GDFLIB_FilterFIRInit_F16.......................................................................................................................... 124
5.3.1
Declaration..................................................................................................................................................... 124
5.3.2
Arguments...................................................................................................................................................... 124
5.3.3
Return.............................................................................................................................................................124
5.3.4
Description..................................................................................................................................................... 124
5.3.5
Re-entrancy.................................................................................................................................................... 125
5.3.6
Code Example................................................................................................................................................ 125
Function GDFLIB_FilterFIR_F16................................................................................................................................127
5.4.1
Declaration..................................................................................................................................................... 127
5.4.2
Arguments...................................................................................................................................................... 127
5.4.3
Return.............................................................................................................................................................127
5.4.4
Description..................................................................................................................................................... 127
5.4.5
Re-entrancy.................................................................................................................................................... 128
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Section number
5.4.6
5.5
5.6
5.7
5.8
Title
Page
Code Example................................................................................................................................................ 129
Function GDFLIB_FilterIIR1Init_F32......................................................................................................................... 130
5.5.1
Declaration..................................................................................................................................................... 130
5.5.2
Arguments...................................................................................................................................................... 130
5.5.3
Return.............................................................................................................................................................131
5.5.4
Description..................................................................................................................................................... 131
5.5.5
Re-entrancy.................................................................................................................................................... 131
5.5.6
Code Example................................................................................................................................................ 131
Function GDFLIB_FilterIIR1_F32...............................................................................................................................132
5.6.1
Declaration..................................................................................................................................................... 132
5.6.2
Arguments...................................................................................................................................................... 132
5.6.3
Return.............................................................................................................................................................132
5.6.4
Description..................................................................................................................................................... 132
5.6.5
Re-entrancy.................................................................................................................................................... 134
5.6.6
Code Example................................................................................................................................................ 134
Function GDFLIB_FilterIIR1Init_F16......................................................................................................................... 135
5.7.1
Declaration..................................................................................................................................................... 135
5.7.2
Arguments...................................................................................................................................................... 135
5.7.3
Return.............................................................................................................................................................136
5.7.4
Description..................................................................................................................................................... 136
5.7.5
Re-entrancy.................................................................................................................................................... 136
5.7.6
Code Example................................................................................................................................................ 136
Function GDFLIB_FilterIIR1_F16...............................................................................................................................137
5.8.1
Declaration..................................................................................................................................................... 137
5.8.2
Arguments...................................................................................................................................................... 137
5.8.3
Return.............................................................................................................................................................137
5.8.4
Description..................................................................................................................................................... 137
5.8.5
Re-entrancy.................................................................................................................................................... 139
5.8.6
Code Example................................................................................................................................................ 139
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Section number
5.9
5.10
5.11
5.12
5.13
Title
Page
Function GDFLIB_FilterIIR2Init_F32......................................................................................................................... 140
5.9.1
Declaration..................................................................................................................................................... 140
5.9.2
Arguments...................................................................................................................................................... 140
5.9.3
Return.............................................................................................................................................................141
5.9.4
Description..................................................................................................................................................... 141
5.9.5
Re-entrancy.................................................................................................................................................... 141
5.9.6
Code Example................................................................................................................................................ 141
Function GDFLIB_FilterIIR2_F32...............................................................................................................................142
5.10.1
Declaration..................................................................................................................................................... 142
5.10.2
Arguments...................................................................................................................................................... 142
5.10.3
Return.............................................................................................................................................................142
5.10.4
Description..................................................................................................................................................... 142
5.10.5
Re-entrancy.................................................................................................................................................... 145
5.10.6
Code Example................................................................................................................................................ 145
Function GDFLIB_FilterIIR2Init_F16......................................................................................................................... 145
5.11.1
Declaration..................................................................................................................................................... 146
5.11.2
Arguments...................................................................................................................................................... 146
5.11.3
Return.............................................................................................................................................................146
5.11.4
Description..................................................................................................................................................... 146
5.11.5
Re-entrancy.................................................................................................................................................... 146
5.11.6
Code Example................................................................................................................................................ 147
Function GDFLIB_FilterIIR2_F16...............................................................................................................................147
5.12.1
Declaration..................................................................................................................................................... 147
5.12.2
Arguments...................................................................................................................................................... 147
5.12.3
Return.............................................................................................................................................................147
5.12.4
Description..................................................................................................................................................... 148
5.12.5
Re-entrancy.................................................................................................................................................... 150
5.12.6
Code Example................................................................................................................................................ 150
Function GDFLIB_FilterMAInit_F32.......................................................................................................................... 151
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Section number
5.14
5.15
5.16
5.17
Title
Page
5.13.1
Declaration..................................................................................................................................................... 151
5.13.2
Arguments...................................................................................................................................................... 151
5.13.3
Return.............................................................................................................................................................151
5.13.4
Description..................................................................................................................................................... 151
5.13.5
Re-entrancy.................................................................................................................................................... 152
5.13.6
Code Example................................................................................................................................................ 152
Function GDFLIB_FilterMA_F32............................................................................................................................... 152
5.14.1
Declaration..................................................................................................................................................... 152
5.14.2
Arguments...................................................................................................................................................... 152
5.14.3
Return.............................................................................................................................................................153
5.14.4
Description..................................................................................................................................................... 153
5.14.5
Re-entrancy.................................................................................................................................................... 154
5.14.6
Code Example................................................................................................................................................ 154
Function GDFLIB_FilterMAInit_F16.......................................................................................................................... 155
5.15.1
Declaration..................................................................................................................................................... 155
5.15.2
Arguments...................................................................................................................................................... 155
5.15.3
Return.............................................................................................................................................................155
5.15.4
Description..................................................................................................................................................... 155
5.15.5
Re-entrancy.................................................................................................................................................... 156
5.15.6
Code Example................................................................................................................................................ 156
Function GDFLIB_FilterMA_F16............................................................................................................................... 156
5.16.1
Declaration..................................................................................................................................................... 156
5.16.2
Arguments...................................................................................................................................................... 156
5.16.3
Return.............................................................................................................................................................157
5.16.4
Description..................................................................................................................................................... 157
5.16.5
Re-entrancy.................................................................................................................................................... 158
5.16.6
Code Example................................................................................................................................................ 158
Function GFLIB_Acos_F32......................................................................................................................................... 159
5.17.1
Declaration..................................................................................................................................................... 159
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NXP Semiconductors
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Section number
5.18
5.19
5.20
5.21
Title
Page
5.17.2
Arguments...................................................................................................................................................... 159
5.17.3
Return.............................................................................................................................................................159
5.17.4
Description..................................................................................................................................................... 159
5.17.5
Re-entrancy.................................................................................................................................................... 163
5.17.6
Code Example................................................................................................................................................ 163
Function GFLIB_Acos_F16......................................................................................................................................... 163
5.18.1
Declaration..................................................................................................................................................... 164
5.18.2
Arguments...................................................................................................................................................... 164
5.18.3
Return.............................................................................................................................................................164
5.18.4
Description..................................................................................................................................................... 164
5.18.5
Re-entrancy.................................................................................................................................................... 168
5.18.6
Code Example................................................................................................................................................ 168
Function GFLIB_Asin_F32.......................................................................................................................................... 168
5.19.1
Declaration..................................................................................................................................................... 168
5.19.2
Arguments...................................................................................................................................................... 168
5.19.3
Return.............................................................................................................................................................169
5.19.4
Description..................................................................................................................................................... 169
5.19.5
Re-entrancy.................................................................................................................................................... 173
5.19.6
Code Example................................................................................................................................................ 173
Function GFLIB_Asin_F16.......................................................................................................................................... 173
5.20.1
Declaration..................................................................................................................................................... 173
5.20.2
Arguments...................................................................................................................................................... 174
5.20.3
Return.............................................................................................................................................................174
5.20.4
Description..................................................................................................................................................... 174
5.20.5
Re-entrancy.................................................................................................................................................... 178
5.20.6
Code Example................................................................................................................................................ 178
Function GFLIB_Atan_F32..........................................................................................................................................178
5.21.1
Declaration..................................................................................................................................................... 178
5.21.2
Arguments...................................................................................................................................................... 178
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Section number
5.22
5.23
5.24
5.25
Title
Page
5.21.3
Return.............................................................................................................................................................179
5.21.4
Description..................................................................................................................................................... 179
5.21.5
Re-entrancy.................................................................................................................................................... 182
5.21.6
Code Example................................................................................................................................................ 182
Function GFLIB_Atan_F16..........................................................................................................................................183
5.22.1
Declaration..................................................................................................................................................... 183
5.22.2
Arguments...................................................................................................................................................... 183
5.22.3
Return.............................................................................................................................................................183
5.22.4
Description..................................................................................................................................................... 183
5.22.5
Re-entrancy.................................................................................................................................................... 186
5.22.6
Code Example................................................................................................................................................ 186
Function GFLIB_AtanYX_F32.................................................................................................................................... 187
5.23.1
Declaration..................................................................................................................................................... 187
5.23.2
Arguments...................................................................................................................................................... 187
5.23.3
Return.............................................................................................................................................................187
5.23.4
Description..................................................................................................................................................... 187
5.23.5
Re-entrancy.................................................................................................................................................... 188
5.23.6
Code Example................................................................................................................................................ 188
Function GFLIB_AtanYX_F16.................................................................................................................................... 189
5.24.1
Declaration..................................................................................................................................................... 189
5.24.2
Arguments...................................................................................................................................................... 189
5.24.3
Return.............................................................................................................................................................189
5.24.4
Description..................................................................................................................................................... 189
5.24.5
Re-entrancy.................................................................................................................................................... 190
5.24.6
Code Example................................................................................................................................................ 190
Function GFLIB_AtanYXShifted_F32........................................................................................................................ 191
5.25.1
Declaration..................................................................................................................................................... 191
5.25.2
Arguments...................................................................................................................................................... 191
5.25.3
Return.............................................................................................................................................................192
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NXP Semiconductors
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Section number
5.26
5.27
5.28
5.29
Title
Page
5.25.4
Description..................................................................................................................................................... 192
5.25.5
Re-entrancy.................................................................................................................................................... 196
5.25.6
Code Example................................................................................................................................................ 196
Function GFLIB_AtanYXShifted_F16........................................................................................................................ 197
5.26.1
Declaration..................................................................................................................................................... 197
5.26.2
Arguments...................................................................................................................................................... 197
5.26.3
Return.............................................................................................................................................................197
5.26.4
Description..................................................................................................................................................... 197
5.26.5
Re-entrancy.................................................................................................................................................... 201
5.26.6
Code Example................................................................................................................................................ 201
Function GFLIB_ControllerPIp_F32........................................................................................................................... 202
5.27.1
Declaration..................................................................................................................................................... 202
5.27.2
Arguments...................................................................................................................................................... 203
5.27.3
Return.............................................................................................................................................................203
5.27.4
Description..................................................................................................................................................... 203
5.27.5
Re-entrancy.................................................................................................................................................... 206
5.27.6
Code Example................................................................................................................................................ 206
Function GFLIB_ControllerPIp_F16........................................................................................................................... 207
5.28.1
Declaration..................................................................................................................................................... 207
5.28.2
Arguments...................................................................................................................................................... 207
5.28.3
Return.............................................................................................................................................................207
5.28.4
Description..................................................................................................................................................... 208
5.28.5
Re-entrancy.................................................................................................................................................... 211
5.28.6
Code Example................................................................................................................................................ 211
Function GFLIB_ControllerPIpAW_F32.....................................................................................................................212
5.29.1
Declaration..................................................................................................................................................... 212
5.29.2
Arguments...................................................................................................................................................... 212
5.29.3
Return.............................................................................................................................................................212
5.29.4
Description..................................................................................................................................................... 212
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NXP Semiconductors
Section number
5.30
5.31
5.32
5.33
Title
Page
5.29.5
Re-entrancy.................................................................................................................................................... 216
5.29.6
Code Example................................................................................................................................................ 216
Function GFLIB_ControllerPIpAW_F16.....................................................................................................................217
5.30.1
Declaration..................................................................................................................................................... 217
5.30.2
Arguments...................................................................................................................................................... 217
5.30.3
Return.............................................................................................................................................................217
5.30.4
Description..................................................................................................................................................... 218
5.30.5
Re-entrancy.................................................................................................................................................... 221
5.30.6
Code Example................................................................................................................................................ 221
Function GFLIB_ControllerPIr_F32............................................................................................................................ 222
5.31.1
Declaration..................................................................................................................................................... 222
5.31.2
Arguments...................................................................................................................................................... 222
5.31.3
Return.............................................................................................................................................................223
5.31.4
Description..................................................................................................................................................... 223
5.31.5
Re-entrancy.................................................................................................................................................... 226
5.31.6
Code Example................................................................................................................................................ 226
Function GFLIB_ControllerPIr_F16............................................................................................................................ 227
5.32.1
Declaration..................................................................................................................................................... 227
5.32.2
Arguments...................................................................................................................................................... 227
5.32.3
Return.............................................................................................................................................................227
5.32.4
Description..................................................................................................................................................... 227
5.32.5
Re-entrancy.................................................................................................................................................... 231
5.32.6
Code Example................................................................................................................................................ 231
Function GFLIB_ControllerPIrAW_F32......................................................................................................................231
5.33.1
Declaration..................................................................................................................................................... 232
5.33.2
Arguments...................................................................................................................................................... 232
5.33.3
Return.............................................................................................................................................................232
5.33.4
Description..................................................................................................................................................... 232
5.33.5
Re-entrancy.................................................................................................................................................... 236
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NXP Semiconductors
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Section number
5.33.6
5.34
5.35
5.36
5.37
Title
Page
Code Example................................................................................................................................................ 236
Function GFLIB_ControllerPIrAW_F16......................................................................................................................237
5.34.1
Declaration..................................................................................................................................................... 237
5.34.2
Arguments...................................................................................................................................................... 237
5.34.3
Return.............................................................................................................................................................237
5.34.4
Description..................................................................................................................................................... 237
5.34.5
Re-entrancy.................................................................................................................................................... 241
5.34.6
Code Example................................................................................................................................................ 241
Function GFLIB_Cos_F32........................................................................................................................................... 242
5.35.1
Declaration..................................................................................................................................................... 242
5.35.2
Arguments...................................................................................................................................................... 242
5.35.3
Return.............................................................................................................................................................243
5.35.4
Description..................................................................................................................................................... 243
5.35.5
Re-entrancy.................................................................................................................................................... 247
5.35.6
Code Example................................................................................................................................................ 247
Function GFLIB_Cos_F16........................................................................................................................................... 247
5.36.1
Declaration..................................................................................................................................................... 247
5.36.2
Arguments...................................................................................................................................................... 247
5.36.3
Return.............................................................................................................................................................248
5.36.4
Description..................................................................................................................................................... 248
5.36.5
Re-entrancy.................................................................................................................................................... 252
5.36.6
Code Example................................................................................................................................................ 252
Function GFLIB_Hyst_F32.......................................................................................................................................... 252
5.37.1
Declaration..................................................................................................................................................... 252
5.37.2
Arguments...................................................................................................................................................... 252
5.37.3
Return.............................................................................................................................................................253
5.37.4
Description..................................................................................................................................................... 253
5.37.5
Re-entrancy.................................................................................................................................................... 254
5.37.6
Code Example................................................................................................................................................ 254
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NXP Semiconductors
Section number
5.38
5.39
5.40
5.41
5.42
Title
Page
Function GFLIB_Hyst_F16.......................................................................................................................................... 255
5.38.1
Declaration..................................................................................................................................................... 255
5.38.2
Arguments...................................................................................................................................................... 255
5.38.3
Return.............................................................................................................................................................255
5.38.4
Description..................................................................................................................................................... 256
5.38.5
Re-entrancy.................................................................................................................................................... 257
5.38.6
Code Example................................................................................................................................................ 257
Function GFLIB_IntegratorTR_F32.............................................................................................................................258
5.39.1
Declaration..................................................................................................................................................... 258
5.39.2
Arguments...................................................................................................................................................... 258
5.39.3
Return.............................................................................................................................................................258
5.39.4
Description..................................................................................................................................................... 258
5.39.5
Re-entrancy.................................................................................................................................................... 260
5.39.6
Code Example................................................................................................................................................ 260
Function GFLIB_IntegratorTR_F16.............................................................................................................................261
5.40.1
Declaration..................................................................................................................................................... 261
5.40.2
Arguments...................................................................................................................................................... 261
5.40.3
Return.............................................................................................................................................................261
5.40.4
Description..................................................................................................................................................... 262
5.40.5
Re-entrancy.................................................................................................................................................... 264
5.40.6
Code Example................................................................................................................................................ 264
Function GFLIB_Limit_F32.........................................................................................................................................264
5.41.1
Declaration..................................................................................................................................................... 264
5.41.2
Arguments...................................................................................................................................................... 265
5.41.3
Return.............................................................................................................................................................265
5.41.4
Description..................................................................................................................................................... 265
5.41.5
Re-entrancy.................................................................................................................................................... 265
5.41.6
Code Example................................................................................................................................................ 266
Function GFLIB_Limit_F16.........................................................................................................................................266
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Section number
5.43
5.44
5.45
5.46
Title
Page
5.42.1
Declaration..................................................................................................................................................... 266
5.42.2
Arguments...................................................................................................................................................... 266
5.42.3
Return.............................................................................................................................................................267
5.42.4
Description..................................................................................................................................................... 267
5.42.5
Re-entrancy.................................................................................................................................................... 267
5.42.6
Code Example................................................................................................................................................ 267
Function GFLIB_LowerLimit_F32.............................................................................................................................. 268
5.43.1
Declaration..................................................................................................................................................... 268
5.43.2
Arguments...................................................................................................................................................... 268
5.43.3
Return.............................................................................................................................................................269
5.43.4
Description..................................................................................................................................................... 269
5.43.5
Re-entrancy.................................................................................................................................................... 269
5.43.6
Code Example................................................................................................................................................ 269
Function GFLIB_LowerLimit_F16.............................................................................................................................. 270
5.44.1
Declaration..................................................................................................................................................... 270
5.44.2
Arguments...................................................................................................................................................... 270
5.44.3
Return.............................................................................................................................................................270
5.44.4
Description..................................................................................................................................................... 270
5.44.5
Re-entrancy.................................................................................................................................................... 271
5.44.6
Code Example................................................................................................................................................ 271
Function GFLIB_Lut1D_F32....................................................................................................................................... 271
5.45.1
Declaration..................................................................................................................................................... 271
5.45.2
Arguments...................................................................................................................................................... 272
5.45.3
Return.............................................................................................................................................................272
5.45.4
Description..................................................................................................................................................... 272
5.45.5
Re-entrancy.................................................................................................................................................... 275
5.45.6
Code Example................................................................................................................................................ 275
Function GFLIB_Lut1D_F16....................................................................................................................................... 277
5.46.1
Declaration..................................................................................................................................................... 277
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Section number
5.47
5.48
5.49
5.50
Title
Page
5.46.2
Arguments...................................................................................................................................................... 277
5.46.3
Return.............................................................................................................................................................277
5.46.4
Description..................................................................................................................................................... 277
5.46.5
Re-entrancy.................................................................................................................................................... 280
5.46.6
Code Example................................................................................................................................................ 281
Function GFLIB_Lut2D_F32....................................................................................................................................... 282
5.47.1
Declaration..................................................................................................................................................... 282
5.47.2
Arguments...................................................................................................................................................... 282
5.47.3
Return.............................................................................................................................................................282
5.47.4
Description..................................................................................................................................................... 282
5.47.5
Re-entrancy.................................................................................................................................................... 288
5.47.6
Code Example................................................................................................................................................ 288
Function GFLIB_Lut2D_F16....................................................................................................................................... 289
5.48.1
Declaration..................................................................................................................................................... 289
5.48.2
Arguments...................................................................................................................................................... 289
5.48.3
Return.............................................................................................................................................................290
5.48.4
Description..................................................................................................................................................... 290
5.48.5
Re-entrancy.................................................................................................................................................... 295
5.48.6
Code Example................................................................................................................................................ 295
Function GFLIB_Ramp_F32........................................................................................................................................ 297
5.49.1
Declaration..................................................................................................................................................... 297
5.49.2
Arguments...................................................................................................................................................... 297
5.49.3
Return.............................................................................................................................................................297
5.49.4
Description..................................................................................................................................................... 297
5.49.5
Re-entrancy.................................................................................................................................................... 298
5.49.6
Code Example................................................................................................................................................ 298
Function GFLIB_Ramp_F16........................................................................................................................................ 299
5.50.1
Declaration..................................................................................................................................................... 299
5.50.2
Arguments...................................................................................................................................................... 299
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Section number
5.51
5.52
5.53
5.54
Title
Page
5.50.3
Return.............................................................................................................................................................299
5.50.4
Description..................................................................................................................................................... 299
5.50.5
Re-entrancy.................................................................................................................................................... 300
5.50.6
Code Example................................................................................................................................................ 301
Function GFLIB_Sign_F32.......................................................................................................................................... 301
5.51.1
Declaration..................................................................................................................................................... 301
5.51.2
Arguments...................................................................................................................................................... 301
5.51.3
Return.............................................................................................................................................................302
5.51.4
Description..................................................................................................................................................... 302
5.51.5
Re-entrancy.................................................................................................................................................... 302
5.51.6
Code Example................................................................................................................................................ 302
Function GFLIB_Sign_F16.......................................................................................................................................... 303
5.52.1
Declaration..................................................................................................................................................... 303
5.52.2
Arguments...................................................................................................................................................... 303
5.52.3
Return.............................................................................................................................................................303
5.52.4
Description..................................................................................................................................................... 303
5.52.5
Re-entrancy.................................................................................................................................................... 304
5.52.6
Code Example................................................................................................................................................ 304
Function GFLIB_Sin_F32............................................................................................................................................ 305
5.53.1
Declaration..................................................................................................................................................... 305
5.53.2
Arguments...................................................................................................................................................... 305
5.53.3
Return.............................................................................................................................................................305
5.53.4
Description..................................................................................................................................................... 305
5.53.5
Re-entrancy.................................................................................................................................................... 309
5.53.6
Code Example................................................................................................................................................ 309
Function GFLIB_Sin_F16............................................................................................................................................ 309
5.54.1
Declaration..................................................................................................................................................... 309
5.54.2
Arguments...................................................................................................................................................... 309
5.54.3
Return.............................................................................................................................................................310
Automotive Math and Motor Control Library Set for NXP MPC560xB devices, Rev. 7
16
NXP Semiconductors
Section number
5.55
5.56
5.57
5.58
Title
Page
5.54.4
Description..................................................................................................................................................... 310
5.54.5
Re-entrancy.................................................................................................................................................... 313
5.54.6
Code Example................................................................................................................................................ 313
Function GFLIB_SinCos_F32...................................................................................................................................... 314
5.55.1
Declaration..................................................................................................................................................... 314
5.55.2
Arguments...................................................................................................................................................... 314
5.55.3
Return.............................................................................................................................................................314
5.55.4
Description..................................................................................................................................................... 314
5.55.5
Re-entrancy.................................................................................................................................................... 319
5.55.6
Code Example................................................................................................................................................ 319
Function GFLIB_SinCos_F16...................................................................................................................................... 319
5.56.1
Declaration..................................................................................................................................................... 320
5.56.2
Arguments...................................................................................................................................................... 320
5.56.3
Return.............................................................................................................................................................320
5.56.4
Description..................................................................................................................................................... 320
5.56.5
Re-entrancy.................................................................................................................................................... 324
5.56.6
Code Example................................................................................................................................................ 324
Function GFLIB_Sqrt_F32...........................................................................................................................................325
5.57.1
Declaration..................................................................................................................................................... 325
5.57.2
Arguments...................................................................................................................................................... 325
5.57.3
Return.............................................................................................................................................................325
5.57.4
Description..................................................................................................................................................... 325
5.57.5
Re-entrancy.................................................................................................................................................... 326
5.57.6
Code Example................................................................................................................................................ 326
Function GFLIB_Sqrt_F16...........................................................................................................................................327
5.58.1
Declaration..................................................................................................................................................... 327
5.58.2
Arguments...................................................................................................................................................... 327
5.58.3
Return.............................................................................................................................................................327
5.58.4
Description..................................................................................................................................................... 328
Automotive Math and Motor Control Library Set for NXP MPC560xB devices, Rev. 7
NXP Semiconductors
17
Section number
5.59
5.60
5.61
5.62
Title
Page
5.58.5
Re-entrancy.................................................................................................................................................... 328
5.58.6
Code Example................................................................................................................................................ 328
Function GFLIB_Tan_F32........................................................................................................................................... 329
5.59.1
Declaration..................................................................................................................................................... 329
5.59.2
Arguments...................................................................................................................................................... 329
5.59.3
Return.............................................................................................................................................................329
5.59.4
Description..................................................................................................................................................... 330
5.59.5
Re-entrancy.................................................................................................................................................... 333
5.59.6
Code Example................................................................................................................................................ 333
Function GFLIB_Tan_F16........................................................................................................................................... 334
5.60.1
Declaration..................................................................................................................................................... 334
5.60.2
Arguments...................................................................................................................................................... 334
5.60.3
Return.............................................................................................................................................................334
5.60.4
Description..................................................................................................................................................... 334
5.60.5
Re-entrancy.................................................................................................................................................... 338
5.60.6
Code Example................................................................................................................................................ 338
Function GFLIB_UpperLimit_F32...............................................................................................................................338
5.61.1
Declaration..................................................................................................................................................... 338
5.61.2
Arguments...................................................................................................................................................... 339
5.61.3
Return.............................................................................................................................................................339
5.61.4
Description..................................................................................................................................................... 339
5.61.5
Re-entrancy.................................................................................................................................................... 339
5.61.6
Code Example................................................................................................................................................ 339
Function GFLIB_UpperLimit_F16...............................................................................................................................340
5.62.1
Declaration..................................................................................................................................................... 340
5.62.2
Arguments...................................................................................................................................................... 340
5.62.3
Return.............................................................................................................................................................340
5.62.4
Description..................................................................................................................................................... 341
5.62.5
Re-entrancy.................................................................................................................................................... 341
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18
NXP Semiconductors
Section number
5.62.6
5.63
5.64
5.65
5.66
Title
Page
Code Example................................................................................................................................................ 341
Function GFLIB_VectorLimit_F32..............................................................................................................................342
5.63.1
Declaration..................................................................................................................................................... 342
5.63.2
Arguments...................................................................................................................................................... 342
5.63.3
Return.............................................................................................................................................................342
5.63.4
Description..................................................................................................................................................... 342
5.63.5
Re-entrancy.................................................................................................................................................... 344
5.63.6
Code Example................................................................................................................................................ 345
Function GFLIB_VectorLimit_F16..............................................................................................................................345
5.64.1
Declaration..................................................................................................................................................... 345
5.64.2
Arguments...................................................................................................................................................... 346
5.64.3
Return.............................................................................................................................................................346
5.64.4
Description..................................................................................................................................................... 346
5.64.5
Re-entrancy.................................................................................................................................................... 348
5.64.6
Code Example................................................................................................................................................ 348
Function GMCLIB_Clark_F32.....................................................................................................................................348
5.65.1
Declaration..................................................................................................................................................... 348
5.65.2
Arguments...................................................................................................................................................... 349
5.65.3
Return.............................................................................................................................................................349
5.65.4
Description..................................................................................................................................................... 349
5.65.5
Re-entrancy.................................................................................................................................................... 350
5.65.6
Code Example................................................................................................................................................ 350
Function GMCLIB_Clark_F16.....................................................................................................................................350
5.66.1
Declaration..................................................................................................................................................... 351
5.66.2
Arguments...................................................................................................................................................... 351
5.66.3
Return.............................................................................................................................................................351
5.66.4
Description..................................................................................................................................................... 351
5.66.5
Re-entrancy.................................................................................................................................................... 352
5.66.6
Code Example................................................................................................................................................ 352
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NXP Semiconductors
19
Section number
5.67
5.68
5.69
5.70
5.71
Title
Page
Function GMCLIB_ClarkInv_F32............................................................................................................................... 352
5.67.1
Declaration..................................................................................................................................................... 353
5.67.2
Arguments...................................................................................................................................................... 353
5.67.3
Return.............................................................................................................................................................353
5.67.4
Description..................................................................................................................................................... 353
5.67.5
Re-entrancy.................................................................................................................................................... 354
5.67.6
Code Example................................................................................................................................................ 354
Function GMCLIB_ClarkInv_F16............................................................................................................................... 354
5.68.1
Declaration..................................................................................................................................................... 355
5.68.2
Arguments...................................................................................................................................................... 355
5.68.3
Return.............................................................................................................................................................355
5.68.4
Description..................................................................................................................................................... 355
5.68.5
Re-entrancy.................................................................................................................................................... 356
5.68.6
Code Example................................................................................................................................................ 356
Function GMCLIB_DecouplingPMSM_F32............................................................................................................... 357
5.69.1
Declaration..................................................................................................................................................... 357
5.69.2
Arguments...................................................................................................................................................... 357
5.69.3
Return.............................................................................................................................................................357
5.69.4
Description..................................................................................................................................................... 357
5.69.5
Re-entrancy.................................................................................................................................................... 361
5.69.6
Code Example................................................................................................................................................ 361
Function GMCLIB_DecouplingPMSM_F16............................................................................................................... 362
5.70.1
Declaration..................................................................................................................................................... 363
5.70.2
Arguments...................................................................................................................................................... 363
5.70.3
Return.............................................................................................................................................................363
5.70.4
Description..................................................................................................................................................... 363
5.70.5
Re-entrancy.................................................................................................................................................... 367
5.70.6
Code Example................................................................................................................................................ 367
Function GMCLIB_ElimDcBusRip_F32..................................................................................................................... 368
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20
NXP Semiconductors
Section number
5.72
5.73
5.74
5.75
Title
Page
5.71.1
Declaration..................................................................................................................................................... 368
5.71.2
Arguments...................................................................................................................................................... 368
5.71.3
Return.............................................................................................................................................................369
5.71.4
Description..................................................................................................................................................... 369
5.71.5
Re-entrancy.................................................................................................................................................... 371
5.71.6
Code Example................................................................................................................................................ 371
Function GMCLIB_ElimDcBusRip_F16..................................................................................................................... 372
5.72.1
Declaration..................................................................................................................................................... 372
5.72.2
Arguments...................................................................................................................................................... 372
5.72.3
Return.............................................................................................................................................................373
5.72.4
Description..................................................................................................................................................... 373
5.72.5
Re-entrancy.................................................................................................................................................... 375
5.72.6
Code Example................................................................................................................................................ 375
Function GMCLIB_Park_F32...................................................................................................................................... 376
5.73.1
Declaration..................................................................................................................................................... 376
5.73.2
Arguments...................................................................................................................................................... 376
5.73.3
Return.............................................................................................................................................................376
5.73.4
Description..................................................................................................................................................... 377
5.73.5
Re-entrancy.................................................................................................................................................... 377
5.73.6
Code Example................................................................................................................................................ 377
Function GMCLIB_Park_F16...................................................................................................................................... 378
5.74.1
Declaration..................................................................................................................................................... 378
5.74.2
Arguments...................................................................................................................................................... 378
5.74.3
Return.............................................................................................................................................................379
5.74.4
Description..................................................................................................................................................... 379
5.74.5
Re-entrancy.................................................................................................................................................... 379
5.74.6
Code Example................................................................................................................................................ 380
Function GMCLIB_ParkInv_F32.................................................................................................................................380
5.75.1
Declaration..................................................................................................................................................... 380
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NXP Semiconductors
21
Section number
5.76
5.77
5.78
5.79
Title
Page
5.75.2
Arguments...................................................................................................................................................... 381
5.75.3
Return.............................................................................................................................................................381
5.75.4
Description..................................................................................................................................................... 381
5.75.5
Re-entrancy.................................................................................................................................................... 382
5.75.6
Code Example................................................................................................................................................ 382
Function GMCLIB_ParkInv_F16.................................................................................................................................382
5.76.1
Declaration..................................................................................................................................................... 382
5.76.2
Arguments...................................................................................................................................................... 383
5.76.3
Return.............................................................................................................................................................383
5.76.4
Description..................................................................................................................................................... 383
5.76.5
Re-entrancy.................................................................................................................................................... 384
5.76.6
Code Example................................................................................................................................................ 384
Function GMCLIB_SvmStd_F32.................................................................................................................................385
5.77.1
Declaration..................................................................................................................................................... 385
5.77.2
Arguments...................................................................................................................................................... 385
5.77.3
Return.............................................................................................................................................................385
5.77.4
Description..................................................................................................................................................... 385
5.77.5
Re-entrancy.................................................................................................................................................... 398
5.77.6
Code Example................................................................................................................................................ 398
Function GMCLIB_SvmStd_F16.................................................................................................................................399
5.78.1
Declaration..................................................................................................................................................... 399
5.78.2
Arguments...................................................................................................................................................... 399
5.78.3
Return.............................................................................................................................................................400
5.78.4
Description..................................................................................................................................................... 400
5.78.5
Re-entrancy.................................................................................................................................................... 413
5.78.6
Code Example................................................................................................................................................ 413
Function MLIB_Abs_F32.............................................................................................................................................414
5.79.1
Declaration..................................................................................................................................................... 414
5.79.2
Arguments...................................................................................................................................................... 414
Automotive Math and Motor Control Library Set for NXP MPC560xB devices, Rev. 7
22
NXP Semiconductors
Section number
5.80
5.81
5.82
5.83
Title
Page
5.79.3
Return.............................................................................................................................................................414
5.79.4
Description..................................................................................................................................................... 415
5.79.5
Re-entrancy.................................................................................................................................................... 415
5.79.6
Code Example................................................................................................................................................ 415
Function MLIB_Abs_F16.............................................................................................................................................416
5.80.1
Declaration..................................................................................................................................................... 416
5.80.2
Arguments...................................................................................................................................................... 416
5.80.3
Return.............................................................................................................................................................416
5.80.4
Description..................................................................................................................................................... 416
5.80.5
Re-entrancy.................................................................................................................................................... 417
5.80.6
Code Example................................................................................................................................................ 417
Function MLIB_AbsSat_F32....................................................................................................................................... 417
5.81.1
Declaration..................................................................................................................................................... 417
5.81.2
Arguments...................................................................................................................................................... 417
5.81.3
Return.............................................................................................................................................................418
5.81.4
Description..................................................................................................................................................... 418
5.81.5
Re-entrancy.................................................................................................................................................... 418
5.81.6
Code Example................................................................................................................................................ 418
Function MLIB_AbsSat_F16....................................................................................................................................... 419
5.82.1
Declaration..................................................................................................................................................... 419
5.82.2
Arguments...................................................................................................................................................... 419
5.82.3
Return.............................................................................................................................................................419
5.82.4
Description..................................................................................................................................................... 420
5.82.5
Re-entrancy.................................................................................................................................................... 420
5.82.6
Code Example................................................................................................................................................ 420
Function MLIB_Add_F32............................................................................................................................................ 421
5.83.1
Declaration..................................................................................................................................................... 421
5.83.2
Arguments...................................................................................................................................................... 421
5.83.3
Return.............................................................................................................................................................421
Automotive Math and Motor Control Library Set for NXP MPC560xB devices, Rev. 7
NXP Semiconductors
23
Section number
5.84
5.85
5.86
5.87
Title
Page
5.83.4
Description..................................................................................................................................................... 421
5.83.5
Re-entrancy:................................................................................................................................................... 422
5.83.6
Code Example:............................................................................................................................................... 422
Function MLIB_Add_F16............................................................................................................................................ 422
5.84.1
Declaration..................................................................................................................................................... 422
5.84.2
Arguments...................................................................................................................................................... 422
5.84.3
Return.............................................................................................................................................................423
5.84.4
Description..................................................................................................................................................... 423
5.84.5
Re-entrancy.................................................................................................................................................... 423
5.84.6
Code Example................................................................................................................................................ 423
Function MLIB_AddSat_F32....................................................................................................................................... 424
5.85.1
Declaration..................................................................................................................................................... 424
5.85.2
Arguments...................................................................................................................................................... 424
5.85.3
Return.............................................................................................................................................................424
5.85.4
Description..................................................................................................................................................... 424
5.85.5
Re-entrancy.................................................................................................................................................... 425
5.85.6
Code Example................................................................................................................................................ 425
Function MLIB_AddSat_F16....................................................................................................................................... 426
5.86.1
Declaration..................................................................................................................................................... 426
5.86.2
Arguments...................................................................................................................................................... 426
5.86.3
Return.............................................................................................................................................................426
5.86.4
Description..................................................................................................................................................... 426
5.86.5
Re-entrancy.................................................................................................................................................... 427
5.86.6
Code Example................................................................................................................................................ 427
Function MLIB_Convert_F32F16................................................................................................................................ 427
5.87.1
Declaration..................................................................................................................................................... 427
5.87.2
Arguments...................................................................................................................................................... 428
5.87.3
Return.............................................................................................................................................................428
5.87.4
Description..................................................................................................................................................... 428
Automotive Math and Motor Control Library Set for NXP MPC560xB devices, Rev. 7
24
NXP Semiconductors
Section number
5.88
5.89
5.90
5.91
Title
Page
5.87.5
Re-entrancy.................................................................................................................................................... 429
5.87.6
Code Example................................................................................................................................................ 429
Function MLIB_Convert_F16F32................................................................................................................................ 429
5.88.1
Declaration..................................................................................................................................................... 429
5.88.2
Arguments...................................................................................................................................................... 429
5.88.3
Return.............................................................................................................................................................430
5.88.4
Description..................................................................................................................................................... 430
5.88.5
Re-entrancy.................................................................................................................................................... 430
5.88.6
Code Example................................................................................................................................................ 431
Function MLIB_ConvertPU_F32F16...........................................................................................................................431
5.89.1
Declaration..................................................................................................................................................... 431
5.89.2
Arguments...................................................................................................................................................... 431
5.89.3
Return.............................................................................................................................................................431
5.89.4
Description..................................................................................................................................................... 432
5.89.5
Re-entrancy.................................................................................................................................................... 432
5.89.6
Code Example................................................................................................................................................ 432
Function MLIB_ConvertPU_F16F32...........................................................................................................................433
5.90.1
Declaration..................................................................................................................................................... 433
5.90.2
Arguments...................................................................................................................................................... 433
5.90.3
Return.............................................................................................................................................................433
5.90.4
Description..................................................................................................................................................... 433
5.90.5
Re-entrancy.................................................................................................................................................... 434
5.90.6
Code Example................................................................................................................................................ 434
Function MLIB_Div_F32............................................................................................................................................. 434
5.91.1
Declaration..................................................................................................................................................... 434
5.91.2
Arguments...................................................................................................................................................... 434
5.91.3
Return.............................................................................................................................................................434
5.91.4
Description..................................................................................................................................................... 435
5.91.5
Re-entrancy.................................................................................................................................................... 435
Automotive Math and Motor Control Library Set for NXP MPC560xB devices, Rev. 7
NXP Semiconductors
25
Section number
5.91.6
5.92
5.93
5.94
5.95
Title
Page
Code Example................................................................................................................................................ 435
Function MLIB_Div_F16............................................................................................................................................. 436
5.92.1
Declaration..................................................................................................................................................... 436
5.92.2
Arguments...................................................................................................................................................... 436
5.92.3
Return.............................................................................................................................................................436
5.92.4
Description..................................................................................................................................................... 436
5.92.5
Re-entrancy.................................................................................................................................................... 437
5.92.6
Code Example................................................................................................................................................ 437
Function MLIB_DivSat_F32........................................................................................................................................ 438
5.93.1
Declaration..................................................................................................................................................... 438
5.93.2
Arguments...................................................................................................................................................... 438
5.93.3
Return.............................................................................................................................................................438
5.93.4
Description..................................................................................................................................................... 438
5.93.5
Re-entrancy.................................................................................................................................................... 439
5.93.6
Code Example................................................................................................................................................ 439
Function MLIB_DivSat_F16........................................................................................................................................ 439
5.94.1
Declaration..................................................................................................................................................... 440
5.94.2
Arguments...................................................................................................................................................... 440
5.94.3
Return.............................................................................................................................................................440
5.94.4
Description..................................................................................................................................................... 440
5.94.5
Re-entrancy.................................................................................................................................................... 440
5.94.6
Code Example................................................................................................................................................ 441
Function MLIB_Mac_F32............................................................................................................................................ 441
5.95.1
Declaration..................................................................................................................................................... 441
5.95.2
Arguments...................................................................................................................................................... 441
5.95.3
Return.............................................................................................................................................................442
5.95.4
Description..................................................................................................................................................... 442
5.95.5
Re-entrancy.................................................................................................................................................... 442
5.95.6
Code Example................................................................................................................................................ 442
Automotive Math and Motor Control Library Set for NXP MPC560xB devices, Rev. 7
26
NXP Semiconductors
Section number
5.96
5.97
5.98
5.99
Title
Page
Function MLIB_Mac_F32F16F16............................................................................................................................... 443
5.96.1
Declaration..................................................................................................................................................... 443
5.96.2
Arguments...................................................................................................................................................... 443
5.96.3
Return.............................................................................................................................................................444
5.96.4
Description..................................................................................................................................................... 444
5.96.5
Re-entrancy.................................................................................................................................................... 444
5.96.6
Code Example................................................................................................................................................ 444
Function MLIB_Mac_F16............................................................................................................................................ 445
5.97.1
Declaration..................................................................................................................................................... 445
5.97.2
Arguments...................................................................................................................................................... 445
5.97.3
Return.............................................................................................................................................................445
5.97.4
Description..................................................................................................................................................... 446
5.97.5
Re-entrancy.................................................................................................................................................... 446
5.97.6
Code Example................................................................................................................................................ 446
Function MLIB_MacSat_F32.......................................................................................................................................447
5.98.1
Declaration..................................................................................................................................................... 447
5.98.2
Arguments...................................................................................................................................................... 447
5.98.3
Return.............................................................................................................................................................447
5.98.4
Description..................................................................................................................................................... 447
5.98.5
Re-entrancy.................................................................................................................................................... 448
5.98.6
Code Example................................................................................................................................................ 448
Function MLIB_MacSat_F32F16F16.......................................................................................................................... 449
5.99.1
Declaration..................................................................................................................................................... 449
5.99.2
Arguments...................................................................................................................................................... 449
5.99.3
Return.............................................................................................................................................................449
5.99.4
Description..................................................................................................................................................... 449
5.99.5
Re-entrancy.................................................................................................................................................... 450
5.99.6
Code Example................................................................................................................................................ 450
5.100 Function MLIB_MacSat_F16.......................................................................................................................................451
Automotive Math and Motor Control Library Set for NXP MPC560xB devices, Rev. 7
NXP Semiconductors
27
Section number
Title
Page
5.100.1 Declaration..................................................................................................................................................... 451
5.100.2 Arguments...................................................................................................................................................... 451
5.100.3 Return.............................................................................................................................................................451
5.100.4 Description..................................................................................................................................................... 451
5.100.5 Re-entrancy.................................................................................................................................................... 452
5.100.6 Code Example................................................................................................................................................ 452
5.101 Function MLIB_Mnac_F32.......................................................................................................................................... 453
5.101.1 Declaration..................................................................................................................................................... 453
5.101.2 Arguments...................................................................................................................................................... 453
5.101.3 Return.............................................................................................................................................................453
5.101.4 Description..................................................................................................................................................... 453
5.101.5 Re-entrancy.................................................................................................................................................... 454
5.101.6 Code Example................................................................................................................................................ 454
5.102 Function MLIB_Mnac_F32F16F16............................................................................................................................. 454
5.102.1 Declaration..................................................................................................................................................... 454
5.102.2 Arguments...................................................................................................................................................... 455
5.102.3 Return.............................................................................................................................................................455
5.102.4 Description..................................................................................................................................................... 455
5.102.5 Re-entrancy.................................................................................................................................................... 456
5.102.6 Code Example................................................................................................................................................ 456
5.103 Function MLIB_Mnac_F16.......................................................................................................................................... 456
5.103.1 Declaration..................................................................................................................................................... 456
5.103.2 Arguments...................................................................................................................................................... 456
5.103.3 Return.............................................................................................................................................................457
5.103.4 Description..................................................................................................................................................... 457
5.103.5 Re-entrancy.................................................................................................................................................... 457
5.103.6 Code Example................................................................................................................................................ 457
5.104 Function MLIB_Msu_F32............................................................................................................................................ 458
5.104.1 Declaration..................................................................................................................................................... 458
Automotive Math and Motor Control Library Set for NXP MPC560xB devices, Rev. 7
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NXP Semiconductors
Section number
Title
Page
5.104.2 Arguments...................................................................................................................................................... 458
5.104.3 Return.............................................................................................................................................................459
5.104.4 Description..................................................................................................................................................... 459
5.104.5 Re-entrancy.................................................................................................................................................... 459
5.104.6 Code Example................................................................................................................................................ 459
5.105 Function MLIB_Msu_F32F16F16............................................................................................................................... 460
5.105.1 Declaration..................................................................................................................................................... 460
5.105.2 Arguments...................................................................................................................................................... 460
5.105.3 Return.............................................................................................................................................................460
5.105.4 Description..................................................................................................................................................... 461
5.105.5 Re-entrancy.................................................................................................................................................... 461
5.105.6 Code Example................................................................................................................................................ 461
5.106 Function MLIB_Msu_F16............................................................................................................................................ 462
5.106.1 Declaration..................................................................................................................................................... 462
5.106.2 Arguments...................................................................................................................................................... 462
5.106.3 Return.............................................................................................................................................................462
5.106.4 Description..................................................................................................................................................... 462
5.106.5 Re-entrancy.................................................................................................................................................... 463
5.106.6 Code Example................................................................................................................................................ 463
5.107 Function MLIB_Mul_F32............................................................................................................................................ 464
5.107.1 Declaration..................................................................................................................................................... 464
5.107.2 Arguments...................................................................................................................................................... 464
5.107.3 Return.............................................................................................................................................................464
5.107.4 Description..................................................................................................................................................... 464
5.107.5 Re-entrancy.................................................................................................................................................... 465
5.107.6 Code Example................................................................................................................................................ 465
5.108 Function MLIB_Mul_F32F16F16................................................................................................................................ 465
5.108.1 Declaration..................................................................................................................................................... 465
5.108.2 Arguments...................................................................................................................................................... 465
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NXP Semiconductors
29
Section number
Title
Page
5.108.3 Return.............................................................................................................................................................466
5.108.4 Description..................................................................................................................................................... 466
5.108.5 Re-entrancy.................................................................................................................................................... 466
5.108.6 Code Example................................................................................................................................................ 466
5.109 Function MLIB_Mul_F16............................................................................................................................................ 467
5.109.1 Declaration..................................................................................................................................................... 467
5.109.2 Arguments...................................................................................................................................................... 467
5.109.3 Return.............................................................................................................................................................467
5.109.4 Description..................................................................................................................................................... 467
5.109.5 Re-entrancy.................................................................................................................................................... 468
5.109.6 Code Example................................................................................................................................................ 468
5.110 Function MLIB_MulSat_F32....................................................................................................................................... 469
5.110.1 Declaration..................................................................................................................................................... 469
5.110.2 Arguments...................................................................................................................................................... 469
5.110.3 Return.............................................................................................................................................................469
5.110.4 Description..................................................................................................................................................... 469
5.110.5 Re-entrancy.................................................................................................................................................... 470
5.110.6 Code Example................................................................................................................................................ 470
5.111 Function MLIB_MulSat_F32F16F16...........................................................................................................................470
5.111.1 Declaration..................................................................................................................................................... 470
5.111.2 Arguments...................................................................................................................................................... 471
5.111.3 Return.............................................................................................................................................................471
5.111.4 Description..................................................................................................................................................... 471
5.111.5 Re-entrancy.................................................................................................................................................... 471
5.111.6 Code Example................................................................................................................................................ 472
5.112 Function MLIB_MulSat_F16....................................................................................................................................... 472
5.112.1 Declaration..................................................................................................................................................... 472
5.112.2 Arguments...................................................................................................................................................... 472
5.112.3 Return.............................................................................................................................................................472
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30
NXP Semiconductors
Section number
Title
Page
5.112.4 Description..................................................................................................................................................... 473
5.112.5 Re-entrancy.................................................................................................................................................... 473
5.112.6 Code Example................................................................................................................................................ 473
5.113 Function MLIB_Neg_F32............................................................................................................................................ 474
5.113.1 Declaration..................................................................................................................................................... 474
5.113.2 Arguments...................................................................................................................................................... 474
5.113.3 Return.............................................................................................................................................................474
5.113.4 Description..................................................................................................................................................... 474
5.113.5 Re-entrancy.................................................................................................................................................... 475
5.113.6 Code Example................................................................................................................................................ 475
5.114 Function MLIB_Neg_F16............................................................................................................................................ 475
5.114.1 Declaration..................................................................................................................................................... 475
5.114.2 Arguments...................................................................................................................................................... 476
5.114.3 Return.............................................................................................................................................................476
5.114.4 Description..................................................................................................................................................... 476
5.114.5 Re-entrancy.................................................................................................................................................... 476
5.114.6 Code Example................................................................................................................................................ 476
5.115 Function MLIB_NegSat_F32....................................................................................................................................... 477
5.115.1 Declaration..................................................................................................................................................... 477
5.115.2 Arguments...................................................................................................................................................... 477
5.115.3 Return.............................................................................................................................................................477
5.115.4 Description..................................................................................................................................................... 478
5.115.5 Re-entrancy.................................................................................................................................................... 478
5.115.6 Code Example................................................................................................................................................ 478
5.116 Function MLIB_NegSat_F16....................................................................................................................................... 479
5.116.1 Declaration..................................................................................................................................................... 479
5.116.2 Arguments...................................................................................................................................................... 479
5.116.3 Return.............................................................................................................................................................479
5.116.4 Description..................................................................................................................................................... 479
Automotive Math and Motor Control Library Set for NXP MPC560xB devices, Rev. 7
NXP Semiconductors
31
Section number
Title
Page
5.116.5 Re-entrancy.................................................................................................................................................... 480
5.116.6 Code Example................................................................................................................................................ 480
5.117 Function MLIB_Norm_F32..........................................................................................................................................480
5.117.1 Declaration..................................................................................................................................................... 480
5.117.2 Arguments...................................................................................................................................................... 481
5.117.3 Return.............................................................................................................................................................481
5.117.4 Description..................................................................................................................................................... 481
5.117.5 Re-entrancy.................................................................................................................................................... 481
5.117.6 Code Example................................................................................................................................................ 481
5.118 Function MLIB_Norm_F16..........................................................................................................................................482
5.118.1 Declaration..................................................................................................................................................... 482
5.118.2 Arguments...................................................................................................................................................... 482
5.118.3 Return.............................................................................................................................................................482
5.118.4 Description..................................................................................................................................................... 482
5.118.5 Re-entrancy.................................................................................................................................................... 482
5.118.6 Code Example................................................................................................................................................ 483
5.119 Function MLIB_RndSat_F16F32................................................................................................................................. 483
5.119.1 Declaration..................................................................................................................................................... 483
5.119.2 Arguments...................................................................................................................................................... 483
5.119.3 Return.............................................................................................................................................................484
5.119.4 Description..................................................................................................................................................... 484
5.119.5 Re-entrancy.................................................................................................................................................... 484
5.119.6 Code Example................................................................................................................................................ 484
5.120 Function MLIB_Round_F32........................................................................................................................................ 484
5.120.1 Declaration..................................................................................................................................................... 484
5.120.2 Arguments...................................................................................................................................................... 484
5.120.3 Return.............................................................................................................................................................485
5.120.4 Description..................................................................................................................................................... 485
5.120.5 Re-entrancy.................................................................................................................................................... 485
Automotive Math and Motor Control Library Set for NXP MPC560xB devices, Rev. 7
32
NXP Semiconductors
Section number
Title
Page
5.120.6 Code Example................................................................................................................................................ 485
5.121 Function MLIB_Round_F16........................................................................................................................................ 486
5.121.1 Declaration..................................................................................................................................................... 486
5.121.2 Arguments...................................................................................................................................................... 486
5.121.3 Return.............................................................................................................................................................487
5.121.4 Description..................................................................................................................................................... 487
5.121.5 Re-entrancy.................................................................................................................................................... 487
5.121.6 Code Example................................................................................................................................................ 487
5.122 Function MLIB_ShBi_F32........................................................................................................................................... 488
5.122.1 Declaration..................................................................................................................................................... 488
5.122.2 Arguments...................................................................................................................................................... 488
5.122.3 Return.............................................................................................................................................................488
5.122.4 Description..................................................................................................................................................... 489
5.122.5 Re-entrancy.................................................................................................................................................... 489
5.122.6 Code Example................................................................................................................................................ 489
5.123 Function MLIB_ShBi_F16........................................................................................................................................... 489
5.123.1 Declaration..................................................................................................................................................... 490
5.123.2 Arguments...................................................................................................................................................... 490
5.123.3 Return.............................................................................................................................................................490
5.123.4 Description..................................................................................................................................................... 490
5.123.5 Re-entrancy.................................................................................................................................................... 490
5.123.6 Code Example................................................................................................................................................ 491
5.124 Function MLIB_ShBiSat_F32...................................................................................................................................... 491
5.124.1 Declaration..................................................................................................................................................... 491
5.124.2 Arguments...................................................................................................................................................... 491
5.124.3 Return.............................................................................................................................................................492
5.124.4 Description..................................................................................................................................................... 492
5.124.5 Re-entrancy.................................................................................................................................................... 492
5.124.6 Code Example................................................................................................................................................ 492
Automotive Math and Motor Control Library Set for NXP MPC560xB devices, Rev. 7
NXP Semiconductors
33
Section number
Title
Page
5.125 Function MLIB_ShBiSat_F16...................................................................................................................................... 493
5.125.1 Declaration..................................................................................................................................................... 493
5.125.2 Arguments...................................................................................................................................................... 493
5.125.3 Return.............................................................................................................................................................493
5.125.4 Description..................................................................................................................................................... 493
5.125.5 Re-entrancy.................................................................................................................................................... 494
5.125.6 Code Example................................................................................................................................................ 494
5.126 Function MLIB_ShL_F32............................................................................................................................................ 494
5.126.1 Declaration..................................................................................................................................................... 494
5.126.2 Arguments...................................................................................................................................................... 494
5.126.3 Return.............................................................................................................................................................495
5.126.4 Description..................................................................................................................................................... 495
5.126.5 Re-entrancy.................................................................................................................................................... 495
5.126.6 Code Example................................................................................................................................................ 495
5.127 Function MLIB_ShL_F16............................................................................................................................................ 496
5.127.1 Declaration..................................................................................................................................................... 496
5.127.2 Arguments...................................................................................................................................................... 496
5.127.3 Return.............................................................................................................................................................496
5.127.4 Description..................................................................................................................................................... 496
5.127.5 Re-entrancy.................................................................................................................................................... 497
5.127.6 Code Example................................................................................................................................................ 497
5.128 Function MLIB_ShLSat_F32....................................................................................................................................... 497
5.128.1 Declaration..................................................................................................................................................... 497
5.128.2 Arguments...................................................................................................................................................... 498
5.128.3 Return.............................................................................................................................................................498
5.128.4 Description..................................................................................................................................................... 498
5.128.5 Re-entrancy.................................................................................................................................................... 498
5.128.6 Code Example................................................................................................................................................ 498
5.129 Function MLIB_ShLSat_F16....................................................................................................................................... 499
Automotive Math and Motor Control Library Set for NXP MPC560xB devices, Rev. 7
34
NXP Semiconductors
Section number
Title
Page
5.129.1 Declaration..................................................................................................................................................... 499
5.129.2 Arguments...................................................................................................................................................... 499
5.129.3 Return.............................................................................................................................................................499
5.129.4 Description..................................................................................................................................................... 500
5.129.5 Re-entrancy.................................................................................................................................................... 500
5.129.6 Code Example................................................................................................................................................ 500
5.130 Function MLIB_ShR_F32............................................................................................................................................ 501
5.130.1 Declaration..................................................................................................................................................... 501
5.130.2 Arguments...................................................................................................................................................... 501
5.130.3 Return.............................................................................................................................................................501
5.130.4 Description..................................................................................................................................................... 501
5.130.5 Re-entrancy.................................................................................................................................................... 501
5.130.6 Code Example................................................................................................................................................ 502
5.131 Function MLIB_ShR_F16............................................................................................................................................ 502
5.131.1 Declaration..................................................................................................................................................... 502
5.131.2 Arguments...................................................................................................................................................... 502
5.131.3 Return.............................................................................................................................................................503
5.131.4 Description..................................................................................................................................................... 503
5.131.5 Re-entrancy.................................................................................................................................................... 503
5.131.6 Code Example................................................................................................................................................ 503
5.132 Function MLIB_Sub_F32.............................................................................................................................................504
5.132.1 Declaration..................................................................................................................................................... 504
5.132.2 Arguments...................................................................................................................................................... 504
5.132.3 Return.............................................................................................................................................................504
5.132.4 Description..................................................................................................................................................... 504
5.132.5 Re-entrancy.................................................................................................................................................... 505
5.132.6 Code Example................................................................................................................................................ 505
5.133 Function MLIB_Sub_F16.............................................................................................................................................506
5.133.1 Declaration..................................................................................................................................................... 506
Automotive Math and Motor Control Library Set for NXP MPC560xB devices, Rev. 7
NXP Semiconductors
35
Section number
Title
Page
5.133.2 Arguments...................................................................................................................................................... 506
5.133.3 Return.............................................................................................................................................................506
5.133.4 Description..................................................................................................................................................... 506
5.133.5 Re-entrancy.................................................................................................................................................... 507
5.133.6 Code Example................................................................................................................................................ 507
5.134 Function MLIB_SubSat_F32........................................................................................................................................507
5.134.1 Declaration..................................................................................................................................................... 507
5.134.2 Arguments...................................................................................................................................................... 507
5.134.3 Return.............................................................................................................................................................508
5.134.4 Description..................................................................................................................................................... 508
5.134.5 Re-entrancy.................................................................................................................................................... 508
5.134.6 Code Example................................................................................................................................................ 508
5.135 Function MLIB_SubSat_F16........................................................................................................................................509
5.135.1 Declaration..................................................................................................................................................... 509
5.135.2 Arguments...................................................................................................................................................... 509
5.135.3 Return.............................................................................................................................................................509
5.135.4 Description..................................................................................................................................................... 510
5.135.5 Re-entrancy.................................................................................................................................................... 510
5.135.6 Code Example................................................................................................................................................ 510
5.136 Function MLIB_VMac_F32......................................................................................................................................... 511
5.136.1 Declaration..................................................................................................................................................... 511
5.136.2 Arguments...................................................................................................................................................... 511
5.136.3 Return.............................................................................................................................................................511
5.136.4 Description..................................................................................................................................................... 511
5.136.5 Re-entrancy.................................................................................................................................................... 512
5.136.6 Code Example................................................................................................................................................ 512
5.137 Function MLIB_VMac_F32F16F16.............................................................................................................................513
5.137.1 Declaration..................................................................................................................................................... 513
5.137.2 Arguments...................................................................................................................................................... 513
Automotive Math and Motor Control Library Set for NXP MPC560xB devices, Rev. 7
36
NXP Semiconductors
Section number
Title
Page
5.137.3 Return.............................................................................................................................................................513
5.137.4 Description..................................................................................................................................................... 513
5.137.5 Re-entrancy.................................................................................................................................................... 514
5.137.6 Code Example................................................................................................................................................ 514
5.138 Function MLIB_VMac_F16......................................................................................................................................... 514
5.138.1 Declaration..................................................................................................................................................... 514
5.138.2 Arguments...................................................................................................................................................... 515
5.138.3 Return.............................................................................................................................................................515
5.138.4 Description..................................................................................................................................................... 515
5.138.5 Re-entrancy.................................................................................................................................................... 515
5.138.6 Code Example................................................................................................................................................ 516
5.139 Function SWLIBS_GetVersion.................................................................................................................................... 516
5.139.1 Declaration..................................................................................................................................................... 516
5.139.2 Return.............................................................................................................................................................516
5.139.3 Description..................................................................................................................................................... 517
5.139.4 Reentrancy..................................................................................................................................................... 517
Chapter 6
6.1
Typedefs Index..............................................................................................................................................................519
Chapter 7
Compound Data Types
7.1
7.2
7.3
GDFLIB_FILTER_IIR1_COEFF_T_F16.................................................................................................................... 523
7.1.1
Description..................................................................................................................................................... 523
7.1.2
Compound Type Members.............................................................................................................................523
GDFLIB_FILTER_IIR1_COEFF_T_F32.................................................................................................................... 524
7.2.1
Description..................................................................................................................................................... 524
7.2.2
Compound Type Members.............................................................................................................................524
GDFLIB_FILTER_IIR1_T_F16...................................................................................................................................524
7.3.1
Description..................................................................................................................................................... 524
7.3.2
Compound Type Members.............................................................................................................................525
Automotive Math and Motor Control Library Set for NXP MPC560xB devices, Rev. 7
NXP Semiconductors
37
Section number
7.4
7.5
7.6
7.7
7.8
7.9
7.10
7.11
7.12
7.13
Title
Page
GDFLIB_FILTER_IIR1_T_F32...................................................................................................................................525
7.4.1
Description..................................................................................................................................................... 525
7.4.2
Compound Type Members.............................................................................................................................525
GDFLIB_FILTER_IIR2_COEFF_T_F16.................................................................................................................... 525
7.5.1
Description..................................................................................................................................................... 526
7.5.2
Compound Type Members.............................................................................................................................526
GDFLIB_FILTER_IIR2_COEFF_T_F32.................................................................................................................... 526
7.6.1
Description..................................................................................................................................................... 526
7.6.2
Compound Type Members.............................................................................................................................526
GDFLIB_FILTER_IIR2_T_F16...................................................................................................................................527
7.7.1
Description..................................................................................................................................................... 527
7.7.2
Compound Type Members.............................................................................................................................527
GDFLIB_FILTER_IIR2_T_F32...................................................................................................................................527
7.8.1
Description..................................................................................................................................................... 528
7.8.2
Compound Type Members.............................................................................................................................528
GDFLIB_FILTER_MA_T_F16................................................................................................................................... 528
7.9.1
Description..................................................................................................................................................... 528
7.9.2
Compound Type Members.............................................................................................................................528
GDFLIB_FILTER_MA_T_F32................................................................................................................................... 528
7.10.1
Description..................................................................................................................................................... 529
7.10.2
Compound Type Members.............................................................................................................................529
GDFLIB_FILTERFIR_PARAM_T_F16..................................................................................................................... 529
7.11.1
Description..................................................................................................................................................... 529
7.11.2
Compound Type Members.............................................................................................................................529
GDFLIB_FILTERFIR_PARAM_T_F32..................................................................................................................... 529
7.12.1
Description..................................................................................................................................................... 530
7.12.2
Compound Type Members.............................................................................................................................530
GDFLIB_FILTERFIR_STATE_T_F16....................................................................................................................... 530
7.13.1
Description..................................................................................................................................................... 530
Automotive Math and Motor Control Library Set for NXP MPC560xB devices, Rev. 7
38
NXP Semiconductors
Section number
7.13.2
7.14
7.15
7.16
7.17
7.18
7.19
7.20
7.21
7.22
7.23
Title
Page
Compound Type Members.............................................................................................................................530
GDFLIB_FILTERFIR_STATE_T_F32....................................................................................................................... 530
7.14.1
Description..................................................................................................................................................... 531
7.14.2
Compound Type Members.............................................................................................................................531
GFLIB_ACOS_T_F16..................................................................................................................................................531
7.15.1
Description..................................................................................................................................................... 531
7.15.2
Compound Type Members.............................................................................................................................531
GFLIB_ACOS_T_F32..................................................................................................................................................531
7.16.1
Description..................................................................................................................................................... 532
7.16.2
Compound Type Members.............................................................................................................................532
GFLIB_ACOS_TAYLOR_COEF_T_F16................................................................................................................... 532
7.17.1
Description..................................................................................................................................................... 532
7.17.2
Compound Type Members.............................................................................................................................532
GFLIB_ACOS_TAYLOR_COEF_T_F32................................................................................................................... 532
7.18.1
Description..................................................................................................................................................... 533
7.18.2
Compound Type Members.............................................................................................................................533
GFLIB_ASIN_T_F16................................................................................................................................................... 533
7.19.1
Description..................................................................................................................................................... 533
7.19.2
Compound Type Members.............................................................................................................................533
GFLIB_ASIN_T_F32................................................................................................................................................... 533
7.20.1
Description..................................................................................................................................................... 534
7.20.2
Compound Type Members.............................................................................................................................534
GFLIB_ASIN_TAYLOR_COEF_T_F16.....................................................................................................................534
7.21.1
Description..................................................................................................................................................... 534
7.21.2
Compound Type Members.............................................................................................................................534
GFLIB_ASIN_TAYLOR_COEF_T_F32.....................................................................................................................534
7.22.1
Description..................................................................................................................................................... 534
7.22.2
Compound Type Members.............................................................................................................................535
GFLIB_ATAN_T_F16................................................................................................................................................. 535
Automotive Math and Motor Control Library Set for NXP MPC560xB devices, Rev. 7
NXP Semiconductors
39
Section number
7.24
7.25
7.26
7.27
7.28
7.29
7.30
7.31
7.32
Title
Page
7.23.1
Description..................................................................................................................................................... 535
7.23.2
Compound Type Members.............................................................................................................................535
GFLIB_ATAN_T_F32................................................................................................................................................. 535
7.24.1
Description..................................................................................................................................................... 535
7.24.2
Compound Type Members.............................................................................................................................536
GFLIB_ATAN_TAYLOR_COEF_T_F16...................................................................................................................536
7.25.1
Description..................................................................................................................................................... 536
7.25.2
Compound Type Members.............................................................................................................................536
GFLIB_ATAN_TAYLOR_COEF_T_F32...................................................................................................................536
7.26.1
Description..................................................................................................................................................... 536
7.26.2
Compound Type Members.............................................................................................................................537
GFLIB_ATANYXSHIFTED_T_F16........................................................................................................................... 537
7.27.1
Description..................................................................................................................................................... 537
7.27.2
Compound Type Members.............................................................................................................................537
GFLIB_ATANYXSHIFTED_T_F32........................................................................................................................... 537
7.28.1
Description..................................................................................................................................................... 538
7.28.2
Compound Type Members.............................................................................................................................538
GFLIB_CONTROLLER_PI_P_T_F16........................................................................................................................ 538
7.29.1
Description..................................................................................................................................................... 538
7.29.2
Compound Type Members.............................................................................................................................538
GFLIB_CONTROLLER_PI_P_T_F32........................................................................................................................ 539
7.30.1
Description..................................................................................................................................................... 539
7.30.2
Compound Type Members.............................................................................................................................539
GFLIB_CONTROLLER_PI_R_T_F16........................................................................................................................539
7.31.1
Description..................................................................................................................................................... 539
7.31.2
Compound Type Members.............................................................................................................................539
GFLIB_CONTROLLER_PI_R_T_F32........................................................................................................................540
7.32.1
Description..................................................................................................................................................... 540
7.32.2
Compound Type Members.............................................................................................................................540
Automotive Math and Motor Control Library Set for NXP MPC560xB devices, Rev. 7
40
NXP Semiconductors
Section number
7.33
7.34
7.35
7.36
7.37
7.38
7.39
7.40
7.41
7.42
Title
Page
GFLIB_CONTROLLER_PIAW_P_T_F16................................................................................................................. 541
7.33.1
Description..................................................................................................................................................... 541
7.33.2
Compound Type Members.............................................................................................................................541
GFLIB_CONTROLLER_PIAW_P_T_F32................................................................................................................. 541
7.34.1
Description..................................................................................................................................................... 541
7.34.2
Compound Type Members.............................................................................................................................542
GFLIB_CONTROLLER_PIAW_R_T_F16................................................................................................................. 542
7.35.1
Description..................................................................................................................................................... 542
7.35.2
Compound Type Members.............................................................................................................................542
GFLIB_CONTROLLER_PIAW_R_T_F32................................................................................................................. 543
7.36.1
Description..................................................................................................................................................... 543
7.36.2
Compound Type Members.............................................................................................................................543
GFLIB_COS_T_F16.................................................................................................................................................... 544
7.37.1
Description..................................................................................................................................................... 544
7.37.2
Compound Type Members.............................................................................................................................544
GFLIB_COS_T_F32.................................................................................................................................................... 544
7.38.1
Description..................................................................................................................................................... 544
7.38.2
Compound Type Members.............................................................................................................................544
GFLIB_HYST_T_F16..................................................................................................................................................545
7.39.1
Description..................................................................................................................................................... 545
7.39.2
Compound Type Members.............................................................................................................................545
GFLIB_HYST_T_F32..................................................................................................................................................545
7.40.1
Description..................................................................................................................................................... 545
7.40.2
Compound Type Members.............................................................................................................................546
GFLIB_INTEGRATOR_TR_T_F16............................................................................................................................546
7.41.1
Description..................................................................................................................................................... 546
7.41.2
Compound Type Members.............................................................................................................................546
GFLIB_INTEGRATOR_TR_T_F32............................................................................................................................546
7.42.1
Description..................................................................................................................................................... 547
Automotive Math and Motor Control Library Set for NXP MPC560xB devices, Rev. 7
NXP Semiconductors
41
Section number
7.42.2
7.43
7.44
7.45
7.46
7.47
7.48
7.49
7.50
7.51
7.52
Title
Page
Compound Type Members.............................................................................................................................547
GFLIB_LIMIT_T_F16................................................................................................................................................. 547
7.43.1
Description..................................................................................................................................................... 547
7.43.2
Compound Type Members.............................................................................................................................547
GFLIB_LIMIT_T_F32................................................................................................................................................. 547
7.44.1
Description..................................................................................................................................................... 548
7.44.2
Compound Type Members.............................................................................................................................548
GFLIB_LOWERLIMIT_T_F16................................................................................................................................... 548
7.45.1
Description..................................................................................................................................................... 548
7.45.2
Compound Type Members.............................................................................................................................548
GFLIB_LOWERLIMIT_T_F32................................................................................................................................... 548
7.46.1
Description..................................................................................................................................................... 548
7.46.2
Compound Type Members.............................................................................................................................549
GFLIB_LUT1D_T_F16................................................................................................................................................549
7.47.1
Description..................................................................................................................................................... 549
7.47.2
Compound Type Members.............................................................................................................................549
GFLIB_LUT1D_T_F32................................................................................................................................................549
7.48.1
Description..................................................................................................................................................... 549
7.48.2
Compound Type Members.............................................................................................................................549
GFLIB_LUT2D_T_F16................................................................................................................................................550
7.49.1
Description..................................................................................................................................................... 550
7.49.2
Compound Type Members.............................................................................................................................550
GFLIB_LUT2D_T_F32................................................................................................................................................550
7.50.1
Description..................................................................................................................................................... 550
7.50.2
Compound Type Members.............................................................................................................................551
GFLIB_RAMP_T_F16................................................................................................................................................. 551
7.51.1
Description..................................................................................................................................................... 551
7.51.2
Compound Type Members.............................................................................................................................551
GFLIB_RAMP_T_F32................................................................................................................................................. 551
Automotive Math and Motor Control Library Set for NXP MPC560xB devices, Rev. 7
42
NXP Semiconductors
Section number
7.53
7.54
7.55
7.56
7.57
7.58
7.59
7.60
7.61
Title
Page
7.52.1
Description..................................................................................................................................................... 551
7.52.2
Compound Type Members.............................................................................................................................552
GFLIB_SIN_T_F16......................................................................................................................................................552
7.53.1
Description..................................................................................................................................................... 552
7.53.2
Compound Type Members.............................................................................................................................552
GFLIB_SIN_T_F32......................................................................................................................................................552
7.54.1
Description..................................................................................................................................................... 552
7.54.2
Compound Type Members.............................................................................................................................553
GFLIB_SINCOS_T_F16.............................................................................................................................................. 553
7.55.1
Description..................................................................................................................................................... 553
7.55.2
Compound Type Members.............................................................................................................................553
GFLIB_SINCOS_T_F32.............................................................................................................................................. 553
7.56.1
Description..................................................................................................................................................... 553
7.56.2
Compound Type Members.............................................................................................................................554
GFLIB_TAN_T_F16.................................................................................................................................................... 554
7.57.1
Description..................................................................................................................................................... 554
7.57.2
Compound Type Members.............................................................................................................................554
GFLIB_TAN_T_F32.................................................................................................................................................... 554
7.58.1
Description..................................................................................................................................................... 554
7.58.2
Compound Type Members.............................................................................................................................555
GFLIB_TAN_TAYLOR_COEF_T_F16......................................................................................................................555
7.59.1
Description..................................................................................................................................................... 555
7.59.2
Compound Type Members.............................................................................................................................555
GFLIB_TAN_TAYLOR_COEF_T_F32......................................................................................................................555
7.60.1
Description..................................................................................................................................................... 556
7.60.2
Compound Type Members.............................................................................................................................556
GFLIB_UPPERLIMIT_T_F16.....................................................................................................................................556
7.61.1
Description..................................................................................................................................................... 556
7.61.2
Compound Type Members.............................................................................................................................556
Automotive Math and Motor Control Library Set for NXP MPC560xB devices, Rev. 7
NXP Semiconductors
43
Section number
7.62
7.63
7.64
7.65
7.66
7.67
7.68
7.69
7.70
7.71
Title
Page
GFLIB_UPPERLIMIT_T_F32.....................................................................................................................................556
7.62.1
Description..................................................................................................................................................... 556
7.62.2
Compound Type Members.............................................................................................................................557
GFLIB_VECTORLIMIT_T_F16................................................................................................................................. 557
7.63.1
Description..................................................................................................................................................... 557
7.63.2
Compound Type Members.............................................................................................................................557
GFLIB_VECTORLIMIT_T_F32................................................................................................................................. 557
7.64.1
Description..................................................................................................................................................... 557
7.64.2
Compound Type Members.............................................................................................................................558
GMCLIB_DECOUPLINGPMSM_T_F16................................................................................................................... 558
7.65.1
Description..................................................................................................................................................... 558
7.65.2
Compound Type Members.............................................................................................................................558
GMCLIB_DECOUPLINGPMSM_T_F32................................................................................................................... 558
7.66.1
Description..................................................................................................................................................... 558
7.66.2
Compound Type Members.............................................................................................................................558
GMCLIB_ELIMDCBUSRIP_T_F16........................................................................................................................... 559
7.67.1
Description..................................................................................................................................................... 559
7.67.2
Compound Type Members.............................................................................................................................559
GMCLIB_ELIMDCBUSRIP_T_F32........................................................................................................................... 559
7.68.1
Description..................................................................................................................................................... 559
7.68.2
Compound Type Members.............................................................................................................................560
SWLIBS_2Syst_F16.....................................................................................................................................................560
7.69.1
Description..................................................................................................................................................... 560
7.69.2
Compound Type Members.............................................................................................................................560
SWLIBS_2Syst_F32.....................................................................................................................................................560
7.70.1
Description..................................................................................................................................................... 560
7.70.2
Compound Type Members.............................................................................................................................560
SWLIBS_3Syst_F16.....................................................................................................................................................561
7.71.1
Description..................................................................................................................................................... 561
Automotive Math and Motor Control Library Set for NXP MPC560xB devices, Rev. 7
44
NXP Semiconductors
Section number
7.71.2
7.72
7.73
Title
Page
Compound Type Members.............................................................................................................................561
SWLIBS_3Syst_F32.....................................................................................................................................................561
7.72.1
Description..................................................................................................................................................... 561
7.72.2
Compound Type Members.............................................................................................................................561
SWLIBS_VERSION_T................................................................................................................................................ 562
7.73.1
Description..................................................................................................................................................... 562
7.73.2
Compound Type Members.............................................................................................................................562
Chapter 8
8.1
Macro Definitions......................................................................................................................................................... 563
8.1.1
Macro Definitions Overview......................................................................................................................... 563
Chapter 9
Macro References
9.1
9.2
9.3
9.4
9.5
9.6
Define GDFLIB_FilterFIRInit......................................................................................................................................571
9.1.1
Macro Definition............................................................................................................................................571
9.1.2
Description..................................................................................................................................................... 571
Define GDFLIB_FilterFIR........................................................................................................................................... 571
9.2.1
Macro Definition............................................................................................................................................571
9.2.2
Description..................................................................................................................................................... 571
Define GDFLIB_FilterIIR1Init.....................................................................................................................................572
9.3.1
Macro Definition............................................................................................................................................572
9.3.2
Description..................................................................................................................................................... 572
Define GDFLIB_FilterIIR1.......................................................................................................................................... 572
9.4.1
Macro Definition............................................................................................................................................572
9.4.2
Description..................................................................................................................................................... 572
Define GDFLIB_FILTER_IIR1_DEFAULT_F32.......................................................................................................572
9.5.1
Macro Definition............................................................................................................................................572
9.5.2
Description..................................................................................................................................................... 573
Define GDFLIB_FILTER_IIR1_DEFAULT_F16.......................................................................................................573
9.6.1
Macro Definition............................................................................................................................................573
Automotive Math and Motor Control Library Set for NXP MPC560xB devices, Rev. 7
NXP Semiconductors
45
Section number
9.6.2
9.7
9.8
9.9
9.10
9.11
9.12
9.13
9.14
9.15
9.16
Title
Page
Description..................................................................................................................................................... 573
Define GDFLIB_FilterIIR2Init.....................................................................................................................................573
9.7.1
Macro Definition............................................................................................................................................573
9.7.2
Description..................................................................................................................................................... 573
Define GDFLIB_FilterIIR2.......................................................................................................................................... 574
9.8.1
Macro Definition............................................................................................................................................574
9.8.2
Description..................................................................................................................................................... 574
Define GDFLIB_FILTER_IIR2_DEFAULT_F32.......................................................................................................574
9.9.1
Macro Definition............................................................................................................................................574
9.9.2
Description..................................................................................................................................................... 574
Define GDFLIB_FILTER_IIR2_DEFAULT_F16.......................................................................................................574
9.10.1
Macro Definition............................................................................................................................................574
9.10.2
Description..................................................................................................................................................... 575
Define GDFLIB_FilterMAInit......................................................................................................................................575
9.11.1
Macro Definition............................................................................................................................................575
9.11.2
Description..................................................................................................................................................... 575
Define GDFLIB_FilterMA........................................................................................................................................... 575
9.12.1
Macro Definition............................................................................................................................................575
9.12.2
Description..................................................................................................................................................... 575
Define GDFLIB_FILTER_MA_DEFAULT_F32........................................................................................................575
9.13.1
Macro Definition............................................................................................................................................575
9.13.2
Description..................................................................................................................................................... 576
Define GDFLIB_FILTER_MA_DEFAULT_F16........................................................................................................576
9.14.1
Macro Definition............................................................................................................................................576
9.14.2
Description..................................................................................................................................................... 576
Define GFLIB_Acos.....................................................................................................................................................576
9.15.1
Macro Definition............................................................................................................................................576
9.15.2
Description..................................................................................................................................................... 576
Define GFLIB_ACOS_DEFAULT_F32...................................................................................................................... 576
Automotive Math and Motor Control Library Set for NXP MPC560xB devices, Rev. 7
46
NXP Semiconductors
Section number
9.17
9.18
9.19
9.20
9.21
9.22
9.23
9.24
9.25
Title
Page
9.16.1
Macro Definition............................................................................................................................................577
9.16.2
Description..................................................................................................................................................... 577
Define GFLIB_ACOS_DEFAULT_F16...................................................................................................................... 577
9.17.1
Macro Definition............................................................................................................................................577
9.17.2
Description..................................................................................................................................................... 577
Define GFLIB_Asin......................................................................................................................................................577
9.18.1
Macro Definition............................................................................................................................................577
9.18.2
Description..................................................................................................................................................... 577
Define GFLIB_ASIN_DEFAULT_F32....................................................................................................................... 578
9.19.1
Macro Definition............................................................................................................................................578
9.19.2
Description..................................................................................................................................................... 578
Define GFLIB_ASIN_DEFAULT_F16....................................................................................................................... 578
9.20.1
Macro Definition............................................................................................................................................578
9.20.2
Description..................................................................................................................................................... 578
Define GFLIB_Atan..................................................................................................................................................... 578
9.21.1
Macro Definition............................................................................................................................................578
9.21.2
Description..................................................................................................................................................... 579
Define GFLIB_ATAN_DEFAULT_F32......................................................................................................................579
9.22.1
Macro Definition............................................................................................................................................579
9.22.2
Description..................................................................................................................................................... 579
Define GFLIB_ATAN_DEFAULT_F16......................................................................................................................579
9.23.1
Macro Definition............................................................................................................................................579
9.23.2
Description..................................................................................................................................................... 579
Define GFLIB_AtanYX................................................................................................................................................579
9.24.1
Macro Definition............................................................................................................................................580
9.24.2
Description..................................................................................................................................................... 580
Define GFLIB_AtanYXShifted.................................................................................................................................... 580
9.25.1
Macro Definition............................................................................................................................................580
9.25.2
Description..................................................................................................................................................... 580
Automotive Math and Motor Control Library Set for NXP MPC560xB devices, Rev. 7
NXP Semiconductors
47
Section number
9.26
9.27
9.28
9.29
9.30
9.31
9.32
9.33
9.34
9.35
Title
Page
Define GFLIB_ControllerPIp....................................................................................................................................... 580
9.26.1
Macro Definition............................................................................................................................................580
9.26.2
Description..................................................................................................................................................... 580
Define GFLIB_CONTROLLER_PI_P_DEFAULT_F32............................................................................................ 581
9.27.1
Macro Definition............................................................................................................................................581
9.27.2
Description..................................................................................................................................................... 581
Define GFLIB_CONTROLLER_PI_P_DEFAULT_F16............................................................................................ 581
9.28.1
Macro Definition............................................................................................................................................581
9.28.2
Description..................................................................................................................................................... 581
Define GFLIB_ControllerPIpAW................................................................................................................................ 581
9.29.1
Macro Definition............................................................................................................................................582
9.29.2
Description..................................................................................................................................................... 582
Define GFLIB_CONTROLLER_PIAW_P_DEFAULT_F32......................................................................................582
9.30.1
Macro Definition............................................................................................................................................582
9.30.2
Description..................................................................................................................................................... 582
Define GFLIB_CONTROLLER_PIAW_P_DEFAULT_F16......................................................................................582
9.31.1
Macro Definition............................................................................................................................................582
9.31.2
Description..................................................................................................................................................... 582
Define GFLIB_ControllerPIr........................................................................................................................................583
9.32.1
Macro Definition............................................................................................................................................583
9.32.2
Description..................................................................................................................................................... 583
Define GFLIB_CONTROLLER_PI_R_DEFAULT_F32............................................................................................ 583
9.33.1
Macro Definition............................................................................................................................................583
9.33.2
Description..................................................................................................................................................... 583
Define GFLIB_CONTROLLER_PI_R_DEFAULT_F16............................................................................................ 583
9.34.1
Macro Definition............................................................................................................................................584
9.34.2
Description..................................................................................................................................................... 584
Define GFLIB_ControllerPIrAW................................................................................................................................. 584
9.35.1
Macro Definition............................................................................................................................................584
Automotive Math and Motor Control Library Set for NXP MPC560xB devices, Rev. 7
48
NXP Semiconductors
Section number
9.35.2
9.36
9.37
9.38
9.39
9.40
9.41
9.42
9.43
9.44
9.45
Title
Page
Description..................................................................................................................................................... 584
Define GFLIB_CONTROLLER_PIAW_R_DEFAULT_F32..................................................................................... 584
9.36.1
Macro Definition............................................................................................................................................584
9.36.2
Description..................................................................................................................................................... 584
Define GFLIB_CONTROLLER_PIAW_R_DEFAULT_F16..................................................................................... 585
9.37.1
Macro Definition............................................................................................................................................585
9.37.2
Description..................................................................................................................................................... 585
Define GFLIB_Cos.......................................................................................................................................................585
9.38.1
Macro Definition............................................................................................................................................585
9.38.2
Description..................................................................................................................................................... 585
Define GFLIB_COS_DEFAULT_F32.........................................................................................................................585
9.39.1
Macro Definition............................................................................................................................................585
9.39.2
Description..................................................................................................................................................... 586
Define GFLIB_COS_DEFAULT_F16.........................................................................................................................586
9.40.1
Macro Definition............................................................................................................................................586
9.40.2
Description..................................................................................................................................................... 586
Define GFLIB_Hyst......................................................................................................................................................586
9.41.1
Macro Definition............................................................................................................................................586
9.41.2
Description..................................................................................................................................................... 586
Define GFLIB_HYST_DEFAULT_F32...................................................................................................................... 586
9.42.1
Macro Definition............................................................................................................................................587
9.42.2
Description..................................................................................................................................................... 587
Define GFLIB_HYST_DEFAULT_F16...................................................................................................................... 587
9.43.1
Macro Definition............................................................................................................................................587
9.43.2
Description..................................................................................................................................................... 587
Define GFLIB_IntegratorTR........................................................................................................................................ 587
9.44.1
Macro Definition............................................................................................................................................587
9.44.2
Description..................................................................................................................................................... 587
Define GFLIB_INTEGRATOR_TR_DEFAULT_F32................................................................................................ 588
Automotive Math and Motor Control Library Set for NXP MPC560xB devices, Rev. 7
NXP Semiconductors
49
Section number
9.46
9.47
9.48
9.49
9.50
9.51
9.52
9.53
9.54
Title
Page
9.45.1
Macro Definition............................................................................................................................................588
9.45.2
Description..................................................................................................................................................... 588
Define GFLIB_INTEGRATOR_TR_DEFAULT_F16................................................................................................ 588
9.46.1
Macro Definition............................................................................................................................................588
9.46.2
Description..................................................................................................................................................... 588
Define GFLIB_Limit.................................................................................................................................................... 588
9.47.1
Macro Definition............................................................................................................................................588
9.47.2
Description..................................................................................................................................................... 589
Define GFLIB_LIMIT_DEFAULT_F32......................................................................................................................589
9.48.1
Macro Definition............................................................................................................................................589
9.48.2
Description..................................................................................................................................................... 589
Define GFLIB_LIMIT_DEFAULT_F16......................................................................................................................589
9.49.1
Macro Definition............................................................................................................................................589
9.49.2
Description..................................................................................................................................................... 589
Define GFLIB_LowerLimit..........................................................................................................................................589
9.50.1
Macro Definition............................................................................................................................................590
9.50.2
Description..................................................................................................................................................... 590
Define GFLIB_LOWERLIMIT_DEFAULT_F32....................................................................................................... 590
9.51.1
Macro Definition............................................................................................................................................590
9.51.2
Description..................................................................................................................................................... 590
Define GFLIB_LOWERLIMIT_DEFAULT_F16....................................................................................................... 590
9.52.1
Macro Definition............................................................................................................................................590
9.52.2
Description..................................................................................................................................................... 590
Define GFLIB_Lut1D...................................................................................................................................................591
9.53.1
Macro Definition............................................................................................................................................591
9.53.2
Description..................................................................................................................................................... 591
Define GFLIB_LUT1D_DEFAULT_F32.................................................................................................................... 591
9.54.1
Macro Definition............................................................................................................................................591
9.54.2
Description..................................................................................................................................................... 591
Automotive Math and Motor Control Library Set for NXP MPC560xB devices, Rev. 7
50
NXP Semiconductors
Section number
9.55
9.56
9.57
9.58
9.59
9.60
9.61
9.62
9.63
9.64
Title
Page
Define GFLIB_LUT1D_DEFAULT_F16.................................................................................................................... 591
9.55.1
Macro Definition............................................................................................................................................591
9.55.2
Description..................................................................................................................................................... 592
Define GFLIB_Lut2D...................................................................................................................................................592
9.56.1
Macro Definition............................................................................................................................................592
9.56.2
Description..................................................................................................................................................... 592
Define GFLIB_LUT2D_DEFAULT_F32.................................................................................................................... 592
9.57.1
Macro Definition............................................................................................................................................592
9.57.2
Description..................................................................................................................................................... 592
Define GFLIB_LUT2D_DEFAULT_F16.................................................................................................................... 592
9.58.1
Macro Definition............................................................................................................................................593
9.58.2
Description..................................................................................................................................................... 593
Define GFLIB_Ramp....................................................................................................................................................593
9.59.1
Macro Definition............................................................................................................................................593
9.59.2
Description..................................................................................................................................................... 593
Define GFLIB_RAMP_DEFAULT_F32..................................................................................................................... 593
9.60.1
Macro Definition............................................................................................................................................593
9.60.2
Description..................................................................................................................................................... 593
Define GFLIB_RAMP_DEFAULT_F16..................................................................................................................... 594
9.61.1
Macro Definition............................................................................................................................................594
9.61.2
Description..................................................................................................................................................... 594
Define GFLIB_Sign......................................................................................................................................................594
9.62.1
Macro Definition............................................................................................................................................594
9.62.2
Description..................................................................................................................................................... 594
Define GFLIB_Sin........................................................................................................................................................594
9.63.1
Macro Definition............................................................................................................................................594
9.63.2
Description..................................................................................................................................................... 595
Define GFLIB_SIN_DEFAULT_F32.......................................................................................................................... 595
9.64.1
Macro Definition............................................................................................................................................595
Automotive Math and Motor Control Library Set for NXP MPC560xB devices, Rev. 7
NXP Semiconductors
51
Section number
9.64.2
9.65
9.66
9.67
9.68
9.69
9.70
9.71
9.72
9.73
9.74
Title
Page
Description..................................................................................................................................................... 595
Define GFLIB_SIN_DEFAULT_F16.......................................................................................................................... 595
9.65.1
Macro Definition............................................................................................................................................595
9.65.2
Description..................................................................................................................................................... 595
Define GFLIB_SinCos..................................................................................................................................................595
9.66.1
Macro Definition............................................................................................................................................596
9.66.2
Description..................................................................................................................................................... 596
Define GFLIB_SINCOS_DEFAULT_F32.................................................................................................................. 596
9.67.1
Macro Definition............................................................................................................................................596
9.67.2
Description..................................................................................................................................................... 596
Define GFLIB_SINCOS_DEFAULT_F16.................................................................................................................. 596
9.68.1
Macro Definition............................................................................................................................................596
9.68.2
Description..................................................................................................................................................... 596
Define GFLIB_Sqrt...................................................................................................................................................... 597
9.69.1
Macro Definition............................................................................................................................................597
9.69.2
Description..................................................................................................................................................... 597
Define GFLIB_Tan.......................................................................................................................................................597
9.70.1
Macro Definition............................................................................................................................................597
9.70.2
Description..................................................................................................................................................... 597
Define GFLIB_TAN_DEFAULT_F32........................................................................................................................ 597
9.71.1
Macro Definition............................................................................................................................................597
9.71.2
Description..................................................................................................................................................... 598
Define GFLIB_TAN_DEFAULT_F16........................................................................................................................ 598
9.72.1
Macro Definition............................................................................................................................................598
9.72.2
Description..................................................................................................................................................... 598
Define GFLIB_UpperLimit.......................................................................................................................................... 598
9.73.1
Macro Definition............................................................................................................................................598
9.73.2
Description..................................................................................................................................................... 598
Define GFLIB_UPPERLIMIT_DEFAULT_F32......................................................................................................... 598
Automotive Math and Motor Control Library Set for NXP MPC560xB devices, Rev. 7
52
NXP Semiconductors
Section number
9.75
9.76
9.77
9.78
9.79
9.80
9.81
9.82
9.83
Title
Page
9.74.1
Macro Definition............................................................................................................................................599
9.74.2
Description..................................................................................................................................................... 599
Define GFLIB_UPPERLIMIT_DEFAULT_F16......................................................................................................... 599
9.75.1
Macro Definition............................................................................................................................................599
9.75.2
Description..................................................................................................................................................... 599
Define GFLIB_VectorLimit......................................................................................................................................... 599
9.76.1
Macro Definition............................................................................................................................................599
9.76.2
Description..................................................................................................................................................... 599
Define GFLIB_VECTORLIMIT_DEFAULT_F32......................................................................................................600
9.77.1
Macro Definition............................................................................................................................................600
9.77.2
Description..................................................................................................................................................... 600
Define GFLIB_VECTORLIMIT_DEFAULT_F16......................................................................................................600
9.78.1
Macro Definition............................................................................................................................................600
9.78.2
Description..................................................................................................................................................... 600
Define GMCLIB_Clark................................................................................................................................................ 600
9.79.1
Macro Definition............................................................................................................................................600
9.79.2
Description..................................................................................................................................................... 601
Define GMCLIB_ClarkInv...........................................................................................................................................601
9.80.1
Macro Definition............................................................................................................................................601
9.80.2
Description..................................................................................................................................................... 601
Define GMCLIB_DecouplingPMSM...........................................................................................................................601
9.81.1
Macro Definition............................................................................................................................................601
9.81.2
Description..................................................................................................................................................... 601
Define GMCLIB_DECOUPLINGPMSM_DEFAULT_F32........................................................................................602
9.82.1
Macro Definition............................................................................................................................................602
9.82.2
Description..................................................................................................................................................... 602
Define GMCLIB_DECOUPLINGPMSM_DEFAULT_F16........................................................................................602
9.83.1
Macro Definition............................................................................................................................................602
9.83.2
Description..................................................................................................................................................... 602
Automotive Math and Motor Control Library Set for NXP MPC560xB devices, Rev. 7
NXP Semiconductors
53
Section number
9.84
9.85
9.86
9.87
9.88
9.89
9.90
9.91
9.92
9.93
Title
Page
Define GMCLIB_ELIMDCBUSRIP_FLT_DNMAX..................................................................................................602
9.84.1
Macro Definition............................................................................................................................................602
9.84.2
Description..................................................................................................................................................... 602
Define GMCLIB_ElimDcBusRip.................................................................................................................................603
9.85.1
Macro Definition............................................................................................................................................603
9.85.2
Description..................................................................................................................................................... 603
Define GMCLIB_ELIMDCBUSRIP_DEFAULT_F32............................................................................................... 603
9.86.1
Macro Definition............................................................................................................................................603
9.86.2
Description..................................................................................................................................................... 603
Define GMCLIB_ELIMDCBUSRIP_DEFAULT_F16............................................................................................... 603
9.87.1
Macro Definition............................................................................................................................................603
9.87.2
Description..................................................................................................................................................... 604
Define GMCLIB_Park..................................................................................................................................................604
9.88.1
Macro Definition............................................................................................................................................604
9.88.2
Description..................................................................................................................................................... 604
Define GMCLIB_ParkInv............................................................................................................................................ 604
9.89.1
Macro Definition............................................................................................................................................604
9.89.2
Description..................................................................................................................................................... 604
Define GMCLIB_SvmStd............................................................................................................................................ 604
9.90.1
Macro Definition............................................................................................................................................605
9.90.2
Description..................................................................................................................................................... 605
Define MLIB_Abs........................................................................................................................................................ 605
9.91.1
Macro Definition............................................................................................................................................605
9.91.2
Description..................................................................................................................................................... 605
Define MLIB_AbsSat................................................................................................................................................... 605
9.92.1
Macro Definition............................................................................................................................................605
9.92.2
Description..................................................................................................................................................... 605
Define MLIB_Add........................................................................................................................................................606
9.93.1
Macro Definition............................................................................................................................................606
Automotive Math and Motor Control Library Set for NXP MPC560xB devices, Rev. 7
54
NXP Semiconductors
Section number
9.93.2
9.94
9.95
9.96
9.97
9.98
9.99
Title
Page
Description..................................................................................................................................................... 606
Define MLIB_AddSat...................................................................................................................................................606
9.94.1
Macro Definition............................................................................................................................................606
9.94.2
Description..................................................................................................................................................... 606
Define MLIB_Convert..................................................................................................................................................606
9.95.1
Macro Definition............................................................................................................................................606
9.95.2
Description..................................................................................................................................................... 607
Define MLIB_ConvertPU.............................................................................................................................................607
9.96.1
Macro Definition............................................................................................................................................607
9.96.2
Description..................................................................................................................................................... 607
Define MLIB_Div.........................................................................................................................................................607
9.97.1
Macro Definition............................................................................................................................................607
9.97.2
Description..................................................................................................................................................... 607
Define MLIB_DivSat....................................................................................................................................................607
9.98.1
Macro Definition............................................................................................................................................608
9.98.2
Description..................................................................................................................................................... 608
Define MLIB_Mac........................................................................................................................................................608
9.99.1
Macro Definition............................................................................................................................................608
9.99.2
Description..................................................................................................................................................... 608
9.100 Define MLIB_MacSat.................................................................................................................................................. 608
9.100.1 Macro Definition............................................................................................................................................608
9.100.2 Description..................................................................................................................................................... 608
9.101 Define MLIB_Mnac......................................................................................................................................................609
9.101.1 Macro Definition............................................................................................................................................609
9.101.2 Description..................................................................................................................................................... 609
9.102 Define MLIB_Msu........................................................................................................................................................609
9.102.1 Macro Definition............................................................................................................................................609
9.102.2 Description..................................................................................................................................................... 609
9.103 Define MLIB_Mul........................................................................................................................................................ 609
Automotive Math and Motor Control Library Set for NXP MPC560xB devices, Rev. 7
NXP Semiconductors
55
Section number
Title
Page
9.103.1 Macro Definition............................................................................................................................................609
9.103.2 Description..................................................................................................................................................... 610
9.104 Define MLIB_MulSat...................................................................................................................................................610
9.104.1 Macro Definition............................................................................................................................................610
9.104.2 Description..................................................................................................................................................... 610
9.105 Define MLIB_Neg........................................................................................................................................................ 610
9.105.1 Macro Definition............................................................................................................................................610
9.105.2 Description..................................................................................................................................................... 610
9.106 Define MLIB_NegSat...................................................................................................................................................610
9.106.1 Macro Definition............................................................................................................................................611
9.106.2 Description..................................................................................................................................................... 611
9.107 Define MLIB_Norm..................................................................................................................................................... 611
9.107.1 Macro Definition............................................................................................................................................611
9.107.2 Description..................................................................................................................................................... 611
9.108 Define MLIB_Round.................................................................................................................................................... 611
9.108.1 Macro Definition............................................................................................................................................611
9.108.2 Description..................................................................................................................................................... 611
9.109 Define MLIB_ShBi.......................................................................................................................................................612
9.109.1 Macro Definition............................................................................................................................................612
9.109.2 Description..................................................................................................................................................... 612
9.110 Define MLIB_ShBiSat..................................................................................................................................................612
9.110.1 Macro Definition............................................................................................................................................612
9.110.2 Description..................................................................................................................................................... 612
9.111 Define MLIB_ShL........................................................................................................................................................ 612
9.111.1 Macro Definition............................................................................................................................................613
9.111.2 Description..................................................................................................................................................... 613
9.112 Define MLIB_ShLSat...................................................................................................................................................613
9.112.1 Macro Definition............................................................................................................................................613
9.112.2 Description..................................................................................................................................................... 613
Automotive Math and Motor Control Library Set for NXP MPC560xB devices, Rev. 7
56
NXP Semiconductors
Section number
Title
Page
9.113 Define MLIB_ShR........................................................................................................................................................613
9.113.1 Macro Definition............................................................................................................................................613
9.113.2 Description..................................................................................................................................................... 613
9.114 Define MLIB_Sub........................................................................................................................................................ 614
9.114.1 Macro Definition............................................................................................................................................614
9.114.2 Description..................................................................................................................................................... 614
9.115 Define MLIB_SubSat................................................................................................................................................... 614
9.115.1 Macro Definition............................................................................................................................................614
9.115.2 Description..................................................................................................................................................... 614
9.116 Define MLIB_VMac.....................................................................................................................................................614
9.116.1 Macro Definition............................................................................................................................................614
9.116.2 Description..................................................................................................................................................... 614
9.117 Define SWLIBS_VERSION.........................................................................................................................................615
9.117.1 Macro Definition............................................................................................................................................615
9.117.2 Description..................................................................................................................................................... 615
9.118 Define SWLIBS_STD_ON...........................................................................................................................................615
9.118.1 Macro Definition............................................................................................................................................615
9.118.2 Description..................................................................................................................................................... 615
9.119 Define SWLIBS_STD_OFF......................................................................................................................................... 615
9.119.1 Macro Definition............................................................................................................................................615
9.119.2 Description..................................................................................................................................................... 615
9.120 Define F32.................................................................................................................................................................... 616
9.120.1 Macro Definition............................................................................................................................................616
9.120.2 Description..................................................................................................................................................... 616
9.121 Define F16.................................................................................................................................................................... 616
9.121.1 Macro Definition............................................................................................................................................616
9.121.2 Description..................................................................................................................................................... 616
9.122 Define FLT....................................................................................................................................................................616
9.122.1 Macro Definition............................................................................................................................................616
Automotive Math and Motor Control Library Set for NXP MPC560xB devices, Rev. 7
NXP Semiconductors
57
Section number
Title
Page
9.122.2 Description..................................................................................................................................................... 616
9.123 Define SWLIBS_DEFAULT_IMPLEMENTATION_F32..........................................................................................617
9.123.1 Macro Definition............................................................................................................................................617
9.123.2 Description..................................................................................................................................................... 617
9.124 Define SWLIBS_DEFAULT_IMPLEMENTATION_F16..........................................................................................617
9.124.1 Macro Definition............................................................................................................................................617
9.124.2 Description..................................................................................................................................................... 617
9.125 Define SWLIBS_DEFAULT_IMPLEMENTATION_FLT.........................................................................................617
9.125.1 Macro Definition............................................................................................................................................617
9.125.2 Description..................................................................................................................................................... 617
9.126 Define SWLIBS_SUPPORT_F32................................................................................................................................ 618
9.126.1 Macro Definition............................................................................................................................................618
9.126.2 Description..................................................................................................................................................... 618
9.127 Define SWLIBS_SUPPORT_F16................................................................................................................................ 618
9.127.1 Macro Definition............................................................................................................................................618
9.127.2 Description..................................................................................................................................................... 618
9.128 Define SWLIBS_SUPPORT_FLT............................................................................................................................... 618
9.128.1 Macro Definition............................................................................................................................................618
9.128.2 Description..................................................................................................................................................... 619
9.129 Define SWLIBS_SUPPORTED_IMPLEMENTATION............................................................................................. 619
9.129.1 Macro Definition............................................................................................................................................619
9.129.2 Description..................................................................................................................................................... 619
9.130 Define SWLIBS_DEFAULT_IMPLEMENTATION.................................................................................................. 619
9.130.1 Macro Definition............................................................................................................................................619
9.130.2 Description..................................................................................................................................................... 619
9.131 Define SFRACT_MIN..................................................................................................................................................620
9.131.1 Macro Definition............................................................................................................................................620
9.131.2 Description..................................................................................................................................................... 620
9.132 Define SFRACT_MAX................................................................................................................................................ 620
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Title
Page
9.132.1 Macro Definition............................................................................................................................................620
9.132.2 Description..................................................................................................................................................... 620
9.133 Define FRACT_MIN.................................................................................................................................................... 620
9.133.1 Macro Definition............................................................................................................................................620
9.133.2 Description..................................................................................................................................................... 621
9.134 Define FRACT_MAX.................................................................................................................................................. 621
9.134.1 Macro Definition............................................................................................................................................621
9.134.2 Description..................................................................................................................................................... 621
9.135 Define FRAC32_0_5.................................................................................................................................................... 621
9.135.1 Macro Definition............................................................................................................................................621
9.135.2 Description..................................................................................................................................................... 621
9.136 Define FRAC16_0_5.................................................................................................................................................... 622
9.136.1 Macro Definition............................................................................................................................................622
9.136.2 Description..................................................................................................................................................... 622
9.137 Define FRAC32_0_25.................................................................................................................................................. 622
9.137.1 Macro Definition............................................................................................................................................622
9.137.2 Description..................................................................................................................................................... 622
9.138 Define FRAC16_0_25.................................................................................................................................................. 622
9.138.1 Macro Definition............................................................................................................................................622
9.138.2 Description..................................................................................................................................................... 622
9.139 Define UINT16_MAX..................................................................................................................................................623
9.139.1 Macro Definition............................................................................................................................................623
9.139.2 Description..................................................................................................................................................... 623
9.140 Define INT16_MAX.....................................................................................................................................................623
9.140.1 Macro Definition............................................................................................................................................623
9.140.2 Description..................................................................................................................................................... 623
9.141 Define INT16_MIN...................................................................................................................................................... 623
9.141.1 Macro Definition............................................................................................................................................624
9.141.2 Description..................................................................................................................................................... 624
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59
Section number
Title
Page
9.142 Define UINT32_MAX..................................................................................................................................................624
9.142.1 Macro Definition............................................................................................................................................624
9.142.2 Description..................................................................................................................................................... 624
9.143 Define INT32_MAX.....................................................................................................................................................624
9.143.1 Macro Definition............................................................................................................................................624
9.143.2 Description..................................................................................................................................................... 624
9.144 Define INT32_MIN...................................................................................................................................................... 625
9.144.1 Macro Definition............................................................................................................................................625
9.144.2 Description..................................................................................................................................................... 625
9.145 Define INT16TOINT32................................................................................................................................................ 625
9.145.1 Macro Definition............................................................................................................................................625
9.145.2 Description..................................................................................................................................................... 625
9.146 Define INT32TOINT16................................................................................................................................................ 625
9.146.1 Macro Definition............................................................................................................................................626
9.146.2 Description..................................................................................................................................................... 626
9.147 Define INT32TOINT64................................................................................................................................................ 626
9.147.1 Macro Definition............................................................................................................................................626
9.147.2 Description..................................................................................................................................................... 626
9.148 Define INT64TOINT32................................................................................................................................................ 626
9.148.1 Macro Definition............................................................................................................................................626
9.148.2 Description..................................................................................................................................................... 626
9.149 Define F16TOINT16.................................................................................................................................................... 627
9.149.1 Macro Definition............................................................................................................................................627
9.149.2 Description..................................................................................................................................................... 627
9.150 Define F32TOINT16.................................................................................................................................................... 627
9.150.1 Macro Definition............................................................................................................................................627
9.150.2 Description..................................................................................................................................................... 627
9.151 Define F64TOINT16.................................................................................................................................................... 627
9.151.1 Macro Definition............................................................................................................................................627
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NXP Semiconductors
Section number
Title
Page
9.151.2 Description..................................................................................................................................................... 628
9.152 Define F16TOINT32.................................................................................................................................................... 628
9.152.1 Macro Definition............................................................................................................................................628
9.152.2 Description..................................................................................................................................................... 628
9.153 Define F32TOINT32.................................................................................................................................................... 628
9.153.1 Macro Definition............................................................................................................................................628
9.153.2 Description..................................................................................................................................................... 628
9.154 Define F64TOINT32.................................................................................................................................................... 628
9.154.1 Macro Definition............................................................................................................................................629
9.154.2 Description..................................................................................................................................................... 629
9.155 Define F16TOINT64.................................................................................................................................................... 629
9.155.1 Macro Definition............................................................................................................................................629
9.155.2 Description..................................................................................................................................................... 629
9.156 Define F32TOINT64.................................................................................................................................................... 629
9.156.1 Macro Definition............................................................................................................................................629
9.156.2 Description..................................................................................................................................................... 629
9.157 Define F64TOINT64.................................................................................................................................................... 630
9.157.1 Macro Definition............................................................................................................................................630
9.157.2 Description..................................................................................................................................................... 630
9.158 Define INT16TOF16.................................................................................................................................................... 630
9.158.1 Macro Definition............................................................................................................................................630
9.158.2 Description..................................................................................................................................................... 630
9.159 Define INT16TOF32.................................................................................................................................................... 630
9.159.1 Macro Definition............................................................................................................................................630
9.159.2 Description..................................................................................................................................................... 631
9.160 Define INT32TOF16.................................................................................................................................................... 631
9.160.1 Macro Definition............................................................................................................................................631
9.160.2 Description..................................................................................................................................................... 631
9.161 Define INT32TOF32.................................................................................................................................................... 631
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Section number
Title
Page
9.161.1 Macro Definition............................................................................................................................................631
9.161.2 Description..................................................................................................................................................... 631
9.162 Define INT64TOF16.................................................................................................................................................... 632
9.162.1 Macro Definition............................................................................................................................................632
9.162.2 Description..................................................................................................................................................... 632
9.163 Define INT64TOF32.................................................................................................................................................... 632
9.163.1 Macro Definition............................................................................................................................................632
9.163.2 Description..................................................................................................................................................... 632
9.164 Define F16_1_DIVBY_SQRT3....................................................................................................................................632
9.164.1 Macro Definition............................................................................................................................................632
9.164.2 Description..................................................................................................................................................... 633
9.165 Define F32_1_DIVBY_SQRT3....................................................................................................................................633
9.165.1 Macro Definition............................................................................................................................................633
9.165.2 Description..................................................................................................................................................... 633
9.166 Define F16_SQRT3_DIVBY_2....................................................................................................................................633
9.166.1 Macro Definition............................................................................................................................................633
9.166.2 Description..................................................................................................................................................... 633
9.167 Define F32_SQRT3_DIVBY_2....................................................................................................................................633
9.167.1 Macro Definition............................................................................................................................................634
9.167.2 Description..................................................................................................................................................... 634
9.168 Define F16_SQRT2_DIVBY_2....................................................................................................................................634
9.168.1 Macro Definition............................................................................................................................................634
9.168.2 Description..................................................................................................................................................... 634
9.169 Define F32_SQRT2_DIVBY_2....................................................................................................................................634
9.169.1 Macro Definition............................................................................................................................................634
9.169.2 Description..................................................................................................................................................... 634
9.170 Define FRAC16............................................................................................................................................................ 635
9.170.1 Macro Definition............................................................................................................................................635
9.170.2 Description..................................................................................................................................................... 635
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Title
Page
9.171 Define FRAC32............................................................................................................................................................ 635
9.171.1 Macro Definition............................................................................................................................................635
9.171.2 Description..................................................................................................................................................... 635
9.172 Define NULL................................................................................................................................................................ 635
9.172.1 Macro Definition............................................................................................................................................636
9.172.2 Description..................................................................................................................................................... 636
9.173 Define FALSE.............................................................................................................................................................. 636
9.173.1 Macro Definition............................................................................................................................................636
9.173.2 Description..................................................................................................................................................... 636
9.174 Define TRUE................................................................................................................................................................ 636
9.174.1 Macro Definition............................................................................................................................................636
9.174.2 Description..................................................................................................................................................... 636
9.175 Define SWLIBS_2Syst................................................................................................................................................. 637
9.175.1 Macro Definition............................................................................................................................................637
9.175.2 Description..................................................................................................................................................... 637
9.176 Define SWLIBS_2Syst................................................................................................................................................. 637
9.176.1 Macro Definition............................................................................................................................................637
9.176.2 Description..................................................................................................................................................... 637
9.177 Define SWLIBS_2Syst................................................................................................................................................. 637
9.177.1 Macro Definition............................................................................................................................................638
9.177.2 Description..................................................................................................................................................... 638
9.178 Define SWLIBS_3Syst................................................................................................................................................. 638
9.178.1 Macro Definition............................................................................................................................................638
9.178.2 Description..................................................................................................................................................... 638
9.179 Define SWLIBS_3Syst................................................................................................................................................. 638
9.179.1 Macro Definition............................................................................................................................................639
9.179.2 Description..................................................................................................................................................... 639
9.180 Define SWLIBS_3Syst................................................................................................................................................. 638
9.180.1 Macro Definition............................................................................................................................................639
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Section number
Title
Page
9.180.2 Description..................................................................................................................................................... 639
9.181 Define SWLIBS_VERSION_DEFAULT.................................................................................................................... 640
9.181.1 Macro Definition............................................................................................................................................640
9.181.2 Description..................................................................................................................................................... 640
9.182 Define SWLIBS_MCID_SIZE..................................................................................................................................... 640
9.182.1 Macro Definition............................................................................................................................................640
9.182.2 Description..................................................................................................................................................... 640
9.183 Define SWLIBS_MCVERSION_SIZE........................................................................................................................ 640
9.183.1 Macro Definition............................................................................................................................................640
9.183.2 Description..................................................................................................................................................... 640
9.184 Define SWLIBS_MCIMPLEMENTATION_SIZE......................................................................................................641
9.184.1 Macro Definition............................................................................................................................................641
9.184.2 Description..................................................................................................................................................... 641
9.185 Define SWLIBS_ID......................................................................................................................................................641
9.185.1 Macro Definition............................................................................................................................................641
9.185.2 Description..................................................................................................................................................... 641
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NXP Semiconductors
Chapter 1
Revision History
Revision
Date
Table 1-1. Revision History
Author
Description
1.0
30/11/2014
Petr Fajmon
Initial version.
2.0
31/03/2015
Jiri Kuhn
The Matlab revision, used for testing, changed to
Matlab 2014a.
3.0
31/07/2015
Petr Fajmon
The Qorivva brand name has been retired and
was removed. All compilers versions were
increased. Number of the significant digits of the
calculated IIR1/IIR2 coefficients in the MATLAB
examples for GDFLIB_IIR1/GDFLIB_IIR2
functions was increased.
4.0
30/09/2015
Jiri Kuhn
Adding the chapters describing the
GFLIB_SinCos function.
5.0
31/12/2015
Petr Fajmon
The Service Release v1.1.3. The GreenHills
compiler version was increased to the latest
v2015.1.4.
6.0
31/03/2016
Jiri Kuhn
Change from Freescale to NXP entity, Service
release 1.1.4.
7.0
30/06/2016
Petr Fajmon
The Service Release v1.1.5. Added support of
the S32 Design Studio for Power Architecture.
Added new MLIB_RndSat_F16F32 function.
Added chapter about possible exceptions.
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NXP Semiconductors
Chapter 2
2.1 ATTACHMENT A - NXP Automotive Software License
Agreement v1.3
IMPORTANT. Read the following NXP Software License Agreement ("Agreement")
completely. By selecting the "I Accept" button at the end of this page, you indicate that
you accept the terms of this Agreement. You may then install the software.
NXP SOFTWARE LICENSE AGREEMENT This is a legal agreement between you
(either as an individual or as an authorized representative of your employer) and
Freescale Semiconductor, Inc., a 100% affiliated company of NXP Semiconductors N.V.,
which will be renamed in due course, on behalf of itself and its Affiliates ("NXP").
"Affiliate" means any corporation, partnership, limited liability company or other entity,
which directly or indirectly controls, is controlled by, or is under common control with,
NXP Semiconductors N.V. It concerns your rights to use this file and any accompanying
written materials (the "Software"). In consideration for NXP allowing you to access the
Software, you are agreeing to be bound by the terms of this Agreement. If you do not
agree to all of the terms of this Agreement, do not download the Software. If you change
your mind later, stop using the Software and delete all copies of the Software in your
possession or control. Any copies of the Software that you have already distributed,
where permitted, and do not destroy will continue to be governed by this Agreement.
Your prior use will also continue to be governed by this Agreement. For the avoidance of
doubt, any third party software indicated in the Quotation Document as being provided is
not Software licensed under this Agreement and is governed solely by the terms and
conditions of the third party licensor. In addition, the parties acknowledge that the
Software may contain Open Source Software components. For the avoidance of doubt, all
Open Source Software components are governed solely by the applicable Open Source
Software licenses.
LICENSE GRANT: Your rights to use this Software vary depending upon the type of
license model you ordered from NXP. The type of license will be set forth in the NXP
Quotation document which formed the basis of your order or, with respect to evaluation
Automotive Math and Motor Control Library Set for NXP MPC560xB devices, Rev. 7
NXP Semiconductors
67
ATTACHMENT A - NXP Automotive Software License Agreement v1.3
licenses, in the correspondence with NXP confirming your request for a copy of the
Software for evaluation. If you do not remember this information, you may contact the
party from whom you obtained the Software or NXP at www.NXP.com.
Definitions: For purposes of this Agreement the following terms are defined as set forth
below: "Authorized System" means the Authorized System set forth in the Quotation
Documents or, if none is specified, Licensee's ECU product containing a NXP processor
or other semiconductor product supplied directly or indirectly from NXP. "Confidential
Information" means any information disclosed by NXP to the Licensee and, if disclosed
in writing or in some other tangible form, that is marked at the time of disclosure as being
"Confidential" or "Proprietary" or with words of similar import; provided, that Software
provided in source code format will be deemed Confidential Information whether or not
identified as such in writing or otherwise. Confidential Information does not include any
information that: (a) is, or becomes, publicly known through no wrongful act on the
Licensee's part; (b) is already known to the Licensee, or becomes lawfully known to the
Licensee without restriction on disclosure; or (c) is independently developed by the
Licensee. "Customer Product Line" means the customer product line specified in the
Quotation Document. "Customer Target Project" means the one customer Target Project
for one automotive vehicle manufacturer specified in the Quotation Document. "Limited
Derivative Works" means Licensee may make derivative works only to the extent the
copyrighted material provided by NXP is not modified. For the avoidance of doubt,
Licensee explicitly has the right to: 1) add source code to source code provided by NXP
without modification to the original source code; 2) compile any source code into object
code, or 3) integrate the NXP source code into its ECU without modifying the original
source code. "Quotation Document" means the NXP or NXP authorized reseller
document offering the goods and/or services which formed the basis of your order and
which is incorporated herein by this reference. "DISM Package" is a commercial offering
bundling a Development License with software support and maintenance services as
described in detail in the Quotation document. "NXP Target Product" means the NXP
processor or other semiconductor product set forth in the Quotation Document. "NXP
Target Product Family" means the NXP processor family or other semiconductor product
family set forth in the Quotation Document. "Open Source Software" means any software
that is subject to terms that, as a condition of use, copying, modification or redistribution,
require such software and/or derivative works thereof to be disclosed or distributed in
source code form, to be licensed for the purpose of making derivative works, or to be
redistributed free of charge, including without limitation software distributed under the
GNU General Public License or GNU Lesser/Library and General Public License,
Apache or BSD.
I. Non-Production License Models:
Automotive Math and Motor Control Library Set for NXP MPC560xB devices, Rev. 7
68
NXP Semiconductors
Chapter 2
a. Evaluation License: NXP grants to you, free of charge, a personal, non-transferable,
non-exclusive, revocable, royalty-free, license to use the Software for ninety (90)
consecutive days from the date of your acceptance as indicated by clicking the "I accept"
button below, internally, solely for the purpose of performing evaluation and testing of
the Software, solely for automotive use, and solely on a NXP Target Product. This
license does not include the right to reproduce, distribute, sell, lease, sublicense or
transfer all or any part of the Software, or to use the Software on non-NXP integrated
circuit devices, or to use the Software for any production purposes whatsoever. NXP
reserves all rights not expressly granted in this Agreement. If you violate any of the terms
or restrictions of this Agreement, NXP may immediately terminate this Agreement, and
require that you stop using and delete all copies of the Software in your possession or
control. b. Development License as part of the DISM Package: Subject to payment of the
fees set forth in the Quotation Document, NXP grants to you a personal, non-transferable,
non-exclusive, revocable, license for 12 months beginning on the date of your registration
or, if you are renewing, the anniversary date of your registration or prior renewal as
indicated by clicking the "I accept" button below, unless a different license term is
specified in the Quotation Document ("Term"), (1) to use the Software on one Target
Product Family for execution on a maximum of 500 sample Authorized Systems, (2) to
reproduce the Software, (3) to prepare Limited Derivative Works of the Licensed
Software (4) to distribute the Software and Limited Derivative Works thereof to
automotive customers in object code only, (5) to sublicense to automotive customers the
right to use the distributed Software in object code only as included within the
Authorized System solely for purposes of testing the Authorized System during the Term,
and (6) to disclose one copy of the Software and Limited Derivative Works thereof in
source code to direct automotive customers solely for internal evaluation and testing or
archiving (and not for further use, reproduction, modification or redistribution) only
where such disclosure is necessary in order to achieve the purpose of the license because
the automotive customer requires disclosure of source code in conjunction with the
testing or purchase of an Authorized System incorporating a NXP Target Product, and
where the direct automotive customer has executed written agreements obligating itself to
observe the limitations set out in this subsection (6) and to protect such Confidential
Information on terms at least as strict as those contained in this Agreement. NXP reserves
all rights not expressly granted in this Agreement. You must prohibit your sublicensees
from translating, reverse engineering, decompiling, or disassembling the Software except
to the extent applicable law specifically prohibits such restriction. If you violate any of
the terms or restrictions of this Agreement, NXP may immediately terminate this
Agreement, and require that you stop using and delete all copies of the Software in your
possession or control. You are solely responsible for systems you design using the
Software.
II. Production License Models:
Automotive Math and Motor Control Library Set for NXP MPC560xB devices, Rev. 7
NXP Semiconductors
69
ATTACHMENT A - NXP Automotive Software License Agreement v1.3
a. Project License: Subject to payment of the fees set forth in the Quotation Document,
exclusively in conjunction with Licensee's development and sale of an Authorized
System, NXP grants to you the non-exclusive, non-transferable right (1) to use the
Software in the Customer Target Project on the Target Product, (2) to reproduce the
Software, (3) to prepare or have prepared through multiple layers of subcontractors
Limited Derivative Works of the Software, (4) to distribute the Software and Limited
Derivative Works thereof in object code only as part of an Authorized System, (5) to
sublicense to others the right to use the distributed Software in object code only as
included within the Authorized System, and (6) to disclose one copy of the Software and
Limited Derivative Works thereof in source code to direct automotive customers solely
for internal evaluation and testing or archiving (and not for further use, reproduction,
modification or redistribution) only where such disclosure is necessary in order to
achieve the purpose of the license because the automotive customer requires disclosure of
source code in conjunction with the testing or purchase of an Authorized System
incorporating a NXP Target Product, and where the direct automotive customer has
executed written agreements obligating itself to observe the limitations set out in this
subsection (6) and to protect such Confidential Information on terms at least as strict as
those contained in this Agreement. Licensee will remain liable for such subcontractor's
adherence to the terms of this Agreement and for any and all acts and omissions of such
subcontractors with respect to this Agreement. Notwithstanding limitation on damages in
this Agreement, Licensee will indemnify, defend, and hold harmless NXP against any
and all claims, costs, damages, liabilities, judgments and attorneys' fees resulting from or
arising out of any breach by the sublicensee, or resulting from or arising out of any action
by the sublicensee inconsistent with this Agreement. You must prohibit your sublicensees
from translating, reverse engineering, decompiling, or disassembling the Software except
to the extent applicable law specifically prohibits such restriction. If you violate any of
the terms or restrictions of this Agreement, NXP may immediately terminate this
Agreement, and require that you stop using and delete all copies of the Software in your
possession or control.
b. Product Line License: Subject to payment of the fees set forth in the Quotation
Document, exclusively in conjunction with Licensee's development and sale of an
Authorized System, NXP grants to you, the non-exclusive, non-transferable right (1) to
use the Software in one Target Product Family in one Customer Product Line, (2) to
reproduce the Software, (3) to prepare or have prepared through multiple layers of
subcontractors Limited Derivative Works of the Software, (4) to distribute the Software
and Limited Derivative Works thereof in object code only as part of an Authorized
System, (5) to sublicense to others the right to use the distributed Software in object code
only as included within the Authorized System and (6) to disclose one copy of the
Software and Limited Derivative Works thereof in source code to direct automotive
customers solely for internal evaluation and testing or archiving (and not for further use,
reproduction, modification or redistribution) only where such disclosure is necessary in
Automotive Math and Motor Control Library Set for NXP MPC560xB devices, Rev. 7
70
NXP Semiconductors
Chapter 2
order to achieve the purpose of the license because the automotive customer requires
disclosure of source code in conjunction with the testing or purchase of an Authorized
System incorporating a NXP Target Product, and where the direct automotive customer
has executed written agreements obligating itself to observe the limitations set out in this
subsection (6) and to protect such Confidential Information on terms at least as strict as
those contained in this Agreement. Licensee will remain liable for such subcontractor's
adherence to the terms of this Agreement and for any and all acts and omissions of such
subcontractors with respect to this Agreement. Notwithstanding limitation on damages in
this Agreement, Licensee will indemnify, defend, and hold harmless NXP against any
and all claims, costs, damages, liabilities, judgments and attorneys' fees resulting from or
arising out of any breach by the sublicensee, or resulting from or arising out of any action
by the sublicensee inconsistent with this Agreement. You must prohibit your sublicensees
from translating, reverse engineering, decompiling, or disassembling the Software except
to the extent applicable law specifically prohibits such restriction. If you violate any of
the terms or restrictions of this Agreement, NXP may immediately terminate this
Agreement, and require that you stop using and delete all copies of the Software in your
possession or control.
c. Family Multi-Project License: Subject to payment of the fees set forth in the Quotation
Document, exclusively in conjunction with Licensee's development and sale of an
Authorized System, NXP grants to you, the non-exclusive, non-transferable right (1) to
use the Software in one Target Product Family, (2) to reproduce the Software, (3) to
prepare or have prepared through multiple layers of subcontractors Limited Derivative
Works of the Software, (4) to distribute the Software and Limited Derivative Works
thereof in object code only as part of an Authorized System, (5) to sublicense to others
the right to use the distributed Software in object code only as included within the
Authorized System and (6) to disclose one copy of the Software and Limited Derivative
Works thereof in source code to direct automotive customers solely for internal
evaluation and testing or archiving (and not for further use, reproduction, modification or
redistribution) only where such disclosure is necessary in order to achieve the purpose of
the license because the automotive customer requires disclosure of source code in
conjunction with the testing or purchase of an Authorized System incorporating a NXP
Target Product, and where the direct automotive customer has executed written
agreements obligating itself to observe the limitations set out in this subsection (6) and to
protect such Confidential Information on terms at least as strict as those contained in this
Agreement. Licensee will remain liable for such subcontractor's adherence to the terms of
this Agreement and for any and all acts and omissions of such subcontractors with respect
to this Agreement. Notwithstanding limitation on damages in this Agreement, Licensee
will indemnify, defend, and hold harmless NXP against any and all claims, costs,
damages, liabilities, judgments and attorneys' fees resulting from or arising out of any
breach by the sublicensee, or resulting from or arising out of any action by the
sublicensee inconsistent with this Agreement. You must prohibit your sublicensees from
Automotive Math and Motor Control Library Set for NXP MPC560xB devices, Rev. 7
NXP Semiconductors
71
ATTACHMENT A - NXP Automotive Software License Agreement v1.3
translating, reverse engineering, decompiling, or disassembling the Software except to
the extent applicable law specifically prohibits such restriction. If you violate any of the
terms or restrictions of this Agreement, NXP may immediately terminate this Agreement,
and require that you stop using and delete all copies of the Software in your possession or
control.
d. Volume License: Subject to payment of the fees set forth in the Quotation Document.,
exclusively in conjunction with Licensee's development and sale of a Authorized System,
NXP grants to you, the non-exclusive, non-transferable right (1) to use the Software in
one Target Product Family on a maximum of the number of Authorized Systems set forth
in the Quotation Document, (2) to reproduce the Software, (3) to prepare or have
prepared through multiple layers of subcontractors Limited Derivative Works of the
Software, (4) to distribute the Software and Limited Derivative Works thereof in object
code only as part of an Authorized System, (5) to sublicense to others the right to use the
distributed Software in object code only as included within the Authorized System and
(6) to disclose one copy of the Software and Limited Derivative Works thereof in source
code to direct automotive customers solely for internal evaluation and testing or archiving
(and not for further use, reproduction, modification or redistribution) only where such
disclosure is necessary in order to achieve the purpose of the license because the
automotive customer requires disclosure of source code in conjunction with the testing or
purchase of an Authorized System incorporating a NXP Target Product, and where the
direct automotive customer has executed written agreements obligating itself to observe
the limitations set out in this subsection (6) and to protect such Confidential Information
on terms at least as strict as those contained in this Agreement. Licensee will remain
liable for such subcontractor's adherence to the terms of this Agreement and for any and
all acts and omissions of such subcontractors with respect to this Agreement.
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Chapter 2
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ATTACHMENT A - NXP Automotive Software License Agreement v1.3
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ATTACHMENT A - NXP Automotive Software License Agreement v1.3
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Chapter 3
Introduction
The aim of this document is to describe the Automotive Math and Motor Control Library
Set for NXP MPC560xB devices. It describes the components of the library, its behavior
and interaction, the API and steps needed to integrate the library into the customer
project.
3.1 Architecture Overview
The Automotive Math and Motor Control Library Set for NXP MPC560xB devices
consists of several sub-libraries, functionally connected as depicted in Figure 3-1.
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General Information
Figure 3-1. AMMCLIB components structure
The Automotive Math and Motor Control Library Set for NXP MPC560xB devices sublibraries are as follows:
• Mathematical Function Library (MLIB) - comprising basic mathematical
operations such as addition, multiplication, etc.
• General Function Library (GFLIB) - comprising basic trigonometric and general
math functions such as sine, cosine, tan, hysteresis, limit, etc.
• General Digital Filters Library (GDFLIB) - comprising digital IIR and FIR filters
designed to be used in a motor control application
• General Motor Control Library (GMCLIB) - comprising standard algorithms
used for motor control such as Clarke/Park transformations, Space Vector
Modulation, etc.
As can be seen in Figure 3-1, the Automotive Math and Motor Control Library Set for
NXP MPC560xB devices libraries form the layer architecture where all upper libraries
utilize the functions from MLIB library. This concept is a key factor for mathematical
operations abstractions allowing to support the highly target-optimized variants.
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3.2 General Information
The Automotive Math and Motor Control Library Set for NXP MPC560xB devices was
developed to support these major implementations:
• Fixed-point 32-bit fractional
• Fixed-point 16-bit fractional
With exception of those functions where the mathematical principle limits the input or
output values, these values are considered to be in the following limits:
• Fixed-point 32-bit fractional: <-1; 1-2-31> in Q1.31 format and with minimum
positive normalized value 2-31.
• Fixed-point 16-bit fractional: <-1; 1-2-15> in Q1.15 format and with minimum
positive normalized value 2-15.
Also those functions which are not relevant for particular implementation, e.g. saturated
functions or shifting for single precision floating point implementation, are not delivered
with this package. For detailed information about available functions please refer to
Function Index.
NOTE
The fixed-point 32-bit fractional and fixed-point 16-bit
fractional functions are implemented based on the unity model.
Which means that the input and output numbers are normalized
to fit between the <-1; 1-2-31> or <-1; 1-2-15> range
representing the Q1.31 or Q1.15 format.
The Automotive Math and Motor Control Library Set for NXP MPC560xB devices was
tested using two different test methods. To test the precision of each function
implementation, the testing based on Matlab reference models was used. This release was
tested using the Matlab R2014a version. To test the implementation on the embedded
side, the target-in-loop testing was performed on the Automotive Math and Motor
Control Library Set for NXP MPC560xB devices. This release was tested using the SFIO
toolbox version 2.2 and Matlab R2014a version.
3.3 Multiple Implementation Support
In order to allow the user to utilize arbitrary implementation within one user application
without any limitations, three different function call methods are supported in the
Automotive Math and Motor Control Library Set for NXP MPC560xB devices:
• Global configuration option
• Additional parameter option
• API postfix option
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Multiple Implementation Support
Each of these method calls the API postfix function. Thus, for each implementation ( 32bit fixed-point, 16-bit fixed point ) only one function is available within the package. This
approach is based on ANSI-C99 ISO/IEC 9899:1999 function overloading.
By default the support of all implementations is turned off, thus the error message
"Define at least one supported implementation in SWLIBS_Config.h file." is displayed
during the compilation if no implementation is selected, preventing the user application
building. Following are the macro definitions enabling or disabling the implementation
support:
• SWLIBS_SUPPORT_F32 for 32-bit fixed-point implementation support selection
• SWLIBS_SUPPORT_F16 for 16-bit fixed-point implementation support selection
These macros are defined in the SWLIBS_Config.h file located in Common directory of
the Automotive Math and Motor Control Library Set for NXP MPC560xB devices
installation destination. To enable the support of each individual implementation the
relevant macro definition has to be set to SWLIBS_STD_ON.
3.3.1 Global Configuration Option
This function call supports the user legacy applications, which were based on older
version of Motor Control Library. Prior to any Automotive Math and Motor Control
Library Set for NXP MPC560xB devices function call using the Global configuration
option, the SWLIBS_DEFAULT_IMPLEMENTATION macro definition has to be setup
properly. This macro definition is not defined by default thus the error message "Define
default implementation in SWLIBS_Config.h file." is displayed during the compilation,
preventing the user application building.
The SWLIBS_DEFAULT_IMPLEMENTATION macro is defined in the SWLIBS_Config.h
file located in Common directory of the Automotive Math and Motor Control Library Set
for NXP MPC560xB devices installation destination. The
SWLIBS_DEFAULT_IMPLEMENTATION can be defined as the one of the following
supported implementations:
• SWLIBS_DEFAULT_IMPLEMENTATION_F32 for 32-bit fixed-point
implementation
• SWLIBS_DEFAULT_IMPLEMENTATION_F16 for 16-bit fixed-point
implementation
After proper definition of SWLIBS_DEFAULT_IMPLEMENTATION macro the
Automotive Math and Motor Control Library Set for NXP MPC560xB devices functions
can be called using standard legacy API convention, e.g. GFLIB_Sin(x).
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For example if the SWLIBS_DEFAULT_IMPLEMENTATION macro definition is set to
SWLIBS_DEFAULT_IMPLEMENTATION_F32, the 32-bit fixed-point implementation of
sine function is invoked after the GFLIB_Sin(x) API call. Note that all standard legacy
API calls will invoke the 32-bit fixed-point implementation in this example.
NOTE
As the Automotive Math and Motor Control Library Set for
NXP MPC560xB devices supports the global configuration
option, it is highly recommended to copy the
SWLIBS_Config.h file to your local structure and refer the
configuration to this local copy. This approach will prevent the
incorrect setup of default configuration option, in case multiple
projects with different default configuration are used.
3.3.2 Additional Parameter Option
In order to support the free selection of used implementation in the user application while
keeping the function name same as in standard legacy API approach, the additional
parameter option is implemented in the Automotive Math and Motor Control Library Set
for NXP MPC560xB devices. In this option the additional parameter is used to
distinguish which implementation shall be invoked. There are the following possible
switches selecting the implementation:
• F32 for 32-bit fixed-point implementation
• F16 for 16-bit fixed-point implementation
For example, if the user application needs to invoke the 16-bit fixed-point
implementation of sine function, the GFLIB_Sin(x, F16) API call needs to be used. Note
that there is a possibility to call any implementation of the functions in user application
without any limitation.
3.3.3 API Postfix Option
In order to support the free selection of used implementation in the user application while
keeping the number of parameters same as in standard legacy API approach, the API
postfix option is implemented in the Automotive Math and Motor Control Library Set for
NXP MPC560xB devices. In this option the implementation postfix is used to distinguish
which implementation shall be invoked. There are the following possible API postfixes
selecting the implementation:
• F32 for 32-bit fixed-point implementation
• F16 for 16-bit fixed-point implementation
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Supported Compilers
For example, if the user application needs to invoke the 32-bit implementation of sine
function, the GFLIB_Sin_F32 API call needs to be used. Note that there is a possibility to
call any implementation of the functions in user application without any limitation.
3.4 Supported Compilers
The Automotive Math and Motor Control Library Set for NXP MPC560xB devices is
written in ANSI-C99 ISO/IEC 9899:1999 standard language. The library was built and
tested using the following compilers:
1. Green Hills MULTI version 2015.1.4
2. Wind River Compiler version 5.9.4.4
3. CodeWarrior Development Studio for Microcontrollers version 10.6.4
4. S32 Design Studio for Power Architecture (GCC) v1.1
The library is delivered in a library module "MPC560xB_AMMCLIB.a" for the Green
Hills compiler. The library module is located in "C:\Freescale\AMMCLIB
\MPC560xB_AMMCLIB_v1.1.5\lib\ghs" folder (considering the default installation path).
For the Wind River compiler, the "MPC560xB_AMMCLIB.a" library module is delivered
within the installation package. The library module is located in "C:\Freescale
\AMMCLIB\MPC560xB_AMMCLIB_v1.1.5\lib\diab" folder (considering the default
installation path).
For the CodeWarrior Eclipse IDE, two library modules are delivered:
• "MPC560xB_AMMCLIB_<MCU_Core>_VLE_SC.a" for signed char data type
• "MPC560xB_AMMCLIB_<MCU_Core>_VLE_UC.a" for unsigned char data type
These library modules are located in "C:\Freescale\AMMCLIB
\MPC560xB_AMMCLIB_v1.1.5\lib\cw10x" folder (considering the default installation
path).
The library is delivered in a library module "MPC560xB_AMMCLIB.a" for the S32
Design Studio for Power Architecture IDE. The library module is located in "C:
\Freescale\AMMCLIB\MPC560xB_AMMCLIB_v1.1.5\lib\s32ds_ppc" folder (considering
the default installation path).
Together with the pre-compiled library modules, these are all the necessary header files.
The interfaces to the algorithms included in this library have been combined into a single
public interface header file for each respective sub-library, i.e. mlib.h, gflib.h, gdflib.h
and gmclib.h. This was done to simplify the number of files required for inclusion by
application programs. Refer to the specific algorithm sections of this document for details
on the software Application Programming Interface (API), definitions and functionality
provided for the individual algorithms.
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3.5 Matlab Integration
In addition to the Automotive Math and Motor Control Library Set for NXP MPC560xB
devices library modules, the Bit Accurate Models (BAM) are delivered in the installation
package. These models can be used in the Matlab Simulink Toolbox to model the
behavior of each function in real implementation. As there are two versions of Matlab
environment depending on the operation system, both 32-bit and 64-bit Bit Accurate
Models are supported. Each model consists of these four files:
1. <libID>_<funcID>_BAM_<implementation>.mdl (e.g.
GFLIB_Acos_BAM_F32.mdl): Contains the Bit Accurate Model (BAM) which can
be included in the user Matlab Simulink model and refers to the S-function C file,
and the S-function executable file.
2. <libID>_<funcID>_SF_<implementation>.c (e.g. GFLIB_Acos_SF_F32.c): The Sfunction C file that calls a simple legacy function during the simulation.
3. <libID>_<funcID>_SF_<implementation>.mexw32 (e.g.
GFLIB_Acos_SF_F32.mexw32): Contains the compiled MATLAB S-function
executable file created from the function C source file compiled for 32-bit Matlab
environment.
4. <libID>_<funcID>_SF_<implementation>.mexw64 (e.g.
GFLIB_Acos_SF_F32.mexw64): Contains the compiled MATLAB S-function
executable file created from the function C source file compiled for 64-bit Matlab
environment.
All delivered functions are provided with Bit Accurate Models in all applicable
implementation versions and were compiled using Matlab 2014a and Windows SDK v7.1
in case of 64-bit models and using LCC compiler in case of 32-bit Bit Accurate Models.
The user is thus responsible for selecting appropriate version of the Bit Accurate Model
considering also the version of the Matlab environment. To include the Bit Accurate
Model in the user Simulink scheme, simply copy the BAM model into the Simulink
scheme. All Matlab/Simulink models are available as a standalone model in the
appropriate library in the "bam" folder or, to make work easier, in one single model
library "ammclib_bam.mdl" file which can be used for Matlab/Simulink scheme creation.
The BAM models can be pulled out from this unified model and can be easily placed into
your Matlab/Simulink scheme. Note that the BAM parameters need to be properly set up.
The structure of the Matlab files delivered with the Automotive Math and Motor Control
Library Set for NXP MPC560xB devices is depicted in Figure 3-2.
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Installation
Figure 3-2. AMMCLib Matlab file structure
An example of Matlab Simulink model utilizing the Automotive Math and Motor Control
Library Set for NXP MPC560xB devices Bit Accurate Models is depicted in Figure 3-3.
Note that this schema is for the illustration only.
Figure 3-3. Example of Matlab Simulink model utilizing the Bit Accurate Models
3.6 Installation
The Automotive Math and Motor Control Library Set for NXP MPC560xB devices is
delivered as a single executable file. To install the Automotive Math and Motor Control
Library Set for NXP MPC560xB devices on a user computer, it is necessary to run the
installation file and follow these steps:
1. On welcome page select the Next to start the installation
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Figure 3-4. AMMCLib installation - step 1. Highlighted "MCU Platform" and "ReleaseID"
identifies the actual release, which is the MPC560xB_AMMCLIB_v1.1.5
2. Accept the license agreement
Figure 3-5. AMMCLib installation - step 2
3. Select the destination directory
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Installation
Figure 3-6. AMMCLib installation - step 3. Highlighted "Platform" and "ReleaseID"
identifies the actual release installation path, which is the MPC560xB_AMMCLIB_v1.1.5
4. Check the destination directory and confirm the installation
Figure 3-7. AMMCLib installation - step 4. Highlighted "Platform" and "ReleaseID"
identifies the actual release installation path, which is the MPC560xB_AMMCLIB_v1.1.5
5. After installation carefully read the Release notes with important additional
information about the release
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Figure 3-8. AMMCLib installation - step 5. Highlighted "Platform" and "ReleaseID"
identifies the actual release, which is the MPC560xB_AMMCLIB_v1.1.5
6. Select Finish to end the installation
Figure 3-9. MCLib installation - step 6
3.7 Library File Structure
After a successful installation, the Automotive Math and Motor Control Library Set for
NXP MPC560xB devices is added by default into the "C:\Freescale\AMMCLIB
\MPC560xB_AMMCLIB_v1.1.5" subfolder. This folder will contain other nested
subfolders and files required by the Automotive Math and Motor Control Library Set for
NXP MPC560xB devices, as shown in Figure 3-10.
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Library File Structure
Figure 3-10. AMMCLIB directory structure
A list of the installed directories/files, and their brief description, is given below:
• bam - contains Bit Accurate Models of all the functions for Matlab/Simulink
• doc - contains the User Manual
• include - contains all the header files, including the master header files of each
library to be included in the user application
• lib - contains the compiled library file to be included in the user application
In order to integrate the Automotive Math and Motor Control Library Set for NXP
MPC560xB devices into a new Green Hills compiler based project, the steps described in
Library Integration into a Green Hills Multi Development Environment section must be
performed.
In order to integrate the Automotive Math and Motor Control Library Set for NXP
MPC560xB devices into a new Wind River Compiler based project, the steps described
in section Library Integration into a Wind River Compiler Environment must be
performed.
For integration of the Automotive Math and Motor Control Library Set for NXP
MPC560xB devices into a new Eclipse-based CodeWarrior based project, the steps
described in section Library Integration into a Freescale CodeWarrior Eclipse IDE must
be performed.
For integration of the Automotive Math and Motor Control Library Set for NXP
MPC560xB devices into a new S32 Design Studio for Power Architecture based project,
the steps described in section Library Integration into a S32 Design Studio for Power
Architecture IDE must be performed.
The header files structure of the Automotive Math and Motor Control Library Set for
NXP MPC560xB devices is depicted in Figure 3-11.
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Figure 3-11. AMMCLIB header file structure
3.8 Integration Assumption
In order to successfully integrate the Automotive Math and Motor Control Library Set for
NXP MPC560xB devices to the customer application, the following assumptions need to
be considered:
1. The C-99 language has to be enabled in the user application (please refer to User
manual of your compiler to enable this feature).
2. The pre-compiled library of the Automotive Math and Motor Control Library Set for
NXP MPC560xB devices was compiled using the VLE option, thus the VLE has to
be enabled in case the pre-compiled version of the Automotive Math and Motor
Control Library Set for NXP MPC560xB devices is used in the user application and
the VLE option is available on target MCU.
3. In case the Freescale CodeWarrior Eclipse IDE is used, the C++ extension has to be
switched off.
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3.9 Library Integration into a Green Hills Multi Development
Environment
The Automotive Math and Motor Control Library Set for NXP MPC560xB devices is
added into a new Green Hills Multi project using the following steps:
1. Open a new empty C project in the Green Hills Multi IDE. See the Green Hills Multi
user manual for instructions.
2. Once you have successfully created and opened a new C project, right click on the
project file *.gpj in the GHS Multi Project Manager. Select <Set Build Options...>
from the pop-up menu, as shown in Figure 3-12
Figure 3-12. Project build options
3. In the <Basic Options> tab of the <Build Options> window, expand section
<Project> and double click on the item <Include Directories (-I)>. Here, the
directory where the builder should look for all the project header files, including the
library header files, shall be specified as shown in Figure 3-13. Considering default
settings, the following path shall be added: "C:\Freescale\AMMCLIB
\MPC560xB_AMMCLIB_v1.1.5\include. "
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Figure 3-13. Adding a path to the library header files
4. While still in the <Project> section, double click on <Libraries (-l)> and enter a path
and a pre-compiled library object file into the dialogue box, as shown in Figure 3-14.
Figure 3-14. Adding a path to the library object files
Considering default settings, you should add "C:\Freescale\AMMCLIB
\MPC560xB_AMMCLIB_v1.1.5\lib\ghs\MPC560xB_AMMCLIB.a"
5. In order to use the library functions, the library master header files must be included
into the application source code. This is done using the pre-processor directive
\#include "<libID>.h", where <libID> can be gdflib, gflib, gmclib, depending on
which library is to be employed.
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The master header files contain several additional header files that are needed for the
Automotive Math and Motor Control Library Set for NXP MPC560xB devices
integration into any user application. They include the "SWLIBS_Typedefs.h" header file
which contains all general purpose data type definitions, the "mlib.h" header file
containing all general math functions, the "SWLIBS_Defines.h" file containing common
macro definitions and the "SWLIBS_MacroDisp.h" allowing the implementation based
API call.
NOTE
Remember that by default there is no default implementation
selected in the "SWLIBS_Config.h" thus the error message will
be displayed during the compilation requesting the default
implementation selection.
Figure 3-15. Opening the C editor for editing the application source code
Figure 3-16. Using the pre-processor directive to include library master header files
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At this point, the Automotive Math and Motor Control Library Set for NXP MPC560xB
devices is linked with the user project file, and hence the library functions can be
exploited and flawlessly compiled/linked with the user application.
3.10 Library Integration into a Wind River Compiler
Environment
As the Wind River Compiler is provided with the Eclipse based IDE called Wind River
Workbench, the following instruction will describe the steps needed to add the
Automotive Math and Motor Control Library Set for NXP MPC560xB devices into a
new project. All described steps assume that there is an existing Wind River Workbench
project ("MCLib_example_diab" name is used in the pictures below).
In order to integrate the Automotive Math and Motor Control Library Set for NXP
MPC560xB devices into an existing Wind River Workbench project, it is necessary to
provide the Wind River Workbench IDE with access paths to the Automotive Math and
Motor Control Library Set for NXP MPC560xB devices files. The following files shall be
added to the user project:
• Library binary files located in the directory "C:\Freescale\AMMCLIB
\MPC560xB_AMMCLIB_v1.1.5\lib\diab" (note: this is the default location and may
be modified during library installation)
• Header files located in the directory "C:\Freescale\AMMCLIB
\MPC560xB_AMMCLIB_v1.1.5\include" (note: this is the default location and may
be modified during library installation)
To add these files, choose your project in <Project Explorer> in the left tab, and from
the <Project> menu select <Properties> as described in Figure 3-17.
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Figure 3-17. Selection of the project property in the Wind River Workbench
In the Properties window, select Build Properties from the left-hand list and choose the
Build Path tab as described in Figure 3-18.
Figure 3-18. Selecting the include paths in the Wind River Workbench
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By selecting the <Add..> button, add the directories, where the builder should look for all
the header files, including the library file. Considering the default settings, the paths
shown in Figure 3-19 and Figure 3-20 shall be added.
Figure 3-19. Including the header files directory to the Wind River Workbench
Figure 3-20. Including the library file directory to the Wind River Workbench
In order to use the library functions, the library master header files must be included into
the application source code. This is done using the pre-processor directive \#include
"<libID>.h", where <libID> can be gdflib, gflib, gmclib, depending on which library is to
be employed.
The master header files contain several additional header files that are needed for the
Automotive Math and Motor Control Library Set for NXP MPC560xB devices
integration into any user application. They include the "SWLIBS_Typedefs.h" header file
which contains all general purpose data type definitions, the "mlib.h" header file
containing all general math functions, the "SWLIBS_Defines.h" file containing common
macro definitions and the "SWLIBS_MacroDisp.h" allowing the implementation based
API call.
NOTE
Remember that by default there is no default implementation
selected in the "SWLIBS_Config.h" thus the error message will
be displayed during the compilation requesting the default
implementation selection.
At this point, the Automotive Math and Motor Control Library Set for NXP MPC560xB
devices is linked with the user project file, and hence the library functions can be
exploited and flawlessly compiled/linked with the user application.
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Library Integration into a Freescale CodeWarrior Eclipse IDE
3.11 Library Integration into a Freescale CodeWarrior Eclipse
IDE
The release provides two library versions for the Eclipse-based CodeWarrior
environment. The library versions are different in the compilation options that were set
while the library was compiled:
• The library file with the suffix: <MCU_Core>_VLE_SC.a, compilation options used:
Power Architecture Embedded ABI, VLE instructions set, char type is signed.
• The library file with the suffix: <MCU_Core>_VLE_UC.a, compilation options
used: Power Architecture EABI, VLE instruction set, char type is unsigned.
The selection of the library version should follow those compilation options set for the
CodeWarrior Eclipse IDE project. If the Automotive Math and Motor Control Library Set
for NXP MPC560xB devices options and project options are different, warnings would
be reported. All described steps assume that there is an existing Eclipse project
("mclib_example_cw10x" name is used on below pictures).
In order to use the Automotive Math and Motor Control Library Set for NXP MPC560xB
devices within a Eclipse-based CodeWarrior GUI environment, it is necessary to provide
the Eclipse-based CodeWarrior GUI with access paths to the Automotive Math and
Motor Control Library Set for NXP MPC560xB devices files. The following files shall be
added to the user project:
• Library binary files located in the directory "C:\Freescale\AMMCLIB
\MPC560xB_AMMCLIB_v1.1.5\lib\cw10x" (note: this is the default location and may
be modified during library installation)
• Header files located in the directory "C:\Freescale\AMMCLIB
\MPC560xB_AMMCLIB_v1.1.5\include" (note: this is the default location and may
be modified during library installation)
To add these files, select your project in the <Project Explorer> in the left tab, and from
the <Project> menu select the <Properties> option as described in Figure 3-21.
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Figure 3-21. Selection of the project property in the CodeWarrior Eclipse IDE
In the <Properties> window, select the <Paths and Symbols> from the left-hand list and
choose the <Includes> tab and <C Source File> under the <Languages> section, as
described in Figure 3-22.
Figure 3-22. Selecting the include paths in the CodeWarrior Eclipse IDE
By selecting the <Add..> button, add the directories, where the builder should look for all
the header files. Considering the default settings, the path shown in Figure 3-23 shall be
added.
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Figure 3-23. Adding the header files path to the CodeWarrior Eclipse IDE project
After adding of the Automotive Math and Motor Control Library Set for NXP
MPC560xB devices header files path, the library object file shall be add to the Eclipsebased CodeWarrior project. In the <Properties> window, select the <Paths and
Symbols> from the left-hand list and choose the <Libraries> tab, as described in Figure
3-24.
Figure 3-24. Selecting the library object in the CodeWarrior Eclipse IDE
By selecting the <Add..> button, add the library object file (consider the project setting
of char data type representation). Considering the default settings, the path shown in
Figure 3-25 shall be added.
Figure 3-25. Adding the library object file to the CodeWarrior Eclipse IDE project
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In order to use the library functions, the library master header files must be included into
the application source code. This is done using the pre-processor directive \#include
"<libID>.h", where <libID> can be gdflib, gflib, gmclib, depending on which library is to
be employed.
The master header files contain several additional header files that are needed for the
Automotive Math and Motor Control Library Set for NXP MPC560xB devices
integration into any user application. They include the "SWLIBS_Typedefs.h" header file
which contains all general purpose data type definitions, the "mlib.h" header file
containing all general math functions, the "SWLIBS_Defines.h" file containing common
macro definitions and the "SWLIBS_MacroDisp.h" allowing the implementation based
API call.
NOTE
Remember that by default there is no default implementation
selected in the "SWLIBS_Config.h" thus the error message will
be displayed during the compilation requesting the default
implementation selection.
At this point, the Automotive Math and Motor Control Library Set for NXP MPC560xB
devices is linked with the user project file, and hence the library functions can be
exploited and flawlessly compiled/linked with the user application.
3.12 Library Integration into a S32 Design Studio for Power
Architecture IDE
In order to use the Automotive Math and Motor Control Library Set for NXP MPC560xB
devices within a S32 Design Studio for Power Architecture GUI environment, it is
necessary to provide the S32 Design Studio GUI with access paths to the Automotive
Math and Motor Control Library Set for NXP MPC560xB devices files. The following
files shall be added to the user project:
• Library binary files located in the directory "C:\Freescale\AMMCLIB
\MPC560xB_AMMCLIB_v1.1.5\lib\s32ds_ppc" (note: this is the default location and
may be modified during library installation)
• Header files located in the directory "C:\Freescale\AMMCLIB
\MPC560xB_AMMCLIB_v1.1.5\include" (note: this is the default location and may
be modified during library installation)
To add these files, select your project in the <Project Explorer> in the left tab, and from
the <Project> menu select the <Properties> option as described in Figure 3-26.
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Library Integration into a S32 Design Studio for Power Architecture IDE
Figure 3-26. Selection of the project property in the S32 Design Studio for Power
Architecture IDE
In the <Properties> window, select the <C/C++ General><Paths and Symbols> from
the left-hand list and choose the <Includes> tab and <GNU C> under the <Languages>
section, as described in Figure 3-27.
Figure 3-27. Selecting the include paths in the S32 Design Studio for Power Architecture
IDE
By selecting the <Add..> button, add the directories, where the builder should look for all
the header files. Considering the default settings, the path shown in Figure 3-28 shall be
added.
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Figure 3-28. Adding the header files path to the S32 Design Studio for Power
Architecture IDE project
After adding of the Automotive Math and Motor Control Library Set for NXP
MPC560xB devices header files path, the library object file shall be add to the S32
Design Studio for Power Architecture project. In the <Properties> window, select the
<C/C++ General><Paths and Symbols> from the left-hand list and choose the
<Libraries> tab, as described in Figure 3-29.
Figure 3-29. Selecting the library object in the S32 Design Studio for Power Architecture
IDE
By selecting the <Add..> button, add the library object file. Considering the default
settings, the path shown in Figure 3-30 shall be added.
Figure 3-30. Adding the library object file to the S32 Design Studio for Power
Architecture IDE project
In order to use the library functions, the library master header files must be included into
the application source code. This is done using the pre-processor directive \#include
"<libID>.h", where <libID> can be gdflib, gflib, gmclib, mlib, depending on which
library is to be employed.
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Library Testing
The master header files contain several additional header files that are needed for the
Automotive Math and Motor Control Library Set for NXP MPC560xB devices
integration into any user application. They include the "SWLIBS_Typedefs.h" header file
which contains all general purpose data type definitions, the "mlib.h" header file
containing all general math functions, the "SWLIBS_Defines.h" file containing common
macro definitions and the "SWLIBS_MacroDisp.h" allowing the implementation based
API call.
NOTE
Remember that, there is no default implementation selected in
the "SWLIBS_Config.h" by default, thus the error message will
be displayed during the compilation requesting the default
implementation selection.
At this point, the Automotive Math and Motor Control Library Set for NXP MPC560xB
devices is linked with the user project file, and hence the library functions can be
exploited and flawlessly compiled/linked with the user application.
3.13 Library Testing
In order to validate the implementation of the Automotive Math and Motor Control
Library Set for NXP MPC560xB devices, the comparison of results from the MATLAB
Reference Model and outputs from the tested library function is used. To ensure the
Automotive Math and Motor Control Library Set for NXP MPC560xB devices precision,
two test methods are used:
• Matlab Simulink Toolbox based testing (refer to AMMCLIB Testing based on the
MATLAB Simulink Toolbox for more details).
• Target-in-loop based testing (refer to AMMCLIB target-in-loop Testing based on the
SFIO Toolbox for detailed information).
The Figure 3-31 shows the testing principle:
• Input vector represents the test vector which enters simultaneously into the
Reference Model and into the Unit Under Test (UUT).
• Reference Model (RM) implements the real model of the UUT. For simple
functions, the models are a part of the MATLAB Simulink Toolbox. Advanced
functions such as filters or controllers had been designed separately.
• By the type of test method used, the Unit Under Test (UUT) may be:
• Bit Accurate Model (BAM) - the "C" implementation of the tested function
compiled in the MATLAB environment. The compilation result, called the
binary MEX-file, is a dynamically-linked subroutine that the MATLAB
interpreter can load and execute.
• SFIO Model represents the tested function running directly on the target MCU.
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Results from the UUT and Reference Model are saved in the final report, together with
the calculated error which is simply the difference between the output value from the
Reference Model and the output value from the UUT, recalculated to an equivalent
precision.
The equivalent precision is the same for all supported implementations of the Automotive
Math and Motor Control Library Set for NXP MPC560xB devices. For the 32-bit and 16bit fixed-point implementations, the output precision of non-approximation function is
greater or equal to +/-1 LSB in 16-bit arithmetic, and is greater or equal to +/-3 LSB in
16-bit arithmetic for approximation functions.
The output value of the function is determined by the following expressions:
• Approximation function with precision +/-3 LSB:
• 32-bit fixed point: <PRECISE_VALUE> +/- 3*2^-15
• 16-bit fixed point: <PRECISE_VALUE> +/- 3*2^-15
• Non-approximation function with precision +/-1 LSB:
• 32-bit fixed point: <PRECISE_VALUE> +/- 2^-15
• 16-bit fixed point: <PRECISE_VALUE> +/- 2^-15
Figure 3-31. Principle of AMMCLIB testing
In order to test the UUT under all conditions, three types of test vector sets are used:
• Deterministic vectors - a specifically defined set of input values over the entire input
range.
• Stochastic vectors - a pseudo-randomly generated set of values (non-deterministic
values fully covering the input range).
• Boundary vectors - a set of input values for which the potential weaknesses of the
tested function are expected. This test is performed only on functions where these
limit conditions might occur.
Each function is considered tested if the required accuracy during deterministic,
stochastic and boundary tests has been achieved. The following two subchapters
AMMCLIB Testing based on the MATLAB Simulink Toolbox and AMMCLIB target-inloop Testing based on the SFIO Toolbox describe the differences between AMMCLIB
testing based on BAM models and target-in-loop testing based on SFIO models.
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Library Testing
3.13.1 AMMCLIB Testing based on the MATLAB Simulink
Toolbox
An example of the testing principle based on the BAM is depicted in the Clark
transformation function (Figure 3-32). The Bit Accurate Model contains the binary MEXfile built from the GMCLIB_Clark function using the MATLAB compiler. This file is
called inside the BAM model, see Figure 3-33. The Reference Model of the Clark
transformation is not included in the MATLAB Simulink Toolbox and hence its
mathematical representation had to be created. A detailed scheme of the Clark RM is in
Figure 3-34.
Figure 3-32. Testing of the GMCLIB_Clark function based on the MATLAB Simulink
Toolbox
Figure 3-33. Bit Accurate Model parameters of the Clark transformation
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Figure 3-34. Reference Model of the GMCLIB_Clark function
3.13.2 AMMCLIB target-in-loop Testing based on the SFIO
Toolbox
The testing method in Figure 3-35 is the similar to that described in the previous chapter
with exception that the BAM model is replaced by the SFIO model. The SFIO Toolbox
realizes the bridge between Matlab and the Embedded target. During testing, the function
GMCLIB_Clark is called directly from the application running on the target MCU.
Unlike testing based on MATLAB, the target-in-loop method verifies that the
implementation of the Automotive Math and Motor Control Library Set for NXP
MPC560xB devices functions works correctly on the target MCU. Moreover, the SFIO
application running on the processor is used to measure performance of the functions.
The SFIO block Set-up allows the setting of communication parameters which are
common to the whole scheme.
Figure 3-35. Target-in-loop testing example based on the SFIO Toolbox
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Functions Precision
3.14 Functions Precision
The maximum allowed error of the Automotive Math and Motor Control Library Set for
NXP MPC560xB devices functions vary based on the implementation, and based on the
character of the function. The output error is calculated as the difference between the
implemented function and double-precision reference model, as described in the Library
Testing section. The actual output error of the function for current input values is smaller
or equal to the maximum allowed error described in the table below. The output error of
the 32-bit and 16-bit fixed-point implementations is calculated as the absolute error.
The following table describes the maximum allowed error of the functions:
Table 3-1. Function precision in [LSB]
Function name
F32
F16
GDFLIB_FilterFIR
3
3
GDFLIB_FilterFIRInit
0
0
GDFLIB_FilterIIR1
1
1
GDFLIB_FilterIIR1Init
0
0
GDFLIB_FilterIIR2
1
1
GDFLIB_FilterIIR2Init
0
0
GDFLIB_FilterMA
1
1
GDFLIB_FilterMAInit
0
0
GFLIB_Acos
3
3
GFLIB_Asin
3
3
GFLIB_Atan
3
3
GFLIB_AtanYX
3
3
GFLIB_AtanYXShifted
3
3
GFLIB_ControllerPIp
3
3
GFLIB_ControllerPIpAW
3
3
GFLIB_ControllerPIr
3
3
GFLIB_ControllerPIrAW
3
3
GFLIB_Cos
3
3
GFLIB_Hyst
1
1
GFLIB_IntegratorTR
3
3
GFLIB_Limit
1
1
GFLIB_LowerLimit
1
1
GFLIB_Lut1D
3
3
GFLIB_Lut2D
3
3
GFLIB_Ramp
1
1
GFLIB_Sign
1
1
Table continues on the next page...
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Table 3-1. Function precision in [LSB]
(continued)
Function name
F32
F16
GFLIB_Sin
3
3
GFLIB_SinCos
3
3
GFLIB_Sqrt
1
3
GFLIB_Tan
3
3
GFLIB_UpperLimit
1
1
GFLIB_VectorLimit
3
3
GMCLIB_Clark
1
3
GMCLIB_ClarkInv
1
3
GMCLIB_DecouplingPMSM
1
3
GMCLIB_ElimDcBusRip
3
3
GMCLIB_Park
1
1
GMCLIB_ParkInv
1
1
GMCLIB_SvmStd
1
3
MLIB_Abs
1
1
MLIB_AbsSat
1
1
MLIB_Add
1
1
MLIB_AddSat
1
1
MLIB_Convert_F16F32
1
1
MLIB_Convert_F32F16
1
1
MLIB_ConvertPU_F16F32
1
1
MLIB_ConvertPU_F32F16
1
1
MLIB_Div
3
1
MLIB_DivSat
3
1
MLIB_Mac
1
1
MLIB_MacSat
1
1
MLIB_Mul
1
1
MLIB_MulSat
1
1
MLIB_Neg
1
1
MLIB_NegSat
1
1
MLIB_Norm
1
1
MLIB_RndSat
1
1
MLIB_Round
1
1
MLIB_ShBi
1
1
MLIB_ShBiSat
1
1
MLIB_ShL
1
1
MLIB_ShLSat
1
1
MLIB_ShR
1
1
MLIB_Sub
1
1
Table continues on the next page...
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Functions Precision
Table 3-1. Function precision in [LSB]
(continued)
Function name
F32
F16
MLIB_SubSat
1
1
MLIB_VMac
1
2
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4.1 Function Index
Table 4-1. Quick function reference
Type
Name
Arguments
void
GDFLIB_FilterFIRInit_F16
const GDFLIB_FILTERFIR_PARAM_T_F16 *const
pParam
GDFLIB_FILTERFIR_STATE_T_F16 *const pState
tFrac16 * pInBuf
void
GDFLIB_FilterFIRInit_F32
const GDFLIB_FILTERFIR_PARAM_T_F32 *const
pParam
GDFLIB_FILTERFIR_STATE_T_F32 *const pState
tFrac32 * pInBuf
tFrac16
GDFLIB_FilterFIR_F16
tFrac16 f16In
const GDFLIB_FILTERFIR_PARAM_T_F16 *const
pParam
GDFLIB_FILTERFIR_STATE_T_F16 *const pState
tFrac32
GDFLIB_FilterFIR_F32
tFrac32 f32In
const GDFLIB_FILTERFIR_PARAM_T_F32 *const
pParam
GDFLIB_FILTERFIR_STATE_T_F32 *const pState
void
GDFLIB_FilterIIR1Init_F16
GDFLIB_FILTER_IIR1_T_F16 *const pParam
void
GDFLIB_FilterIIR1Init_F32
GDFLIB_FILTER_IIR1_T_F32 *const pParam
tFrac16
GDFLIB_FilterIIR1_F16
tFrac16 f16In
GDFLIB_FILTER_IIR1_T_F16 *const pParam
tFrac32
GDFLIB_FilterIIR1_F32
tFrac32 f32In
GDFLIB_FILTER_IIR1_T_F32 *const pParam
void
GDFLIB_FilterIIR2Init_F16
GDFLIB_FILTER_IIR2_T_F16 *const pParam
void
GDFLIB_FilterIIR2Init_F32
GDFLIB_FILTER_IIR2_T_F32 *const pParam
tFrac16
GDFLIB_FilterIIR2_F16
tFrac16 f16In
GDFLIB_FILTER_IIR2_T_F16 *const pParam
tFrac32
GDFLIB_FilterIIR2_F32
tFrac32 f32In
GDFLIB_FILTER_IIR2_T_F32 *const pParam
void
GDFLIB_FilterMAInit_F16
GDFLIB_FILTER_MA_T_F16 * pParam
void
GDFLIB_FilterMAInit_F32
GDFLIB_FILTER_MA_T_F32 * pParam
tFrac16
GDFLIB_FilterMA_F16
tFrac16 f16In
GDFLIB_FILTER_MA_T_F16 * pParam
tFrac32
GDFLIB_FilterMA_F32
tFrac32 f32In
Table continues on the next page...
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Function Index
Table 4-1. Quick function reference (continued)
Type
Name
Arguments
GDFLIB_FILTER_MA_T_F32 * pParam
tFrac16
GFLIB_Acos_F16
tFrac16 f16In
const GFLIB_ACOS_T_F16 *const pParam
tFrac32
GFLIB_Acos_F32
tFrac32 f32In
const GFLIB_ACOS_T_F32 *const pParam
tFrac16
GFLIB_Asin_F16
tFrac16 f16In
const GFLIB_ASIN_T_F16 *const pParam
tFrac32
GFLIB_Asin_F32
tFrac32 f32In
const GFLIB_ASIN_T_F32 *const pParam
tFrac16
GFLIB_AtanYXShifted_F16
tFrac16 f16InY
tFrac16 f16InX
const GFLIB_ATANYXSHIFTED_T_F16 * pParam
tFrac32
GFLIB_AtanYXShifted_F32
tFrac32 f32InY
tFrac32 f32InX
const GFLIB_ATANYXSHIFTED_T_F32 * pParam
tFrac16
GFLIB_AtanYX_F16
tFrac16 f16InY
tFrac16 f16InX
tFrac32
GFLIB_AtanYX_F32
tFrac32 f32InY
tFrac32 f32InX
tFrac16
GFLIB_Atan_F16
tFrac16 f16In
const GFLIB_ATAN_T_F16 *const pParam
tFrac32
GFLIB_Atan_F32
tFrac32 f32In
const GFLIB_ATAN_T_F32 *const pParam
tFrac16
GFLIB_ControllerPIpAW_F16
tFrac16 f16InErr
GFLIB_CONTROLLER_PIAW_P_T_F16 *const
pParam
tFrac32
GFLIB_ControllerPIpAW_F32
tFrac32 f32InErr
GFLIB_CONTROLLER_PIAW_P_T_F32 *const
pParam
tFrac16
GFLIB_ControllerPIp_F16
tFrac16 f16InErr
GFLIB_CONTROLLER_PI_P_T_F16 *const pParam
tFrac32
GFLIB_ControllerPIp_F32
tFrac32 f32InErr
GFLIB_CONTROLLER_PI_P_T_F32 *const pParam
tFrac16
GFLIB_ControllerPIrAW_F16
tFrac16 f16InErr
GFLIB_CONTROLLER_PIAW_R_T_F16 *const
pParam
tFrac32
GFLIB_ControllerPIrAW_F32
tFrac32 f32InErr
GFLIB_CONTROLLER_PIAW_R_T_F32 *const
pParam
tFrac16
GFLIB_ControllerPIr_F16
tFrac16 f16InErr
GFLIB_CONTROLLER_PI_R_T_F16 *const pParam
tFrac32
GFLIB_ControllerPIr_F32
tFrac32 f32InErr
GFLIB_CONTROLLER_PI_R_T_F32 *const pParam
tFrac16
GFLIB_Cos_F16
tFrac16 f16In
const GFLIB_COS_T_F16 *const pParam
tFrac32
GFLIB_Cos_F32
tFrac32 f32In
const GFLIB_COS_T_F32 *const pParam
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Chapter 4
Table 4-1. Quick function reference (continued)
Type
Name
Arguments
tFrac16
GFLIB_Hyst_F16
tFrac16 f16In
GFLIB_HYST_T_F16 *const pParam
tFrac32
GFLIB_Hyst_F32
tFrac32 f32In
GFLIB_HYST_T_F32 *const pParam
tFrac16
GFLIB_IntegratorTR_F16
tFrac16 f16In
GFLIB_INTEGRATOR_TR_T_F16 *const pParam
tFrac32
GFLIB_IntegratorTR_F32
tFrac32 f32In
GFLIB_INTEGRATOR_TR_T_F32 *const pParam
tFrac16
GFLIB_Limit_F16
tFrac16 f16In
const GFLIB_LIMIT_T_F16 *const pParam
tFrac32
GFLIB_Limit_F32
tFrac32 f32In
const GFLIB_LIMIT_T_F32 *const pParam
tFrac16
GFLIB_LowerLimit_F16
tFrac16 f16In
const GFLIB_LOWERLIMIT_T_F16 *const pParam
tFrac32
GFLIB_LowerLimit_F32
tFrac32 f32In
const GFLIB_LOWERLIMIT_T_F32 *const pParam
tFrac16
GFLIB_Lut1D_F16
tFrac16 f16In
const GFLIB_LUT1D_T_F16 *const pParam
tFrac32
GFLIB_Lut1D_F32
tFrac32 f32In
const GFLIB_LUT1D_T_F32 *const pParam
tFrac16
GFLIB_Lut2D_F16
tFrac16 f16In1
tFrac16 f16In2
const GFLIB_LUT2D_T_F16 *const pParam
tFrac32
GFLIB_Lut2D_F32
tFrac32 f32In1
tFrac32 f32In2
const GFLIB_LUT2D_T_F32 *const pParam
tFrac16
GFLIB_Ramp_F16
tFrac16 f16In
GFLIB_RAMP_T_F16 *const pParam
tFrac32
GFLIB_Ramp_F32
tFrac32 f32In
GFLIB_RAMP_T_F32 *const pParam
tFrac16
GFLIB_Sign_F16
tFrac16 f16In
tFrac32
GFLIB_Sign_F32
tFrac32 f32In
void
GFLIB_SinCos_F16
tFrac16 f16In
SWLIBS_2Syst_F16 * pOut
const GFLIB_SINCOS_T_F16 *const pParam
void
GFLIB_SinCos_F32
tFrac32 f32In
SWLIBS_2Syst_F32 * pOut
const GFLIB_SINCOS_T_F32 *const pParam
tFrac16
GFLIB_Sin_F16
tFrac16 f16In
const GFLIB_SIN_T_F16 *const pParam
tFrac32
GFLIB_Sin_F32
tFrac32 f32In
const GFLIB_SIN_T_F32 *const pParam
tFrac16
GFLIB_Sqrt_F16
tFrac16 f16In
tFrac32
GFLIB_Sqrt_F32
tFrac32 f32In
tFrac16
GFLIB_Tan_F16
tFrac16 f16In
const GFLIB_TAN_T_F16 *const pParam
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Function Index
Table 4-1. Quick function reference (continued)
Type
Name
Arguments
tFrac32
GFLIB_Tan_F32
tFrac32 f32In
const GFLIB_TAN_T_F32 *const pParam
tFrac16
GFLIB_UpperLimit_F16
tFrac16 f16In
const GFLIB_UPPERLIMIT_T_F16 *const pParam
tFrac32
GFLIB_UpperLimit_F32
tFrac32 f32In
const GFLIB_UPPERLIMIT_T_F32 *const pParam
tBool
GFLIB_VectorLimit_F16
const SWLIBS_2Syst_F16 *const pIn
SWLIBS_2Syst_F16 *const pOut
const GFLIB_VECTORLIMIT_T_F16 *const pParam
tBool
GFLIB_VectorLimit_F32
const SWLIBS_2Syst_F32 *const pIn
SWLIBS_2Syst_F32 *const pOut
const GFLIB_VECTORLIMIT_T_F32 *const pParam
void
GMCLIB_ClarkInv_F16
const SWLIBS_2Syst_F16 *const pIn
SWLIBS_3Syst_F16 *const pOut
void
GMCLIB_ClarkInv_F32
const SWLIBS_2Syst_F32 *const pIn
SWLIBS_3Syst_F32 *const pOut
void
GMCLIB_Clark_F16
const SWLIBS_3Syst_F16 *const pIn
SWLIBS_2Syst_F16 *const pOut
void
GMCLIB_Clark_F32
const SWLIBS_3Syst_F32 *const pIn
SWLIBS_2Syst_F32 *const pOut
void
GMCLIB_DecouplingPMSM_F16
SWLIBS_2Syst_F16 *const pUdqDec
const SWLIBS_2Syst_F16 *const pUdq
const SWLIBS_2Syst_F16 *const pIdq
tFrac16 f16AngularVel
const GMCLIB_DECOUPLINGPMSM_T_F16 *const
pParam
void
GMCLIB_DecouplingPMSM_F32
SWLIBS_2Syst_F32 *const pUdqDec
const SWLIBS_2Syst_F32 *const pUdq
const SWLIBS_2Syst_F32 *const pIdq
tFrac32 f32AngularVel
const GMCLIB_DECOUPLINGPMSM_T_F32 *const
pParam
void
GMCLIB_ElimDcBusRip_F16
SWLIBS_2Syst_F16 *const pOut
const SWLIBS_2Syst_F16 *const pIn
const GMCLIB_ELIMDCBUSRIP_T_F16 *const
pParam
void
GMCLIB_ElimDcBusRip_F32
SWLIBS_2Syst_F32 *const pOut
const SWLIBS_2Syst_F32 *const pIn
const GMCLIB_ELIMDCBUSRIP_T_F32 *const
pParam
void
GMCLIB_ParkInv_F16
SWLIBS_2Syst_F16 *const pOut
const SWLIBS_2Syst_F16 *const pInAngle
const SWLIBS_2Syst_F16 *const pIn
void
GMCLIB_ParkInv_F32
SWLIBS_2Syst_F32 *const pOut
const SWLIBS_2Syst_F32 *const pInAngle
const SWLIBS_2Syst_F32 *const pIn
void
GMCLIB_Park_F16
SWLIBS_2Syst_F16 * pOut
const SWLIBS_2Syst_F16 *const pInAngle
const SWLIBS_2Syst_F16 *const pIn
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Table 4-1. Quick function reference (continued)
Type
Name
Arguments
void
GMCLIB_Park_F32
SWLIBS_2Syst_F32 * pOut
const SWLIBS_2Syst_F32 *const pInAngle
const SWLIBS_2Syst_F32 *const pIn
tU16
GMCLIB_SvmStd_F16
SWLIBS_3Syst_F16 * pOut
const SWLIBS_2Syst_F16 *const pIn
tU32
GMCLIB_SvmStd_F32
SWLIBS_3Syst_F32 * pOut
const SWLIBS_2Syst_F32 *const pIn
tFrac16
MLIB_AbsSat_F16
register tFrac16 f16In
tFrac32
MLIB_AbsSat_F32
register tFrac32 f32In
tFrac16
MLIB_Abs_F16
register tFrac16 f16In
tFrac32
MLIB_Abs_F32
register tFrac32 f32In
tFrac16
MLIB_AddSat_F16
register tFrac16 f16In1
register tFrac16 f16In2
tFrac32
MLIB_AddSat_F32
register tFrac32 f32In1
register tFrac32 f32In2
tFrac16
MLIB_Add_F16
register tFrac16 f16In1
register tFrac16 f16In2
tFrac32
MLIB_Add_F32
register tFrac32 f32In1
register tFrac32 f32In2
tFrac16
MLIB_ConvertPU_F16F32
register tFrac32 f32In
tFrac32
MLIB_ConvertPU_F32F16
register tFrac16 f16In
tFrac16
MLIB_Convert_F16F32
register tFrac32 f32In1
register tFrac32 f32In2
tFrac32
MLIB_Convert_F32F16
register tFrac16 f16In1
register tFrac16 f16In2
tFrac16
MLIB_DivSat_F16
register tFrac16 f16In1
register tFrac16 f16In2
tFrac32
MLIB_DivSat_F32
register tFrac32 f32In1
register tFrac32 f32In2
tFrac16
MLIB_Div_F16
register tFrac16 f16In1
register tFrac16 f16In2
tFrac32
MLIB_Div_F32
register tFrac32 f32In1
register tFrac32 f32In2
tFrac16
MLIB_MacSat_F16
register tFrac16 f16In1
register tFrac16 f16In2
register tFrac16 f16In3
tFrac32
MLIB_MacSat_F32
register tFrac32 f32In1
register tFrac32 f32In2
register tFrac32 f32In3
tFrac32
MLIB_MacSat_F32F16F16
register tFrac32 f32In1
register tFrac16 f16In2
register tFrac16 f16In3
tFrac16
MLIB_Mac_F16
register tFrac16 f16In1
register tFrac16 f16In2
register tFrac16 f16In3
tFrac32
MLIB_Mac_F32
register tFrac32 f32In1
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Function Index
Table 4-1. Quick function reference (continued)
Type
Name
Arguments
register tFrac32 f32In2
register tFrac32 f32In3
tFrac32
MLIB_Mac_F32F16F16
register tFrac32 f32In1
register tFrac16 f16In2
register tFrac16 f16In3
tFrac16
MLIB_Mnac_F16
register tFrac16 f16In1
register tFrac16 f16In2
register tFrac16 f16In3
tFrac32
MLIB_Mnac_F32
register tFrac32 f32In1
register tFrac32 f32In2
register tFrac32 f32In3
tFrac32
MLIB_Mnac_F32F16F16
register tFrac32 f32In1
register tFrac16 f16In2
register tFrac16 f16In3
tFrac16
MLIB_Msu_F16
register tFrac16 f16In1
register tFrac16 f16In2
register tFrac16 f16In3
tFrac32
MLIB_Msu_F32
register tFrac32 f32In1
register tFrac32 f32In2
register tFrac32 f32In3
tFrac32
MLIB_Msu_F32F16F16
register tFrac32 f32In1
register tFrac16 f16In2
register tFrac16 f16In3
tFrac16
MLIB_MulSat_F16
register tFrac16 f16In1
register tFrac16 f16In2
tFrac32
MLIB_MulSat_F32
register tFrac32 f32In1
register tFrac32 f32In2
tFrac32
MLIB_MulSat_F32F16F16
register tFrac16 f16In1
register tFrac16 f16In2
tFrac16
MLIB_Mul_F16
register tFrac16 f16In1
register tFrac16 f16In2
tFrac32
MLIB_Mul_F32
register tFrac32 f32In1
register tFrac32 f32In2
tFrac32
MLIB_Mul_F32F16F16
register tFrac16 f16In1
register tFrac16 f16In2
tFrac16
MLIB_NegSat_F16
register tFrac16 f16In
tFrac32
MLIB_NegSat_F32
register tFrac32 f32In
tFrac16
MLIB_Neg_F16
register tFrac16 f16In
tFrac32
MLIB_Neg_F32
register tFrac32 f32In
tU16
MLIB_Norm_F16
register tFrac16 f16In
tU16
MLIB_Norm_F32
register tFrac32 f32In
tFrac16
MLIB_RndSat_F16F32
register tFrac32 f32In
tFrac16
MLIB_Round_F16
register tFrac16 f16In1
register tU16 u16In2
tFrac32
MLIB_Round_F32
register tFrac32 f32In1
register tU16 u16In2
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Chapter 4
Table 4-1. Quick function reference (continued)
Type
Name
Arguments
tFrac16
MLIB_ShBiSat_F16
register tFrac16 f16In1
register tS16 s16In2
tFrac32
MLIB_ShBiSat_F32
register tFrac32 f32In1
register tS16 s16In2
tFrac16
MLIB_ShBi_F16
register tFrac16 f16In1
register tS16 s16In2
tFrac32
MLIB_ShBi_F32
register tFrac32 f32In1
register tS16 s16In2
tFrac16
MLIB_ShLSat_F16
register tFrac16 f16In1
register tU16 u16In2
tFrac32
MLIB_ShLSat_F32
register tFrac32 f32In1
register tU16 u16In2
tFrac16
MLIB_ShL_F16
register tFrac16 f16In1
register tU16 u16In2
tFrac32
MLIB_ShL_F32
register tFrac32 f32In1
register tU16 u16In2
tFrac16
MLIB_ShR_F16
register tFrac16 f16In1
register tU16 u16In2
tFrac32
MLIB_ShR_F32
register tFrac32 f32In1
register tU16 u16In2
tFrac16
MLIB_SubSat_F16
register tFrac16 f16In1
register tFrac16 f16In2
tFrac32
MLIB_SubSat_F32
register tFrac32 f32In1
register tFrac32 f32In2
tFrac16
MLIB_Sub_F16
register tFrac16 f16In1
register tFrac16 f16In2
tFrac32
MLIB_Sub_F32
register tFrac32 f32In1
register tFrac32 f32In2
tFrac16
MLIB_VMac_F16
register tFrac16 f16In1
register tFrac16 f16In2
register tFrac16 f16In3
register tFrac16 f16In4
tFrac32
MLIB_VMac_F32
register tFrac32 f32In1
register tFrac32 f32In2
register tFrac32 f32In3
register tFrac32 f32In4
tFrac32
MLIB_VMac_F32F16F16
register tFrac16 f16In1
register tFrac16 f16In2
register tFrac16 f16In3
register tFrac16 f16In4
SWLIBS_GetVersion
const
SWLIBS_VERSION_
T*
void
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Function Index
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Chapter 5
API References
This section describes in details the Application Interface for all functions available in
Automotive Math and Motor Control Library Set for NXP MPC560xB devices.
5.1 Function GDFLIB_FilterFIRInit_F32
This function initializes the FIR filter buffers.
5.1.1 Declaration
void GDFLIB_FilterFIRInit_F32(const GDFLIB_FILTERFIR_PARAM_T_F32 *const pParam,
GDFLIB_FILTERFIR_STATE_T_F32 *const pState, tFrac32 *pInBuf);
5.1.2 Arguments
Table 5-1. GDFLIB_FilterFIRInit_F32 arguments
Type
Name
Direction
Description
const
pParam
GDFLIB_FILTERFIR_P
ARAM_T_F32 *const
input
Pointer to the parameters structure.
GDFLIB_FILTERFIR_S pState
TATE_T_F32 *const
input,
output
Pointer to the state structure.
tFrac32 *
input,
output
Pointer to a buffer for storing filter input signal values, must
point to a R/W memory region and must be a filter order + 1
long.
pInBuf
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Function GDFLIB_FilterFIRInit_F32
5.1.3 Return
void
5.1.4 Description
The function performs the initialization procedure for the GDFLIB_FilterFIR_F32
function. In particular, the function performs the following operations:
1. Resets the input buffer index to zero.
2. Initializes the input buffer pointer to the pointer provided as an argument.
3. Resets the input buffer.
After initialization, made by the function, the parameters and state structures should be
provided as arguments to calls of the GDFLIB_FilterFIR_F32 function.
Note
The input/output pointers must contain valid addresses
otherwise an exception may occur (Data TLB Error, Data
Storage, Alignment, Machine Check).
The input buffer pointer (State->pInBuf) must point to a Read/
Write memory region, which must be at least the number of the
filter taps long. The number of taps in a filter is equal to the
filter order + 1. There is no restriction as to the location of the
parameters structure as long as it is readable.
CAUTION
No check is performed for R/W capability and the length of the
input buffer (pState->pInBuf). In case of passing incorrect
pointer to the function, an unexpected behavior of the function
might be expected including the incorrect memory access
exception.
5.1.5 Re-entrancy
The function is re-entrant only if the calling code is provided with a distinct instance of
the structure pointed to by pState.
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Chapter 5 API References
5.1.6 Code Example
#include "gdflib.h"
#define FIR_NUMTAPS 16
#define FIR_NUMTAPS_MAX 64
#define FIR_ORDER (FIR_NUMTAPS - 1)
GDFLIB_FILTERFIR_PARAM_T_F32 Param;
GDFLIB_FILTERFIR_STATE_T_F32 State0, State1, State2;
tFrac32 f32InBuf[FIR_NUMTAPS_MAX];
tFrac32 f32CoefBuf[FIR_NUMTAPS_MAX];
#define OUT_LEN 16
void main(void)
{
int ii;
tFrac32 f32OutBuf0[OUT_LEN];
tFrac32 f32OutBuf1[OUT_LEN];
tFrac32 f32OutBuf2[OUT_LEN];
// Define a simple low-pass filter
// The filter coefficients were calculated by the following
// Matlab function (coefficients are contained in Hd.Numerator):
//
// function Hd = fir_example
// FIR_EXAMPLE Returns a discrete-time filter object.
// N
= 15;
// F6dB = 0.5;
//
// h = fdesign.lowpass('n,fc', N, F6dB);
//
// Hd = design(h, 'window');
// return;
ii = 0;
f32CoefBuf[ii++] = 0xFFB10C14;
f32CoefBuf[ii++] = 0xFF779D25;
f32CoefBuf[ii++] = 0x01387DD7;
f32CoefBuf[ii++] = 0x028E6845;
f32CoefBuf[ii++] = 0xFB245142;
f32CoefBuf[ii++] = 0xF7183CC7;
f32CoefBuf[ii++] = 0x11950A3C;
f32CoefBuf[ii++] = 0x393ED867;
f32CoefBuf[ii++] = 0x393ED867;
f32CoefBuf[ii++] = 0x11950A3C;
f32CoefBuf[ii++] = 0xF7183CC7;
f32CoefBuf[ii++] = 0xFB245142;
f32CoefBuf[ii++] = 0x028E6845;
f32CoefBuf[ii++] = 0x01387DD7;
f32CoefBuf[ii++] = 0xFF779D25;
f32CoefBuf[ii++] = 0xFFB10C14;
Param.u32Order = 15;
Param.pCoefBuf = &f32CoefBuf[0];
// Initialize FIR filter
GDFLIB_FilterFIRInit_F32 (&Param, &State0, &f32InBuf[0]);
// Initialize FIR filter
GDFLIB_FilterFIRInit (&Param, &State1, &f32InBuf[0], F32);
//
//
//
//
##############################################################
Available only if 32-bit fractional implementation selected
as default
##############################################################
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Function GDFLIB_FilterFIR_F32
// Initialize FIR filter
GDFLIB_FilterFIRInit (&Param, &State2, &f32InBuf[0]);
// Compute step response of the filter
for(ii=0; ii < OUT_LEN; ii++)
{
// f32OutBuf0 contains step response of the filter
f32OutBuf0[ii] = GDFLIB_FilterFIR_F32 (0x7FFFFFFF, &Param, &State0);
// f32OutBuf1 contains step response of the filter
f32OutBuf1[ii] = GDFLIB_FilterFIR (0x7FFFFFFF, &Param, &State1, F32);
//
//
//
//
##############################################################
Available only if 32-bit fractional implementation selected
as default
##############################################################
// f32OutBuf2 contains step response of the filter
f32OutBuf2[ii] = GDFLIB_FilterFIR (0x7FFFFFFF, &Param, &State2);
}
// After the loop the f32OutBuf0, f32OutBuf1, f32OutBuf2 shall contains
the following values:
// {0xFFB1009E, 0xFF2801B0, 0x005FFF40, 0x02EDFA24, 0xFE1203DC,
0xF52A15AC, 0x06BEF282, 0x3FFC8006,
// 0x793A0D8A, 0x7FFFFFFF, 0x7FFFFFFF, 0x7D0B05E8, 0x7F9900CC,
0x7FFFFFFF, 0x7FFFFFFF, 0x7FF9000C}
}
5.2 Function GDFLIB_FilterFIR_F32
The function performs a single iteration of an FIR filter.
5.2.1 Declaration
tFrac32 GDFLIB_FilterFIR_F32(tFrac32 f32In, const GDFLIB_FILTERFIR_PARAM_T_F32 *const pParam,
GDFLIB_FILTERFIR_STATE_T_F32 *const pState);
5.2.2 Arguments
Table 5-2. GDFLIB_FilterFIR_F32 arguments
Type
Name
Direction
Description
input
Input value.
const
pParam
GDFLIB_FILTERFIR_P
ARAM_T_F32 *const
input
Pointer to the parameter structure.
GDFLIB_FILTERFIR_S pState
TATE_T_F32 *const
input,
output
Pointer to the filter state structure.
tFrac32
f32In
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Chapter 5 API References
5.2.3 Return
The value of a filtered signal after processing by an FIR filter.
5.2.4 Description
The function performs the operation of an FIR filter on a sample-by-sample basis. At
each new input to the FIR filter, the function should be called, which will return a new
filtered value.
The FIR filter is defined by the following formula:
Equation GDFLIB_FilterFIR_Eq1
where: x[n] is the input signal, y[n] is the output signal, h i are the filter coefficients, and
N is the filter order. It should be noted, that the number of taps of the filter is N + 1 in
this case.
The multiply and accumulate operations are performed with 64 accumulation, which
means that no saturation is performed during computations. However, if the final value
cannot fit in the return data type, saturation may occur. It should be noted, although rather
theoretically, that no saturation is performed on the accumulation guard bits and an
overflow over the accumulation guard bits may occur.
The function assumes that the filter order is at least one, which is equivalent to two taps.
The filter also cannot contain more than 0xffffffff(hexadecimal) taps, which is equivalent
to the order of 0xfffffffe (hexadecimal).
The input values are recorded by the function in the provided state structure in a circular
buffer, pointed to by the state structure member pState->pInBuf. The buffer index is
stored in pState->u32Idx, which points to the buffer element where a new input signal
sample will be stored.
The filter coefficients are stored in the parameter structure, in the structure member
pParam->pCoefBuf.
The first call to the function must be preceded by an initialization, which can be made
through the GDFLIB_FilterFIRInit_F32 function. The GDFLIB_FilterFIRInit_F32 and
then the GDFLIB_FilterFIR_F32 functions should be called with the same parameters.
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Function GDFLIB_FilterFIR_F32
Note
The input/output pointers must contain valid addresses
otherwise an exception may occur (Data TLB Error, Data
Storage, Alignment, Machine Check).
5.2.5 Re-entrancy
The function is re-entrant only if the calling code is provided with a distinct instance of
the structure pointed to by pState.
Note
From the performance point of view, the function is designed to
work with filters with a larger number of taps (equal order + 1).
As a rule of thumb, if the number of taps is lower than 5, a
different algorithm should be considered.
CAUTION
No check is performed for R/W capability and the length of the
input buffer (pState->pInBuf). In case of passing incorrect
pointer to the function, an unexpected behavior of the function
might be expected including the incorrect memory access
exception.
5.2.6 Code Example
#include "gdflib.h"
#define FIR_NUMTAPS 16
#define FIR_NUMTAPS_MAX 64
#define FIR_ORDER (FIR_NUMTAPS - 1)
GDFLIB_FILTERFIR_PARAM_T_F32 Param;
GDFLIB_FILTERFIR_STATE_T_F32 State0, State1, State2;
tFrac32 f32InBuf[FIR_NUMTAPS_MAX];
tFrac32 f32CoefBuf[FIR_NUMTAPS_MAX];
#define OUT_LEN 16
void main(void)
{
int ii;
tFrac32 f32OutBuf0[OUT_LEN];
tFrac32 f32OutBuf1[OUT_LEN];
tFrac32 f32OutBuf2[OUT_LEN];
// Define a simple low-pass filter
// The filter coefficients were calculated by the following
// Matlab function (coefficients are contained in Hd.Numerator):
//
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// function Hd = fir_example
// FIR_EXAMPLE Returns a discrete-time filter object.
// N
= 15;
// F6dB = 0.5;
//
// h = fdesign.lowpass('n,fc', N, F6dB);
//
// Hd = design(h, 'window');
// return;
ii = 0;
f32CoefBuf[ii++] = 0xFFB10C14;
f32CoefBuf[ii++] = 0xFF779D25;
f32CoefBuf[ii++] = 0x01387DD7;
f32CoefBuf[ii++] = 0x028E6845;
f32CoefBuf[ii++] = 0xFB245142;
f32CoefBuf[ii++] = 0xF7183CC7;
f32CoefBuf[ii++] = 0x11950A3C;
f32CoefBuf[ii++] = 0x393ED867;
f32CoefBuf[ii++] = 0x393ED867;
f32CoefBuf[ii++] = 0x11950A3C;
f32CoefBuf[ii++] = 0xF7183CC7;
f32CoefBuf[ii++] = 0xFB245142;
f32CoefBuf[ii++] = 0x028E6845;
f32CoefBuf[ii++] = 0x01387DD7;
f32CoefBuf[ii++] = 0xFF779D25;
f32CoefBuf[ii++] = 0xFFB10C14;
Param.u32Order = 15;
Param.pCoefBuf = &f32CoefBuf[0];
// Initialize FIR filter
GDFLIB_FilterFIRInit_F32 (&Param, &State0, &f32InBuf[0]);
// Initialize FIR filter
GDFLIB_FilterFIRInit (&Param, &State1, &f32InBuf[0], F32);
//
//
//
//
##############################################################
Available only if 32-bit fractional implementation selected
as default
##############################################################
// Initialize FIR filter
GDFLIB_FilterFIRInit (&Param, &State2, &f32InBuf[0]);
// Compute step response of the filter
for(ii=0; ii < OUT_LEN; ii++)
{
// f32OutBuf0 contains step response of the filter
f32OutBuf0[ii] = GDFLIB_FilterFIR_F32 (0x7FFFFFFF, &Param, &State0);
// f32OutBuf1 contains step response of the filter
f32OutBuf1[ii] = GDFLIB_FilterFIR (0x7FFFFFFF, &Param, &State1, F32);
//
//
//
//
##############################################################
Available only if 32-bit fractional implementation selected
as default
##############################################################
// f32OutBuf2 contains step response of the filter
f32OutBuf2[ii] = GDFLIB_FilterFIR (0x7FFFFFFF, &Param, &State2);
}
// After the loop the f32OutBuf0, f32OutBuf1, f32OutBuf2 shall contains
the following values:
// {0xFFB1009E, 0xFF2801B0, 0x005FFF40, 0x02EDFA24, 0xFE1203DC,
0xF52A15AC, 0x06BEF282, 0x3FFC8006,
// 0x793A0D8A, 0x7FFFFFFF, 0x7FFFFFFF, 0x7D0B05E8, 0x7F9900CC,
0x7FFFFFFF, 0x7FFFFFFF, 0x7FF9000C}
}
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Function GDFLIB_FilterFIRInit_F16
5.3 Function GDFLIB_FilterFIRInit_F16
This function initializes the FIR filter buffers.
5.3.1 Declaration
void GDFLIB_FilterFIRInit_F16(const GDFLIB_FILTERFIR_PARAM_T_F16 *const pParam,
GDFLIB_FILTERFIR_STATE_T_F16 *const pState, tFrac16 *pInBuf);
5.3.2 Arguments
Table 5-3. GDFLIB_FilterFIRInit_F16 arguments
Type
Name
Direction
Description
const
pParam
GDFLIB_FILTERFIR_P
ARAM_T_F16 *const
input
Pointer to the parameters structure.
GDFLIB_FILTERFIR_S pState
TATE_T_F16 *const
input,
output
Pointer to the state structure.
tFrac16 *
input,
output
Pointer to a buffer for storing filter input signal values, must
point to a R/W memory region and must be a filter order + 1
long.
pInBuf
5.3.3 Return
void
5.3.4 Description
The function performs the initialization procedure for the GDFLIB_FilterFIR_F16
function. In particular, the function performs the following operations:
1. Resets the input buffer index to zero.
2. Initializes the input buffer pointer to the pointer provided as an argument.
3. Resets the input buffer.
After initialization, made by the function, the parameters and state structures should be
provided as arguments to calls of the GDFLIB_FilterFIR_F16 function.
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Note
The input/output pointers must contain valid addresses
otherwise an exception may occur (Data TLB Error, Data
Storage, Alignment, Machine Check).
The input buffer pointer (State->pInBuf) must point to a Read/
Write memory region, which must be at least the number of the
filter taps long. The number of taps in a filter is equal to the
filter order + 1. There is no restriction as to the location of the
parameters structure as long as it is readable.
CAUTION
No check is performed for R/W capability and the length of the
input buffer (pState->pInBuf). In case of passing incorrect
pointer to the function, an unexpected behavior of the function
might be expected including the incorrect memory access
exception.
5.3.5 Re-entrancy
The function is re-entrant only if the calling code is provided with a distinct instance of
the structure pointed to by pState.
5.3.6 Code Example
#include "gdflib.h"
#define FIR_NUMTAPS 16
#define FIR_NUMTAPS_MAX 64
#define FIR_ORDER (FIR_NUMTAPS - 1)
GDFLIB_FILTERFIR_PARAM_T_F16 Param;
GDFLIB_FILTERFIR_STATE_T_F16 State0, State1, State2;
tFrac16 f16InBuf[FIR_NUMTAPS_MAX];
tFrac16 f16CoefBuf[FIR_NUMTAPS_MAX];
#define OUT_LEN 16
void main(void)
{
int ii;
tFrac16 f16OutBuf0[OUT_LEN];
tFrac16 f16OutBuf1[OUT_LEN];
tFrac16 f16OutBuf2[OUT_LEN];
// Define a simple low-pass filter
// The filter coefficients were calculated by the following
// Matlab function (coefficients are contained in Hd.Numerator):
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Function GDFLIB_FilterFIRInit_F16
//
// function Hd = fir_example
// FIR_EXAMPLE Returns a discrete-time filter object.
// N
= 15;
// F6dB = 0.5;
//
// h = fdesign.lowpass('n,fc', N, F6dB);
//
// Hd = design(h, 'window');
// return;
ii = 0;
f16CoefBuf[ii++] = 0xFFB1;
f16CoefBuf[ii++] = 0xFF77;
f16CoefBuf[ii++] = 0x0138;
f16CoefBuf[ii++] = 0x028E;
f16CoefBuf[ii++] = 0xFB24;
f16CoefBuf[ii++] = 0xF718;
f16CoefBuf[ii++] = 0x1195;
f16CoefBuf[ii++] = 0x393E;
f16CoefBuf[ii++] = 0x393E;
f16CoefBuf[ii++] = 0x1195;
f16CoefBuf[ii++] = 0xF718;
f16CoefBuf[ii++] = 0xFB24;
f16CoefBuf[ii++] = 0x028E;
f16CoefBuf[ii++] = 0x0138;
f16CoefBuf[ii++] = 0xFF77;
f16CoefBuf[ii++] = 0xFFB1;
Param.u16Order = 15;
Param.pCoefBuf = &f16CoefBuf[0];
// Initialize FIR filter
GDFLIB_FilterFIRInit_F16 (&Param, &State0, &f16InBuf[0]);
// Initialize FIR filter
GDFLIB_FilterFIRInit (&Param, &State1, &f16InBuf[0], F16);
//
//
//
//
##############################################################
Available only if 16-bit fractional implementation selected
as default
##############################################################
// Initialize FIR filter
GDFLIB_FilterFIRInit (&Param, &State2, &f16InBuf[0]);
// Compute step response of the filter
for(ii=0; ii < OUT_LEN; ii++)
{
// f16OutBuf0 contains step response of the filter
f16OutBuf0[ii] = GDFLIB_FilterFIR_F16 (0x7FFF, &Param, &State0);
// f16OutBuf1 contains step response of the filter
f16OutBuf1[ii] = GDFLIB_FilterFIR (0x7FFF, &Param, &State1, F16);
//
//
//
//
##############################################################
Available only if 16-bit fractional implementation selected
as default
##############################################################
// f16OutBuf2 contains step response of the filter
f16OutBuf2[ii] = GDFLIB_FilterFIR (0x7FFF, &Param, &State2);
}
// After the loop the f16OutBuf0, f16OutBuf1, f16OutBuf2 shall contains
the following values:
// {0xFFB1, 0xFF28, 0x005F, 0x02ED, 0xFE12, 0xF52A, 0x06BE, 0x3FFC,
// 0x793A, 0x7FFF, 0x7FFF, 0x7D0B, 0x7F99, 0x7FFF, 0x7FFF, 0x7FF9}
}
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5.4 Function GDFLIB_FilterFIR_F16
The function performs a single iteration of an FIR filter.
5.4.1 Declaration
tFrac16 GDFLIB_FilterFIR_F16(tFrac16 f16In, const GDFLIB_FILTERFIR_PARAM_T_F16 *const pParam,
GDFLIB_FILTERFIR_STATE_T_F16 *const pState);
5.4.2 Arguments
Table 5-4. GDFLIB_FilterFIR_F16 arguments
Type
Name
Direction
Description
input
Input value.
const
pParam
GDFLIB_FILTERFIR_P
ARAM_T_F16 *const
input
Pointer to the parameter structure.
GDFLIB_FILTERFIR_S pState
TATE_T_F16 *const
input,
output
Pointer to the filter state structure.
tFrac16
f16In
5.4.3 Return
The value of a filtered signal after processing by an FIR filter.
5.4.4 Description
The function performs the operation of an FIR filter on a sample-by-sample basis. At
each new input to the FIR filter, the function should be called, which will return a new
filtered value.
The FIR filter is defined by the following formula:
Equation GDFLIB_FilterFIR_Eq1
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Function GDFLIB_FilterFIR_F16
where: x[n] is the input signal, y[n] is the output signal, h i are the filter coefficients, and
N is the filter order. It should be noted, that the number of taps of the filter is N + 1 in
this case.
The multiply and accumulate operations are performed with 32 accumulation, which
means that no saturation is performed during computations. However, if the final value
cannot fit in the return data type, saturation may occur. It should be noted, although rather
theoretically, that no saturation is performed on the accumulation guard bits and an
overflow over the accumulation guard bits may occur.
The function assumes that the filter order is at least one, which is equivalent to two taps.
The filter also cannot contain more than 0xffff(hexadecimal) taps, which is equivalent to
the order of 0xfffe (hexadecimal).
The input values are recorded by the function in the provided state structure in a circular
buffer, pointed to by the state structure member pState->pInBuf. The buffer index is
stored in pState->u16Idx, which points to the buffer element where a new input signal
sample will be stored.
The filter coefficients are stored in the parameter structure, in the structure member
pParam->pCoefBuf.
The first call to the function must be preceded by an initialization, which can be made
through the GDFLIB_FilterFIRInit_F16 function. The GDFLIB_FilterFIRInit_F16 and
then the GDFLIB_FilterFIR_F16 functions should be called with the same parameters.
Note
The input/output pointers must contain valid addresses
otherwise an exception may occur (Data TLB Error, Data
Storage, Alignment, Machine Check).
5.4.5 Re-entrancy
The function is re-entrant only if the calling code is provided with a distinct instance of
the structure pointed to by pState.
Note
From the performance point of view, the function is designed to
work with filters with a larger number of taps (equal order + 1).
As a rule of thumb, if the number of taps is lower than 5, a
different algorithm should be considered.
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CAUTION
No check is performed for R/W capability and the length of the
input buffer (pState->pInBuf). In case of passing incorrect
pointer to the function, an unexpected behavior of the function
might be expected including the incorrect memory access
exception.
5.4.6 Code Example
#include "gdflib.h"
#define FIR_NUMTAPS 16
#define FIR_NUMTAPS_MAX 64
#define FIR_ORDER (FIR_NUMTAPS - 1)
GDFLIB_FILTERFIR_PARAM_T_F16 Param;
GDFLIB_FILTERFIR_STATE_T_F16 State0, State1, State2;
tFrac16 f16InBuf[FIR_NUMTAPS_MAX];
tFrac16 f16CoefBuf[FIR_NUMTAPS_MAX];
#define OUT_LEN 16
void main(void)
{
int ii;
tFrac16 f16OutBuf0[OUT_LEN];
tFrac16 f16OutBuf1[OUT_LEN];
tFrac16 f16OutBuf2[OUT_LEN];
// Define a simple low-pass filter
// The filter coefficients were calculated by the following
// Matlab function (coefficients are contained in Hd.Numerator):
//
// function Hd = fir_example
// FIR_EXAMPLE Returns a discrete-time filter object.
// N
= 15;
// F6dB = 0.5;
//
// h = fdesign.lowpass('n,fc', N, F6dB);
//
// Hd = design(h, 'window');
// return;
ii = 0;
f16CoefBuf[ii++] = 0xFFB1;
f16CoefBuf[ii++] = 0xFF77;
f16CoefBuf[ii++] = 0x0138;
f16CoefBuf[ii++] = 0x028E;
f16CoefBuf[ii++] = 0xFB24;
f16CoefBuf[ii++] = 0xF718;
f16CoefBuf[ii++] = 0x1195;
f16CoefBuf[ii++] = 0x393E;
f16CoefBuf[ii++] = 0x393E;
f16CoefBuf[ii++] = 0x1195;
f16CoefBuf[ii++] = 0xF718;
f16CoefBuf[ii++] = 0xFB24;
f16CoefBuf[ii++] = 0x028E;
f16CoefBuf[ii++] = 0x0138;
f16CoefBuf[ii++] = 0xFF77;
f16CoefBuf[ii++] = 0xFFB1;
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Function GDFLIB_FilterIIR1Init_F32
Param.u16Order = 15;
Param.pCoefBuf = &f16CoefBuf[0];
// Initialize FIR filter
GDFLIB_FilterFIRInit_F16 (&Param, &State0, &f16InBuf[0]);
// Initialize FIR filter
GDFLIB_FilterFIRInit (&Param, &State1, &f16InBuf[0], F16);
//
//
//
//
##############################################################
Available only if 16-bit fractional implementation selected
as default
##############################################################
// Initialize FIR filter
GDFLIB_FilterFIRInit (&Param, &State2, &f16InBuf[0]);
// Compute step response of the filter
for(ii=0; ii < OUT_LEN; ii++)
{
// f16OutBuf0 contains step response of the filter
f16OutBuf0[ii] = GDFLIB_FilterFIR_F16 (0x7FFF, &Param, &State0);
// f16OutBuf1 contains step response of the filter
f16OutBuf1[ii] = GDFLIB_FilterFIR (0x7FFF, &Param, &State1, F16);
//
//
//
//
##############################################################
Available only if 16-bit fractional implementation selected
as default
##############################################################
// f16OutBuf2 contains step response of the filter
f16OutBuf2[ii] = GDFLIB_FilterFIR (0x7FFF, &Param, &State2);
}
// After the loop the f16OutBuf0, f16OutBuf1, f16OutBuf2 shall contains
the following values:
// {0xFFB1, 0xFF28, 0x005F, 0x02ED, 0xFE12, 0xF52A, 0x06BE, 0x3FFC,
// 0x793A, 0x7FFF, 0x7FFF, 0x7D0B, 0x7F99, 0x7FFF, 0x7FFF, 0x7FF9}
}
5.5 Function GDFLIB_FilterIIR1Init_F32
This function initializes the first order IIR filter buffers.
5.5.1 Declaration
void GDFLIB_FilterIIR1Init_F32(GDFLIB_FILTER_IIR1_T_F32 *const pParam);
5.5.2 Arguments
Table 5-5. GDFLIB_FilterIIR1Init_F32 arguments
Type
GDFLIB_FILTER_IIR1_ pParam
T_F32 *const
Name
Direction
input,
output
Description
Pointer to filter structure with filter buffer and filter parameters.
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5.5.3 Return
Function returns no value.
5.5.4 Description
This function clears the internal buffers of a first order IIR filter. It shall be called after
filter parameter initialization and whenever the filter initialization is required.
Note
The input pointer must contain a valid address otherwise an
exception may occur (Data TLB Error, Data Storage,
Alignment, Machine Check).
This function shall not be called together with
GDFLIB_FilterIIR1_F32 unless periodic clearing of filter
buffers is required.
5.5.5 Re-entrancy
The function is re-entrant.
5.5.6 Code Example
#include "gdflib.h"
GDFLIB_FILTER_IIR1_T_F32 f32trMyIIR1 = GDFLIB_FILTER_IIR1_DEFAULT_F32;
void main(void)
{
// function returns no value
GDFLIB_FilterIIR1Init_F32 (&f32trMyIIR1);
// function returns no value
GDFLIB_FilterIIR1Init (&f32trMyIIR1, F32);
//
//
//
//
}
##############################################################
Available only if 32-bit fractional implementation selected
as default
##############################################################
// function returns no value
GDFLIB_FilterIIR1Init (&f32trMyIIR1);
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Function GDFLIB_FilterIIR1_F32
5.6 Function GDFLIB_FilterIIR1_F32
This function implements the first order IIR filter.
5.6.1 Declaration
tFrac32 GDFLIB_FilterIIR1_F32(tFrac32 f32In, GDFLIB_FILTER_IIR1_T_F32 *const pParam);
5.6.2 Arguments
Table 5-6. GDFLIB_FilterIIR1_F32 arguments
Type
tFrac32
Name
f32In
GDFLIB_FILTER_IIR1_ pParam
T_F32 *const
Direction
Description
input
Value of input signal to be filtered in step (k). The value is a
32-bit number in the 1.31 fractional format.
input,
output
Pointer to the filter structure with a filter buffer and filter
parameters.
5.6.3 Return
The function returns a 32-bit value in fractional format 1.31, representing the filtered
value of the input signal in step (k).
5.6.4 Description
This function calculates the first order infinite impulse (IIR) filter. The IIR filters are also
called recursive filters because both the input and the previously calculated output values
are used for calculation of the filter equation in each step. This form of feedback enables
transfer of the energy from the output to the input, which theoretically leads to an
infinitely long impulse response (IIR).
A general form of the IIR filter expressed as a transfer function in the Z-domain is
described as follows:
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Equation GDFLIB_FilterIIR1_Eq1
where N denotes the filter order. The first order IIR filter in the Z-domain is therefore
given from equation GDFLIB_FilterIIR1_Eq1 as:
Equation GDFLIB_FilterIIR1_Eq2
In order to implement the first order IIR filter on a microcontroller, the discrete time
domain representation of the filter, described by equation GDFLIB_FilterIIR1_Eq2, must
be transformed into a time difference equation as follows:
Equation GDFLIB_FilterIIR1_Eq3
Equation GDFLIB_FilterIIR1_Eq3 represents a Direct Form I implementation of a first
order IIR filter. It is well known that Direct Form I (DF-I) and Direct Form II (DF-II)
implementations of an IIR filter are generally sensitive to parameter quantization if a
finite precision arithmetic is considered. This, however, can be neglected when the filter
transfer function is broken down into low order sections, i.e. first or second order. The
main difference between DF-I and DF-II implementations of an IIR filter is in the number
of delay buffers and in the number of guard bits required to handle the potential overflow.
The DF-II implementation requires less delay buffers than DF-I, hence less data memory
is utilized. On the other hand, since the poles come first in the DF-II realization, the
signal entering the state delay-line typically requires a larger dynamic range than the
output signal y(k). Therefore, overflow can occur at the delay-line input of the DF-II
implementation, unlike in the DF-I implementation.
Because there are two delay buffers necessary for both DF-I and DF-II implementation of
the first order IIR filter, the DF-I implementation was chosen to be used in the
GDFLIB_FilterIIR1_F32 function.
Figure 5-1. Direct Form 1 first order IIR filter
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Function GDFLIB_FilterIIR1_F32
The coefficients of the filter depicted in Figure 5-1 can be designed to meet the
requirements for the first order Low (LPF) or High Pass (HPF) filters. Filter coefficients
can be calculated using various tools, for example, the Matlab butter function. In order to
avoid overflow during the calculation of the GDFLIB_FilterIIR1_F32 function, filter
coefficients must be divided by eight. The coefficient quantization error due to finite
precision arithmetic can be neglected in the case of a first order filter. Therefore, the
calculation of coefficients can be done using Matlab as follows:
freq_cut = 100;
T_sampling = 100e-6;
[b,a]=butter(1,[freq_cut*T_sampling*2],'low');
sys=tf(b,a,T_sampling);
bode(sys)
f32B0 = b(1);
f32B1 = b(2);
f32A1 = a(2);
disp('Coefficients for GDFLIB_FilterIIR1 function:');
disp(['f32B0 = FRAC32 (' num2str(f32B0,'%1.15f') '/8);']);
disp(['f32B1 = FRAC32 (' num2str(f32B1,'%1.15f') '/8);']);
disp(['f32A1 = FRAC32 (' num2str(f32A1,'%1.15f') '/8);']);
Note
The input pointer must contain a valid address otherwise an
exception may occur (Data TLB Error, Data Storage,
Alignment, Machine Check).
The filter delay line includes two delay buffers which should be
reset after filter initialization. This can be done by assigning to
the filter instance a GDFLIB_FILTER_IIR1_DEFAULT_F32
macro during instance declaration or by calling the
GDFLIB_FilterIIR1Init_F32 function.
CAUTION
Because of fixed point implementation, and to avoid overflow
during the calculation of the GDFLIB_FilterIIR1_F32 function,
filter coefficients must be divided by eight. Function output is
internally multiplied by eight to correct the coefficient scaling.
5.6.5 Re-entrancy
The function is re-entrant.
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5.6.6 Code Example
#include "gdflib.h"
tFrac32 f32In;
tFrac32 f32Out;
GDFLIB_FILTER_IIR1_T_F32 f32trMyIIR1 = GDFLIB_FILTER_IIR1_DEFAULT_F32;
void main(void)
{
// input value = 0.25
f32In = FRAC32 (0.25);
// filter coefficients (LPF 100Hz, Ts=100e-6)
f32trMyIIR1.trFiltCoeff.f32B0 = FRAC32 (0.030468747091254/8);
f32trMyIIR1.trFiltCoeff.f32B1 = FRAC32 (0.030468747091254/8);
f32trMyIIR1.trFiltCoeff.f32A1 = FRAC32 (-0.939062505817492/8);
// output should be 0x00F99998 ~ FRAC32(0.007617)
GDFLIB_FilterIIR1Init_F32 (&f32trMyIIR1);
f32Out = GDFLIB_FilterIIR1_F32 (f32In, &f32trMyIIR1);
// output should be 0x00F99998 ~ FRAC32(0.007617)
GDFLIB_FilterIIR1Init (&f32trMyIIR1, F32);
f32Out = GDFLIB_FilterIIR1 (f32In, &f32trMyIIR1, F32);
//
//
//
//
}
##############################################################
Available only if 32-bit fractional implementation selected
as default
##############################################################
// output should be 0x00F99998 ~ FRAC32(0.007617)
GDFLIB_FilterIIR1Init (&f32trMyIIR1);
f32Out = GDFLIB_FilterIIR1 (f32In, &f32trMyIIR1);
5.7 Function GDFLIB_FilterIIR1Init_F16
This function initializes the first order IIR filter buffers.
5.7.1 Declaration
void GDFLIB_FilterIIR1Init_F16(GDFLIB_FILTER_IIR1_T_F16 *const pParam);
5.7.2 Arguments
Table 5-7. GDFLIB_FilterIIR1Init_F16 arguments
Type
GDFLIB_FILTER_IIR1_ pParam
T_F16 *const
Name
Direction
input,
output
Description
Pointer to filter structure with filter buffer and filter parameters.
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Function GDFLIB_FilterIIR1Init_F16
5.7.3 Return
Function returns no value.
5.7.4 Description
This function clears the internal buffers of a first order IIR filter. It shall be called after
filter parameter initialization and whenever the filter initialization is required.
Note
The input pointer must contain a valid address otherwise an
exception may occur (Data TLB Error, Data Storage,
Alignment, Machine Check).
This function shall not be called together with
GDFLIB_FilterIIR1_F16 unless periodic clearing of filter
buffers is required.
5.7.5 Re-entrancy
The function is re-entrant.
5.7.6 Code Example
#include "gdflib.h"
GDFLIB_FILTER_IIR1_T_F16 f16trMyIIR1 = GDFLIB_FILTER_IIR1_DEFAULT_F16;
void main(void)
{
// function returns no value
GDFLIB_FilterIIR1Init_F16 (&f16trMyIIR1);
// function returns no value
GDFLIB_FilterIIR1Init (&f16trMyIIR1, F16);
//
//
//
//
}
##############################################################
Available only if 16-bit fractional implementation selected
as default
##############################################################
// function returns no value
GDFLIB_FilterIIR1Init (&f16trMyIIR1);
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5.8 Function GDFLIB_FilterIIR1_F16
This function implements the first order IIR filter.
5.8.1 Declaration
tFrac16 GDFLIB_FilterIIR1_F16(tFrac16 f16In, GDFLIB_FILTER_IIR1_T_F16 *const pParam);
5.8.2 Arguments
Table 5-8. GDFLIB_FilterIIR1_F16 arguments
Type
tFrac16
Name
f16In
GDFLIB_FILTER_IIR1_ pParam
T_F16 *const
Direction
Description
input
Value of input signal to be filtered in step (k). The value is a
16-bit number in the 1.15 fractional format.
input,
output
Pointer to the filter structure with a filter buffer and filter
parameters.
5.8.3 Return
The function returns a 16-bit value in fractional format 1.15, representing the filtered
value of the input signal in step (k).
5.8.4 Description
This function calculates the first order infinite impulse (IIR) filter. The IIR filters are also
called recursive filters because both the input and the previously calculated output values
are used for calculation of the filter equation in each step. This form of feedback enables
transfer of the energy from the output to the input, which theoretically leads to an
infinitely long impulse response (IIR).
A general form of the IIR filter expressed as a transfer function in the Z-domain is
described as follows:
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Function GDFLIB_FilterIIR1_F16
Equation GDFLIB_FilterIIR1_Eq1
where N denotes the filter order. The first order IIR filter in the Z-domain is therefore
given from equation GDFLIB_FilterIIR1_Eq1 as:
Equation GDFLIB_FilterIIR1_Eq2
In order to implement the first order IIR filter on a microcontroller, the discrete time
domain representation of the filter, described by equation GDFLIB_FilterIIR1_Eq2, must
be transformed into a time difference equation as follows:
Equation GDFLIB_FilterIIR1_Eq3
Equation GDFLIB_FilterIIR1_Eq3 represents a Direct Form I implementation of a first
order IIR filter. It is well known that Direct Form I (DF-I) and Direct Form II (DF-II)
implementations of an IIR filter are generally sensitive to parameter quantization if a
finite precision arithmetic is considered. This, however, can be neglected when the filter
transfer function is broken down into low order sections, i.e. first or second order. The
main difference between DF-I and DF-II implementations of an IIR filter is in the number
of delay buffers and in the number of guard bits required to handle the potential overflow.
The DF-II implementation requires less delay buffers than DF-I, hence less data memory
is utilized. On the other hand, since the poles come first in the DF-II realization, the
signal entering the state delay-line typically requires a larger dynamic range than the
output signal y(k). Therefore, overflow can occur at the delay-line input of the DF-II
implementation, unlike in the DF-I implementation.
Because there are two delay buffers necessary for both DF-I and DF-II implementation of
the first order IIR filter, the DF-I implementation was chosen to be used in the
GDFLIB_FilterIIR1_F16 function.
Figure 5-2. Direct Form 1 first order IIR filter
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Chapter 5 API References
The coefficients of the filter depicted in Figure 5-2 can be designed to meet the
requirements for the first order Low (LPF) or High Pass (HPF) filters. Filter coefficients
can be calculated using various tools, for example, the Matlab butter function. The
coefficient quantization error due to finite precision arithmetic can be neglected in the
case of a first order filter. Therefore, the calculation of coefficients can be done using
Matlab as follows:
freq_cut
T_sampling
= 100;
= 100e-6;
[b,a]=butter(1,[freq_cut*T_sampling*2],'low');
sys=tf(b,a,T_sampling);
bode(sys)
f16B0 = b(1);
f16B1 = b(2);
f16A1 = a(2);
disp('Coefficients for GDFLIB_FilterIIR1 function:');
disp(['f16B0 = FRAC16 (' num2str(f16B0,'%1.15f') '/8);']);
disp(['f16B1 = FRAC16 (' num2str(f16B1,'%1.15f') '/8);']);
disp(['f16A1 = FRAC16 (' num2str(f16A1,'%1.15f') '/8);']);
Note
The input pointer must contain a valid address otherwise an
exception may occur (Data TLB Error, Data Storage,
Alignment, Machine Check).
The filter delay line includes two delay buffers which should be
reset after filter initialization. This can be done by assigning to
the filter instance a GDFLIB_FILTER_IIR1_DEFAULT_F16
macro during instance declaration or by calling the
GDFLIB_FilterIIR1Init_F16 function.
CAUTION
Because of fixed point implementation, and to avoid overflow
during the calculation of the GDFLIB_FilterIIR1_F16 function,
filter coefficients must be divided by eight. Function output is
internally multiplied by eight to correct the coefficient scaling.
5.8.5 Re-entrancy
The function is re-entrant.
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Function GDFLIB_FilterIIR2Init_F32
5.8.6 Code Example
#include "gdflib.h"
tFrac16 f16In;
tFrac16 f16Out;
GDFLIB_FILTER_IIR1_T_F16 f16trMyIIR1 = GDFLIB_FILTER_IIR1_DEFAULT_F16;
void main(void)
{
// input value = 0.25
f16In = FRAC16 (0.25);
// filter coefficients (LPF 100Hz, Ts=100e-6)
f16trMyIIR1.trFiltCoeff.f16B0 = FRAC16 (0.030468747091254/8);
f16trMyIIR1.trFiltCoeff.f16B1 = FRAC16 (0.030468747091254/8);
f16trMyIIR1.trFiltCoeff.f16A1 = FRAC16 (-0.939062505817492/8);
// output should be 0x00F9 ~ FRAC16(0.007617)
GDFLIB_FilterIIR1Init_F16 (&f16trMyIIR1);
f16Out = GDFLIB_FilterIIR1_F16 (f16In, &f16trMyIIR1);
// output should be 0x00F9 ~ FRAC16(0.007617)
GDFLIB_FilterIIR1Init (&f16trMyIIR1, F16);
f16Out = GDFLIB_FilterIIR1 (f16In, &f16trMyIIR1, F16);
//
//
//
//
}
##############################################################
Available only if 16-bit fractional implementation selected
as default
##############################################################
// output should be 0x00F9 ~ FRAC16(0.007617)
GDFLIB_FilterIIR1Init (&f16trMyIIR1);
f16Out = GDFLIB_FilterIIR1 (f16In, &f16trMyIIR1);
5.9 Function GDFLIB_FilterIIR2Init_F32
This function initializes the second order IIR filter buffers.
5.9.1 Declaration
void GDFLIB_FilterIIR2Init_F32(GDFLIB_FILTER_IIR2_T_F32 *const pParam);
5.9.2 Arguments
Table 5-9. GDFLIB_FilterIIR2Init_F32 arguments
Type
GDFLIB_FILTER_IIR2_ pParam
T_F32 *const
Name
Direction
input,
output
Description
Pointer to the filter structure with a filter buffer and filter
parameters.
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5.9.3 Return
Function returns no value.
5.9.4 Description
This function clears the internal buffers of a second order IIR filter. It shall be called after
filter parameter initialization and whenever the filter initialization is required.
Note
The input pointer must contain a valid address otherwise an
exception may occur (Data TLB Error, Data Storage,
Alignment, Machine Check).
This function shall not be called together with
GDFLIB_FilterIIR2_F32 unless periodic clearing of filter
buffers is required.
5.9.5 Re-entrancy
The function is re-entrant.
5.9.6 Code Example
#include "gdflib.h"
GDFLIB_FILTER_IIR2_T_F32 f32trMyIIR2 = GDFLIB_FILTER_IIR2_DEFAULT_F32;
void main(void)
{
// function returns no value
GDFLIB_FilterIIR2Init_F32 (&f32trMyIIR2);
// function returns no value
GDFLIB_FilterIIR2Init (&f32trMyIIR2, F32);
//
//
//
//
}
##############################################################
Available only if 32-bit fractional implementation selected
as default
##############################################################
// function returns no value
GDFLIB_FilterIIR2Init (&f32trMyIIR2);
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Function GDFLIB_FilterIIR2_F32
5.10 Function GDFLIB_FilterIIR2_F32
This function implements the second order IIR filter.
5.10.1 Declaration
tFrac32 GDFLIB_FilterIIR2_F32(tFrac32 f32In, GDFLIB_FILTER_IIR2_T_F32 *const pParam);
5.10.2 Arguments
Table 5-10. GDFLIB_FilterIIR2_F32 arguments
Type
tFrac32
Name
f32In
GDFLIB_FILTER_IIR2_ pParam
T_F32 *const
Direction
Description
input
Value of input signal to be filtered in step (k). The value is a
32-bit number in the 1.31 fractional format.
input,
output
Pointer to the filter structure with a filter buffer and filter
parameters.
5.10.3 Return
The function returns a 32-bit value in fractional format 1.31, representing the filtered
value of the input signal in step (k).
5.10.4 Description
This function calculates the second order infinite impulse (IIR) filter. The IIR filters are
also called recursive filters because both the input and the previously calculated output
values are used for calculation of the filter equation in each step. This form of feedback
enables transfer of the energy from the output to the input, which theoretically leads to an
infinitely long impulse response (IIR).
A general form of the IIR filter expressed as a transfer function in the Z-domain is
described as follows:
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Equation GDFLIB_FilterIIR2_Eq1
where N denotes the filter order. The second order IIR filter in the Z-domain is therefore
given from eq. GDFLIB_FilterIIR2_Eq1 as:
Equation GDFLIB_FilterIIR2_Eq2
In order to implement the second order IIR filter on a microcontroller, the discrete time
domain representation of the filter, described by eq. GDFLIB_FilterIIR2_Eq2, must be
transformed into a time difference equation as follows:
Equation GDFLIB_FilterIIR2_Eq3
Equation GDFLIB_FilterIIR2_Eq3 represents a Direct Form I implementation of a
second order IIR filter. It is well known that Direct Form I (DF-I) and Direct Form II
(DF-II) implementations of an IIR filter are generally sensitive to parameter quantization
if a finite precision arithmetic is considered. This, however, can be neglected when the
filter transfer function is broken down into low order sections, i.e. first or second order.
The main difference between DF-I and DF-II implementations of an IIR filter is in the
number of delay buffers and in the number of guard bits required to handle the potential
overflow. The DF-II implementation requires less delay buffers than DF-I, hence less
data memory is utilized. On the other hand, since the poles come first in the DF-II
realization, the signal entering the state delay-line typically requires a larger dynamic
range than the output signal y(k). Therefore, overflow can occur at the delay-line input of
the DF-II implementation, unlike in the DF-I implementation.
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Function GDFLIB_FilterIIR2_F32
Figure 5-3. Direct Form 1 second order IIR filter
The coefficients of the filter depicted in Figure 5-3 can be designed to meet the
requirements for the second order Band Pass (BPF) or Band Stop (BSF) filters. Filter
coefficients can be calculated using various tools, for example the Matlab butter function.
In order to avoid overflow during the calculation of the GDFLIB_FilterIIR2_F32
function, filter coefficients must be divided by eight. The coefficient quantization error
due to finite precision arithmetic can be neglected in the case of a second order filter.
Therefore, calculation of coefficients can be done using Matlab as follows:
freq_bot
freq_top
T_sampling
= 400;
= 625;
= 100e-6;
[b,a]= butter(1,[freq_bot freq_top]*T_sampling *2, 'bandpass');
sys =tf(b,a,T_sampling);
bode(sys,[freq_bot:1:freq_top]*2*pi)
f32B0 =
f32B1 =
f32B2 =
f32A1 =
f32A2 =
disp ('
disp ([
disp ([
disp ([
disp ([
disp ([
b(1);
b(2);
b(3);
a(2);
a(3);
Coefficients for GDFLIB_FilterIIR2 function
'f32B0 = FRAC32(' num2str( f32B0,'%1.15f' )
'f32B1 = FRAC32(' num2str( f32B1,'%1.15f' )
'f32B2 = FRAC32(' num2str( f32B2,'%1.15f' )
'f32A1 = FRAC32(' num2str( f32A1,'%1.15f' )
'f32A2 = FRAC32(' num2str( f32A2,'%1.15f' )
:');
'/8);']);
'/8);']);
'/8);']);
'/8);']);
'/8);']);
Note
The input pointer must contain a valid address otherwise an
exception may occur (Data TLB Error, Data Storage,
Alignment, Machine Check).
The filter delay line includes four delay buffers which should
be reset after filter initialization. This can be done by assigning
to the filter instance a
GDFLIB_FILTER_IIR2_DEFAULT_F32 macro during
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instance declaration or by calling the
GDFLIB_FilterIIR2Init_F32 function.
CAUTION
Because of fixed point implementation, and to avoid overflow
during the calculation of the GDFLIB_FilterIIR2_F32 function,
filter coefficients must be divided by eight. Function output is
internally multiplied by eight to correct the coefficient scaling.
5.10.5 Re-entrancy
The function is re-entrant.
5.10.6 Code Example
#include "gdflib.h"
tFrac32 f32In;
tFrac32 f32Out;
GDFLIB_FILTER_IIR2_T_F32 f32trMyIIR2 = GDFLIB_FILTER_IIR2_DEFAULT_F32;
void main(void)
{
// input value = 0.25
f32In = FRAC32 (0.25);
// filter coefficients (BPF 400-625Hz,
f32trMyIIR2.trFiltCoeff.f32B0 = FRAC32
f32trMyIIR2.trFiltCoeff.f32B1 = FRAC32
f32trMyIIR2.trFiltCoeff.f32B2 = FRAC32
f32trMyIIR2.trFiltCoeff.f32A1 = FRAC32
f32trMyIIR2.trFiltCoeff.f32A2 = FRAC32
Ts=100e-6)
(0.066122101544579/8);
(0/8);
(-0.066122101544579/8);
(-1.776189018043779/8);
(0.867755796910841/8);
// output should be 0x021DAC18 ~ FRAC32(0.0165305)
GDFLIB_FilterIIR2Init_F32 (&f32trMyIIR2);
f32Out = GDFLIB_FilterIIR2_F32 (f32In, &f32trMyIIR2);
// output should be 0x021DAC18 ~ FRAC32(0.0165305)
GDFLIB_FilterIIR2Init (&f32trMyIIR2, F32);
f32Out = GDFLIB_FilterIIR2 (f32In, &f32trMyIIR2, F32);
//
//
//
//
}
##############################################################
Available only if 32-bit fractional implementation selected
as default
##############################################################
// output should be 0x021DAC18 ~ FRAC32(0.0165305)
GDFLIB_FilterIIR2Init (&f32trMyIIR2);
f32Out = GDFLIB_FilterIIR2 (f32In, &f32trMyIIR2);
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Function GDFLIB_FilterIIR2Init_F16
5.11 Function GDFLIB_FilterIIR2Init_F16
This function initializes the second order IIR filter buffers.
5.11.1 Declaration
void GDFLIB_FilterIIR2Init_F16(GDFLIB_FILTER_IIR2_T_F16 *const pParam);
5.11.2 Arguments
Table 5-11. GDFLIB_FilterIIR2Init_F16 arguments
Type
Name
GDFLIB_FILTER_IIR2_ pParam
T_F16 *const
Direction
input,
output
Description
Pointer to the filter structure with a filter buffer and filter
parameters.
5.11.3 Return
Function returns no value.
5.11.4 Description
This function clears the internal buffers of a second order IIR filter. The function shall be
called after filter parameter initialization and whenever the filter initialization is required.
Note
The input pointer must contain a valid address otherwise an
exception may occur (Data TLB Error, Data Storage,
Alignment, Machine Check).
This function shall not be called together with
GDFLIB_FilterIIR2_F16 unless periodic clearing of filter
buffers is required.
5.11.5 Re-entrancy
The function is re-entrant.
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5.11.6 Code Example
#include "gdflib.h"
GDFLIB_FILTER_IIR2_T_F16 f16trMyIIR2 = GDFLIB_FILTER_IIR2_DEFAULT_F16;
void main(void)
{
// function returns no value
GDFLIB_FilterIIR2Init_F16 (&f16trMyIIR2);
// function returns no value
GDFLIB_FilterIIR2Init (&f16trMyIIR2, F16);
//
//
//
//
}
##############################################################
Available only if 16-bit fractional implementation selected
as default
##############################################################
// function returns no value
GDFLIB_FilterIIR2Init (&f16trMyIIR2);
5.12 Function GDFLIB_FilterIIR2_F16
This function implements the second order IIR filter.
5.12.1 Declaration
tFrac16 GDFLIB_FilterIIR2_F16(tFrac16 f16In, GDFLIB_FILTER_IIR2_T_F16 *const pParam);
5.12.2 Arguments
Table 5-12. GDFLIB_FilterIIR2_F16 arguments
Type
tFrac16
Name
f16In
GDFLIB_FILTER_IIR2_ pParam
T_F16 *const
Direction
Description
input
Value of input signal to be filtered in step (k). The value is a
16-bit number in the 1.15 fractional format.
input,
output
Pointer to the filter structure with a filter buffer and filter
parameters.
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Function GDFLIB_FilterIIR2_F16
5.12.3 Return
The function returns a 16-bit value in fractional format 1.15, representing the filtered
value of the input signal in step (k).
5.12.4 Description
This function calculates the second order infinite impulse (IIR) filter. The IIR filters are
also called recursive filters because both the input and the previously calculated output
values are used for calculation of the filter equation in each step. This form of feedback
enables transfer of the energy from the output to the input, which theoretically leads to an
infinitely long impulse response (IIR).
A general form of the IIR filter expressed as a transfer function in the Z-domain is
described as follows:
Equation GDFLIB_FilterIIR2_Eq1
where N denotes the filter order. The second order IIR filter in the Z-domain is therefore
given from eq. GDFLIB_FilterIIR2_Eq1 as:
Equation GDFLIB_FilterIIR2_Eq2
In order to implement the second order IIR filter on a microcontroller, the discrete time
domain representation of the filter, described by eq. GDFLIB_FilterIIR2_Eq2, must be
transformed into a time difference equation as follows:
Equation GDFLIB_FilterIIR2_Eq3
Equation GDFLIB_FilterIIR2_Eq3 represents a Direct Form I implementation of a
second order IIR filter. It is well known that Direct Form I (DF-I) and Direct Form II
(DF-II) implementations of an IIR filter are generally sensitive to parameter quantization
if a finite precision arithmetic is considered. This, however, can be neglected when the
filter transfer function is broken down into low order sections, i.e. first or second order.
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The main difference between DF-I and DF-II implementations of an IIR filter is in the
number of delay buffers and in the number of guard bits required to handle the potential
overflow. The DF-II implementation requires less delay buffers than DF-I, hence less
data memory is utilized. On the other hand, since the poles come first in the DF-II
realization, the signal entering the state delay-line typically requires a larger dynamic
range than the output signal y(k). Therefore, overflow can occur at the delay-line input of
the DF-II implementation, unlike in the DF-I implementation.
Figure 5-4. Direct Form 1 second order IIR filter
The coefficients of the filter depicted in Figure 5-4 can be designed to meet the
requirements for the second order Band Pass (BPF) or Band Stop (BSF) filters. Filter
coefficients can be calculated using various tools, for example the Matlab butter function.
In order to avoid overflow during the calculation of the GDFLIB_FilterIIR2_F16
function, filter coefficients must be divided by eight. The coefficient quantization error
due to finite precision arithmetic can be neglected in the case of a second order filter.
Therefore, calculation of coefficients can be done using Matlab as follows:
freq_bot
freq_top
T_sampling
= 400;
= 625;
= 100e-6;
[b,a]= butter(1,[freq_bot freq_top]*T_sampling *2, 'bandpass');
sys =tf(b,a,T_sampling);
bode(sys,[freq_bot:1:freq_top]*2*pi)
f16B0 =
f16B1 =
f16B2 =
f16A1 =
f16A2 =
disp ('
disp ([
disp ([
disp ([
disp ([
disp ([
b(1);
b(2);
b(3);
a(2);
a(3);
Coefficients for GDFLIB_FilterIIR2 function
'f16B0 = FRAC16(' num2str( f16B0,'%1.15f' )
'f16B1 = FRAC16(' num2str( f16B1,'%1.15f' )
'f16B2 = FRAC16(' num2str( f16B2,'%1.15f' )
'f16A1 = FRAC16(' num2str( f16A1,'%1.15f' )
'f16A2 = FRAC16(' num2str( f16A2,'%1.15f' )
:');
'/8);']);
'/8);']);
'/8);']);
'/8);']);
'/8);']);
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Function GDFLIB_FilterIIR2_F16
Note
The input pointer must contain a valid address otherwise an
exception may occur (Data TLB Error, Data Storage,
Alignment, Machine Check).
The filter delay line includes four delay buffers which should
be reset after filter initialization. This can be done by assigning
to the filter instance a
GDFLIB_FILTER_IIR2_DEFAULT_F16 macro during
instance declaration or by calling the
GDFLIB_FilterIIR2Init_F16 function.
CAUTION
Because of fixed point implementation, and to avoid overflow
during the calculation of the GDFLIB_FilterIIR2_F16 function,
filter coefficients must be divided by eight. Function output is
internally multiplied by eight to correct the coefficient scaling.
5.12.5 Re-entrancy
The function is re-entrant.
5.12.6 Code Example
#include "gdflib.h"
tFrac16 f16In;
tFrac16 f16Out;
GDFLIB_FILTER_IIR2_T_F16 f16trMyIIR2 = GDFLIB_FILTER_IIR2_DEFAULT_F16;
void main(void)
{
// input value = 0.25
f16In = FRAC16 (0.25);
// filter coefficients (BPF 400-625Hz,
f16trMyIIR2.trFiltCoeff.f16B0 = FRAC16
f16trMyIIR2.trFiltCoeff.f16B1 = FRAC16
f16trMyIIR2.trFiltCoeff.f16B2 = FRAC16
f16trMyIIR2.trFiltCoeff.f16A1 = FRAC16
f16trMyIIR2.trFiltCoeff.f16A2 = FRAC16
Ts=100e-6)
(0.066122101544579/8);
(0/8);
(-0.066122101544579/8);
(-1.776189018043779/8);
(0.867755796910841/8);
// output should be 0x021D ~ FRAC16(0.01651)
GDFLIB_FilterIIR2Init_F16 (&f16trMyIIR2);
f16Out = GDFLIB_FilterIIR2_F16 (f16In, &f16trMyIIR2);
// output should be 0x021D ~ FRAC16(0.01651)
GDFLIB_FilterIIR2Init (&f16trMyIIR2, F16);
f16Out = GDFLIB_FilterIIR2 (f16In, &f16trMyIIR2, F16);
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//
//
//
//
}
##############################################################
Available only if 16-bit fractional implementation selected
as default
##############################################################
// output should be 0x021D ~ FRAC16(0.01651)
GDFLIB_FilterIIR2Init (&f16trMyIIR2);
f16Out = GDFLIB_FilterIIR2 (f16In, &f16trMyIIR2);
5.13 Function GDFLIB_FilterMAInit_F32
This function clears the internal filter accumulator.
5.13.1 Declaration
void GDFLIB_FilterMAInit_F32(GDFLIB_FILTER_MA_T_F32 *pParam);
5.13.2 Arguments
Table 5-13. GDFLIB_FilterMAInit_F32 arguments
Type
Name
GDFLIB_FILTER_MA_ pParam
T_F32 *
Direction
input,
output
Description
Pointer to the filter structure with a filter accumulator and a
smoothing factor.
5.13.3 Return
void
5.13.4 Description
This function clears the internal accumulator of a moving average filter. It shall be called
after filter parameter initialization and whenever the filter initialization is required.
Note
The input pointer must contain a valid address otherwise an
exception may occur (Data TLB Error, Data Storage,
Alignment, Machine Check).
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Function GDFLIB_FilterMA_F32
This function shall not be called together with
GDFLIB_FilterMA_F32 unless periodic clearing of filter
buffers is required.
5.13.5 Re-entrancy
The function is re-entrant.
5.13.6 Code Example
#include "gdflib.h"
GDFLIB_FILTER_MA_T_F32 f32trMyMA = GDFLIB_FILTER_MA_DEFAULT_F32;
void main(void)
{
// filter window = 2^5 = 32 samples
f32trMyMA.u16NSamples = 5;
GDFLIB_FilterMAInit_F32 (&f32trMyMA);
GDFLIB_FilterMAInit (&f32trMyMA,F32);
//
//
//
//
}
##############################################################
Available only if 32-bit fractional implementation selected
as default
##############################################################
GDFLIB_FilterMAInit (&f32trMyMA);
5.14 Function GDFLIB_FilterMA_F32
This function implements an exponential moving average filter.
5.14.1 Declaration
tFrac32 GDFLIB_FilterMA_F32(tFrac32 f32In, GDFLIB_FILTER_MA_T_F32 *pParam);
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5.14.2 Arguments
Table 5-14. GDFLIB_FilterMA_F32 arguments
Type
tFrac32
Name
f32In
GDFLIB_FILTER_MA_ pParam
T_F32 *
Direction
Description
input
Value of input signal to be filtered in step (k). The value is a
32-bit number in the Q1.31 format.
input,
output
Pointer to the filter structure with a filter accumulator and a
smoothing factor.
5.14.3 Return
The function returns a 32-bit value in format Q1.31, representing the filtered value of the
input signal in step (k).
5.14.4 Description
This function calculates one iteration of an exponential moving average filter (also
known as the exponentially weighted moving average, EWMA). The filter is
characterized by the following difference equation:
Equation GDFLIB_FilterMA_Eq2
where x(k) is the filter input, y(k) is the filter output in the current step, y(k-1) is the filter
output of the previous step and λ is a smoothing factor, 0 < λ < 1. Values of λ close to
one lead to less smoothing and give greater weight to recent changes in the input data,
while values of λ closer to zero cause greater smoothing and the filter is less responsive
to recent changes.
There is no direct equivalence between the smoothing factor λ of the exponential moving
average filter and the number of averaged samples N of a uniform sliding-window
moving average filter. Nevertheless, the implementation uses the following
approximation to relate the two filtering approaches:
Equation GDFLIB_FilterMA_Eq3
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Function GDFLIB_FilterMA_F32
The library function expects the smoothing factor to be supplied in the form of the
u16NSamples variable stored within the filter structure. This variable represents the
binary logarithm of the number of averaged samples N of the corresponding uniform
sliding-window moving average filter:
Equation GDFLIB_FilterMA_Eq4
Note
The input pointer must contain a valid address otherwise an
exception may occur (Data TLB Error, Data Storage,
Alignment, Machine Check).
The recalculated smoothing factor u16NSamples needs to be
defined prior to calling this function and must be equal to or
greater than 0, and equal to or smaller than 31 (0 <
u16NSamples < 31). Incorrect setting of this parameter will
yield meaningless results.
5.14.5 Re-entrancy
The function is re-entrant.
5.14.6 Code Example
#include "gdflib.h"
tFrac32 f32Input;
tFrac32 f32Output;
GDFLIB_FILTER_MA_T_F32 f32trMyMA = GDFLIB_FILTER_MA_DEFAULT_F32;
void main(void)
{
// input value = 0.25
f32Input = FRAC32 (0.25);
// filter window = 2^5 = 32 samples
f32trMyMA.u16NSamples = 5;
GDFLIB_FilterMAInit_F32 (&f32trMyMA);
// output should be 0x1000000 = FRAC32(0.0078125)
f32Output = GDFLIB_FilterMA_F32 (f32Input,&f32trMyMA);
// output should be 0x1000000 = FRAC32(0.0078125)
f32Output = GDFLIB_FilterMA (f32Input,&f32trMyMA,F32);
// ##############################################################
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// Available only if 32-bit fractional implementation selected
// as default
// ##############################################################
}
// output should be 0x1000000 = FRAC32(0.0078125)
f32Output = GDFLIB_FilterMA (f32Input,&f32trMyMA);
5.15 Function GDFLIB_FilterMAInit_F16
This function clears the internal filter accumulator.
5.15.1 Declaration
void GDFLIB_FilterMAInit_F16(GDFLIB_FILTER_MA_T_F16 *pParam);
5.15.2 Arguments
Table 5-15. GDFLIB_FilterMAInit_F16 arguments
Type
Name
GDFLIB_FILTER_MA_ pParam
T_F16 *
Direction
input,
output
Description
Pointer to the filter structure with a filter accumulator and a
smoothing factor.
5.15.3 Return
void
5.15.4 Description
This function clears the internal accumulator of a moving average filter. It shall be called
after filter parameter initialization and whenever the filter initialization is required.
Note
The input pointer must contain a valid address otherwise an
exception may occur (Data TLB Error, Data Storage,
Alignment, Machine Check).
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Function GDFLIB_FilterMA_F16
This function shall not be called together with
GDFLIB_FilterMA_F16 unless periodic clearing of filter
buffers is required.
5.15.5 Re-entrancy
The function is re-entrant.
5.15.6 Code Example
#include "gdflib.h"
GDFLIB_FILTER_MA_T_F16 f16trMyMA = GDFLIB_FILTER_MA_DEFAULT_F16;
void main(void)
{
// filter window = 2^3 = 8 samples
f16trMyMA.u16NSamples = 3;
GDFLIB_FilterMAInit_F16 (&f16trMyMA);
GDFLIB_FilterMAInit (&f16trMyMA,F16);
//
//
//
//
}
##############################################################
Available only if 16-bit fractional implementation selected
as default
##############################################################
GDFLIB_FilterMAInit (&f16trMyMA);
5.16 Function GDFLIB_FilterMA_F16
This function implements an exponential moving average filter.
5.16.1 Declaration
tFrac16 GDFLIB_FilterMA_F16(tFrac16 f16In, GDFLIB_FILTER_MA_T_F16 *pParam);
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5.16.2 Arguments
Table 5-16. GDFLIB_FilterMA_F16 arguments
Type
tFrac16
Name
f16In
GDFLIB_FILTER_MA_ pParam
T_F16 *
Direction
Description
input
Value of input signal to be filtered in step (k). The value is a
16-bit number in the Q1.15 format.
input,
output
Pointer to the filter structure with a filter accumulator and a
smoothing factor.
5.16.3 Return
The function returns a 16-bit value in format Q1.15, representing the filtered value of the
input signal in step (k).
5.16.4 Description
This function calculates one iteration of an exponential moving average filter (also
known as the exponentially weighted moving average, EWMA). The filter is
characterized by the following difference equation:
Equation GDFLIB_FilterMA_Eq2
where x(k) is the filter input, y(k) is the filter output in the current step, y(k-1) is the filter
output of the previous step and λ is a smoothing factor, 0 < λ < 1. Values of λ close to
one lead to less smoothing and give greater weight to recent changes in the input data,
while values of λ closer to zero cause greater smoothing and the filter is less responsive
to recent changes.
There is no direct equivalence between the smoothing factor λ of the exponential moving
average filter and the number of averaged samples N of a uniform sliding-window
moving average filter. Nevertheless, the implementation uses the following
approximation to relate the two filtering approaches:
Equation GDFLIB_FilterMA_Eq3
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Function GDFLIB_FilterMA_F16
The library function expects the smoothing factor to be supplied in the form of the
u16NSamples variable stored within the filter structure. This variable represents the
binary logarithm of the number of averaged samples N of the corresponding uniform
sliding-window moving average filter:
Equation GDFLIB_FilterMA_Eq4
Note
The input pointer must contain a valid address otherwise an
exception may occur (Data TLB Error, Data Storage,
Alignment, Machine Check).
The recalculated smoothing factor u16NSamples needs to be
defined prior to calling this function and must be equal to or
greater than 0, and equal to or smaller than 16 (0 <
u16NSamples < 16). Incorrect setting of this parameter will
yield meaningless results. In case the filter window size is
greater than 8, the output error may exceed the guaranteed
range.
5.16.5 Re-entrancy
The function is re-entrant.
5.16.6 Code Example
#include "gdflib.h"
tFrac16 f16Input;
tFrac16 f16Output;
GDFLIB_FILTER_MA_T_F16 f16trMyMA = GDFLIB_FILTER_MA_DEFAULT_F16;
void main(void)
{
// input value = 0.25
f16Input = FRAC16 (0.25);
// filter window = 2^3 = 8 samples
f16trMyMA.u16NSamples = 3;
GDFLIB_FilterMAInit_F16 (&f16trMyMA);
// output should be 0x0400 = FRAC16(0.03125)
f16Output = GDFLIB_FilterMA_F16 (f16Input,&f16trMyMA);
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// output should be 0x0400 = FRAC16(0.03125)
f16Output = GDFLIB_FilterMA (f16Input,&f16trMyMA,F16);
//
//
//
//
}
##############################################################
Available only if 16-bit fractional implementation selected
as default
##############################################################
// output should be 0x0400 = FRAC16(0.03125)
f16Output = GDFLIB_FilterMA (f16Input,&f16trMyMA);
5.17 Function GFLIB_Acos_F32
This function implements polynomial approximation of arccosine function.
5.17.1 Declaration
tFrac32 GFLIB_Acos_F32(tFrac32 f32In, const GFLIB_ACOS_T_F32 *const pParam);
5.17.2 Arguments
Table 5-17. GFLIB_Acos_F32 arguments
Type
Name
Direction
Description
tFrac32
f32In
input
Input argument is a 32-bit number that contains a value
between [-1,1).
const
GFLIB_ACOS_T_F32
*const
pParam
input
Pointer to an array of Taylor coefficients.
5.17.3 Return
The function returns arccos(f32In)/ π as a fixed point 32-bit number, normalized between
[0,1).
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Function GFLIB_Acos_F32
5.17.4 Description
The GFLIB_Acos_F32 function provides a computational method for calculation of the
standard inverse trigonometric arccosine function arccos(x), using the piece-wise
polynomial approximation. Function arccos(x) takes the ratio of the length of the adjacent
side to the length of the hypotenuse and returns the angle.
Figure 5-5. Course of the function GFLIB_Acos
The computational algorithm uses the symmetry of the arccos(x) function around the
point (0, π/2), which allows for computing the function values just in the interval [0, 1)
and to compute the function values in the interval [-1, 0) by the simple formula:
Equation GFLIB_Acos_Eq1
where:
• y[-1, 0) is the arccos(x) function value in the interval [-1, 0)
• y[0, 1) is the arccos(x) function value in the interval [0, 1)
Additionally, because the arccos(x) function is difficult for polynomial approximation for
x approaching 1 (or -1 by symmetry), due to its derivatives approaching infinity, a special
transformation is used to transform the range of x from [0.5, 1) to (0, 0.5]:
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Equation GFLIB_Acos_Eq2
In this way, the computation of the arccos(x) function in the range [0.5, 1) can be
replaced by the computation in the range (0, 0.5], in which approximation is easier.
Moreover for interval [0.997, 1), different approximation coeficients are used to eliminate
the imprecision of the polynom in this range.
For the interval (0, 0.5], the algorithm uses a polynomial approximation as follows:
Equation GFLIB_Acos_Eq3
Equation GFLIB_Acos_Eq4
The division of the [0,1) interval into three sub-intervals, with polynomial coefficients
calculated for each sub-interval, is noted in Table 5-18.
Table 5-18. Integer polynomial coefficients for each interval
Interval
a0
a1
a2
a3
a4
<0, 1/2)
91918582
66340080
9729967
682829947
12751
<1/2, 0.997)
-52453538
-36708911
-15136243
-964576326
1073630175
<0.997, 1)
-52453538
-36708911
-15136243
-966167437
1073739175
The implementation of the GFLIB_Acos_F32 is almost the same as in the function
GFLIB_Asin_F32. However, the output of the GFLIB_Acos_F32 is corrected as follows:
Equation GFLIB_Acos_Eq5
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Function GFLIB_Acos_F32
The polynomial coefficients were obtained using the Matlab fitting function, where a
polynomial of 5th order was used for the fitting of each respective sub-interval. The
functions arcsine and arccosine are similar, therefore the GFLIB_Acos_F32 function
uses the same polynomial coefficients as he GFLIB_Asin_F32 function.
Figure 5-6. acos(x) vs. GFLIB_Acos(s32In)
Note
The input pointer must contain a valid address otherwise an
exception may occur (Data TLB Error, Data Storage,
Alignment, Machine Check).
The output angle is normalized into the range [0,1). The
function call is slightly different from common approach in the
library set. The function can be called in four different ways:
• With implementation postfix (i.e. GFLIB_Acos_F32(f32In,
&pParam)), where the &pParam is pointer to
approximation coefficients. In case the default
approximation coefficients are used, the &pParam must be
replaced with GFLIB_ACOS_DEFAULT_F32 symbol.
The &pParam parameter is mandatory.
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• With additional implementation parameter (i.e.
GFLIB_Acos(f32In, &pParam, F32), where the &pParam
is pointer to approximation coefficients. In case the default
approximation coefficients are used, the &pParam must be
replaced with GFLIB_ACOS_DEFAULT_F32 symbol.
The &pParam parameter is mandatory.
• With preselected default implementation (i.e.
GFLIB_Acos(f32In, &pParam), where the &pParam is
pointer to approximation coefficients. The &pParam
parameter is optional and in case it is not used, the default
GFLIB_ACOS_DEFAULT_F32 approximation
coefficients are used.
5.17.5 Re-entrancy
The function is re-entrant.
5.17.6 Code Example
#include "gflib.h"
tFrac32 f32Input;
tFrac32 f32Angle;
void main(void)
{
// input f32Input = 0
f32Input = FRAC32 (0);
// output should be 0x400031CE = 0.5 => pi/2
f32Angle = GFLIB_Acos_F32 (f32Input, GFLIB_ACOS_DEFAULT_F32);
// output should be 0x400031CE = 0.5 => pi/2
f32Angle = GFLIB_Acos (f32Input, GFLIB_ACOS_DEFAULT_F32, F32);
//
//
//
//
}
##############################################################
Available only if 32-bit fractional implementation selected
as default
##############################################################
// output should be 0x400031CE = 0.5 => pi/2
f32Angle = GFLIB_Acos (f32Input);
5.18 Function GFLIB_Acos_F16
This function implements polynomial approximation of arccosine function.
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Function GFLIB_Acos_F16
5.18.1 Declaration
tFrac16 GFLIB_Acos_F16(tFrac16 f16In, const GFLIB_ACOS_T_F16 *const pParam);
5.18.2 Arguments
Table 5-19. GFLIB_Acos_F16 arguments
Type
Name
Direction
Description
tFrac16
f16In
input
Input argument is a 16-bit number that contains a value
between [-1,1).
const
GFLIB_ACOS_T_F16
*const
pParam
input
Pointer to an array of Taylor coefficients.
5.18.3 Return
The function returns arccos(f16In)/ π as a fixed point 16-bit number, normalized between
[0,1).
5.18.4 Description
The GFLIB_Acos_F16 function provides a computational method for calculation of the
standard inverse trigonometric arccosine function arccos(x), using the piece-wise
polynomial approximation. Function arccos(x) takes the ratio of the length of the adjacent
side to the length of the hypotenuse and returns the angle.
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Figure 5-7. Course of the function GFLIB_Acos
The computational algorithm uses the symmetry of the arccos(x) function around the
point (0, π/2), which allows for computing the function values just in the interval [0, 1)
and to compute the function values in the interval [-1, 0) by the simple formula:
Equation GFLIB_Acos_Eq1
where:
• y[-1, 0) is the arccos(x) function value in the interval [-1, 0)
• y[0, 1) is the arccos(x) function value in the interval [0, 1)
Additionally, because the arccos(x) function is difficult for polynomial approximation for
x approaching 1 (or -1 by symmetry), due to its derivatives approaching infinity, a special
transformation is used to transform the range of x from [0.5, 1) to (0, 0.5]:
Equation GFLIB_Acos_Eq2
In this way, the computation of the arccos(x) function in the range [0.5, 1) can be
replaced by the computation in the range (0, 0.5], in which approximation is easier.
For the interval (0, 0.5], the algorithm uses a polynomial approximation as follows:
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Function GFLIB_Acos_F16
Equation GFLIB_Acos_Eq3
Equation GFLIB_Acos_Eq4
The division of the [0,1) interval into two sub-intervals, with polynomial coefficients
calculated for each sub-interval, is noted in Table 5-20.
Table 5-20. Integer polynomial coefficients for each interval
Interval
a0
a1
a2
a3
a4
<0, 1/2)
1403
1012
148
10419
1
<1/2, 1)
-800
-560
-231
-14718
16384
The implementation of the GFLIB_Acos_F16 is almost the same as in the function
GFLIB_Asin_F16. However, the output of the GFLIB_Acos_F16 is corrected as follows:
Equation GFLIB_Acos_Eq5
The polynomial coefficients were obtained using the Matlab fitting function, where a
polynomial of 5th order was used for the fitting of each respective sub-interval. The
functions arcsine and arccosine are similar, therefore the GFLIB_Acos_F16 function
uses the same polynomial coefficients as the GFLIB_Asin_F16 function.
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Figure 5-8. acos(x) vs. GFLIB_Acos(f16In)
Note
The input pointer must contain a valid address otherwise an
exception may occur (Data TLB Error, Data Storage,
Alignment, Machine Check).
The output angle is normalized into the range [0,1). The
function call is slightly different from common approach in the
library set. The function can be called in four different ways:
• With implementation postfix (i.e. GFLIB_Acos_F16(f16In,
&pParam)), where the &pParam is pointer to
approximation coefficients. In case the default
approximation coefficients are used, the &pParam must be
replaced with GFLIB_ACOS_DEFAULT_F16 symbol.
The &pParam parameter is mandatory.
• With additional implementation parameter (i.e.
GFLIB_Acos(f16In, &pParam, F16), where the &pParam
is pointer to approximation coefficients. In case the default
approximation coefficients are used, the &pParam must be
replaced with GFLIB_ACOS_DEFAULT_F16 symbol.
The &pParam parameter is mandatory.
• With preselected default implementation (i.e.
GFLIB_Acos(f16In, &pParam), where the &pParam is
pointer to approximation coefficients. The &pParam
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Function GFLIB_Asin_F32
parameter is optional and in case it is not used, the default
GFLIB_ACOS_DEFAULT_F16 approximation
coefficients are used.
5.18.5 Re-entrancy
The function is re-entrant.
5.18.6 Code Example
#include "gflib.h"
tFrac16 f16Input;
tFrac16 f16Angle;
void main(void)
{
// input f16Input = 0
f16Input = FRAC16 (0);
// output should be 0x4000 = 0.5 => pi/2
f16Angle = GFLIB_Acos_F16 (f16Input, GFLIB_ACOS_DEFAULT_F16);
// output should be 0x4000 = 0.5 => pi/2
f16Angle = GFLIB_Acos (f16Input, GFLIB_ACOS_DEFAULT_F16, F16);
//
//
//
//
}
##############################################################
Available only if 16-bit fractional implementation selected
as default
##############################################################
// output should be 0x4000 = 0.5 => pi/2
f16Angle = GFLIB_Acos (f16Input);
5.19 Function GFLIB_Asin_F32
This function implements polynomial approximation of arcsine function.
5.19.1 Declaration
tFrac32 GFLIB_Asin_F32(tFrac32 f32In, const GFLIB_ASIN_T_F32 *const pParam);
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5.19.2 Arguments
Table 5-21. GFLIB_Asin_F32 arguments
Type
Name
Direction
Description
tFrac32
f32In
input
Input argument is a 32-bit number that contains a value
between [-1,1).
const
GFLIB_ASIN_T_F32
*const
pParam
input
Pointer to an array of Taylor coefficients.
5.19.3 Return
The function returns arcsin(f32In)/ π as a fixed point 32-bit number, normalized between
[-1,1).
5.19.4 Description
The GFLIB_Asin_F32 function provides a computational method for calculation of a
standard inverse trigonometric arcsine function arcsin(x), using the piece-wise
polynomial approximation. Function arcsin(x) takes the ratio of the length of the opposite
side to the length of the hypotenuse and returns the angle.
Figure 5-9. Course of the function GFLIB_Asin
The computational algorithm uses the symmetry of the arcsin(x) function around the
point (0, π/2), which allows to for computing the function values just in the interval [0,
1 ) and to compute the function values in the interval [-1, 0) by the simple formula:
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Function GFLIB_Asin_F32
Equation GFLIB_Asin_Eq1
where:
• y[-1, 0) is the arcsin(x) function value in the interval [-1, 0)
• y[1, 0) is the arcsin(x) function value in the interval [1, 0 )
Additionally, because the arcsin(x) function is difficult for polynomial approximation for
x approaching 1 (or -1 by symmetry), due to its derivatives approaching infinity, a special
transformation is used to transform the range of x from [0.5, 1) to (0, 0.5] :
Equation GFLIB_Asin_Eq2
In this way, the computation of the arcsin(x) function in the range [0.5, 1) can be replaced
by the computation in the range (0, 0.5], in which approximation is easier.
Moreover for interval [0.997, 1), different approximation coeficients are used to eliminate
the imprecision of the polynom in this range.
For the interval (0, 0.5], the algorithm uses polynomial approximation as follows:
Equation GFLIB_Asin_Eq3
Equation GFLIB_Asin_Eq4
The division of the [0,1) interval into two sub-intervals, with polynomial coefficients
calculated for each sub-interval, is noted in Table 5-22.
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Table 5-22. Integer polynomial coefficients for each interval
Interval
a0
a1
a2
a3
a4
<0 , 1/2)
91918582
66340080
9729967
682829947
12751
<1/2, 0.997)
-52453538
-36708911
-15136243
-964576326
1073630175
<0.997, 1)
-52453538
-36708911
-15136243
-966167437
1073739175
Polynomial coefficients were obtained using the Matlab fitting function, where a
polynomial of the 5th order was used for the fitting of each respective sub-interval. The
Matlab was used as follows:
clear all
clc
number_of_range = 2;
i = 1;
range = 0;
Range = 1 / number_of_range;
x(i,:) = (((i-1)*Range):(1/(2^15)):((i)*Range))';
y(i,:) = asin(x(i,:))/pi;
p(i,:) = polyfit((x(i,:)),(y(i,:)),4);
i=i+1;
Range = 1 / number_of_range;
x(i,:) = (((i-1)*Range):(1/(2^15)):((i)*Range))';
y(i,:) = asin(x(i,:))/pi;
x1(i,:) = ((x(i,:) - ((i-1)*Range)));
x1(i,:) = 0.5 - x1(i,:);
x2(i,:) = sqrt(x1(i,:));
p(i,:) = polyfit((x2(i,:)),(y(i,:)),4);
i=i+1;
f(2,:) = polyval(p(2,:),x2(2,:));
f(1,:) = polyval(p(1,:),x(1,:));
error_1 = abs(f(2,:) - y(2,:));
max(error_1 * (2^15))
error_2 = abs(f(1,:) - y(1,:));
max(error_2 * (2^15))
plot(x(2,:),y(2,:),'-',x(2,:),f(2,:),'-',x(1,:),y(1,:),'-',x(1,:),f(1,:),'-');
coef = round(p * (2^31))
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Function GFLIB_Asin_F32
Figure 5-10. asin(x) vs. GFLIB_Asin(f32In)
Note
The input pointer must contain a valid address otherwise an
exception may occur (Data TLB Error, Data Storage,
Alignment, Machine Check).
The output angle is normalized into the range [-0.5,0.5). The
function call is slightly different from common approach in the
library set. The function can be called in four different ways:
• With implementation postfix (i.e. GFLIB_Asin_F32(f32In,
&pParam)), where the &pParam is pointer to
approximation coefficients. In case the default
approximation coefficients are used, the &pParam must be
replaced with GFLIB_ASIN_DEFAULT_F32 symbol. The
&pParam parameter is mandatory.
• With additional implementation parameter (i.e.
GFLIB_Asin(f32In, &pParam, F32), where the &pParam is
pointer to approximation coefficients. In case the default
approximation coefficients are used, the &pParam must be
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replaced with GFLIB_ASIN_DEFAULT_F32 symbol. The
&pParam parameter is mandatory.
• With preselected default implementation (i.e.
GFLIB_Asin(f32In, &pParam), where the &pParam is
pointer to approximation coefficients. The &pParam
parameter is optional and in case it is not used, the default
GFLIB_ASIN_DEFAULT_F32 approximation coefficients
are used.
5.19.5 Re-entrancy
The function is re-entrant.
5.19.6 Code Example
#include "gflib.h"
tFrac32 f32Input;
tFrac32 f32Angle;
void main(void)
{
// input f32Input = (1-(2^-31))
f32Input = (tFrac32)(0x7FFFFFFF);
// output should be 0x3FFFF5A7 = 0.4999987665
f32Angle = GFLIB_Asin_F32 (f32Input, GFLIB_ASIN_DEFAULT_F32);
// output should be 0x3FFFF5A7 = 0.4999987665
f32Angle = GFLIB_Asin (f32Input, GFLIB_ASIN_DEFAULT_F32, F32);
//
//
//
//
}
##############################################################
Available only if 32-bit fractional implementation selected
as default
##############################################################
// output should be 0x3FFFF5A7 = 0.4999987665
f32Angle = GFLIB_Asin (f32Input);
5.20 Function GFLIB_Asin_F16
This function implements polynomial approximation of arcsine function.
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Function GFLIB_Asin_F16
5.20.1 Declaration
tFrac16 GFLIB_Asin_F16(tFrac16 f16In, const GFLIB_ASIN_T_F16 *const pParam);
5.20.2 Arguments
Table 5-23. GFLIB_Asin_F16 arguments
Type
Name
Direction
Description
tFrac16
f16In
input
Input argument is a 16-bit number that contains a value
between [-1,1).
const
GFLIB_ASIN_T_F16
*const
pParam
input
Pointer to an array of Taylor coefficients.
5.20.3 Return
The function returns arcsin(f16In)/ π as a fixed point 16-bit number, normalized between
[-1,1).
5.20.4 Description
The GFLIB_Asin_F16 function provides a computational method for calculation of a
standard inverse trigonometric arcsine function arcsin(x), using the piece-wise
polynomial approximation. Function arcsin(x) takes the ratio of the length of the opposite
side to the length of the hypotenuse and returns the angle.
Figure 5-11. Course of the function GFLIB_Asin
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The computational algorithm uses the symmetry of the arcsin(x) function around the
point (0, π/2), which allows to for computing the function values just in the interval [0, 1)
and to compute the function values in the interval [-1, 0) by the simple formula:
Equation GFLIB_Asin_Eq1
where:
• y[-1, 0) is the arcsin(x) function value in the interval [-1, 0)
• y[1, 0) is the arcsin(x) function value in the interval [1, 0)
Additionally, because the arcsin(x) function is difficult for polynomial approximation for
x approaching 1 (or -1 by symmetry), due to its derivatives approaching infinity, a special
transformation is used to transform the range of x from [0.5, 1) to (0, 0.5]:
Equation GFLIB_Asin_Eq2
In this way, the computation of the arcsin(x) function in the range [0.5, 1) can be replaced
by the computation in the range (0, 0.5], in which approximation is easier.
For the interval (0, 0.5], the algorithm uses polynomial approximation as follows:
Equation GFLIB_Asin_Eq3
Equation GFLIB_Asin_Eq4
The division of the [0,1) interval into two sub-intervals, with polynomial coefficients
calculated for each sub-interval, is noted in Table 5-24.
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Function GFLIB_Asin_F16
Table 5-24. Integer polynomial coefficients for each interval
Interval
a0
a1
a2
a3
a4
<0 , 1/2)
1403
1012
148
10419
1
<1/2, 1)
-800
-560
-231
-14718
16384
Polynomial coefficients were obtained using the Matlab fitting function, where a
polynomial of the 5th order was used for the fitting of each respective sub-interval. The
Matlab was used as follows:
clear all
clc
number_of_range = 2;
i = 1;
range = 0;
Range = 1 / number_of_range;
x(i,:) = (((i-1)*Range):(1/(2^15)):((i)*Range))';
y(i,:) = asin(x(i,:))/pi;
p(i,:) = polyfit((x(i,:)),(y(i,:)),4);
i=i+1;
Range = 1 / number_of_range;
x(i,:) = (((i-1)*Range):(1/(2^15)):((i)*Range))';
y(i,:) = asin(x(i,:))/pi;
x1(i,:) = ((x(i,:) - ((i-1)*Range)));
x1(i,:) = 0.5 - x1(i,:);
x2(i,:) = sqrt(x1(i,:));
p(i,:) = polyfit((x2(i,:)),(y(i,:)),4);
i=i+1;
f(2,:) = polyval(p(2,:),x2(2,:));
f(1,:) = polyval(p(1,:),x(1,:));
error_1 = abs(f(2,:) - y(2,:));
max(error_1 * (2^15))
error_2 = abs(f(1,:) - y(1,:));
max(error_2 * (2^15))
plot(x(2,:),y(2,:),'-',x(2,:),f(2,:),'-',x(1,:),y(1,:),'-',x(1,:),f(1,:),'-');
coef = round(p * (2^31))
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Figure 5-12. asin(x) vs. GFLIB_Asin(f16In)
Note
The input pointer must contain a valid address otherwise an
exception may occur (Data TLB Error, Data Storage,
Alignment, Machine Check).
The output angle is normalized into the range [-0.5,0.5). The
function call is slightly different from common approach in the
library set. The function can be called in four different ways:
• With implementation postfix (i.e. GFLIB_Asin_F16(f16In,
&pParam)), where the &pParam is pointer to
approximation coefficients. In case the default
approximation coefficients are used, the &pParam must be
replaced with GFLIB_ASIN_DEFAULT_F16 symbol. The
&pParam parameter is mandatory.
• With additional implementation parameter (i.e.
GFLIB_Asin(f16In, &pParam, F16), where the &pParam is
pointer to approximation coefficients. In case the default
approximation coefficients are used, the &pParam must be
replaced with GFLIB_ASIN_DEFAULT_F16 symbol. The
&pParam parameter is mandatory.
• With preselected default implementation (i.e.
GFLIB_Asin(f16In, &pParam), where the &pParam is
pointer to approximation coefficients. The &pParam
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Function GFLIB_Atan_F32
parameter is optional and in case it is not used, the default
GFLIB_ASIN_DEFAULT_F16 approximation coefficients
are used.
5.20.5 Re-entrancy
The function is re-entrant.
5.20.6 Code Example
#include "gflib.h"
tFrac16 f16Input;
tFrac16 f16Angle;
void main(void)
{
// input f16Input = (1-(2^-15))
f16Input = (tFrac16)(0x7FFF);
// output should be 0x3FAE = 0.4974975
f16Angle = GFLIB_Asin_F16 (f16Input, GFLIB_ASIN_DEFAULT_F16);
// output should be 0x3FAE = 0.4974975
f16Angle = GFLIB_Asin (f16Input, GFLIB_ASIN_DEFAULT_F16, F16);
//
//
//
//
}
##############################################################
Available only if 16-bit fractional implementation selected
as default
##############################################################
// output should be 0x3FAE = 0.4974975
f16Angle = GFLIB_Asin (f16Input);
5.21 Function GFLIB_Atan_F32
This function implements minimax polynomial approximation of arctangent function.
5.21.1 Declaration
tFrac32 GFLIB_Atan_F32(tFrac32 f32In, const GFLIB_ATAN_T_F32 *const pParam);
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5.21.2 Arguments
Table 5-25. GFLIB_Atan_F32 arguments
Type
Name
Direction
Description
tFrac32
f32In
input
Input argument is a 32-bit number between [-1,1).
const
GFLIB_ATAN_T_F32
*const
pParam
input
Pointer to an array of minimax approximation coefficients.
5.21.3 Return
The function returns the atan of the input argument as a fixed point 32-bit number that
contains the angle in radians between [- π/4, π/4), normalized between [-0.25,0.25).
5.21.4 Description
The GFLIB_Atan_F32 function provides a computational method for calculation of a
standard trigonometric arctangent function arctan(x), using the piece-wise minimax
polynomial approximation. Function arctan(x) takes a ratio and returns the angle of two
sides of a right-angled triangle. The ratio is the length of the side opposite the angle
divided by the length of the side adjacent to the angle. The graph of arctan(x) is shown in
Figure 5-13.
Figure 5-13. Course of the function GFLIB_Atan
The GFLIB_Atan_F32 function is implemented with consideration to fixed point
fractional arithmetic. As can be further seen from Figure 5-13, the arctangent values are
identical for the input ranges [-1, 0) and [0, 1).
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Function GFLIB_Atan_F32
Moreover, it can be observed from Figure 5-13 that the course of the arctan(x) function
output for a ratio in interval 1. is identical, but with the opposite sign, to the output for a
ratio in interval 2. Therefore, the approximation of the arctangent function over the entire
defined range of input ratios can be simplified to the approximation for a ratio in range
[0, 1), and then, depending on the input ratio, the result will be negated. In order to
increase the accuracy of approximation without the need for a higher order polynomial,
the interval [0, 1) is further divided into eight equally spaced sub intervals, and minimax
polynomial approximation is done for each interval respectively. Such a division results
in eight sets of polynomial coefficients. Moreover, it allows using a polynomial of only
the 3rd order to achieve an accuracy of less than 0.5LSB (on the upper 16 bits of 32-bit
results) across the entire range of input ratios.
The GFLIB_Atan_F32 function uses fixed point fractional arithmetic, so to cast the
fractional value of the output angle [-0.25, 0.25) into the correct range [- π/4, π/4), the
fixed point output angle can be multiplied by π for an angle in radians. Then, the fixed
point fractional implementation of the minimax approximation polynomial, used for
calculation of each sub sector, is defined as follows:
Equation GFLIB_Atan_Eq1
Equation GFLIB_Atan_Eq2
The division of the [0, 1) interval into eight sub-intervals, with polynomial coefficients
calculated for each sub-interval, is noted in Table 5-26. Polynomial coefficients were
obtained using the Matlab fitting function, where a polynomial of the 3rd order was used
for the fitting of each respective sub-interval.
Table 5-26. Integer minimax polynomial coefficients for each interval
Interval
a1
a2
a3
<0, 1/8)
-164794
42515925
42667172
<1/8, 2/8)
-465182
41238272
126697014
<2/8, 3/8)
-690034
38899574
207041074
<3/8, 4/8)
-820713
35848645
281909001
<4/8, 5/8)
-865105
32453241
350251355
<5/8, 6/8)
-845462
29016149
411702516
Table continues on the next page...
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Table 5-26. Integer minimax polynomial coefficients for each interval (continued)
<6/8, 7/8)
-786689
25743137
466407809
<7/8, 1)
-708969
22748418
514828039
Figure 5-14. atan(x) vs. GFLIB_Atan(f32In)
Figure 5-14 depicts a floating point arctangent function generated from Matlab and the
approximated value of the arctangent function obtained from GFLIB_Atan_F32, plus
their difference. The course of calculation accuracy as a function of the input value can
be observed from this figure. The achieved accuracy with consideration to the 3rd order
piece-wise minimax polynomial approximation and described fixed point scaling is less
than 0.5LSB on the upper 16 bits of the 32-bit result.
Note
The input pointer must contain a valid address otherwise an
exception may occur (Data TLB Error, Data Storage,
Alignment, Machine Check).
The output angle is normalized into the range [-0.25, 0.25). The
function call is slightly different from common approach in the
library set. The function can be called in four different ways:
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Function GFLIB_Atan_F32
• With implementation postfix (i.e. GFLIB_Atan_F32(f32In,
&pParam)), where the &pParam is pointer to
approximation coefficients. In case the default
approximation coefficients are used, the &pParam must be
replaced with GFLIB_ATAN_DEFAULT_F32 symbol.
The &pParam parameter is mandatory.
• With additional implementation parameter (i.e.
GFLIB_Atan(f32In, &pParam, F32), where the &pParam is
pointer to approximation coefficients. In case the default
approximation coefficients are used, the &pParam must be
replaced with GFLIB_ATAN_DEFAULT_F32 symbol.
The &pParam parameter is mandatory.
• With preselected default implementation (i.e.
GFLIB_Atan(f32In, &pParam), where the &pParam is
pointer to approximation coefficients. The &pParam
parameter is optional and in case it is not used, the default
GFLIB_ATAN_DEFAULT_F32 approximation
coefficients are used.
5.21.5 Re-entrancy
The function is re-entrant.
5.21.6 Code Example
#include "gflib.h"
tFrac32 f32Input;
tFrac32 f32Angle;
void main(void)
{
// input ratio = 0x7FFFFFFF
f32Input = (tFrac32)(0x7FFFFFFF);
// output angle should be 0x1FFFF29F = 0.249999 => pi/4
f32Angle = GFLIB_Atan_F32 (f32Input, GFLIB_ATAN_DEFAULT_F32);
// output angle should be 0x1FFFF29F = 0.249999 => pi/4
f32Angle = GFLIB_Atan (f32Input, GFLIB_ATAN_DEFAULT_F32, F32);
//
//
//
//
##############################################################
Available only if 32-bit fractional implementation selected
as default
##############################################################
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}
// output angle should be 0x1FFFF29F = 0.249999 => pi/4
f32Angle = GFLIB_Atan (f32Input);
5.22 Function GFLIB_Atan_F16
This function implements minimax polynomial approximation of arctangent function.
5.22.1 Declaration
tFrac16 GFLIB_Atan_F16(tFrac16 f16In, const GFLIB_ATAN_T_F16 *const pParam);
5.22.2 Arguments
Table 5-27. GFLIB_Atan_F16 arguments
Type
Name
Direction
Description
tFrac16
f16In
input
Input argument is a 16-bit number between [-1, 1).
const
GFLIB_ATAN_T_F16
*const
pParam
input
Pointer to an array of minimax approximation coefficients.
5.22.3 Return
The function returns the atan of the input argument as a fixed point 16-bit number that
contains the angle in radians between [- π/4, π/4), normalized between [-0.25, 0.25).
5.22.4 Description
The GFLIB_Atan_F16 function provides a computational method for calculation of a
standard trigonometric arctangent function arctan(x), using the piece-wise minimax
polynomial approximation. Function arctan(x) takes a ratio and returns the angle of two
sides of a right-angled triangle. The ratio is the length of the side opposite the angle
divided by the length of the side adjacent to the angle. The graph of arctan(x) is shown in
Figure 5-15.
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Function GFLIB_Atan_F16
Figure 5-15. Course of the function GFLIB_Atan
The GFLIB_Atan_F16 function is implemented with consideration to fixed point
fractional arithmetic. As can be further seen from Figure 5-15, the arctangent values are
identical for the input ranges [-1, 0) and [0, 1).
Moreover, it can be observed from Figure 5-15 that the course of the arctan(x) function
output for a ratio in interval 1. is identical, but with the opposite sign, to the output for a
ratio in interval 2. Therefore, the approximation of the arctangent function over the entire
defined range of input ratios can be simplified to the approximation for a ratio in range
[0, 1), and then, depending on the input ratio, the result will be negated. In order to
increase the accuracy of approximation without the need for a higher order polynomial,
the interval [0, 1) is further divided into eight equally spaced sub intervals, and minimax
polynomial approximation is done for each interval respectively. Such a division results
in eight sets of polynomial coefficients. Moreover, it allows using a minimax polynomial
of only the 3rd order to achieve an accuracy of less than 0.5LSB across the entire range
of input ratios.
The GFLIB_Atan_F16 function uses fixed point fractional arithmetic, so to cast the
fractional value of the output angle [-0.25, 0.25) into the correct range [- π/4, π/4), the
fixed point output angle can be multiplied by π for an angle in radians. Then, the fixed
point fractional implementation of the minimax approximation polynomial, used for
calculation of each sub sector, is defined as follows:
Equation GFLIB_Atan_Eq1
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Equation GFLIB_Atan_Eq2
The division of the [0, 1) interval into eight sub-intervals, with minimax polynomial
coefficients calculated for each sub-interval, is noted in Table 5-28. Minimax polynomial
coefficients were obtained using the Matlab fitting function, where a polynomial of the
3rd order was used for the fitting of each respective sub-interval.
Table 5-28. Integer polynomial coefficients for each interval
Interval
a1
a2
a3
<0, 1/8)
-3
649
652
<1/8, 2/8)
-7
630
1934
<2/8, 3/8)
-11
594
3160
<3/8, 4/8)
-13
547
4302
<4/8, 5/8)
-13
495
5345
<5/8, 6/8)
-13
443
6283
<6/8, 7/8)
-12
393
7117
<7/8, 1)
-11
347
7856
Figure 5-16. atan(x) vs. GFLIB_Atan(f16In)
Note
The input pointer must contain a valid address otherwise an
exception may occur (Data TLB Error, Data Storage,
Alignment, Machine Check).
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Function GFLIB_Atan_F16
The output angle is normalized into the range [-0.25,0.25). The
function call is slightly different from common approach in the
library set. The function can be called in four different ways:
• With implementation postfix (i.e. GFLIB_Atan_F16(f16In,
&pParam)), where the &pParam is pointer to
approximation coefficients. In case the default
approximation coefficients are used, the &pParam must be
replaced with GFLIB_ATAN_DEFAULT_F16 symbol.
The &pParam parameter is mandatory.
• With additional implementation parameter (i.e.
GFLIB_Atan(f16In, &pParam, F16), where the &pParam is
pointer to approximation coefficients. In case the default
approximation coefficients are used, the &pParam must be
replaced with GFLIB_ATAN_DEFAULT_F16 symbol.
The &pParam parameter is mandatory.
• With preselected default implementation (i.e.
GFLIB_Atan(f16In, &pParam), where the &pParam is
pointer to approximation coefficients. The &pParam
parameter is optional and in case it is not used, the default
GFLIB_ATAN_DEFAULT_F16 approximation
coefficients are used.
5.22.5 Re-entrancy
The function is re-entrant.
5.22.6 Code Example
#include "gflib.h"
tFrac16 f16Input;
tFrac16 f16Angle;
void main(void)
{
// input ratio = 0x7FFF
f16Input = (tFrac16)(0x7FFF);
// output angle should be 0x1FFF = 0.249999 => pi/4
f16Angle = GFLIB_Atan_F16 (f16Input, GFLIB_ATAN_DEFAULT_F16);
// output angle should be 0x1FFF = 0.249999 => pi/4
f16Angle = GFLIB_Atan (f16Input, GFLIB_ATAN_DEFAULT_F16, F16);
// ##############################################################
// Available only if 16-bit fractional implementation selected
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// as default
// ##############################################################
}
// output angle should be 0x1FFF = 0.249999 => pi/4
f16Angle = GFLIB_Atan (f16Input);
5.23 Function GFLIB_AtanYX_F32
This function calculate the angle between the positive x-axis and the direction of a vector
given by the (x, y) coordinates.
5.23.1 Declaration
tFrac32 GFLIB_AtanYX_F32(tFrac32 f32InY, tFrac32 f32InX);
5.23.2 Arguments
Table 5-29. GFLIB_AtanYX_F32 arguments
Type
Name
Direction
Description
tFrac32
f32InY
input
The ordinate of the input vector (y coordinate).
tFrac32
f32InX
input
The abscissa of the input vector (x coordinate).
5.23.3 Return
The function returns the angle between the positive x-axis of a plane and the direction of
the vector given by the x and y coordinates provided as parameters.
5.23.4 Description
The function returns the angle between the positive x-axis of a plane and the direction of
the vector given by the x and y coordinates provided as parameters. The first parameter,
f32InY, is the ordinate (the y coordinate) and the second one, f32InX, is the abscissa (the
x coordinate).
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Function GFLIB_AtanYX_F32
Both the input parameters are assumed to be in the fractional range of [-1, 1). The
computed angle is limited by the fractional range of [-1, 1), which corresponds to the real
range of [- π, π). The counter-clockwise direction is assumed to be positive and thus a
positive angle will be computed if the provided ordinate (f32InY) is positive. Similarly, a
negative angle will be computed for the negative ordinate.
The calculations are performed in a few steps.
In the first step, the angle is positioned within the correct half-quarter of the
circumference of a circle by dividing the angle into two parts: the integral multiple of 45
deg (half-quarter) and the remaining offset within the 45 deg range. Simple geometric
properties of the Cartesian coordinate system are used to calculate the coordinates of the
vector with the calculated angle offset.
In the second step, the vector ordinate is divided by the vector abscissa (y/x) to obtain the
tangent value of the angle offset. The angle offset is computed by applying the ordinary
arctangent function.
The sum of the integral multiple of half-quarters and the angle offset within a single halfquarter form the angle to be computed. The function will return 0 if both input arguments
are 0.
In comparison to the GFLIB_Atan_F32 function, the GFLIB_AtanYX_F32 function
correctly places the calculated angle within the whole fractional range of [-1, 1), which
corresponds to the real angle range of [- π, π).
Note
The function calls the GFLIB_Atan_F32 function. The
computed value is within the range of [-1, 1).
5.23.5 Re-entrancy
The function is re-entrant.
5.23.6 Code Example
#include "gflib.h"
tFrac32 f32InY;
tFrac32 f32InX;
tFrac32 f32Ang;
void main(void)
{
// Angle 45 deg = PI/4 rad
f32InY = FRAC32 (0.5);
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f32InX = FRAC32 (0.5);
// output should be close to 0x200034EA
f32Ang = GFLIB_AtanYX_F32 (f32InY, f32InX);
// output should be close to 0x200034EA
f32Ang = GFLIB_AtanYX (f32InY, f32InX, F32);
//
//
//
//
}
##############################################################
Available only if 32-bit fractional implementation selected
as default
##############################################################
// output should be close to 0x200034EA
f32Ang = GFLIB_AtanYX (f32InY, f32InX);
5.24 Function GFLIB_AtanYX_F16
This function calculate the angle between the positive x-axis and the direction of a vector
given by the (x, y) coordinates.
5.24.1 Declaration
tFrac16 GFLIB_AtanYX_F16(tFrac16 f16InY, tFrac16 f16InX);
5.24.2 Arguments
Table 5-30. GFLIB_AtanYX_F16 arguments
Type
Name
Direction
Description
tFrac16
f16InY
input
The ordinate of the input vector (y coordinate).
tFrac16
f16InX
input
The abscissa of the input vector (x coordinate).
5.24.3 Return
The function returns the angle between the positive x-axis of a plane and the direction of
the vector given by the x and y coordinates provided as parameters.
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Function GFLIB_AtanYX_F16
5.24.4 Description
The function returns the angle between the positive x-axis of a plane and the direction of
the vector given by the x and y coordinates provided as parameters. The first parameter,
f16InY, is the ordinate (the y coordinate) and the second one, f16InX, is the abscissa (the
x coordinate).
Both the input parameters are assumed to be in the fractional range of [-1, 1). The
computed angle is limited by the fractional range of [-1, 1), which corresponds to the real
range of [- π, π). The counter-clockwise direction is assumed to be positive and thus a
positive angle will be computed if the provided ordinate (f16InY) is positive. Similarly, a
negative angle will be computed for the negative ordinate.
The calculations are performed in a few steps.
In the first step, the angle is positioned within the correct half-quarter of the
circumference of a circle by dividing the angle into two parts: the integral multiple of 45
deg (half-quarter) and the remaining offset within the 45 deg range. Simple geometric
properties of the Cartesian coordinate system are used to calculate the coordinates of the
vector with the calculated angle offset.
In the second step, the vector ordinate is divided by the vector abscissa (y/x) to obtain the
tangent value of the angle offset. The angle offset is computed by applying the ordinary
arctangent function.
The sum of the integral multiple of half-quarters and the angle offset within a single halfquarter form the angle to be computed. The function will return 0 if both input arguments
are 0.
In comparison to the GFLIB_Atan_F16 function, the GFLIB_AtanYX_F16 function
correctly places the calculated angle within the whole fractional range of [-1, 1), which
corresponds to the real angle range of [- π, π).
Note
The function calls the GFLIB_Atan_F16 function. The
computed value is within the range of [-1, 1).
5.24.5 Re-entrancy
The function is re-entrant.
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5.24.6 Code Example
#include "gflib.h"
tFrac16 f16InY;
tFrac16 f16InX;
tFrac16 f16Ang;
void main(void)
{
// Angle 45 deg = PI/4 rad
f16InY = FRAC16 (0.5);
f16InX = FRAC16 (0.5);
// output should be close to 0x2000
f16Ang = GFLIB_AtanYX_F16 (f16InY, f16InX);
// output should be close to 0x2000
f16Ang = GFLIB_AtanYX (f16InY, f16InX, F16);
//
//
//
//
}
##############################################################
Available only if 16-bit fractional implementation selected
as default
##############################################################
// output should be close to 0x2000
f16Ang = GFLIB_AtanYX (f16InY, f16InX);
5.25 Function GFLIB_AtanYXShifted_F32
This function calculates the angle of two sine waves shifted in phase to each other.
5.25.1 Declaration
tFrac32 GFLIB_AtanYXShifted_F32(tFrac32 f32InY, tFrac32 f32InX, const
GFLIB_ATANYXSHIFTED_T_F32 *pParam);
5.25.2 Arguments
Table 5-31. GFLIB_AtanYXShifted_F32 arguments
Type
Name
Direction
Description
tFrac32
f32InY
input
The value of the first signal, assumed to be sin( θ).
tFrac32
f32InX
input
The value of the second signal, assumed to be sin( θ + Δθ).
input,
output
The parameters for the function.
const
pParam
GFLIB_ATANYXSHIFT
ED_T_F32 *
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Function GFLIB_AtanYXShifted_F32
5.25.3 Return
The function returns the angle of two sine waves shifted in phase to each other.
5.25.4 Description
The function calculates the angle of two sinusoidal signals, one shifted in phase to the
other. The phase shift between sinusoidal signals does not have to be π/2 and can be any
value.
It is assumed that the arguments of the function are as follows:
Equation GFLIB_AtanYXShifted_Eq1
where:
• x, y are respectively, the f32InX, and f32InY arguments
• θ is the angle to be computed by the function
• Δθ is the phase difference between the x, y signals
At the end of computations, an angle offset θOffset is added to the computed angle θ. The
angle offset is an additional parameter, which can be used to set the zero of the θ axis. If
θOffset is zero, then the angle computed by the function will be exactly θ.
The GFLIB_AtanYXShifted_F32 function does not directly use the angle offset θOffset
and the phase difference θ. The function's parameters, contained in the function
parameters structure GFLIB_ATANYXSHIFTED_T_F32, need to be computed by
means of the provided Matlab function (see below).
If Δθ= π/2 or Δθ=- π/2, then the function is similar to the GFLIB_AtanYX_F32 function,
however, the GFLIB_AtanYX_F32 function in this case is more effective with regard to
execution time and accuracy.
In order to use the function, the following necessary steps need to be completed:
• define Δθ and θOffset, the Δθ shall be known from the input sinusoidal signals, the
θOffset needs to be set arbitrarily
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• compute values for the function parameters structure by means of the provided
Matlab function
• convert the computed values into integer format and insert them into the C code (see
also the C code example)
The function uses the following algorithm for computing the angle:
Equation GFLIB_AtanYXShifted_Eq2
where:
•
•
•
•
•
•
x, y are respectively, the f32InX, and f32InY
θ is the angle to be computed by the function, see the previous equation
Δθ is the phase difference between the x, y signals, see the previous equation
S is a scaling coefficient, S is almost 1, (S < 1), see also the explanation below
a, b intermediate variables
θOffset is the additional phase shift, the computed angle will be θ + θOffset
The scale coefficient S is used to prevent overflow and to assure symmetry around 0 for
the entire fractional range. S shall be less than 1.0, but as large as possible. The algorithm
implemented in this function uses the value of 1 - 2 -15.
The algorithm can be easily justified by proving the trigonometric identity:
Equation GFLIB_AtanYXShifted_Eq3
For the purposes of fractional arithmetic, the algorithm is implemented such that
additional values are used as shown in the equation below:
Equation GFLIB_AtanYXShifted_Eq4
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Function GFLIB_AtanYXShifted_F32
where:
• C y, C x are the algorithm coefficients for y and x signals
• K y is multiplication coefficient of the y signal, represented by the parameters
structure member pParam->f32Ky
• K x is multiplication coefficient of the x signal, represented by the parameters
structure member pParam->f32Kx
• N y is scaling coefficient of the y signal, represented the by parameters structure
member pParam->s32Ny
• N x is scaling coefficient of the x signal, represented by the parameters structure
member pParam->s32Nx
• θadj is an adjusting angle, represented by the parameters structure member pParam>f32ThetaAdj
The multiplication and scaling coefficients, and the adjusting angle, shall be defined in a
parameters structure provided as the function input parameter.
The function initialization parameters can be calculated as shown in the following Matlab
code:
function [KY, KX, NY, NX, THETAADJ] = atanyxshiftedpar(dthdeg, thoffsetdeg)
// ATANYXSHIFTEDPAR calculation of parameters for atanyxshifted() function
//
// [KY, KX, NY, NX, THETAADJ] = atanyxshiftedpar(dthdeg, thoffsetdeg)
//
// dthdeg = phase shift (delta theta) between sine waves in degrees
// thoffsetdeg = angle offset (theta offset) in degrees
// NY - scaling coefficient of y signal
// NX - scaling coefficient of x signal
// KY - multiplication coefficient of y signal
// KX - multiplication coefficient of x signal
// THETAADJ - adjusting angle in radians, scaled from [-pi, pi) to [-1, 1)
if (dthdeg < -180) || (dthdeg >= 180)
error('atanyxshiftedpar: dthdeg out of range');
end
if (thoffsetdeg < -180) || (thoffsetdeg >= 180)
error('atanyxshiftedpar: thoffsetdeg out of range');
end
dth2 = ((dthdeg/2)/180*pi);
thoffset = (thoffsetdeg/180*pi);
CY = (1 - 2^-15)/(2*cos(dth2));
CX = (1 - 2^-15)/(2*sin(dth2));
if(abs(CY) >= 1) NY = ceil(log2(abs(CY)));
else NY = 0;
end
if(abs(CX) >= 1) NX = ceil(log2(abs(CX)));
else NX = 0;
end
KY = CY/2^NY;
KX = CX/2^NX;
THETAADJ = dthdeg/2 - thoffsetdeg;
if THETAADJ >= 180
THETAADJ = THETAADJ - 360;
elseif THETAADJ < -180
THETAADJ = THETAADJ + 360;
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end
THETAADJ = THETAADJ/180;
return;
While applying the function, some general guidelines should be considered as stated
below.
At some values of the phase shift, and particularly at phase shift approaching -180, 0 or
180 degrees, the algorithm may become numerically unstable, causing any error,
contributed by input signal imperfections or through finite precision arithmetic, to be
magnified significantly. Therefore, some care should be taken to avoid error where
possible. The detailed error analysis of the algorithm is beyond the scope of this
documentation, however, general guidelines are provided.
There are several sources of error in the function:
•
•
•
•
error of the supplied signal values due to the finite resolution of the AD conversion
error contributed by higher order harmonics appearing in the input signals
computational error of the multiplication due to the finite length of registers
error of the phase shift Δθ representation in the finite precision arithmetic and in the
values
• error due to differences in signal amplitudes
It should be noted that the function requires both signals to have the same amplitude. To
minimize the output error, the amplitude of both signals should be as close to 1.0 as much
as possible.
The function has been tested to be reliable at a phase shift in the range of [-165, -15] and
[15, 165] degrees for perfectly sinusoidal input signals. Beyond this range, the function
operates correctly, however, the output error can be beyond the guaranteed value. In a
real application, an error, contributed by an AD conversion and by higher order
harmonics of the input signals, should be also taken into account.
Note
The input pointer must contain a valid address otherwise an
exception may occur (Data TLB Error, Data Storage,
Alignment, Machine Check).
The function calls the GFLIB_AtanYX_F32 function. The
function may become numerically unstable for a phase shift
approaching -180, 0 or 180 degrees. The function accuracy is
guaranteed for a phase shift in the range of [-165, -15] and [15,
165] degrees at perfect input signals.
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Function GFLIB_AtanYXShifted_F32
CAUTION
Due to the cyclic character of the GFLIB_AtanYX_F16, in case
the difference between the adjusting angle θadj and the input
vector angle is approaching to 1-2 -15 or -1, the
GFLIB_AtanYX_F16 function operates correctly, however the
output error might exceed the guaranteed limits comparing to
the double precision reference.
5.25.5 Re-entrancy
The function is re-entrant.
5.25.6 Code Example
#include "gflib.h"
tFrac32 f32InY;
tFrac32 f32InX;
tFrac32 f32Ang;
GFLIB_ATANYXSHIFTED_T_F32 Param;
void main(void)
{
// dtheta = 69.33deg, thetaoffset = 10deg
// CY = (1 - 2^-15)/(2*cos((69.33/2)/180*pi))= 0.60789036201452440
// CX = (1 - 2^-15)/(2*sin((69.33/2)/180*pi))= 0.87905201358520957
// NY = 0 (abs(CY) < 1)
// NX = 0 (abs(CX) < 1)
// KY = 0.60789/2^0 = 0.60789036201452440
// KX = 0.87905/2^0 = 0.87905201358520957
// THETAADJ = 10/180 = 0.05555555555
Param.f32Ky = FRAC32 (0.60789036201452440);
Param.f32Kx = FRAC32 (0.87905201358520957);
Param.s32Ny = 0;
Param.s32Nx = 0;
Param.f32ThetaAdj = FRAC32 (0.05555555555);
// theta = 15 deg
// Y = sin(theta) = 0.2588190
// X = sin(theta + dtheta) = 0.9951074
f32InY = FRAC32 (0.2588190);
f32InX = FRAC32 (0.9951074);
// f32Ang output should be close to 0x1C34824A
f32Ang = GFLIB_AtanYXShifted_F32 (f32InY, f32InX, &Param);
// f32Ang output should be close to 0x1C34824A
f32Ang = GFLIB_AtanYXShifted (f32InY, f32InX, &Param, F32);
//
//
//
//
##############################################################
Available only if 32-bit fractional implementation selected
as default
##############################################################
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}
// f32Ang output should be close to 0x1C34824A
f32Ang = GFLIB_AtanYXShifted (f32InY, f32InX, &Param);
5.26 Function GFLIB_AtanYXShifted_F16
This function calculates the angle of two sine waves shifted in phase to each other.
5.26.1 Declaration
tFrac16 GFLIB_AtanYXShifted_F16(tFrac16 f16InY, tFrac16 f16InX, const
GFLIB_ATANYXSHIFTED_T_F16 *pParam);
5.26.2 Arguments
Table 5-32. GFLIB_AtanYXShifted_F16 arguments
Type
Name
Direction
Description
tFrac16
f16InY
input
The value of the first signal, assumed to be sin( θ).
tFrac16
f16InX
input
The value of the second signal, assumed to be sin( θ + Δθ).
input,
output
The parameters for the function.
const
pParam
GFLIB_ATANYXSHIFT
ED_T_F16 *
5.26.3 Return
The function returns the angle of two sine waves shifted in phase to each other.
5.26.4 Description
The function calculates the angle of two sinusoidal signals, one shifted in phase to the
other. The phase shift between sinusoidal signals does not have to be π/2 and can be any
value.
It is assumed that the arguments of the function are as follows:
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Function GFLIB_AtanYXShifted_F16
Equation GFLIB_AtanYXShifted_Eq1
where:
• x, y are respectively, the f16InX, and f16InY arguments
• θ is the angle to be computed by the function
• Δθ is the phase difference between the x, y signals
At the end of computations, an angle offset θOffset is added to the computed angle θ. The
angle offset is an additional parameter, which can be used to set the zero of the θ axis. If
θOffset is zero, then the angle computed by the function will be exactly θ.
The GFLIB_AtanYXShifted_F16 function does not directly use the angle offset θOffset
and the phase difference θ. The function's parameters, contained in the function
parameters structure GFLIB_ATANYXSHIFTED_T_F16, need to be computed by
means of the provided Matlab function (see below).
If Δθ= π/2 or Δθ=- π/2, then the function is similar to the GFLIB_AtanYX_F16 function,
however, the GFLIB_AtanYX_F16 function in this case is more effective with regard to
execution time and accuracy.
In order to use the function, the following necessary steps need to be completed:
• define Δθ and θOffset, the Δθ shall be known from the input sinusoidal signals, the
θOffset needs to be set arbitrarily
• compute values for the function parameters structure by means of the provided
Matlab function
• convert the computed values into integer format and insert them into the C code (see
also the C code example)
The function uses the following algorithm for computing the angle:
Equation GFLIB_AtanYXShifted_Eq2
where:
• x, y are respectively, the f16InX, and f16InY
• θ is the angle to be computed by the function, see the previous equation
• Δθ is the phase difference between the x, y signals, see the previous equation
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• S is a scaling coefficient, S is almost 1, (S < 1), see also the explanation below
• a, b intermediate variables
• θOffset is the additional phase shift, the computed angle will be θ + θOffset
The scale coefficient S is used to prevent overflow and to assure symmetry around 0 for
the entire fractional range. S shall be less than 1.0, but as large as possible. The algorithm
implemented in this function uses the value of 1 - 2 -15.
The algorithm can be easily justified by proving the trigonometric identity:
Equation GFLIB_AtanYXShifted_Eq3
For the purposes of fractional arithmetic, the algorithm is implemented such that
additional values are used as shown in the equation below:
Equation GFLIB_AtanYXShifted_Eq4
where:
• C y, C x are the algorithm coefficients for y and x signals
• K y is multiplication coefficient of the y signal, represented by the parameters
structure member pParam->f16Ky
• K x is multiplication coefficient of the x signal, represented by the parameters
structure member pParam->f16Kx
• N y is scaling coefficient of the y signal, represented the by parameters structure
member pParam->s16Ny
• N x is scaling coefficient of the x signal, represented by the parameters structure
member pParam->s16Nx
• θadj is an adjusting angle, represented by the parameters structure member pParam>f16ThetaAdj
The multiplication and scaling coefficients, and the adjusting angle, shall be defined in a
parameters structure provided as the function input parameter.
The function initialization parameters can be calculated as shown in the following Matlab
code:
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Function GFLIB_AtanYXShifted_F16
function [KY, KX, NY, NX, THETAADJ] = atanyxshiftedpar(dthdeg, thoffsetdeg)
// ATANYXSHIFTEDPAR calculation of parameters for atanyxshifted() function
//
// [KY, KX, NY, NX, THETAADJ] = atanyxshiftedpar(dthdeg, thoffsetdeg)
//
// dthdeg = phase shift (delta theta) between sine waves in degrees
// thoffsetdeg = angle offset (theta offset) in degrees
// NY - scaling coefficient of y signal
// NX - scaling coefficient of x signal
// KY - multiplication coefficient of y signal
// KX - multiplication coefficient of x signal
// THETAADJ - adjusting angle in radians, scaled from [-pi, pi) to [-1, 1)
if (dthdeg < -180) || (dthdeg >= 180)
error('atanyxshiftedpar: dthdeg out of range');
end
if (thoffsetdeg < -180) || (thoffsetdeg >= 180)
error('atanyxshiftedpar: thoffsetdeg out of range');
end
dth2 = ((dthdeg/2)/180*pi);
thoffset = (thoffsetdeg/180*pi);
CY = (1 - 2^-15)/(2*cos(dth2));
CX = (1 - 2^-15)/(2*sin(dth2));
if(abs(CY) >= 1) NY = ceil(log2(abs(CY)));
else NY = 0;
end
if(abs(CX) >= 1) NX = ceil(log2(abs(CX)));
else NX = 0;
end
KY = CY/2^NY;
KX = CX/2^NX;
THETAADJ = dthdeg/2 - thoffsetdeg;
if THETAADJ >= 180
THETAADJ = THETAADJ - 360;
elseif THETAADJ < -180
THETAADJ = THETAADJ + 360;
end
THETAADJ = THETAADJ/180;
return;
While applying the function, some general guidelines should be considered as stated
below.
At some values of the phase shift, and particularly at phase shift approaching -180, 0 or
180 degrees, the algorithm may become numerically unstable, causing any error,
contributed by input signal imperfections or through finite precision arithmetic, to be
magnified significantly. Therefore, some care should be taken to avoid error where
possible. The detailed error analysis of the algorithm is beyond the scope of this
documentation, however, general guidelines are provided.
There are several sources of error in the function:
• error of the supplied signal values due to the finite resolution of the AD conversion
• error contributed by higher order harmonics appearing in the input signals
• computational error of the multiplication due to the finite length of registers
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• error of the phase shift Δθ representation in the finite precision arithmetic and in the
values
• error due to differences in signal amplitudes
It should be noted that the function requires both signals to have the same amplitude. To
minimize the output error, the amplitude of both signals should be as close to 1.0 as much
as possible.
The function has been tested to be reliable at a phase shift in the range of [-165, -15] and
[15, 165] degrees for perfectly sinusoidal input signals. Beyond this range, the function
operates correctly, however, the output error can be beyond the guaranteed value. In a
real application, an error, contributed by an AD conversion and by higher order
harmonics of the input signals, should be also taken into account.
Note
The input pointer must contain a valid address otherwise an
exception may occur (Data TLB Error, Data Storage,
Alignment, Machine Check).
The function calls the GFLIB_AtanYX_F16 function. The
function may become numerically unstable for a phase shift
approaching -180, 0 or 180 degrees. The function accuracy is
guaranteed for a phase shift in the range of [-175, -5] and [5,
175] degrees at perfect input signals. To eliminate the
calculation error the function uses the 32-bit internal
accumulators.
CAUTION
Due to the cyclic character of the GFLIB_AtanYX_F16, in case
the difference between the adjusting angle θadj and the input
vector angle is approaching to 1-2 -15 or -1, the
GFLIB_AtanYX_F16 function operates correctly, however the
output error might exceed the guaranteed limits comparing to
the double precision reference.
5.26.5 Re-entrancy
The function is re-entrant.
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Function GFLIB_ControllerPIp_F32
5.26.6 Code Example
#include "gflib.h"
tFrac16 f16InY;
tFrac16 f16InX;
tFrac16 f16Ang;
GFLIB_ATANYXSHIFTED_T_F16 Param;
void main(void)
{
// dtheta = 69.33deg, thetaoffset = 10deg
// CY = (1 - 2^-15)/(2*cos((69.33/2)/180*pi))= 0.60789036201452440
// CX = (1 - 2^-15)/(2*sin((69.33/2)/180*pi))= 0.87905201358520957
// NY = 0 (abs(CY) < 1)
// NX = 0 (abs(CX) < 1)
// KY = 0.60789/2^0 = 0.60789036201452440
// KX = 0.87905/2^0 = 0.87905201358520957
// THETAADJ = 10/180 = 0.05555555555
Param.f16Ky = FRAC16 (0.60789036201452440);
Param.f16Kx = FRAC16 (0.87905201358520957);
Param.s16Ny = 0;
Param.s16Nx = 0;
Param.f16ThetaAdj = FRAC16 (0.05555555555);
// theta = 15 deg
// Y = sin(theta) = 0.2588190
// X = sin(theta + dtheta) = 0.9951074
f16InY = FRAC16 (0.2588190);
f16InX = FRAC16 (0.9951074);
// f16Ang output should be close to 0x1C34
f16Ang = GFLIB_AtanYXShifted_F16 (f16InY, f16InX, &Param);
// f16Ang output should be close to 0x1C34
f16Ang = GFLIB_AtanYXShifted (f16InY, f16InX, &Param, F16);
//
//
//
//
}
##############################################################
Available only if 16-bit fractional implementation selected
as default
##############################################################
// f16Ang output should be close to 0x1C34
f16Ang = GFLIB_AtanYXShifted (f16InY, f16InX, &Param);
5.27 Function GFLIB_ControllerPIp_F32
This function calculates a parallel form of the Proportional-Integral controller, without
integral anti-windup.
5.27.1 Declaration
tFrac32 GFLIB_ControllerPIp_F32(tFrac32 f32InErr, GFLIB_CONTROLLER_PI_P_T_F32 *const pParam);
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5.27.2 Arguments
Table 5-33. GFLIB_ControllerPIp_F32 arguments
Type
tFrac32
Name
f32InErr
GFLIB_CONTROLLER pParam
_PI_P_T_F32 *const
Direction
Description
input
Input error signal to the controller is a 32-bit number
normalized between [-1, 1).
input,
output
Pointer to the controller parameters structure.
5.27.3 Return
The function returns a 32-bit value in format 1.31, representing the signal to be applied to
the controlled system so that the input error is forced to zero.
5.27.4 Description
A PI controller attempts to correct the error between a measured process variable and a
desired set-point by calculating and then outputting a corrective action that can adjust the
process accordingly. The GFLIB_ControllerPIp_F32 function calculates the
Proportional-Integral (PI) algorithm according to the equations below. The PI algorithm
is implemented in the parallel (non-interacting) form, allowing the user to define the P
and I parameters independently without interaction.
An anti-windup strategy is not implemented in this function. Nevertheless, the
accumulator overflow is prevented by correct saturation of the controller output at
maximal values: [-1, 1) in fractional interpretation, or [-2 31,2 31-1) in integer
interpretation.
The PI algorithm in the continuous time domain can be described as:
Equation GFLIB_ControllerPIp_Eq1
where
• e(t) - input error in the continuous time domain
• u(t) - controller output in the continuous time domain
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Function GFLIB_ControllerPIp_F32
• K P - proportional gain
• K I - integral gain
Equation GFLIB_ControllerPIp_Eq1 can be described using the Laplace transformation
as follows:
Equation GFLIB_ControllerPIp_Eq2
The proportional part of equation GFLIB_ControllerPIp_Eq2 is transformed into the
discrete time domain simply as:
Equation GFLIB_ControllerPIp_Eq3
Transforming the integral part of equation GFLIB_ControllerPIp_Eq2 into a discrete time
domain using the Bilinear method, also known as trapezoidal approximation, leads to the
following equation:
Equation GFLIB_ControllerPIp_Eq4
where T s [sec] is the sampling time.
In order to implement the discrete equation of the controller on the fixed point arithmetic
platform, the maximal values (scales) of the input and output signals have to be known a
priori. This is essential for correct casting of the physical signal values into fixed point
values:
• E MAX - maximal value of the controller input error signal
• U MAX - maximal value of the controller output signal
The fractional representation of both input and output signals, normalized between [-1,
1), is obtained as follows:
Equation GFLIB_ControllerPIp_Eq5
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Equation GFLIB_ControllerPIp_Eq6
Applying such scaling (normalization) on the proportional term of equation
GFLIB_ControllerPIp_Eq3 results in:
Equation GFLIB_ControllerPIp_Eq7
where K P_sc is the proportional gain parameter considering input/output scaling.
Analogically, scaling the integral term of equation GFLIB_ControllerPIp_Eq4 results in:
Equation GFLIB_ControllerPIp_Eq8
where K I_sc is the integral gain parameter considering input/output scaling.
The sum of the scaled proportional and integral terms gives a complete equation of the
controller:
Equation GFLIB_ControllerPIp_Eq9
The problem is however, that either of the gain parameters K P_sc, K I_sc can be out of the
[-1, 1) range, hence cannot be directly interpreted as fractional values. To overcome this,
it is necessary to scale these gain parameters using the shift values as follows:
Equation GFLIB_ControllerPIp_Eq10
and
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Function GFLIB_ControllerPIp_F32
Equation GFLIB_ControllerPIp_Eq11
where
•
•
•
•
f32PropGain - is the scaled value of proportional gain [-1, 1)
s16PropGainShift - is the scaling shift for proportional gain [-31,31]
f32IntegGain - is the scaled value of integral gain [-1, 1)
s16IntegGainShift - is the scaling shift for integral gain [-31,31]
Note
The input pointer must contain a valid address otherwise an
exception may occur (Data TLB Error, Data Storage,
Alignment, Machine Check).
All controller parameters and states can be reset during
declaration using the
GFLIB_CONTROLLER_PI_P_DEFAULT_F32 macro. As the
GFLIB_ControllerPIp also contains the integration part, the
output result is saddled by cumulative error. To enumerate the
computation error in one calculation cycle, the internal
integration accumulator is not used for testing purposes and is
replaced by output from the previous calculation step of the
reference model.
5.27.5 Re-entrancy
The function is re-entrant.
5.27.6 Code Example
#include "gflib.h"
tFrac32 f32InErr;
tFrac32 f32Output;
GFLIB_CONTROLLER_PI_P_T_F32 trMyPI = GFLIB_CONTROLLER_PI_P_DEFAULT_F32;
void main(void)
{
// input error = 0.25
f32InErr = FRAC32 (0.25);
// controller parameters
trMyPI.f32PropGain
trMyPI.f32IntegGain
trMyPI.s16PropGainShift
= FRAC32 (0.01);
= FRAC32 (0.02);
= 1;
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trMyPI.s16IntegGainShift
trMyPI.f32IntegPartK_1
= 1;
= 0;
// output should be 0x01EB851E
f32Output = GFLIB_ControllerPIp_F32 (f32InErr, &trMyPI);
// clearing of internal states
trMyPI.f32IntegPartK_1 = (tFrac32)0;
trMyPI.f32InK_1 = (tFrac32)0;
// output should be 0x01EB851E
f32Output = GFLIB_ControllerPIp (f32InErr, &trMyPI, F32);
//
//
//
//
##############################################################
Available only if 32-bit fractional implementation selected
as default
##############################################################
// clearing of internal states
trMyPI.f32IntegPartK_1 = (tFrac32)0;
trMyPI.f32InK_1 = (tFrac32)0;
}
// output should be 0x01EB851E
f32Output = GFLIB_ControllerPIp (f32InErr, &trMyPI);
5.28 Function GFLIB_ControllerPIp_F16
This function calculates a parallel form of the Proportional-Integral controller, without
integral anti-windup.
5.28.1 Declaration
tFrac16 GFLIB_ControllerPIp_F16(tFrac16 f16InErr, GFLIB_CONTROLLER_PI_P_T_F16 *const pParam);
5.28.2 Arguments
Table 5-34. GFLIB_ControllerPIp_F16 arguments
Type
tFrac16
Name
f16InErr
GFLIB_CONTROLLER pParam
_PI_P_T_F16 *const
Direction
Description
input
Input error signal to the controller is a 16-bit number
normalized between [-1, 1).
input,
output
Pointer to the controller parameters structure.
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Function GFLIB_ControllerPIp_F16
5.28.3 Return
The function returns a 16-bit value in format 1.15, representing the signal to be applied to
the controlled system so that the input error is forced to zero.
5.28.4 Description
A PI controller attempts to correct the error between a measured process variable and a
desired set-point by calculating and then outputting a corrective action that can adjust the
process accordingly. The GFLIB_ControllerPIp_F16 function calculates the
Proportional-Integral (PI) algorithm according to the equations below. The PI algorithm
is implemented in the parallel (non-interacting) form, allowing the user to define the P
and I parameters independently without interaction.
An anti-windup strategy is not implemented in this function. Nevertheless, the
accumulator overflow is prevented by correct saturation of the controller output at
maximal values: [-1, 1) in fractional interpretation, or [-2 15,2 15-1) in integer
interpretation.
The PI algorithm in the continuous time domain can be described as:
Equation GFLIB_ControllerPIp_Eq1
where
•
•
•
•
e(t) - input error in the continuous time domain
u(t) - controller output in the continuous time domain
K P - proportional gain
K I - integral gain
Equation GFLIB_ControllerPIp_Eq1 can be described using the Laplace transformation
as follows:
Equation GFLIB_ControllerPIp_Eq2
The proportional part of equation GFLIB_ControllerPIp_Eq2 is transformed into the
discrete time domain simply as:
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Equation GFLIB_ControllerPIp_Eq3
Transforming the integral part of equation GFLIB_ControllerPIp_Eq2 into a discrete time
domain using the Bilinear method, also known as trapezoidal approximation, leads to the
following equation:
Equation GFLIB_ControllerPIp_Eq4
where T s [sec] is the sampling time.
In order to implement the discrete equation of the controller on the fixed point arithmetic
platform, the maximal values (scales) of the input and output signals have to be known a
priori. This is essential for correct casting of the physical signal values into fixed point
values:
• E MAX - maximal value of the controller input error signal
• U MAX - maximal value of the controller output signal
The fractional representation of both input and output signals, normalized between [-1,
1), is obtained as follows:
Equation GFLIB_ControllerPIp_Eq5
Equation GFLIB_ControllerPIp_Eq6
Applying such scaling (normalization) on the proportional term of equation
GFLIB_ControllerPIp_Eq3 results in:
Equation GFLIB_ControllerPIp_Eq7
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Function GFLIB_ControllerPIp_F16
where K P_sc is the proportional gain parameter considering input/output scaling.
Analogically, scaling the integral term of equation GFLIB_ControllerPIp_Eq4 results in:
Equation GFLIB_ControllerPIp_Eq8
where K I_sc is the integral gain parameter considering input/output scaling.
The sum of the scaled proportional and integral terms gives a complete equation of the
controller:
Equation GFLIB_ControllerPIp_Eq9
The problem is however, that either of the gain parameters K P_sc, K I_sc can be out of the
[-1, 1) range, hence cannot be directly interpreted as fractional values. To overcome this,
it is necessary to scale these gain parameters using the shift values as follows:
Equation GFLIB_ControllerPIp_Eq10
and
Equation GFLIB_ControllerPIp_Eq11
where
•
•
•
•
f16PropGain - is the scaled value of proportional gain [-1, 1)
s16PropGainShift - is the scaling shift for proportional gain [-15, 15)
f16IntegGain - is the scaled value of integral gain [-1, 1)
s16IntegGainShift - is the scaling shift for integral gain [-15, 15)
Note
The input pointer must contain a valid address otherwise an
exception may occur (Data TLB Error, Data Storage,
Alignment, Machine Check).
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All controller parameters and states can be reset during
declaration using the
GFLIB_CONTROLLER_PI_P_DEFAULT_F16 macro. As the
GFLIB_ControllerPIp also contains the integration part, the
output result is saddled by cumulative error. To enumerate the
computation error in one calculation cycle, the internal
integration accumulator is not used for testing purposes and is
replaced by output from the previous calculation step of the
reference model.
5.28.5 Re-entrancy
The function is re-entrant.
5.28.6 Code Example
#include "gflib.h"
tFrac16 f16InErr;
tFrac16 f16Output;
GFLIB_CONTROLLER_PI_P_T_F16 trMyPI = GFLIB_CONTROLLER_PI_P_DEFAULT_F16;
void main(void)
{
// input error = 0.25
f16InErr = FRAC16 (0.25);
// controller parameters
trMyPI.f16PropGain
trMyPI.f16IntegGain
trMyPI.s16PropGainShift
trMyPI.s16IntegGainShift
trMyPI.f32IntegPartK_1
=
=
=
=
=
FRAC16 (0.01);
FRAC16 (0.02);
1;
1;
0;
// output should be 0x01EB
f16Output = GFLIB_ControllerPIp_F16 (f16InErr, &trMyPI);
// clearing of internal states
trMyPI.f32IntegPartK_1 = (tFrac32)0;
trMyPI.f16InK_1 = (tFrac16)0;
// output should be 0x01EB
f16Output = GFLIB_ControllerPIp (f16InErr, &trMyPI, F16);
//
//
//
//
##############################################################
Available only if 16-bit fractional implementation selected
as default
##############################################################
// clearing of internal states
trMyPI.f32IntegPartK_1 = (tFrac32)0;
trMyPI.f16InK_1 = (tFrac16)0;
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Function GFLIB_ControllerPIpAW_F32
}
// output should be 0x01EB
f16Output = GFLIB_ControllerPIp (f16InErr, &trMyPI);
5.29 Function GFLIB_ControllerPIpAW_F32
The function calculates the parallel form of the Proportional-Integral (PI) controller with
implemented integral anti-windup functionality.
5.29.1 Declaration
tFrac32 GFLIB_ControllerPIpAW_F32(tFrac32 f32InErr, GFLIB_CONTROLLER_PIAW_P_T_F32 *const
pParam);
5.29.2 Arguments
Table 5-35. GFLIB_ControllerPIpAW_F32 arguments
Type
tFrac32
Name
f32InErr
GFLIB_CONTROLLER pParam
_PIAW_P_T_F32
*const
Direction
Description
input
Input error signal to the controller is a 32-bit number
normalized between [-1, 1).
input,
output
Pointer to the controller parameters structure.
5.29.3 Return
The function returns a 32-bit value in format 1.31, representing the signal to be applied to
the controlled system so that the input error is forced to zero.
5.29.4 Description
A PI controller attempts to correct the error between a measured process variable and a
desired set-point by calculating and then outputting a corrective action that can adjust the
process accordingly. The GFLIB_ControllerPIpAW function calculates the ProportionalIntegral (PI) algorithm according to the equations below. The PI algorithm is
implemented in the parallel (non-interacting) form, allowing the user to define the P and I
parameters independently without interaction. The controller output is limited and the
limit values (f32UpperLimit and f32LowerLimit) are defined by the user. The PI
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controller algorithm also returns a limitation flag. This flag (u16LimitFlag) is a member
of the structure of the PI controller parameters
(GFLIB_CONTROLLER_PIAW_P_T_F32). If the PI controller output reaches the upper
or lower limit then u16LimitFlag = 1, otherwise u16LimitFlag = 0 (integer values). An
anti-windup strategy is implemented by limiting the integral portion. The integral state is
limited by the controller limits, in the same way as the controller output.
The PI algorithm in the continuous time domain can be described as:
Equation GFLIB_ControllerPIpAW_Eq1
where
•
•
•
•
e(t) - input error in the continuous time domain
u(t) - controller output in the continuous time domain
K P - proportional gain
K I - integral gain
Equation GFLIB_ControllerPIpAW_Eq1 can be described using the Laplace
transformation as follows:
Equation GFLIB_ControllerPIpAW_Eq2
The proportional part of equation GFLIB_ControllerPIpAW_Eq2 is transformed into the
discrete time domain simply as:
Equation GFLIB_ControllerPIpAW_Eq3
Transforming the integral part of equation GFLIB_ControllerPIpAW_Eq2 into a discrete
time domain using the Bilinear method, also known as trapezoidal approximation, leads
to the following equation:
Equation GFLIB_ControllerPIpAW_Eq4
where T s [sec] is the sampling time.
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Function GFLIB_ControllerPIpAW_F32
In order to implement the discrete equation of the controller on the fixed point arithmetic
platform, the maximal values (scales) of input and output signals have to be known a
priori. This is essential for correct casting of the physical signal values into fixed point
values:
• E MAX - maximal value of the controller input error signal
• U MAX - maximal value of the controller output signal
The fractional representation of both input and output signals, normalized between [-1,
1), is obtained as follows:
Equation GFLIB_ControllerPIpAW_Eq5
Equation GFLIB_ControllerPIpAW_Eq6
Applying such scaling (normalization) on the proportional term of equation
GFLIB_ControllerPIpAW_Eq3 results in:
Equation GFLIB_ControllerPIpAW_Eq7
where K P_sc is the proportional gain parameter considering input/output scaling.
Analogically, scaling the integral term of equation GFLIB_ControllerPIpAW_Eq4 results
in:
Equation GFLIB_ControllerPIpAW_Eq8
where K I_sc is the integral gain parameter considering input/output scaling.
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The sum of the scaled proportional and integral terms gives a complete equation of the
controller. The problem is however, that either of the gain parameters K P_sc, K I_sc can
be out of the [-1, 1) range, hence can not be directly interpreted as fractional values. To
overcome this, it is necessary to scale these gain parameters using the shift values as
follows:
Equation GFLIB_ControllerPIpAW_Eq9
Equation GFLIB_ControllerPIpAW_Eq10
where
•
•
•
•
f16PropGain - is the scaled value of proportional gain [-1, 1)
s16PropGainShift - is the scaling shift for proportional gain [-31, 31)
f16IntegGain - is the scaled value of integral gain [-1, 1)
s16IntegGainShift - is the scaling shift for integral gain [-31, 31)
The sum of the scaled proportional and integral terms gives a complete equation of the
controller:
Equation GFLIB_ControllerPIpAW_Eq11
The output signal limitation is implemented in this controller. The actual output u(k) is
bounded not to exceed the given limit values f32UpperLimit, f32LowerLimit. This is due
to either the bounded power of the actuator or to the physical constraints of the plant.
Equation GFLIB_ControllerPIpAW_Eq12
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Function GFLIB_ControllerPIpAW_F32
The bounds are described by a limitation element equation
GFLIB_ControllerPIpAW_Eq12. When the bounds are exceeded the non-linear
saturation characteristic will take effect and influence the dynamic behavior. The
described limitation is implemented on the integral part accumulator (limitation during
the calculation) and on the overall controller output. Therefore, if the limitation occurs,
the controller output is clipped to its bounds and the wind-up occurrence of the
accumulator portion is avoided by saturating the actual sum.
Note
The input pointer must contain a valid address otherwise an
exception may occur (Data TLB Error, Data Storage,
Alignment, Machine Check).
All controller parameters and states can be reset during
declaration using the
GFLIB_CONTROLLER_PIAW_P_DEFAULT_F32 macro. As
the GFLIB_ControllerPIp also contains the integration part, the
output result is saddled by cumulative error. To enumerate the
computation error in one calculation cycle, the internal
integration accumulator is not used for testing purposes and is
replaced by output from the previous calculation step of the
reference model.
5.29.5 Re-entrancy
The function is re-entrant.
5.29.6 Code Example
#include "gflib.h"
tFrac32 f32InErr;
tFrac32 f32Output;
GFLIB_CONTROLLER_PIAW_P_T_F32 trMyPI = GFLIB_CONTROLLER_PIAW_P_DEFAULT_F32;
void main(void)
{
// input error = 0.25
f32InErr = FRAC32 (0.25);
// controller parameters
trMyPI.f32PropGain
trMyPI.f32IntegGain
trMyPI.s16PropGainShift
trMyPI.s16IntegGainShift
trMyPI.f32IntegPartK_1
=
=
=
=
=
FRAC32 (0.01);
FRAC32 (0.02);
1;
1;
FRAC32 (0);
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trMyPI.f32UpperLimit
trMyPI.f32LowerLimit
= FRAC32 (1.0);
= FRAC32 (-1.0);
// output should be 0x01EB851E
f32Output = GFLIB_ControllerPIpAW_F32 (f32InErr, &trMyPI);
// clearing of internal states
trMyPI.f32IntegPartK_1 = (tFrac32)0;
trMyPI.f32InK_1 = (tFrac32)0;
// output should be 0x01EB851E
f32Output = GFLIB_ControllerPIpAW (f32InErr, &trMyPI, F32);
//
//
//
//
##############################################################
Available only if 32-bit fractional implementation selected
as default
##############################################################
// clearing of internal states
trMyPI.f32IntegPartK_1 = (tFrac32)0;
trMyPI.f32InK_1 = (tFrac32)0;
}
// output should be 0x01EB851E
f32Output = GFLIB_ControllerPIpAW (f32InErr, &trMyPI);
5.30 Function GFLIB_ControllerPIpAW_F16
The function calculates the parallel form of the Proportional-Integral (PI) controller with
implemented integral anti-windup functionality.
5.30.1 Declaration
tFrac16 GFLIB_ControllerPIpAW_F16(tFrac16 f16InErr, GFLIB_CONTROLLER_PIAW_P_T_F16 *const
pParam);
5.30.2 Arguments
Table 5-36. GFLIB_ControllerPIpAW_F16 arguments
Type
tFrac16
Name
f16InErr
GFLIB_CONTROLLER pParam
_PIAW_P_T_F16
*const
Direction
Description
input
Input error signal to the controller is a 16-bit number
normalized between [-1, 1).
input,
output
Pointer to the controller parameters structure.
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Function GFLIB_ControllerPIpAW_F16
5.30.3 Return
The function returns a 16-bit value in format 1.15, representing the signal to be applied to
the controlled system so that the input error is forced to zero.
5.30.4 Description
A PI controller attempts to correct the error between a measured process variable and a
desired set-point by calculating and then outputting a corrective action that can adjust the
process accordingly. The GFLIB_ControllerPIpAW function calculates the ProportionalIntegral (PI) algorithm according to the equations below. The PI algorithm is
implemented in the parallel (non-interacting) form, allowing the user to define the P and I
parameters independently without interaction. The controller output is limited and the
limit values (f16UpperLimit and f16LowerLimit) are defined by the user. The PI
controller algorithm also returns a limitation flag. This flag (u16LimitFlag) is a member
of the structure of the PI controller parameters
(GFLIB_CONTROLLER_PIAW_P_T_F16). If the PI controller output reaches the upper
or lower limit then u16LimitFlag = 1, otherwise u16LimitFlag = 0 (integer values). An
anti- windup strategy is implemented by limiting the integral portion. The integral state is
limited by the controller limits, in the same way as the controller output.
The PI algorithm in the continuous time domain can be described as:
Equation GFLIB_ControllerPIpAW_Eq1
where
•
•
•
•
e(t) - input error in the continuous time domain
u(t) - controller output in the continuous time domain
K P - proportional gain
K I - integral gain
Equation GFLIB_ControllerPIpAW_Eq1 can be described using the Laplace
transformation as follows:
Equation GFLIB_ControllerPIpAW_Eq2
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The proportional part of equation GFLIB_ControllerPIpAW_Eq2 is transformed into the
discrete time domain simply as:
Equation GFLIB_ControllerPIpAW_Eq3
Transforming the integral part of equation GFLIB_ControllerPIpAW_Eq2 into a discrete
time domain using the Bilinear method, also known as trapezoidal approximation, leads
to the following equation:
Equation GFLIB_ControllerPIpAW_Eq4
where T s [sec] is the sampling time.
In order to implement the discrete equation of the controller on the fixed point arithmetic
platform, the maximal values (scales) of input and output signals have to be known a
priori. This is essential for correct casting of the physical signal values into fixed point
values:
• E MAX - maximal value of the controller input error signal
• U MAX - maximal value of the controller output signal
The fractional representation of both input and output signals, normalized between [-1,
1), is obtained as follows:
Equation GFLIB_ControllerPIpAW_Eq5
Equation GFLIB_ControllerPIpAW_Eq6
Applying such scaling (normalization) on the proportional term of equation
GFLIB_ControllerPIpAW_Eq3 results in:
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Function GFLIB_ControllerPIpAW_F16
Equation GFLIB_ControllerPIpAW_Eq7
where K P_sc is the proportional gain parameter considering input/output scaling.
Analogically, scaling the integral term of equation GFLIB_ControllerPIpAW_Eq4 results
in:
Equation GFLIB_ControllerPIpAW_Eq8
where K I_sc is the integral gain parameter considering input/output scaling.
The sum of the scaled proportional and integral terms gives a complete equation of the
controller. The problem is however, that either of the gain parameters K P_sc, K I_sc can
be out of the [-1, 1) range, hence can not be directly interpreted as fractional values. To
overcome this, it is necessary to scale these gain parameters using the shift values as
follows:
Equation GFLIB_ControllerPIpAW_Eq9
Equation GFLIB_ControllerPIpAW_Eq10
where
•
•
•
•
f16PropGain - is the scaled value of proportional gain [-1, 1)
s16PropGainShift - is the scaling shift for proportional gain [-31, 31)
f16IntegGain - is the scaled value of integral gain [-1, 1)
s16IntegGainShift - is the scaling shift for integral gain [-31, 31)
The sum of the scaled proportional and integral terms gives a complete equation of the
controller:
Equation GFLIB_ControllerPIpAW_Eq11
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The output signal limitation is implemented in this controller. The actual output u(k) is
bounded not to exceed the given limit values f16UpperLimit, f16LowerLimit. This is due
to either the bounded power of the actuator or to the physical constraints of the plant.
Equation GFLIB_ControllerPIpAW_Eq12
The bounds are described by a limitation element equation
GFLIB_ControllerPIpAW_Eq12. When the bounds are exceeded the non-linear
saturation characteristic will take effect and influence the dynamic behavior. The
described limitation is implemented on the integral part accumulator (limitation during
the calculation) and on the overall controller output. Therefore, if the limitation occurs,
the controller output is clipped to its bounds and the wind-up occurrence of the
accumulator portion is avoided by saturating the actual sum.
Note
The input pointer must contain a valid address otherwise an
exception may occur (Data TLB Error, Data Storage,
Alignment, Machine Check).
All controller parameters and states can be reset during
declaration using the
GFLIB_CONTROLLER_PIAW_P_DEFAULT_F16 macro. To
effectively reach the target precision the internal calculation is
done in 32-bit fractional arithmetic and internal accumulator is
32-bit wide. As the GFLIB_ControllerPIp also contains the
integration part, the output result is saddled by cumulative
error. To enumerate the computation error in one calculation
cycle, the internal integration accumulator is not used for
testing purposes and is replaced by output from the previous
calculation step of the reference model.
5.30.5 Re-entrancy
The function is re-entrant.
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Function GFLIB_ControllerPIr_F32
5.30.6 Code Example
#include "gflib.h"
tFrac16 f16InErr;
tFrac16 f16Output;
GFLIB_CONTROLLER_PIAW_P_T_F16 trMyPI = GFLIB_CONTROLLER_PIAW_P_DEFAULT_F16;
void main(void)
{
// input error = 0.25
f16InErr = FRAC16 (0.25);
// controller parameters
trMyPI.f16PropGain
trMyPI.f16IntegGain
trMyPI.s16PropGainShift
trMyPI.s16IntegGainShift
trMyPI.f32IntegPartK_1
trMyPI.f16UpperLimit
trMyPI.f16LowerLimit
=
=
=
=
=
=
=
FRAC16
FRAC16
1;
1;
FRAC32
FRAC16
FRAC16
(0.01);
(0.02);
(0);
(1.0);
(-1.0);
// output should be 0x01EB
f16Output = GFLIB_ControllerPIpAW_F16 (f16InErr, &trMyPI);
// clearing of internal states
trMyPI.f32IntegPartK_1 = (tFrac32)0;
trMyPI.f16InK_1 = (tFrac16)0;
// output should be 0x01EB
f16Output = GFLIB_ControllerPIpAW (f16InErr, &trMyPI, F16);
//
//
//
//
##############################################################
Available only if 16-bit fractional implementation selected
as default
##############################################################
// clearing of internal states
trMyPI.f32IntegPartK_1 = (tFrac32)0;
trMyPI.f16InK_1 = (tFrac16)0;
}
// output should be 0x01EB
f16Output = GFLIB_ControllerPIpAW (f16InErr, &trMyPI);
5.31 Function GFLIB_ControllerPIr_F32
This function calculates a standard recurrent form of the Proportional-Integral controller,
without integral anti-windup.
5.31.1 Declaration
tFrac32 GFLIB_ControllerPIr_F32(tFrac32 f32InErr, GFLIB_CONTROLLER_PI_R_T_F32 *const pParam);
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5.31.2 Arguments
Table 5-37. GFLIB_ControllerPIr_F32 arguments
Type
tFrac32
Name
f32InErr
GFLIB_CONTROLLER pParam
_PI_R_T_F32 *const
Direction
Description
input
Input error signal to the controller is a 32-bit number
normalized between [-1, 1).
input,
output
Pointer to the controller parameters structure.
5.31.3 Return
The function returns a 32-bit value in fractional format 1.31, representing the signal to be
applied to the controlled system so that the input error is forced to zero.
5.31.4 Description
The function GFLIB_ControllerPIr_F32 calculates a standard recurrent form of the
Proportional-Integral controller, without integral anti-windup.
The continuous time domain representation of the PI controller is defined as:
Equation GFLIB_ControllerPIr_Eq1
The transfer function for this kind of PI controller, in a continuous time domain, is
described using the Laplace transformation as follows:
Equation GFLIB_ControllerPIr_Eq2
Transforming equation GFLIB_ControllerPIr_Eq2 into a discrete time domain leads to
the following equation:
Equation GFLIB_ControllerPIr_Eq3
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Function GFLIB_ControllerPIr_F32
where Kp is proportional gain, Ki is integral gain, Ts is the sampling period, u(k) is the
controller output, e(k) is the controller input error signal, CC1 and CC2 are controller
coefficients calculated depending on the discretization method used, as shown in Table
5-38.
Table 5-38. Calculation of coefficients CC1 and CC2 using various discretization methods
Trapezoidal
Backward Rect.
Forward Rect.
CC1=
K p+K IT S/2
K p+K IT S
Kp
CC2=
-K p+K IT S/2
-K p
-K p+K IT S
In order to implement the discrete equation of the controller GFLIB_ControllerPIr_Eq3
on the fixed point arithmetic platform, the maximal values (scales) of the input and
output signals
• E MAX - maximal value of the controller input error signal
• U MAX - maximal value of the controller output signal
have to be known a priori. This is essential for correct casting of the physical signal
values into fixed point values [-1, 1).
Then the fractional representation [-1, 1) of both input and output signals is obtained as
follows:
Equation GFLIB_ControllerPIr_Eq4
Equation GFLIB_ControllerPIr_Eq5
The resulting controller discrete time domain equation in fixed point fractional
representation is therefore given as:
Equation GFLIB_ControllerPIr_Eq6
which can be rearranged into the following form:
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Equation GFLIB_ControllerPIr_Eq7
where
Equation GFLIB_ControllerPIr_Eq8
are the controller coefficients adapted according to the input and output scale values. In
order to implement both coefficients as fractional numbers, both CC1 f and CC2 f must
reside in the fractional range [-1, 1). However, depending on values CC1, CC2, E MAX, U
MAX, the calculation of CC1 and CC2 may result in values outside this fractional range.
f
f
Therefore, a scaling of CC1 f, CC2 f is introduced as follows:
Equation GFLIB_ControllerPIr_Eq9
Equation GFLIB_ControllerPIr_Eq10
The introduced scaling shift u16NShift is chosen such that both coefficients f32CC1sc,
f32CC2sc reside in the range [-1, 1). To simplify the implementation, this scaling shift is
chosen to be a power of 2, so the final scaling is a simple shift operation. Moreover, the
scaling shift cannot be a negative number, so the operation of scaling is always to scale
numbers with an absolute value larger than 1 down to fit in the range [-1, 1).
Equation GFLIB_ControllerPIr_Eq11
The final, scaled, fractional equation of a recurrent PI controller on a 32-bit fixed point
platform is therefore implemented as follows:
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Function GFLIB_ControllerPIr_F32
Equation GFLIB_ControllerPIr_Eq12
where:
•
•
•
•
•
u f(k) - fractional representation [-1, 1) of the controller output
e f(k) - fractional representation [-1, 1) of the controller input (error)
f32CC1sc - fractional representation [-1, 1) of the 1st controller coefficient
f32CC2sc - fractional representation [-1, 1) of the 2nd controller coefficient
u16NShift - in range [0,31] - is chosen such that both coefficients f32CC1sc and
f32CC2sc are in the range [-1, 1)
Note
The input pointer must contain a valid address otherwise an
exception may occur (Data TLB Error, Data Storage,
Alignment, Machine Check).
All controller parameters and states can be reset during
declaration using the
GFLIB_CONTROLLER_PI_R_DEFAULT_F32 macro.
5.31.5 Re-entrancy
The function is re-entrant.
5.31.6 Code Example
#include "gflib.h"
tFrac32 f32InErr;
tFrac32 f32Output;
GFLIB_CONTROLLER_PI_R_T_F32 trMyPI = GFLIB_CONTROLLER_PI_R_DEFAULT_F32;
void main(void)
{
// input error = 0.25
f32InErr = FRAC32 (0.25);
// controller parameters
trMyPI.f32CC1sc = FRAC32 (0.01);
trMyPI.f32CC2sc = FRAC32 (0.02);
trMyPI.u16NShift = 1;
// output should be 0x00A3D70A
f32Output = GFLIB_ControllerPIr_F32 (f32InErr,&trMyPI);
// clearing of internal states
trMyPI.f32Acc = (tFrac32)0;
trMyPI.f32InErrK1 = (tFrac32)0;
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// output should be 0x00A3D70A
f32Output = GFLIB_ControllerPIr (f32InErr,&trMyPI, F32);
//
//
//
//
##############################################################
Available only if 32-bit fractional implementation selected
as default
##############################################################
// clearing of internal states
trMyPI.f32Acc = (tFrac32)0;
trMyPI.f32InErrK1 = (tFrac32)0;
}
// output should be 0x00A3D70A
f32Output = GFLIB_ControllerPIr (f32InErr,&trMyPI);
5.32 Function GFLIB_ControllerPIr_F16
This function calculates a standard recurrent form of the Proportional-Integral controller,
without integral anti-windup.
5.32.1 Declaration
tFrac16 GFLIB_ControllerPIr_F16(tFrac16 f16InErr, GFLIB_CONTROLLER_PI_R_T_F16 *const pParam);
5.32.2 Arguments
Table 5-39. GFLIB_ControllerPIr_F16 arguments
Type
tFrac16
Name
f16InErr
GFLIB_CONTROLLER pParam
_PI_R_T_F16 *const
Direction
Description
input
Input error signal to the controller is a 16-bit number
normalized between [-1, 1).
input,
output
Pointer to the controller parameters structure.
5.32.3 Return
The function returns a 16-bit value in fractional format 1.15, representing the signal to be
applied to the controlled system so that the input error is forced to zero.
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Function GFLIB_ControllerPIr_F16
5.32.4 Description
The function GFLIB_ControllerPIr_F16 calculates a standard recurrent form of the
Proportional-Integral controller, without integral anti-windup.
The continuous time domain representation of the PI controller is defined as:
Equation GFLIB_ControllerPIr_Eq1
The transfer function for this kind of PI controller, in a continuous time domain, is
described using the Laplace transformation as follows:
Equation GFLIB_ControllerPIr_Eq2
Transforming equation GFLIB_ControllerPIr_Eq2 into a discrete time domain leads to
the following equation:
Equation GFLIB_ControllerPIr_Eq3
where Kp is proportional gain, Ki is integral gain, Ts is the sampling period, u(k) is the
controller output, e(k) is the controller input error signal, CC1 and CC2 are controller
coefficients calculated depending on the discretization method used, as shown in Table
5-40.
Table 5-40. Calculation of coefficients CC1 and CC2 using various discretization methods
Trapezoidal
Backward Rect.
Forward Rect.
CC1=
K p+K IT S/2
K p+K IT S
Kp
CC2=
-K p+K IT S/2
-K p
-K p+K IT S
In order to implement the discrete equation of the controller GFLIB_ControllerPIr_Eq3
on the fixed point arithmetic platform, the maximal values (scales) of the input and
output signals
• E MAX - maximal value of the controller input error signal
• U MAX - maximal value of the controller output signal
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have to be known a priori. This is essential for correct casting of the physical signal
values into fixed point values [-1, 1).
Then the fractional representation [-1, 1) of both input and output signals is obtained as
follows:
Equation GFLIB_ControllerPIr_Eq4
Equation GFLIB_ControllerPIr_Eq5
The resulting controller discrete time domain equation in fixed point fractional
representation is therefore given as:
Equation GFLIB_ControllerPIr_Eq6
which can be rearranged into the following form:
Equation GFLIB_ControllerPIr_Eq7
where
Equation GFLIB_ControllerPIr_Eq8
are the controller coefficients adapted according to the input and output scale values. In
order to implement both coefficients as fractional numbers, both CC1 f and CC2 f must
reside in the fractional range [-1, 1). However, depending on values CC1, CC2, E MAX, U
MAX, the calculation of CC1 and CC2 may result in values outside this fractional range.
f
f
Therefore, a scaling of CC1 f, CC2 f is introduced as follows:
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Function GFLIB_ControllerPIr_F16
Equation GFLIB_ControllerPIr_Eq9
Equation GFLIB_ControllerPIr_Eq10
The introduced scaling shift u16NShift is chosen such that both coefficients f16CC1sc,
f16CC2sc reside in the range [-1, 1). To simplify the implementation, this scaling shift is
chosen to be a power of 2, so the final scaling is a simple shift operation. Moreover, the
scaling shift cannot be a negative number, so the operation of scaling is always to scale
numbers with an absolute value larger than 1 down to fit in the range [-1, 1).
Equation GFLIB_ControllerPIr_Eq11
The final, scaled, fractional equation of a recurrent PI controller on a 16-bit fixed point
platform is therefore implemented as follows:
Equation GFLIB_ControllerPIr_Eq12
where:
•
•
•
•
•
u f(k) - fractional representation [-1, 1) of the controller output
e f(k) - fractional representation [-1, 1) of the controller input (error)
f16CC1sc - fractional representation [-1, 1) of the 1st controller coefficient
f16CC2sc - fractional representation [-1, 1) of the 2nd controller coefficient
u16NShift - in range [0,15] - is chosen such that both coefficients f16CC1sc and
f16CC2sc are in the range [-1, 1)
Note
The input pointer must contain a valid address otherwise an
exception may occur (Data TLB Error, Data Storage,
Alignment, Machine Check).
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All controller parameters and states can be reset during
declaration using the
GFLIB_CONTROLLER_PI_R_DEFAULT_F16 macro.
5.32.5 Re-entrancy
The function is re-entrant.
5.32.6 Code Example
#include "gflib.h"
tFrac16 f16InErr;
tFrac16 f16Output;
GFLIB_CONTROLLER_PI_R_T_F16 trMyPI = GFLIB_CONTROLLER_PI_R_DEFAULT_F16;
void main(void)
{
// input error = 0.25
f16InErr = FRAC16 (0.25);
// controller parameters
trMyPI.f16CC1sc = FRAC16 (0.01);
trMyPI.f16CC2sc = FRAC16 (0.02);
trMyPI.u16NShift = 1;
// output should be 0x00A3
f16Output = GFLIB_ControllerPIr_F16 (f16InErr,&trMyPI);
// clearing of internal states
trMyPI.f32Acc = (tFrac32)0;
trMyPI.f16InErrK1 = (tFrac16)0;
// output should be 0x00A3
f16Output = GFLIB_ControllerPIr (f16InErr,&trMyPI, F16);
//
//
//
//
##############################################################
Available only if 16-bit fractional implementation selected
as default
##############################################################
// clearing of internal states
trMyPI.f32Acc = (tFrac32)0;
trMyPI.f16InErrK1 = (tFrac16)0;
}
// output should be 0x00A3
f16Output = GFLIB_ControllerPIr (f16InErr,&trMyPI);
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Function GFLIB_ControllerPIrAW_F32
5.33 Function GFLIB_ControllerPIrAW_F32
This function calculates a standard recurrent form of the Proportional-Integral controller,
with integral anti-windup.
5.33.1 Declaration
tFrac32 GFLIB_ControllerPIrAW_F32(tFrac32 f32InErr, GFLIB_CONTROLLER_PIAW_R_T_F32 *const
pParam);
5.33.2 Arguments
Table 5-41. GFLIB_ControllerPIrAW_F32 arguments
Type
tFrac32
Name
f32InErr
GFLIB_CONTROLLER pParam
_PIAW_R_T_F32
*const
Direction
Description
input
Input error signal to the controller is a 32-bit number
normalized between [-1, 1).
input,
output
Pointer to the controller parameters structure.
5.33.3 Return
The function returns a 32-bit value in fractional format 1.31, representing the signal to be
applied to the controlled system so that the input error is forced to zero.
5.33.4 Description
The function GFLIB_ControllerPIrAW calculates a standard recurrent form of the
Proportional-Integral controller, with integral anti-windup.
The continuous time domain representation of the PI controller is defined as:
Equation GFLIB_ControllerPIrAW_Eq1
The transfer function for this kind of PI controller, in a continuous time domain is
described using the Laplace transformation as follows:
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Equation GFLIB_ControllerPIrAW_Eq2
Transforming equation GFLIB_ControllerPIrAW_Eq2 into a discrete time domain leads
to the following equation:
Equation GFLIB_ControllerPIrAW_Eq3
where Kp is proportional gain, Ki is integral gain, Ts is the sampling period, u(k) is the
controller output, e(k) is the controller input error signal, CC1 and CC2 are the controller
coefficients calculated depending on the discretization method used, as shown in Table
5-42.
Table 5-42. Calculation of coefficients CC1 and CC2 using various discretization methods
Trapezoidal
Backward Rect.
Forward Rect.
CC1=
K p+K iT s/2
K p+K iT s
Kp
CC2=
-K p+K iT s/2
-K p
-K p+K iT s
In order to implement the discrete equation of the controller
GFLIB_ControllerPIrAW_Eq3 on the fixed point arithmetic platform, the maximal
values (scales) of input and output signals
• E MAX - maximal value of the controller input error signal
• U MAX - maximal value of the controller output signal
have to be known a priori. This is essential for correct casting of the physical signal
values into fixed point values [-1, 1).
Then the fractional representation [-1, 1) of both input and output signals is obtained as
follows:
Equation GFLIB_ControllerPIrAW_Eq4
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Function GFLIB_ControllerPIrAW_F32
Equation GFLIB_ControllerPIrAW_Eq5
The resulting controller discrete time domain equation in fixed point fractional
representation is therefore given as:
Equation GFLIB_ControllerPIrAW_Eq6
which can be rearranged into the following form:
Equation GFLIB_ControllerPIrAW_Eq7
where
Equation GFLIB_ControllerPIrAW_Eq8
are the controller coefficients adapted according to the input and output scale values. In
order to implement both coefficients as fractional numbers, both CC1 f and CC2 f must
reside in the fractional range [-1, 1). However, depending on values CC1, CC2, E MAX, U
MAX, the calculation of CC1 and CC2 may result in values outside this fractional range.
f
f
Therefore, a scaling of CC1 f, CC2 f is introduced as follows:
Equation GFLIB_ControllerPIrAW_Eq9
Equation GFLIB_ControllerPIrAW_Eq10
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The introduced scaling shift u16NShift is chosen such that both coefficients
f32CC1sc,f32CC2sc reside in the range [-1, 1). To simplify the implementation, this
scaling shift is chosen to be a power of 2, so the final scaling is a simple shift operation.
Moreover, the scaling shift cannot be a negative number, so the operation of scaling is
always to scale numbers with an absolute value larger than 1 down to fit in the range [-1,
1).
Equation GFLIB_ControllerPIrAW_Eq11
The final, scaled, fractional equation of the recurrent PI controller on a 32-bit fixed point
platform is therefore implemented as follows:
Equation GFLIB_ControllerPIrAW_Eq12
where:
•
•
•
•
•
u f(k) - fractional representation [-1, 1) of the controller output
e f(k) - fractional representation [-1, 1) of the controller input (error)
f32CC1sc - fractional representation [-1, 1) of the 1st controller coefficient
f32CC2sc - fractional representation [-1, 1) of the 2nd controller coefficient
u16NShift - in range [0,31] - is chosen such that both coefficients f32CC1sc and
f32CC2sc are in the range [-1, 1)
The output signal limitation is implemented in this controller. The actual output u(k) is
bounded not to exceed the given limit values UpperLimit, LowerLimit. This is due to
either the bounded power of the actuator or to the physical constraints of the plant.
Equation GFLIB_ControllerPIrAW_Eq13
The bounds are described by a limitation element equation
GFLIB_ControllerPIrAW_Eq13. When the bounds are exceeded, the non-linear
saturation characteristic will take effect and influence the dynamic behavior. The
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Function GFLIB_ControllerPIrAW_F32
described limitation is implemented on the output sum. Therefore, if the limitation
occurs, the controller output is clipped to its bounds and the wind-up occurrence of the
accumulator is avoided by saturating the output sum.
Note
The input pointer must contain a valid address otherwise an
exception may occur (Data TLB Error, Data Storage,
Alignment, Machine Check).
All controller parameters and states can be reset during
declaration using the
GFLIB_CONTROLLER_PIAW_R_DEFAULT_F32 macro. As
the GFLIB_ControllerPIrAW_F32 also contains the internal
accumulator, the output result is saddled by cumulative error.
To enumerate the computation error in one calculation cycle,
the internal accumulator is not used for testing purposes and is
replaced by output from the previous calculation step of the
reference model. The anti-windup mechanism is implemented
based on the output limitation.
5.33.5 Re-entrancy
The function is re-entrant.
5.33.6 Code Example
#include "gflib.h"
tFrac32 f32InErr;
tFrac32 f32Output;
GFLIB_CONTROLLER_PIAW_R_T_F32 trMyPI = GFLIB_CONTROLLER_PIAW_R_DEFAULT_F32;
void main(void)
{
// input error = 0.25
f32InErr = FRAC32 (0.25);
// controller parameters
trMyPI.f32CC1sc
trMyPI.f32CC2sc
trMyPI.u16NShift
trMyPI.f32UpperLimit
trMyPI.f32LowerLimit
=
=
=
=
=
FRAC32
FRAC32
1;
FRAC32
FRAC32
(0.01);
(0.02);
(1.0);
(-1.0);
// output should be 0x00A3D70A
f32Output = GFLIB_ControllerPIrAW_F32 (f32InErr, &trMyPI);
// clearing of internal states
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trMyPI.f32Acc = (tFrac32)0;
trMyPI.f32InErrK1 = (tFrac32)0;
// output should be 0x00A3D70A
f32Output = GFLIB_ControllerPIrAW (f32InErr, &trMyPI, F32);
//
//
//
//
##############################################################
Available only if 32-bit fractional implementation selected
as default
##############################################################
// clearing of internal states
trMyPI.f32Acc = (tFrac32)0;
trMyPI.f32InErrK1 = (tFrac32)0;
}
// output should be 0x00A3D70A
f32Output = GFLIB_ControllerPIrAW (f32InErr, &trMyPI);
5.34 Function GFLIB_ControllerPIrAW_F16
This function calculates a standard recurrent form of the Proportional-Integral controller,
with integral anti-windup.
5.34.1 Declaration
tFrac16 GFLIB_ControllerPIrAW_F16(tFrac16 f16InErr, GFLIB_CONTROLLER_PIAW_R_T_F16 *const
pParam);
5.34.2 Arguments
Table 5-43. GFLIB_ControllerPIrAW_F16 arguments
Type
tFrac16
Name
f16InErr
GFLIB_CONTROLLER pParam
_PIAW_R_T_F16
*const
Direction
Description
input
Input error signal to the controller is a 16-bit number
normalized between [-1, 1).
input,
output
Pointer to the controller parameters structure.
5.34.3 Return
The function returns a 16-bit value in fractional format 1.16, representing the signal to be
applied to the controlled system so that the input error is forced to zero.
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Function GFLIB_ControllerPIrAW_F16
5.34.4 Description
The function GFLIB_ControllerPIrAW calculates a standard recurrent form of the
Proportional-Integral controller, with integral anti-windup.
The continuous time domain representation of the PI controller is defined as:
Equation GFLIB_ControllerPIrAW_Eq1
The transfer function for this kind of PI controller, in a continuous time domain is
described using the Laplace transformation as follows:
Equation GFLIB_ControllerPIrAW_Eq2
Transforming equation GFLIB_ControllerPIrAW_Eq2 into a discrete time domain leads
to the following equation:
Equation GFLIB_ControllerPIrAW_Eq3
where Kp is proportional gain, Ki is integral gain, Ts is the sampling period, u(k) is the
controller output, e(k) is the controller input error signal, CC1 and CC2 are the controller
coefficients calculated depending on the discretization method used, as shown in Table
5-44.
Table 5-44. Calculation of coefficients CC1 and CC2 using various discretization methods
Trapezoidal
Backward Rect.
Forward Rect.
CC1=
K p+K iT s/2
K p+K iT s
Kp
CC2=
-K p+K iT s/2
-K p
-K p+K iT s
In order to implement the discrete equation of the controller
GFLIB_ControllerPIrAW_Eq3 on the fixed point arithmetic platform, the maximal
values (scales) of input and output signals
• E MAX - maximal value of the controller input error signal
• U MAX - maximal value of the controller output signal
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have to be known a priori. This is essential for correct casting of the physical signal
values into fixed point values [-1, 1).
Then the fractional representation [-1, 1) of both input and output signals is obtained as
follows:
Equation GFLIB_ControllerPIrAW_Eq4
Equation GFLIB_ControllerPIrAW_Eq5
The resulting controller discrete time domain equation in fixed point fractional
representation is therefore given as:
Equation GFLIB_ControllerPIrAW_Eq6
which can be rearranged into the following form:
Equation GFLIB_ControllerPIrAW_Eq7
where
Equation GFLIB_ControllerPIrAW_Eq8
are the controller coefficients adapted according to the input and output scale values. In
order to implement both coefficients as fractional numbers, both CC1 f and CC2 f must
reside in the fractional range [-1, 1). However, depending on values CC1, CC2, E MAX, U
MAX , the calculation of CC1 and CC2 may result in values outside this fractional
f
f
range. Therefore, a scaling of CC1 f, CC2 f is introduced as follows:
Automotive Math and Motor Control Library Set for NXP MPC560xB devices, Rev. 7
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Function GFLIB_ControllerPIrAW_F16
Equation GFLIB_ControllerPIrAW_Eq9
Equation GFLIB_ControllerPIrAW_Eq10
The introduced scaling shift u16NShift is chosen such that both coefficients
f16CC1sc,f16CC2sc reside in the range [-1, 1). To simplify the implementation, this
scaling shift is chosen to be a power of 2, so the final scaling is a simple shift operation.
Moreover, the scaling shift cannot be a negative number, so the operation of scaling is
always to scale numbers with an absolute value larger than 1 down to fit in the range [-1,
1).
Equation GFLIB_ControllerPIrAW_Eq11
The final, scaled, fractional equation of the recurrent PI controller on a 16-bit fixed point
platform is therefore implemented as follows:
Equation GFLIB_ControllerPIrAW_Eq12
where:
•
•
•
•
•
u f(k) - fractional representation [-1, 1) of the controller output
e f(k) - fractional representation [-1, 1) of the controller input (error)
f16CC1sc - fractional representation [-1, 1) of the 1st controller coefficient
f16CC2sc - fractional representation [-1, 1) of the 2nd controller coefficient
u16NShift - in range [0,15] - is chosen such that both coefficients f16CC1sc and
f16CC2sc are in the range [-1, 1)
The output signal limitation is implemented in this controller. The actual output u(k) is
bounded not to exceed the given limit values UpperLimit, LowerLimit. This is due to
either the bounded power of the actuator or to the physical constraints of the plant.
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Equation GFLIB_ControllerPIrAW_Eq13
The bounds are described by a limitation element equation
GFLIB_ControllerPIrAW_Eq13. When the bounds are exceeded, the non-linear
saturation characteristic will take effect and influence the dynamic behavior. The
described limitation is implemented on the output sum. Therefore, if the limitation
occurs, the controller output is clipped to its bounds and the wind-up occurrence of the
accumulator is avoided by saturating the output sum.
Note
The input pointer must contain a valid address otherwise an
exception may occur (Data TLB Error, Data Storage,
Alignment, Machine Check).
All controller parameters and states can be reset during
declaration using the
GFLIB_CONTROLLER_PIAW_R_DEFAULT_F16 macro. As
the GFLIB_ControllerPIrAW_F16 also contains the internal
accumulator, the output result is saddled by cumulative error.
To enumerate the computation error in one calculation cycle,
the internal accumulator is not used for testing purposes and is
replaced by output from the previous calculation step of the
reference model. To eliminate the calculation error the
GFLIB_ControllerPIrAW_F16 uses the 32-bit wide internal
accumulator. The anti-windup mechanism is implemented
based on the output limitation.
5.34.5 Re-entrancy
The function is re-entrant.
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Function GFLIB_Cos_F32
5.34.6 Code Example
#include "gflib.h"
tFrac16 f16InErr;
tFrac16 f16Output;
GFLIB_CONTROLLER_PIAW_R_T_F16 trMyPI = GFLIB_CONTROLLER_PIAW_R_DEFAULT_F16;
void main(void)
{
// input error = 0.25
f16InErr = FRAC16 (0.25);
// controller parameters
trMyPI.f16CC1sc
trMyPI.f16CC2sc
trMyPI.u16NShift
trMyPI.f16UpperLimit
trMyPI.f16LowerLimit
=
=
=
=
=
FRAC16
FRAC16
1;
FRAC16
FRAC16
(0.01);
(0.02);
(1.0);
(-1.0);
// output should be 0x00A3
f16Output = GFLIB_ControllerPIrAW_F16 (f16InErr, &trMyPI);
// clearing of internal states
trMyPI.f32Acc = (tFrac32)0;
trMyPI.f16InErrK1 = (tFrac16)0;
// output should be 0x00A3
f16Output = GFLIB_ControllerPIrAW (f16InErr, &trMyPI, F16);
//
//
//
//
##############################################################
Available only if 16-bit fractional implementation selected
as default
##############################################################
// clearing of internal states
trMyPI.f32Acc = (tFrac32)0;
trMyPI.f16InErrK1 = (tFrac16)0;
}
// output should be 0x00A3
f16Output = GFLIB_ControllerPIrAW (f16InErr, &trMyPI);
5.35 Function GFLIB_Cos_F32
This function implements polynomial approximation of cosine function.
5.35.1 Declaration
tFrac32 GFLIB_Cos_F32(tFrac32 f32In, const GFLIB_COS_T_F32 *const pParam);
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5.35.2 Arguments
Table 5-45. GFLIB_Cos_F32 arguments
Type
Name
Direction
Description
tFrac32
f32In
input
Input argument is a 32-bit number that contains an angle in
radians between [- π, π) normalized between [-1, 1).
const
GFLIB_COS_T_F32
*const
pParam
input
Pointer to an array of Taylor coefficients.
5.35.3 Return
The function returns the cos of the input argument as a fixed point 32-bit number,
normalized between [-1, 1).
5.35.4 Description
The GFLIB_Cos_F32 function provides a computational method for calculation of a
standard trigonometric cosine function cos(x), using the 9th order Taylor polynomial
approximation of the sine function. The following two equations describe the chosen
approach of calculating the cosine function:
Equation GFLIB_Cos_Eq1
Equation GFLIB_Cos_Eq2
The 9th order polynomial approximation is chosen as sufficient an order to achieve the
best ratio between calculation accuracy and speed of calculation. Accuracy criterion is to
have the output error within 3LSB on the upper 16 bits of the 32-bit result.
Because the GFLIB_Cos_F32 function is implemented with consideration to fixed point
fractional arithmetic, all variables are normalized to fit into the [-1, 1) range. Therefore,
in order to cast the fractional value of the input angle f32In [-1, 1) into the correct range
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Function GFLIB_Cos_F32
[- π, π), the input f32In must be multiplied by π. So, the fixed point fractional
implementation of the GFLIB_Sin_F32 function, using optimized 9th order Taylor
approximation, is given as follows:
Equation GFLIB_Cos_Eq3
The 9th order polynomial approximation of the sine function has a very good accuracy in
the range [- π/2, π/2) of the argument, but in wider ranges the calculation error quickly
increases. To minimize the error without having to use a higher order polynomial, the
symmetry of the sine function sin(x) = sin( π - x) is utilized. Therefore, the input
argument is transferred to be always in the range [- π/2, π/2) and the Taylor polynomial is
calculated only in the range of the argument [- π/2, π/2).
To make calculations more precise, the given argument value f32In (that is to be
transferred into the range [-0.5, 0.5) due to the sine function symmetry) is shifted by 1 bit
to the left (multiplied by 2). Then, the value of f32In 2, used in the calculations, is in the
range [-1, 1) instead of [-0.25, 0.25]. Shifting the input value by 1 bit to the left will
increase the accuracy of the calculated sin( π * f32In) function. Implementing such a
scale on the approximation function described by equation GFLIB_Cos_Eq2, results in
the following:
Equation GFLIB_Cos_Eq4
Equation GFLIB_Cos_Eq3 can be further rewritten into the following form:
Equation GFLIB_Cos_Eq5
where a 1...a 5 are coefficients of the approximation polynomial, which are calculated as
follows (represented as 32-bit signed fractional numbers):
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Equation GFLIB_Cos_Eq6
Therefore, the resulting equation has the following form:
Equation GFLIB_Cos_Eq7
Figure 5-17 depicts a floating point cosine function generated from Matlab and the
approximated value of the cosine function obtained from GFLIB_Cos_F32, plus their
difference. The course of calculation accuracy as a function of the input angle can be
observed from this figure.
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Function GFLIB_Cos_F32
Figure 5-17. cos(x) vs. GFLIB_Cos(f32In)
Note
The input pointer must contain a valid address otherwise an
exception may occur (Data TLB Error, Data Storage,
Alignment, Machine Check).
The input angle (f32In) is normalized into the range [-1, 1). The
function call is slightly different from common approach in the
library set. The function can be called in three different ways:
• With implementation postfix (i.e. GFLIB_Cos_F32(f32In,
&pParam)), where the &pParam is pointer to
approximation coefficients. In case the default
approximation coefficients are used, the &pParam must be
replaced with GFLIB_COS_DEFAULT_F32 symbol. The
&pParam parameter is mandatory.
• With additional implementation parameter (i.e.
GFLIB_Cos(f32In, &pParam, F32), where the &pParam is
pointer to approximation coefficients. In case the default
approximation coefficients are used, the &pParam must be
replaced with GFLIB_COS_DEFAULT_F32 symbol. The
&pParam parameter is mandatory.
• With preselected default implementation (i.e.
GFLIB_Cos(f32In, &pParam), where &pParam is pointer
to approximation coefficients. The &pParam parameter is
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optional and in case it is not used, the default
GFLIB_COS_DEFAULT_F32 approximation coefficients
are used.
5.35.5 Re-entrancy
The function is re-entrant.
5.35.6 Code Example
#include "gflib.h"
tFrac32 f32Angle;
tFrac32 f32Output;
void main(void)
{
// input angle = 0.25 => pi/4
f32Angle = FRAC32 (0.25);
// output should be 0x5A827E94
f32Output = GFLIB_Cos_F32 (f32Angle, GFLIB_COS_DEFAULT_F32);
// output should be 0x5A827E94
f32Output = GFLIB_Cos (f32Angle, GFLIB_COS_DEFAULT_F32, F32);
//
//
//
//
}
##############################################################
Available only if 32-bit fractional implementation selected
as default
##############################################################
// output should be 0x5A827E94
f32Output = GFLIB_Cos (f32Angle);
5.36 Function GFLIB_Cos_F16
This function implements polynomial approximation of cosine function.
5.36.1 Declaration
tFrac16 GFLIB_Cos_F16(tFrac16 f16In, const GFLIB_COS_T_F16 *const pParam);
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Function GFLIB_Cos_F16
5.36.2 Arguments
Table 5-46. GFLIB_Cos_F16 arguments
Type
Name
Direction
Description
tFrac16
f16In
input
Input argument is a 16-bit number that contains an angle in
radians between [- π, π) normalized between [-1, 1).
const
GFLIB_COS_T_F16
*const
pParam
input
Pointer to an array of Taylor coefficients.
5.36.3 Return
The function returns the cos of the input argument as a fixed point 16-bit number,
normalized between [-1, 1).
5.36.4 Description
The GFLIB_Cos_F16 function provides a computational method for calculation of a
standard trigonometric cosine function cos(x), using the 7th order Taylor polynomial
approximation of the sine function. The following two equations describe the chosen
approach of calculating the cosine function:
Equation GFLIB_Cos_Eq1
Equation GFLIB_Cos_Eq2
The 7th order polynomial approximation is chosen as sufficient an order to achieve the
best ratio between calculation accuracy and speed of calculation.
Because the GFLIB_Cos_F16 function is implemented with consideration to fixed point
fractional arithmetic, all variables are normalized to fit into the [-1, 1) range. Therefore,
in order to cast the fractional value of the input angle f16In [-1, 1) into the correct range
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[- π, π ), the input f16In must be multiplied by π. So, the fixed point fractional
implementation of the GFLIB_Sin_F16 function, using 9th order Taylor approximation,
is given as follows:
Equation GFLIB_Cos_Eq3
The 7th order polynomial approximation of the sine function has a good accuracy in the
range [- π/2, π/2) of the argument, but in wider ranges the calculation error quickly
increases. To minimize the error without having to use a higher order polynomial, the
symmetry of the sine function sin(x) = sin( π - x) is utilized. Therefore, the input
argument is transferred to be always in the range [- π/2, π/2) and the Taylor polynomial is
calculated only in the range of the argument [- π/2, π/2).
To make calculations more precise, the given argument value f16In (that is to be
transferred into the range [-0.5,0.5) due to the sine function symmetry) is shifted by 1 bit
to the left (multiplied by 2). Then, the value of f16In 2, used in the calculations, is in the
range [-1, 1) instead of [-0.25, 0.25]. Shifting the input value by 1 bit to the left will
increase the accuracy of the calculated sin( π * f16In) function. Implementing such a
scale on the approximation function described by equation GFLIB_Cos_Eq2, results in
the following:
Equation GFLIB_Cos_Eq4
Equation GFLIB_Cos_Eq3 can be further rewritten into the following form:
Equation GFLIB_Cos_Eq5
where a 1...a 5 are coefficients of the approximation polynomial, which are calculated as
follows (represented as 16-bit signed fractional numbers):
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Function GFLIB_Cos_F16
Equation GFLIB_Cos_Eq6
Therefore, the resulting equation has the following form:
Equation GFLIB_Cos_Eq7
Figure 5-18 depicts a floating point cosine function generated from Matlab and the
approximated value of the cosine function obtained from GFLIB_Cos_F16, plus their
difference. The course of calculation accuracy as a function of the input angle can be
observed from this figure.
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Figure 5-18. cos(x) vs. GFLIB_Cos(f16In)
Note
The input pointer must contain a valid address otherwise an
exception may occur (Data TLB Error, Data Storage,
Alignment, Machine Check).
The input angle (f16In) is normalized into the range [-1, 1). The
function call is slightly different from common approach in the
library set. The function can be called in three different ways:
• With implementation postfix (i.e. GFLIB_Cos_F16(f16In,
&pParam)), where the &pParam is pointer to
approximation coefficients. In case the default
approximation coefficients are used, the &pParam must be
replaced with GFLIB_COS_DEFAULT_F16 symbol. The
&pParam parameter is mandatory.
• With additional implementation parameter (i.e.
GFLIB_Cos(f16In, &pParam, F16), where the &pParam is
pointer to approximation coefficients. In case the default
approximation coefficients are used, the &pParam must be
replaced with GFLIB_COS_DEFAULT_F16 symbol. The
&pParam parameter is mandatory.
• With preselected default implementation (i.e.
GFLIB_Cos(f16In, &pParam), where the &pParam is
pointer to approximation coefficients. The &pParam
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Function GFLIB_Hyst_F32
parameter is optional and in case it is not used, the default
GFLIB_COS_DEFAULT_F16 approximation coefficients
are used.
5.36.5 Re-entrancy
The function is re-entrant.
5.36.6 Code Example
#include "gflib.h"
tFrac16 f16Angle;
tFrac16 f16Output;
void main(void)
{
// input angle = 0.25 => pi/4
f16Angle = FRAC16 (0.25);
// output should be 0x5A82
f16Output = GFLIB_Cos_F16 (f16Angle, GFLIB_COS_DEFAULT_F16);
// output should be 0x5A82
f16Output = GFLIB_Cos (f16Angle, GFLIB_COS_DEFAULT_F16, F16);
//
//
//
//
}
##############################################################
Available only if 16-bit fractional implementation selected
as default
##############################################################
// output should be 0x5A82
f16Output = GFLIB_Cos (f16Angle);
5.37 Function GFLIB_Hyst_F32
This function implements the hysteresis functionality.
5.37.1 Declaration
tFrac32 GFLIB_Hyst_F32(tFrac32 f32In, GFLIB_HYST_T_F32 *const pParam);
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5.37.2 Arguments
Table 5-47. GFLIB_Hyst_F32 arguments
Type
Name
Direction
Description
tFrac32
f32In
input
Input signal in the form of a 32-bit fixed point number,
normalized between [-1, 1).
GFLIB_HYST_T_F32
*const
pParam
input,
output
Pointer to the structure with parameters and states of the
hysteresis function. Arguments of the structure contain fixed
point 32-bit values, normalized between [-1, 1).
5.37.3 Return
The function returns the value of the hysteresis output, which is equal to either
f32OutValOn or f32OutValOff depending on the value of the input and the state of the
function output in the previous calculation step. The output value is interpreted as a fixed
point 32-bit number, normalized between [-1, 1).
5.37.4 Description
The GFLIB_Hyst function provides a computational method for the calculation of a
hysteresis (relay) function. The function switches the output between the two predefined
values stored in the f32OutValOn and f32OutValOff members of structure
GFLIB_HYST_T_F32. When the value of the input is higher than the upper threshold
f32HystOn, then the output value is equal to f32OutValOn. On the other hand, when the
input value is lower than the lower threshold f32HystOff, then the output value is equal to
f32OutValOff. When the input value is between these two threshold values then the
output retains its value (the previous state).
Equation GFLIB_Hyst_Eq1
A graphical description of GFLIB_Hyst functionality is shown in Figure 5-19.
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Function GFLIB_Hyst_F32
Figure 5-19. Hysteresis function
Note
The input pointer must contain a valid address otherwise an
exception may occur (Data TLB Error, Data Storage,
Alignment, Machine Check).
CAUTION
For correct functionality, the threshold f32HystOn value must
be greater than the f32HystOff value.
Note
All parameters and states used by the function can be reset
during declaration using the GFLIB_HYST_DEFAULT_F32
macro.
5.37.5 Re-entrancy
The function is re-entrant.
5.37.6 Code Example
#include "gflib.h"
tFrac32 f32In;
tFrac32 f32Out;
GFLIB_HYST_T_F32 f32trMyHyst = GFLIB_HYST_DEFAULT_F32;
void main(void)
{
// Setting parameters for hysteresis
f32trMyHyst.f32HystOn = FRAC32 (0.1289);
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f32trMyHyst.f32HystOff = FRAC32 (-0.3634);
f32trMyHyst.f32OutValOn = FRAC32 (0.589);
f32trMyHyst.f32OutValOff = FRAC32 (-0.123);
f32trMyHyst.f32OutState = FRAC32 (-0.3333);
// input value = -0.41115
f32In = FRAC32 (-0.41115);
// output should be 0x8FBE76C8 ~ FRAC32(-0.123)
f32Out = GFLIB_Hyst_F32 (f32In,&f32trMyHyst);
// output should be 0x8FBE76C8 ~ FRAC32(-0.123)
f32trMyHyst.f32OutState = FRAC32 (0);
f32Out = GFLIB_Hyst (f32In, &f32trMyHyst, F32);
//
//
//
//
}
##############################################################
Available only if 32-bit fractional implementation selected
as default
##############################################################
// output should be 0x8FBE76C8 ~ FRAC32(-0.123)
f32trMyHyst.f32OutState = FRAC32 (0);
f32Out = GFLIB_Hyst (f32In, &f32trMyHyst);
5.38 Function GFLIB_Hyst_F16
This function implements the hysteresis functionality.
5.38.1 Declaration
tFrac16 GFLIB_Hyst_F16(tFrac16 f16In, GFLIB_HYST_T_F16 *const pParam);
5.38.2 Arguments
Table 5-48. GFLIB_Hyst_F16 arguments
Type
Name
Direction
Description
tFrac16
f16In
input
Input signal in the form of a 16-bit fixed point number,
normalized between [-1, 1).
GFLIB_HYST_T_F16
*const
pParam
input,
output
Pointer to the structure with parameters and states of the
hysteresis function. Arguments of the structure contain fixed
point 16-bit values, normalized between [-1, 1).
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Function GFLIB_Hyst_F16
5.38.3 Return
The function returns the value of the hysteresis output, which is equal to either
f16OutValOn or f16OutValOff depending on the value of the input and the state of the
function output in the previous calculation step. The output value is interpreted as a fixed
point 16-bit number, normalized between [-1, 1).
5.38.4 Description
The GFLIB_Hyst function provides a computational method for the calculation of a
hysteresis (relay) function. The function switches the output between the two predefined
values stored in the f16OutValOn and f16OutValOff members of structure
GFLIB_HYST_T_F16. When the value of the input is higher than the upper threshold
f16HystOn, then the output value is equal to f16OutValOn. On the other hand, when the
input value is lower than the lower threshold f16HystOff, then the output value is equal to
f16OutValOff. When the input value is between these two threshold values then the
output retains its value (the previous state).
Equation GFLIB_Hyst_Eq1
A graphical description of GFLIB_Hyst functionality is shown in Figure 5-20.
Figure 5-20. Hysteresis function
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Note
The input pointer must contain a valid address otherwise an
exception may occur (Data TLB Error, Data Storage,
Alignment, Machine Check).
CAUTION
For correct functionality, the threshold f16HystOn value must
be greater than the f16HystOff value.
Note
All parameters and states used by the function can be reset
during declaration using the GFLIB_HYST_DEFAULT_F16
macro.
5.38.5 Re-entrancy
The function is re-entrant.
5.38.6 Code Example
#include "gflib.h"
tFrac16 f16In;
tFrac16 f16Out;
GFLIB_HYST_T_F16 f16trMyHyst = GFLIB_HYST_DEFAULT_F16;
void main(void)
{
// Setting parameters for hysteresis
f16trMyHyst.f16HystOn = FRAC16 (0.1289);
f16trMyHyst.f16HystOff = FRAC16 (-0.3634);
f16trMyHyst.f16OutValOn = FRAC16 (0.589);
f16trMyHyst.f16OutValOff = FRAC16 (-0.123);
f16trMyHyst.f16OutState = FRAC16 (-0.3333);
// input value = -0.41115
f16In = FRAC16 (-0.41115);
// output should be 0x8FBE ~ FRAC16(-0.123)
f16Out = GFLIB_Hyst_F16 (f16In,&f16trMyHyst);
// output should be 0x8FBE ~ FRAC16(-0.123)
f16trMyHyst.f16OutState = FRAC16 (0);
f16Out = GFLIB_Hyst (f16In, &f16trMyHyst, F16);
//
//
//
//
}
##############################################################
Available only if 16-bit fractional implementation selected
as default
##############################################################
// output should be 0x8FBE ~ FRAC16(-0.123)
f16trMyHyst.f16OutState = FRAC16 (0);
f16Out = GFLIB_Hyst (f16In, &f16trMyHyst);
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Function GFLIB_IntegratorTR_F32
5.39 Function GFLIB_IntegratorTR_F32
The function calculates a discrete implementation of the integrator (sum), discretized
using a trapezoidal (Bilinear) transformation with overflow on range boundaries.
5.39.1 Declaration
tFrac32 GFLIB_IntegratorTR_F32(tFrac32 f32In, GFLIB_INTEGRATOR_TR_T_F32 *const pParam);
5.39.2 Arguments
Table 5-49. GFLIB_IntegratorTR_F32 arguments
Type
tFrac32
Name
f32In
GFLIB_INTEGRATOR_ pParam
TR_T_F32 *const
Direction
Description
input
Input argument to be integrated.
input,
output
Pointer to the integrator parameters structure.
5.39.3 Return
The function returns a 32-bit value in format Q1.31, which represents the actual
integrated value of the input signal with overflow on range boundaries.
5.39.4 Description
The function GFLIB_IntegratorTR_F32 implements a discrete integrator using
trapezoidal (Bilinear) transformation with overflow on range boundaries.
The continuous time domain representation of the integrator is defined as:
Equation GFLIB_IntegratorTR_Eq1
The transfer function for this integrator, in a continuous time domain, is described using
the Laplace transformation as follows:
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Equation GFLIB_IntegratorTR_Eq2
Transforming equation GFLIB_IntegratorTR_Eq2 into a digital time domain using
Bilinear transformation, leads to the following transfer function:
Equation GFLIB_IntegratorTR_Eq3
where T s is the sampling period of the system. The discrete implementation of the digital
transfer function GFLIB_IntegratorTR_Eq3 is as follows:
Equation GFLIB_IntegratorTR_Eq4
Considering fractional maths implementation, the integrator input and output maximal
values (scales) must be known. Then the discrete implementation is given as follows:
Equation GFLIB_IntegratorTR_Eq5
where E MAX is the input scale and U MAX is the output scale. Then integrator constant
C1 is defined as:
Equation GFLIB_IntegratorTR_Eq6
In order to implement the discrete form integrator as in GFLIB_IntegratorTR_Eq5 on a
fixed point platform, the value of C1 f coefficient must reside in a the fractional range
[-1,1). Therefore, scaling must be introduced as follows:
Equation GFLIB_IntegratorTR_Eq7
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Function GFLIB_IntegratorTR_F32
The introduced scaling is chosen such that coefficient f32C1 fits into fractional range
[-1,1). To simplify the implementation, this scaling is chosen to be a power of 2, so the
final scaling is a simple shift operation using the u16NShift variable. Hence, the shift is
calculated as:
Equation GFLIB_IntegratorTR_Eq8
If the output exceeds the fractional range [-1,1), an overflow occurs. This behavior allows
continual integration of an angular velocity of a rotor to obtain the actual rotor position,
assuming the output range corresponds to one complete revolution.
Note
The input pointer must contain a valid address otherwise an
exception may occur (Data TLB Error, Data Storage,
Alignment, Machine Check).
All parameters and states used by the function can be reset
during declaration using the
GFLIB_INTEGRATOR_TR_DEFAULT_F32 macro.
The specified accuracy of the function is not guaranteed in
cases when any of the terms in GFLIB_IntegratorTR_Eq5
overflows.
5.39.5 Re-entrancy
The function is re-entrant.
5.39.6 Code Example
#include "gflib.h"
tFrac32 f32In;
tFrac32 f32Out;
// Definition of one integrator instance
GFLIB_INTEGRATOR_TR_T_F32 trMyIntegrator = GFLIB_INTEGRATOR_TR_DEFAULT_F32;
void main(void)
{
// Setting parameters for integrator, Ts = 100e-4, E_MAX=U_MAX=1
trMyIntegrator.f32C1
= FRAC32 (100e-4/2);
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trMyIntegrator.u16NShift = (tU16)0;
// input value = 0.5
f32In = FRAC32 (0.5);
// output should be 0x0051EB85
f32Out = GFLIB_IntegratorTR_F32 (f32In, &trMyIntegrator);
// clearing of the internal states
trMyIntegrator.f32State = (tFrac32)0;
trMyIntegrator.f32InK1 = (tFrac32)0;
// output should be 0x0051EB85
f32Out = GFLIB_IntegratorTR (f32In, &trMyIntegrator, F32);
//
//
//
//
##############################################################
Available only if 32-bit fractional implementation selected
as default
##############################################################
// clearing of the internal states
trMyIntegrator.f32State = (tFrac32)0;
trMyIntegrator.f32InK1 = (tFrac32)0;
}
// output should be 0x0051EB85
f32Out = GFLIB_IntegratorTR (f32In, &trMyIntegrator);
5.40 Function GFLIB_IntegratorTR_F16
The function calculates a discrete implementation of the integrator (sum), discretized
using a trapezoidal (Bilinear) transformation with overflow on range boundaries.
5.40.1 Declaration
tFrac16 GFLIB_IntegratorTR_F16(tFrac16 f16In, GFLIB_INTEGRATOR_TR_T_F16 *const pParam);
5.40.2 Arguments
Table 5-50. GFLIB_IntegratorTR_F16 arguments
Type
tFrac16
Name
f16In
GFLIB_INTEGRATOR_ pParam
TR_T_F16 *const
Direction
Description
input
Input argument to be integrated.
input,
output
Pointer to the integrator parameters structure.
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Function GFLIB_IntegratorTR_F16
5.40.3 Return
The function returns a 16-bit value in format Q1.15, which represents the actual
integrated value of the input signal with overflow on range boundaries.
5.40.4 Description
The function GFLIB_IntegratorTR_F16 implements a discrete integrator using
trapezoidal (Bilinear) transformation with overflow on range boundaries.
The continuous time domain representation of the integrator is defined as:
Equation GFLIB_IntegratorTR_Eq1
The transfer function for this integrator, in a continuous time domain, is described using
the Laplace transformation as follows:
Equation GFLIB_IntegratorTR_Eq2
Transforming equation GFLIB_IntegratorTR_Eq2 into a digital time domain using
Bilinear transformation, leads to the following transfer function:
Equation GFLIB_IntegratorTR_Eq3
where T s is the sampling period of the system. The discrete implementation of the digital
transfer function GFLIB_IntegratorTR_Eq3 is as follows:
Equation GFLIB_IntegratorTR_Eq4
Considering fractional maths implementation, the integrator input and output maximal
values (scales) must be known. Then the discrete implementation is given as follows:
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Equation GFLIB_IntegratorTR_Eq5
where E MAX is the input scale and U MAX is the output scale. Then integrator constant
C1 is defined as:
Equation GFLIB_IntegratorTR_Eq6
In order to implement the discrete form integrator as in GFLIB_IntegratorTR_Eq5 on a
fixed point platform, the value of C1 f coefficient must reside in a the fractional range
[-1,1). Therefore, scaling must be introduced as follows:
Equation GFLIB_IntegratorTR_Eq7
The introduced scaling is chosen such that coefficient f16C1 fits into fractional range
[-1,1). To simplify the implementation, this scaling is chosen to be a power of 2, so the
final scaling is a simple shift operation using the u16NShift variable. Hence, the shift is
calculated as:
Equation GFLIB_IntegratorTR_Eq8
If the output exceeds the fractional range [-1,1), an overflow occurs. This behavior allows
continual integration of an angular velocity of a rotor to obtain the actual rotor position,
assuming the output range corresponds to one complete revolution.
Note
The input pointer must contain a valid address otherwise an
exception may occur (Data TLB Error, Data Storage,
Alignment, Machine Check).
All parameters and states used by the function can be reset
during declaration using the
GFLIB_INTEGRATOR_TR_DEFAULT_F16 macro.
The specified accuracy of the function is not guaranteed in
cases when any of the terms in GFLIB_IntegratorTR_Eq5
overflows.
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Function GFLIB_Limit_F32
5.40.5 Re-entrancy
The function is re-entrant.
5.40.6 Code Example
#include "gflib.h"
tFrac16 f16In;
tFrac16 f16Out;
// Definition of one integrator instance
GFLIB_INTEGRATOR_TR_T_F16 trMyIntegrator = GFLIB_INTEGRATOR_TR_DEFAULT_F16;
void main(void)
{
// Setting parameters for integrator, Ts = 100e-4, E_MAX=U_MAX=1
trMyIntegrator.f16C1
= FRAC16 (100e-4/2);
trMyIntegrator.u16NShift = (tU16)0;
// input value = 0.5
f16In = FRAC16 (0.5);
// output should be 0x0051
f16Out = GFLIB_IntegratorTR_F16 (f16In, &trMyIntegrator);
// clearing of the internal states
trMyIntegrator.f32State = (tFrac32)0;
trMyIntegrator.f16InK1 = (tFrac16)0;
// output should be 0x0051
f16Out = GFLIB_IntegratorTR (f16In, &trMyIntegrator, F16);
//
//
//
//
##############################################################
Available only if 16-bit fractional implementation selected
as default
##############################################################
// clearing of the internal states
trMyIntegrator.f32State = (tFrac32)0;
trMyIntegrator.f16InK1 = (tFrac16)0;
}
// output should be 0x0051
f16Out = GFLIB_IntegratorTR (f16In, &trMyIntegrator);
5.41 Function GFLIB_Limit_F32
This function tests whether the input value is within the upper and lower limits.
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5.41.1 Declaration
tFrac32 GFLIB_Limit_F32(tFrac32 f32In, const GFLIB_LIMIT_T_F32 *const pParam);
5.41.2 Arguments
Table 5-51. GFLIB_Limit_F32 arguments
Type
Name
Direction
Description
tFrac32
f32In
input
Input value.
const
GFLIB_LIMIT_T_F32
*const
pParam
input
Pointer to the limits structure.
5.41.3 Return
The input value in case the input value is below the limits, or the upper or lower limit if
the input value is above these limits.
5.41.4 Description
The GFLIB_Limit function tests whether the input value is within the upper and lower
limits. If so, the input value will be returned. If the input value is above the upper limit,
the upper limit will be returned. Similarly, if the input value is below the lower limit, the
lower limit will be returned.
The upper and lower limits can be found in the limits structure, supplied to the function
as a pointer pParam.
Note
The input pointer must contain a valid address otherwise an
exception may occur (Data TLB Error, Data Storage,
Alignment, Machine Check).
The function assumes that the upper limit f32UpperLimit is
greater than the lower limit f32LowerLimit. Otherwise, the
function returns an undefined value.
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Function GFLIB_Limit_F16
5.41.5 Re-entrancy
The function is re-entrant.
5.41.6 Code Example
#include "gflib.h"
tFrac32 f32In;
tFrac32 f32Out;
GFLIB_LIMIT_T_F32 f32trMyLimit = GFLIB_LIMIT_DEFAULT_F32;
void main(void)
{
// upper/lower limits
f32trMyLimit.f32UpperLimit = FRAC32 (0.5);
f32trMyLimit.f32LowerLimit = FRAC32 (-0.5);
// input value = 0.75
f32In = FRAC32 (0.75);
// output should be 0x40000000 ~ FRAC32(0.5)
f32Out = GFLIB_Limit_F32 (f32In, &f32trMyLimit);
// output should be 0x40000000 ~ FRAC32(0.5)
f32Out = GFLIB_Limit (f32In, &f32trMyLimit, F32);
//
//
//
//
}
##############################################################
Available only if 32-bit fractional implementation selected
as default
##############################################################
// output should be 0x40000000 ~ FRAC32(0.5)
f32Out = GFLIB_Limit (f32In, &f32trMyLimit);
5.42 Function GFLIB_Limit_F16
This function tests whether the input value is within the upper and lower limits.
5.42.1 Declaration
tFrac16 GFLIB_Limit_F16(tFrac16 f16In, const GFLIB_LIMIT_T_F16 *const pParam);
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5.42.2 Arguments
Table 5-52. GFLIB_Limit_F16 arguments
Type
Name
Direction
Description
tFrac16
f16In
input
Input value.
const
GFLIB_LIMIT_T_F16
*const
pParam
input
Pointer to the limits structure.
5.42.3 Return
The input value in case the input value is below the limits, or the upper or lower limit if
the input value is above these limits.
5.42.4 Description
The GFLIB_Limit function tests whether the input value is within the upper and lower
limits. If so, the input value will be returned. If the input value is above the upper limit,
the upper limit will be returned. Similarly, if the input value is below the lower limit, the
lower limit will be returned.
The upper and lower limits can be found in the limits structure, supplied to the function
as a pointer pParam.
Note
The input pointer must contain a valid address otherwise an
exception may occur (Data TLB Error, Data Storage,
Alignment, Machine Check).
The function assumes that the upper limit f16UpperLimit is
greater than the lower limit f16LowerLimit. Otherwise, the
function returns an undefined value.
5.42.5 Re-entrancy
The function is re-entrant.
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Function GFLIB_LowerLimit_F32
5.42.6 Code Example
#include "gflib.h"
tFrac16 f16In;
tFrac16 f16Out;
GFLIB_LIMIT_T_F16 f16trMyLimit = GFLIB_LIMIT_DEFAULT_F16;
void main(void)
{
// upper/lower limits
f16trMyLimit.f16UpperLimit = FRAC16 (0.5);
f16trMyLimit.f16LowerLimit = FRAC16 (-0.5);
// input value = 0.75
f16In = FRAC16 (0.75);
// output should be 0x4000 ~ FRAC16(0.5)
f16Out = GFLIB_Limit_F16 (f16In, &f16trMyLimit);
// output should be 0x4000 ~ FRAC16(0.5)
f16Out = GFLIB_Limit (f16In, &f16trMyLimit, F16);
//
//
//
//
}
##############################################################
Available only if 16-bit fractional implementation selected
as default
##############################################################
// output should be 0x4000 ~ FRAC16(0.5)
f16Out = GFLIB_Limit (f16In, &f16trMyLimit);
5.43 Function GFLIB_LowerLimit_F32
This function tests whether the input value is above the lower limit.
5.43.1 Declaration
tFrac32 GFLIB_LowerLimit_F32(tFrac32 f32In, const GFLIB_LOWERLIMIT_T_F32 *const pParam);
5.43.2 Arguments
Table 5-53. GFLIB_LowerLimit_F32 arguments
Type
tFrac32
Name
f32In
const
pParam
GFLIB_LOWERLIMIT_
T_F32 *const
Direction
Description
input
Input value.
input
Pointer to the limits structure.
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5.43.3 Return
The input value in case the input value is above the limit, or the lower limit if the input
value is below the limit.
5.43.4 Description
The function tests whether the input value is above the lower limit. If so, the input value
will be returned. Otherwise, if the input value is below the lower limit, the lower limit
will be returned.
The lower limit f32LowerLimit can be found in the limits structure, supplied to the
function as a pointer pParam.
Note
The input pointer must contain a valid address otherwise an
exception may occur (Data TLB Error, Data Storage,
Alignment, Machine Check).
5.43.5 Re-entrancy
The function is re-entrant.
5.43.6 Code Example
#include "gflib.h"
tFrac32 f32In;
tFrac32 f32Out;
GFLIB_LOWERLIMIT_T_F32 f32trMyLowerLimit = GFLIB_LOWERLIMIT_DEFAULT_F32;
void main(void)
{
// lower limit
f32trMyLowerLimit.f32LowerLimit = FRAC32 (0.5);
// input value = 0.75
f32In = FRAC32 (0.75);
// output should be 0x60000000 ~ FRAC32(0.75)
f32Out = GFLIB_LowerLimit_F32 (f32In,&f32trMyLowerLimit);
// output should be 0x60000000 ~ FRAC32(0.75)
f32Out = GFLIB_LowerLimit (f32In,&f32trMyLowerLimit,F32);
// ##############################################################
// Available only if 32-bit fractional implementation selected
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Function GFLIB_LowerLimit_F16
// as default
// ##############################################################
}
// output should be 0x60000000 ~ FRAC32(0.75)
f32Out = GFLIB_LowerLimit (f32In,&f32trMyLowerLimit);
5.44 Function GFLIB_LowerLimit_F16
This function tests whether the input value is above the lower limit.
5.44.1 Declaration
tFrac16 GFLIB_LowerLimit_F16(tFrac16 f16In, const GFLIB_LOWERLIMIT_T_F16 *const pParam);
5.44.2 Arguments
Table 5-54. GFLIB_LowerLimit_F16 arguments
Type
tFrac16
Name
f16In
const
pParam
GFLIB_LOWERLIMIT_
T_F16 *const
Direction
Description
input
Input value.
input
Pointer to the limits structure.
5.44.3 Return
The input value in case the input value is above the limit, or the lower limit if the input
value is below the limit.
5.44.4 Description
The function tests whether the input value is above the lower limit. If so, the input value
will be returned. Otherwise, if the input value is below the lower limit, the lower limit
will be returned.
The lower limit f32LowerLimit can be found in the limits structure, supplied to the
function as a pointer pParam.
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Note
The input pointer must contain a valid address otherwise an
exception may occur (Data TLB Error, Data Storage,
Alignment, Machine Check).
5.44.5 Re-entrancy
The function is re-entrant.
5.44.6 Code Example
#include "gflib.h"
tFrac16 f16In;
tFrac16 f16Out;
GFLIB_LOWERLIMIT_T_F16 f16trMyLowerLimit = GFLIB_LOWERLIMIT_DEFAULT_F16;
void main(void)
{
// lower limit
f16trMyLowerLimit.f16LowerLimit = FRAC16 (0.5);
// input value = 0.75
f16In = FRAC16 (0.75);
// output should be 0x6000 ~ FRAC16(0.75)
f16Out = GFLIB_LowerLimit_F16 (f16In,&f16trMyLowerLimit);
// output should be 0x6000 ~ FRAC16(0.75)
f16Out = GFLIB_LowerLimit (f16In,&f16trMyLowerLimit,F16);
//
//
//
//
}
##############################################################
Available only if 16-bit fractional implementation selected
as default
##############################################################
// output should be 0x6000 ~ FRAC16(0.75)
f16Out = GFLIB_LowerLimit (f16In,&f16trMyLowerLimit);
5.45 Function GFLIB_Lut1D_F32
This function implements the one-dimensional look-up table.
5.45.1 Declaration
tFrac32 GFLIB_Lut1D_F32(tFrac32 f32In, const GFLIB_LUT1D_T_F32 *const pParam);
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Function GFLIB_Lut1D_F32
5.45.2 Arguments
Table 5-55. GFLIB_Lut1D_F32 arguments
Type
Name
Direction
Description
tFrac32
f32In
input
The abscissa for which 1D interpolation is performed.
const
GFLIB_LUT1D_T_F32
*const
pParam
input
Pointer to the parameters structure with parameters of the
look-up table function.
5.45.3 Return
The interpolated value from the look-up table with 16-bit accuracy.
5.45.4 Description
The GFLIB_Lut1D_F32 function performs one dimensional linear interpolation over a
table of data. The data is assumed to represent a one dimensional function sampled at
equidistant points. The following interpolation formula is used:
Equation GFLIB_Lut1D_Eq1
where:
• y is the interpolated value
• y 1 and y 2 are the ordinate values at, respectively, the beginning and the end of the
interpolating interval
• x 1 and x 2 are the abscissa values at, respectively, the beginning and the end of the
interpolating interval
• the x is the input value provided to the function in the f32In argument
The interpolating intervals are defined in the table provided by the pf32Table member of
the parameters structure. The table contains ordinate values consecutively over the entire
interpolating range. The abscissa values are assumed to be defined implicitly by a single
interpolating interval length and a table index, while the interpolating index zero is the
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table element pointed to by the pf32Table parameter. The abscissa value is equal to the
multiplication of the interpolating index and the interpolating interval length. For
example, let's consider the following interpolating table:
Table 5-56. GFLIB_Lut1D example table
ordinate (y)
interpolating index
abscissa (x)
-0.5
-1
-1*(2 -1)
pf32Table{rarrow} 0.0
0
0*(2 -1)
0.25
1
1*(2 -1)
0.5
N/A
2*(2 -1)
The Table 5-56 contains 4 interpolating points (note four rows). The interpolating
interval length in this example is equal to 2 -1 . The pf32Table parameter points to the
second row, defining also the interpolating index 0. The x-coordinates of the interpolating
points are calculated in the right column.
It should be noted that the pf32Table pointer does not have to point to the start of the
memory area of ordinate values. Therefore, the interpolating index can be positive or
negative or, even, does not have to have zero in its range.
A special algorithm is used to make the computation efficient, however, under some
additional assumptions, as provided below:
• the values of the interpolated function are 32 bits long
• the length of each interpolating interval is equal to 2 -n, where n is an integer in the
range of 1, 2, ... 29
• the provided abscissa for interpolation is 32 bits long
The algorithm performs the following steps:
1. Compute the index representing the interval, in which the linear interpolation will be
performed:
Equation GFLIB_Lut1D_Eq2
where I is the interval index and the s Interval the shift amount provided in the
parameters structure as the member s32ShamIntvl. The operator >> represents the
binary arithmetic right shift.
2. Compute the abscissa offset within an interpolating interval:
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Function GFLIB_Lut1D_F32
Equation GFLIB_Lut1D_Eq3
where Δ{x} is the abscissa offset within an interval and the s Offset is the shift amount
provided in the parameters structure. The operators << and & represent, respectively,
the binary left shift and the bitwise logical conjunction. It should be noted that the
computation represents the extraction of some least significant bits of the x with the
sign bit cleared.
3. Compute the interpolated value by the linear interpolation between the ordinates read
from the table at the start and the end of the computed interval. The computed
abscissa offset is used for the linear interpolation.
Equation GFLIB_Lut1D_Eq4
where y, y 1 and y 2 are, respectively, the interpolated value, the ordinate at the start of
the interpolating interval, the ordinate at the end of the interpolating interval. The pTable
is the address provided in the parameters structure pParam->f32Table. It should be noted
that due to assumption of equidistant data points, division by the interval length is
avoided.
It should be noted that the computations are performed with a 16-bit accuracy. In
particular, the 16 least significant bits are ignored in all multiplications.
The shift amounts shall be provided in the parameters structure (pParam>u32ShamOffset). The address of the table with the data, the pTable, shall be defined by
the parameter structure member pParam->pf32Table.
The shift amounts, the s Interval and s Offset, can be computed with the following formulas:
Equation GFLIB_Lut1D_Eq5
where n is the integer defining the length of the interpolating interval in the range of -1,
-2, ... -29.
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The computation of the abscissa offset and the interval index can be viewed also in the
following way. The input abscissa value can be divided into two parts. The first n most
significant bits of the 32-bit word, after the sign bit, compose the interval index, in which
interpolation is performed. The rest of the bits form the abscissa offset within the
interpolating interval. This simple way to calculate the interpolating interval index and
the abscissa offset is the consequence of assuming that all interpolating interval lengths
equal 2 -n.
It should be noted that the input abscissa value can be positive or negative. If it is,
positive then the ordinate values are read as in the ordinary data array, that is, at or after
the data pointer provided in the parameters structure (pParam->pf32Table). However, if it
is negative, then the ordinate values are read from the memory, which is located behind
the pParam->pf32Table pointer.
Note
The input pointer must contain a valid address and the range of
the input abscissa values must fall within the range of the
interpolating data table otherwise an exception may occur (Data
TLB Error, Data Storage, Alignment, Machine Check).
The function performs a linear interpolation.
CAUTION
The function does not check whether the input abscissa value is
within the range allowed by the interpolating data table
pParam->pf32Table. If the computed interval index points to
data outside the provided data table, then the interpolation will
be computed with invalid data. The range of the input abscissa
value depends on the position of the pointer in the interpolating
data table. Sum of the absolute values of the lower and upper
border values is equal to the FRACT_MAX. For a better
understanding, please, see the extended code example.
5.45.5 Re-entrancy
The function is re-entrant.
5.45.6 Code Example
#include "gflib.h"
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Function GFLIB_Lut1D_F32
tFrac32 f32In;
tFrac32 f32Out;
GFLIB_LUT1D_T_F32 trf32MyLut1D = GFLIB_LUT1D_DEFAULT_F32;
tFrac32 pf32Table1D[9] = {FRAC32 (0.8),FRAC32 (0.1),FRAC32 (-0.2),FRAC32
(0.7),FRAC32 (0.2),FRAC32 (-0.3),FRAC32 (-0.8),FRAC32 (0.91),FRAC32 (0.99)};
void main(void)
{
// ####################################################################
// Pointer is located in the middle of the interpolating data table.
// ####################################################################
// setting parameters for Lut1D function
trf32MyLut1D.u32ShamOffset = (tU32)3;
trf32MyLut1D.pf32Table = &(pf32Table1D[4]);
// input vector = -0.5
f32In = FRAC32 (-0.5);
// output should be 0x66666666 ~ FRAC32(0.8)
f32Out = GFLIB_Lut1D_F32 (f32In,&trf32MyLut1D);
// output should be 0x66666666 ~ FRAC32(0.8)
f32Out = GFLIB_Lut1D (f32In,&trf32MyLut1D,F32);
// available only if 32-bit fractional implementation selected as default
// output should be 0x66666666 ~ FRAC32(0.8)
f32Out = GFLIB_Lut1D (f32In,&trf32MyLut1D);
// ####################################################################
// Pointer is located at the beginning of the interpolating data table.
// ####################################################################
// setting parameters for Lut1D function
trf32MyLut1D.u32ShamOffset = (tU32)3;
trf32MyLut1D.pf32Table = &(pf32Table1D[0]);
// input vector = 0
f32In = FRAC32 (0);
// output should be 0x66666666 ~ FRAC32(0.8)
f32Out = GFLIB_Lut1D_F32 (f32In,&trf32MyLut1D);
// output should be 0x66666666 ~ FRAC32(0.8)
f32Out = GFLIB_Lut1D (f32In,&trf32MyLut1D,F32);
// available only if 32-bit fractional implementation selected as default
// output should be 0x66666666 ~ FRAC32(0.8)
f32Out = GFLIB_Lut1D (f32In,&trf32MyLut1D);
// ####################################################################
// Pointer is located at the end of the interpolating data table.
// ####################################################################
// setting parameters for Lut1D function
trf32MyLut1D.u32ShamOffset = (tU32)3;
trf32MyLut1D.pf32Table = &(pf32Table1D[8]);
// input vector = -1
f32In = FRAC32 (-1);
// output should be 0x66666666 ~ FRAC32(0.8)
f32Out = GFLIB_Lut1D_F32 (f32In,&trf32MyLut1D);
// output should be 0x66666666 ~ FRAC32(0.8)
f32Out = GFLIB_Lut1D (f32In,&trf32MyLut1D,F32);
}
// available only if 32-bit fractional implementation selected as default
// output should be 0x66666666 ~ FRAC32(0.8)
f32Out = GFLIB_Lut1D (f32In,&trf32MyLut1D);
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5.46 Function GFLIB_Lut1D_F16
This function implements the one-dimensional look-up table.
5.46.1 Declaration
tFrac16 GFLIB_Lut1D_F16(tFrac16 f16In, const GFLIB_LUT1D_T_F16 *const pParam);
5.46.2 Arguments
Table 5-57. GFLIB_Lut1D_F16 arguments
Type
Name
Direction
Description
tFrac16
f16In
input
The abscissa for which 1D interpolation is performed.
const
GFLIB_LUT1D_T_F16
*const
pParam
input
Pointer to the parameters structure with parameters of the
look-up table function.
5.46.3 Return
The interpolated value from the look-up table.
5.46.4 Description
The GFLIB_Lut1D_F16 function performs one dimensional linear interpolation over a
table of data. The data is assumed to represent a one dimensional function sampled at
equidistant points. The following interpolation formula is used:
Equation GFLIB_Lut1D_Eq1
where:
• y is the interpolated value
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Function GFLIB_Lut1D_F16
• y 1 and y 2 are the ordinate values at, respectively, the beginning and the end of the
interpolating interval
• x 1 and x 2 are the abscissa values at, respectively, the beginning and the end of the
interpolating interval
• the x is the input value provided to the function in the f16In argument
The interpolating intervals are defined in the table provided by the pf16Table member of
the parameters structure. The table contains ordinate values consecutively over the entire
interpolating range. The abscissa values are assumed to be defined implicitly by a single
interpolating interval length and a table index, while the interpolating index zero is the
table element pointed to by the pf16Table parameter. The abscissa value is equal to the
multiplication of the interpolating index and the interpolating interval length. For
example, let's consider the following interpolating table:
Table 5-58. GFLIB_Lut1D example table
ordinate (y)
interpolating index
abscissa (x)
-0.5
-1
-1*(2 -1)
pf16Table{rarrow} 0.0
0
0*(2 -1)
0.25
1
1*(2 -1)
0.5
N/A
2*(2 -1)
The Table 5-58 contains 4 interpolating points (note four rows). The interpolating
interval length in this example is equal to 2 -1. The pf16Table parameter points to the
second row, defining also the interpolating index 0. The x-coordinates of the interpolating
points are calculated in the right column.
It should be noted that the pf16Table pointer does not have to point to the start of the
memory area of ordinate values. Therefore, the interpolating index can be positive or
negative or, even, does not have to have zero in its range.
A special algorithm is used to make the computation efficient, however, under some
additional assumptions, as provided below:
• the values of the interpolated function are 16 bits long
• the length of each interpolating interval is equal to 2 -n, where n is an integer in the
range of 1, 2, ... 13
• the provided abscissa for interpolation is 16 bits long
The algorithm performs the following steps:
1. Compute the index representing the interval, in which the linear interpolation will be
performed:
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Equation GFLIB_Lut1D_Eq2
where I is the interval index and the s Interval the shift amount provided in the
parameters structure as the member s16ShamIntvl. The operator >> represents the
binary arithmetic right shift.
2. Compute the abscissa offset within an interpolating interval:
Equation GFLIB_Lut1D_Eq3
where Δ{x} is the abscissa offset within an interval and the s Offset is the shift amount
provided in the parameters structure. The operators << and & represent, respectively,
the binary left shift and the bitwise logical conjunction. It should be noted that the
computation represents the extraction of some least significant bits of the x with the
sign bit cleared.
3. Compute the interpolated value by the linear interpolation between the ordinates read
from the table at the start and the end of the computed interval. The computed
abscissa offset is used for the linear interpolation.
Equation GFLIB_Lut1D_Eq4
where y, y 1 and y 2 are, respectively, the interpolated value, the ordinate at the start of
the interpolating interval, the ordinate at the end of the interpolating interval. The pTable
is the address provided in the parameters structure pParam->f16Table. It should be noted
that due to assumption of equidistant data points, division by the interval length is
avoided.
It should be noted that the computations are performed with a 16-bit accuracy. In
particular, the 16 least significant bits are ignored in all multiplications.
The shift amounts shall be provided in the parameters structure (pParam>u16ShamOffset). The address of the table with the data, the pTable, shall be defined by
the parameter structure member pParam->pf16Table.
The shift amounts, the s Interval and s Offset, can be computed with the following formulas:
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Function GFLIB_Lut1D_F16
Equation GFLIB_Lut1D_Eq5
where n is the integer defining the length of the interpolating interval in the range of -1,
-2, ... -15.
The computation of the abscissa offset and the interval index can be viewed also in the
following way. The input abscissa value can be divided into two parts. The first n most
significant bits of the 16-bit halfword, after the sign bit, compose the interval index, in
which interpolation is performed. The rest of the bits form the abscissa offset within the
interpolating interval. This simple way to calculate the interpolating interval index and
the abscissa offset is the consequence of assuming that all interpolating interval lengths
equal 2 -n.
It should be noted that the input abscissa value can be positive or negative. If it is,
positive then the ordinate values are read as in the ordinary data array, that is, at or after
the data pointer provided in the parameters structure (pParam->pf16Table). However, if it
is negative, then the ordinate values are read from the memory, which is located behind
the pParam->pf16Table pointer.
Note
The input pointer must contain a valid address and the range of
the input abscissa values must fall within the range of the
interpolating data table otherwise an exception may occur (Data
TLB Error, Data Storage, Alignment, Machine Check).
The function performs a linear interpolation.
CAUTION
The function does not check whether the input abscissa value is
within the range allowed by the interpolating data table
pParam->pf16Table. If the computed interval index points to
data outside the provided data table, then the interpolation will
be computed with invalid data. The range of the input abscissa
value depends on the position of the pointer in the interpolating
data table. Sum of the absolute values of the lower and upper
border values is equal to the SFRACT_MAX. For a better
understanding, please, see the extended code example.
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5.46.5 Re-entrancy
The function is re-entrant.
5.46.6 Code Example
#include "gflib.h"
tFrac16 f16In;
tFrac16 f16Out;
GFLIB_LUT1D_T_F16 trf16MyLut1D = GFLIB_LUT1D_DEFAULT_F16;
tFrac16 pf16Table1D[9] = {FRAC16 (0.8),FRAC16 (0.1),FRAC16 (-0.2),FRAC16
(0.7),FRAC16 (0.2),FRAC16 (-0.3),FRAC16 (-0.8),FRAC16 (0.91),FRAC16 (0.99)};
void main(void)
{
// ####################################################################
// Pointer is located in the middle of the interpolating data table.
// ####################################################################
// setting parameters for Lut1D function
trf16MyLut1D.u16ShamOffset = (tU16)3;
trf16MyLut1D.pf16Table = &(pf16Table1D[4]);
// input vector = -0.5
f16In = FRAC16 (-0.5);
// output should be 0x6666 ~ FRAC16(0.8)
f16Out = GFLIB_Lut1D_F16 (f16In,&trf16MyLut1D);
// output should be 0x6666 ~ FRAC16(0.8)
f16Out = GFLIB_Lut1D (f16In,&trf16MyLut1D,F16);
// available only if 16-bit fractional implementation selected as default
// output should be 0x6666 ~ FRAC16(0.8)
f16Out = GFLIB_Lut1D (f16In,&trf16MyLut1D);
// ####################################################################
// Pointer is located at the beginning of the interpolating data table.
// ####################################################################
// setting parameters for Lut1D function
trf16MyLut1D.u16ShamOffset = (tU16)3;
trf16MyLut1D.pf16Table = &(pf16Table1D[0]);
// input vector = 0
f16In = FRAC16 (0);
// output should be 0x6666 ~ FRAC16(0.8)
f16Out = GFLIB_Lut1D_F16 (f16In,&trf16MyLut1D);
// output should be 0x6666 ~ FRAC16(0.8)
f16Out = GFLIB_Lut1D (f16In,&trf16MyLut1D,F16);
// available only if 16-bit fractional implementation selected as default
// output should be 0x6666 ~ FRAC16(0.8)
f16Out = GFLIB_Lut1D (f16In,&trf16MyLut1D);
// ####################################################################
// Pointer is located at the end of the interpolating data table.
// ####################################################################
// setting parameters for Lut1D function
trf16MyLut1D.u16ShamOffset = (tU16)3;
trf16MyLut1D.pf16Table = &(pf16Table1D[8]);
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Function GFLIB_Lut2D_F32
// input vector = -1
f16In = FRAC16 (-1);
// output should be 0x6666 ~ FRAC16(0.8)
f16Out = GFLIB_Lut1D_F16 (f16In,&trf16MyLut1D);
// output should be 0x6666 ~ FRAC16(0.8)
f16Out = GFLIB_Lut1D (f16In,&trf16MyLut1D,F16);
}
// available only if 16-bit fractional implementation selected as default
// output should be 0x6666 ~ FRAC16(0.8)
f16Out = GFLIB_Lut1D (f16In,&trf16MyLut1D);
5.47 Function GFLIB_Lut2D_F32
This function implements the two-dimensional look-up table.
5.47.1 Declaration
tFrac32 GFLIB_Lut2D_F32(tFrac32 f32In1, tFrac32 f32In2, const GFLIB_LUT2D_T_F32 *const
pParam);
5.47.2 Arguments
Table 5-59. GFLIB_Lut2D_F32 arguments
Type
Name
Direction
Description
tFrac32
f32In1
input
First input variable for which 2D interpolation is performed.
tFrac32
f32In2
input
Second input variable for which 2D interpolation is performed.
const
GFLIB_LUT2D_T_F32
*const
pParam
input
Pointer to the parameters structure with parameters of the two
dimensional look-up table function.
5.47.3 Return
The interpolated value from the look-up table with 16-bit accuracy.
5.47.4 Description
The GFLIB_Lut2D_F32 function performs two dimensional linear interpolation over a
2D table of data.
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The following interpolation formulas are used:
Equation GFLIB_Lut2D_Eq1
Equation GFLIB_Lut2D_Eq2
Equation GFLIB_Lut2D_Eq3
where:
• f[x,y] is the interpolated value
• f[x,y 1] and f[x,y 2] are the ordinate values at, respectively, the beginning and the end
of the final interpolating interval
• x 1, x 2, y 1 and y 2 are the area values, respectively, the interpolated area
• the x, y are the input values provided to the function in the f32In1 and f32In2
arguments
The interpolating intervals are defined in the table provided by the pf32Table member of
the parameters structure. The table contains ordinate values consecutively over the whole
interpolating range. The abscissa values are assumed to be defined implicitly by a single
interpolating interval length and a table index while the interpolating index zero is the
table element pointed to by the pf32Table parameter. The abscissa value is equal to the
multiplication of the interpolating index and the interpolating interval length. For
example let's consider the following interpolating table:
Table 5-60. GFLIB_Lut2D example table
ordinate (f[x,y])
interpolating index
abscissa (x)
-1)
abscissa (y)
-1*(2 -1)
-0.5
-1
-1*(2
pf32Table{rarrow} 0.0
0
0*(2 -1)
0*(2 -1)
0.5
1
1*(2 -1)
1*(2 -1)
1.0
N/A
2*(2 -1)
2*(2 -1)
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Function GFLIB_Lut2D_F32
The Table 5-60 contains 4 interpolating points (note four rows). Interpolating interval
length in this example is equal to 2 -1 . The pf32Table parameter points to the second
row, defining also the interpolating index 0. The x-coordinates of the interpolating points
are calculated in the right column. It should be noticed that the pf32Table pointer does
not have to point to the start of the memory area with ordinate values. Therefore the
interpolating index can be positive or negative or, even, does not have to have zero in its
range.
Special algorithm is used to make the computation efficient, however under some
additional assumptions as provided below:
• the values of the interpolated function are 32-bit long
• the length of each interpolating interval is equal to 2 -n, where n is an integer in the
range of 1, 2, ... 29
• the provided abscissa for interpolation is 32-bit long
The algorithm performs the following steps:
1. Compute the index representing the interval, in which the bilinear interpolation will
be performed in each axis:
Equation GFLIB_Lut2D_Eq4
Equation GFLIB_Lut2D_Eq5
where I x and I y is the interval index and the s IntervalX and s IntervalY are the shift
amounts provided in the parameters structure as a member u32ShamOffset1 or
u32ShamOffset2. The operator >> represents the binary arithmetic right shift.
2. Compute the abscissas offset for both axis within an interpolating intervals:
Equation GFLIB_Lut2D_Eq6
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Equation GFLIB_Lut2D_Eq7
where Δ{x} and Δ{y} are the abscissas offset within an Xinterval and Yinterval. The
s Offset1 and s Offset2 are the shift amounts provided in the parameters structure. The
operators << and & represent the binary left shift and the bitwise logical conjunction.
It should be noted that the computation represents extraction of some least significant
bits of the x and y with the sign bit cleared.
3. Compute the interpolated value by the linear interpolation in X-axis by y 1 value
between the ordinates x1 and x 2 readed from the table at the start and the end of the
computed interval in X-axis way. The computed abscissa offset is used for the linear
interpolation:
Equation GFLIB_Lut2D_Eq8
Equation GFLIB_Lut2D_Eq9
Equation GFLIB_Lut2D_Eq10
where f[x,y 1] is interpolated value, f[x 1,y 1] and f[x 2,y 1] are, the ordinate at the
start of the interpolating interval and the ordinate at the end of the interpolating
interval. The pTable} is the address provided in the parameters structure pParam>f32Table.
4. The same computation as shown above in X-axis by y 2 value. Interpolation formulas
are the same as paragraph 3:
Equation GFLIB_Lut2D_Eq11
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Function GFLIB_Lut2D_F32
Equation GFLIB_Lut2D_Eq12
Equation GFLIB_Lut2D_Eq13
5. Final linear interpolation in Y-axis way Interpolation formulas are the same as
paragraph 3 or 4:
Equation GFLIB_Lut2D_Eq14
Equation GFLIB_Lut2D_Eq15
Equation GFLIB_Lut2D_Eq16
It should be noted that due to assumption of the equidistant data points, the division
by the interval length is avoided.
It should be noted that the computations are performed with the 16-bit accuracy. In
particular the 16 least significant bits are ignored in all multiplications.
The shift amounts shall be provided in the parameters structure (pParam>u32ShamOffset1 and pParam->u32ShamOffset2). The address of the table with the
data, the pTable}, shall be defined by the parameter structure member pParam>pf32Table.
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The shift amounts, the s Interval1,2 and s Offset1,2, can be computed with the following
formulas:
Equation GFLIB_Lut2D_Eq17
where n is the integer defining the length of the interpolating interval in the range of -1,
-2, ... -29.
The computation of the abscissa offset and the interval index can be viewed also in the
following way. The input abscissa value can be divided into two parts. The first n most
significant bits of the 32-bit word, after the sign bit, compose the interval index, in which
interpolation is performed. The rest of the bits form the abscissa offset within the
interpolating interval. This simple way to calculate the interpolating interval index and
the abscissa offset is the consequence of assumption of all interpolating interval lengths
equal 2 -n.
It should be noted that the input abscissa value can be positive or negative. If it is positive
then the ordinate values are read as in the ordinary data array, that is at or after the data
pointer provided in the parameters structure (pParam->pf32Table). However, if it is
negative, then the ordinate values are read from the memory, which is located behind the
pParam->pf32Table pointer.
Note
The input pointer must contain a valid address and the range of
the input values must fall within the range of the interpolating
data table otherwise an exception may occur (Data TLB Error,
Data Storage, Alignment, Machine Check).
The function performs the bilinear interpolation with 16-bit
accuracy.
CAUTION
The function does not check whether the input values are within
a range allowed by the interpolating data table pParam>pf32Table. If the computed interval index points to data
outside the provided data table then the interpolation will be
computed with invalid data. The range of the input abscissa
value depends on the position of the pointer in the interpolating
data table. Sum of the absolute values of the lower and upper
border values is equal to the FRACT_MAX. For a better
understanding, please, see the extended code example.
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Function GFLIB_Lut2D_F32
5.47.5 Re-entrancy
The function is re-entrant.
5.47.6 Code Example
#include "gflib.h"
(0.03), FRAC32
(0.13), FRAC32
(0.23), FRAC32
(0.33), FRAC32
(0.43), FRAC32
(0.53), FRAC32
(0.63), FRAC32
(0.73), FRAC32
(0.83), FRAC32
tFrac32 f32In1;
tFrac32 f32In2;
tFrac32 f32Out;
GFLIB_LUT2D_T_F32 tr32tMyLut2D = GFLIB_LUT2D_DEFAULT_F32;
tFrac32 pf32Table2D[81] = {FRAC32 (0.9), FRAC32 (0.01), FRAC32 (0.02),
(0.04), FRAC32 (0.05), FRAC32 (0.06), FRAC32 (0.07), FRAC32 (0.08),
FRAC32 (0.1), FRAC32 (0.11), FRAC32 (0.12),
(0.14), FRAC32 (0.15), FRAC32 (0.16), FRAC32 (0.17), FRAC32 (0.18),
FRAC32 (0.2), FRAC32 (0.21), FRAC32 (0.22),
(0.24), FRAC32 (0.25), FRAC32 (0.26), FRAC32 (0.27), FRAC32 (0.28),
FRAC32 (0.3), FRAC32 (0.31), FRAC32 (0.32),
(0.34), FRAC32 (0.35), FRAC32 (0.36), FRAC32 (0.37), FRAC32 (0.38),
FRAC32 (0.4), FRAC32 (0.41), FRAC32 (0.42),
(0.44), FRAC32 (0.45), FRAC32 (0.46), FRAC32 (0.47), FRAC32 (0.48),
FRAC32 (0.5), FRAC32 (0.51), FRAC32 (0.52),
(0.54), FRAC32 (0.55), FRAC32 (0.56), FRAC32 (0.57), FRAC32 (0.58),
FRAC32 (0.6), FRAC32 (0.61), FRAC32 (0.62),
(0.64), FRAC32 (0.65), FRAC32 (0.66), FRAC32 (0.67), FRAC32 (0.68),
FRAC32 (0.7), FRAC32 (0.71), FRAC32 (0.72),
(0.74), FRAC32 (0.75), FRAC32 (0.76), FRAC32 (0.77), FRAC32 (0.78),
FRAC32 (0.8), FRAC32 (0.81), FRAC32 (0.82),
(0.84), FRAC32 (0.85), FRAC32 (0.86), FRAC32 (0.87), FRAC32 (0.88)};
FRAC32
FRAC32
FRAC32
FRAC32
FRAC32
FRAC32
FRAC32
FRAC32
FRAC32
void main(void)
{
// ####################################################################
// Pointer is located in the middle of the interpolating data table.
// ####################################################################
// setting parameters for Lut2D function
tr32tMyLut2D.u32ShamOffset1 = (tU32)3;
tr32tMyLut2D.u32ShamOffset2 = (tU32)3;
tr32tMyLut2D.pf32Table = &(pf32Table2D[40]);
// input vector
f32In1 = FRAC32 (-0.5);
f32In2 = FRAC32 (-0.5);
// output should be 0x73333333 ~ FRAC32(0.9)
f32Out = GFLIB_Lut2D_F32 (f32In1,f32In2,&tr32tMyLut2D);
// output should be 0x73333333 ~ FRAC32(0.9)
f32Out = GFLIB_Lut2D (f32In1,f32In2,&tr32tMyLut2D,F32);
// available only if 32-bit fractional implementation selected as default
// output should be 0x73333333 ~ FRAC32(0.9)
f32Out = GFLIB_Lut2D (f32In1,f32In2,&tr32tMyLut2D);
// ####################################################################
// Pointer is located at the beginning of the interpolating data table.
// ####################################################################
// setting parameters for Lut2D function
tr32tMyLut2D.u32ShamOffset1 = (tU32)3;
tr32tMyLut2D.u32ShamOffset2 = (tU32)3;
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tr32tMyLut2D.pf32Table = &(pf32Table2D[0]);
// input vector
f32In1 = FRAC32 (0);
f32In2 = FRAC32 (0);
// output should be 0x73333333 ~ FRAC32(0.9)
f32Out = GFLIB_Lut2D_F32 (f32In1,f32In2,&tr32tMyLut2D);
// output should be 0x73333333 ~ FRAC32(0.9)
f32Out = GFLIB_Lut2D (f32In1,f32In2,&tr32tMyLut2D,F32);
// available only if 32-bit fractional implementation selected as default
// output should be 0x73333333 ~ FRAC32(0.9)
f32Out = GFLIB_Lut2D (f32In1,f32In2,&tr32tMyLut2D);
// ####################################################################
// Pointer is located at the end of the interpolating data table.
// ####################################################################
// setting parameters for Lut2D function
tr32tMyLut2D.u32ShamOffset1 = (tU32)3;
tr32tMyLut2D.u32ShamOffset2 = (tU32)3;
tr32tMyLut2D.pf32Table = &(pf32Table2D[80]);
// input vector
f32In1 = FRAC32 (-1);
f32In2 = FRAC32 (-1);
// output should be 0x73333333 ~ FRAC32(0.9)
f32Out = GFLIB_Lut2D_F32 (f32In1,f32In2,&tr32tMyLut2D);
// output should be 0x73333333 ~ FRAC32(0.9)
f32Out = GFLIB_Lut2D (f32In1,f32In2,&tr32tMyLut2D,F32);
}
// available only if 32-bit fractional implementation selected as default
// output should be 0x73333333 ~ FRAC32(0.9)
f32Out = GFLIB_Lut2D (f32In1,f32In2,&tr32tMyLut2D);
5.48 Function GFLIB_Lut2D_F16
This function implements the two-dimensional look-up table.
5.48.1 Declaration
tFrac16 GFLIB_Lut2D_F16(tFrac16 f16In1, tFrac16 f16In2, const GFLIB_LUT2D_T_F16 *const
pParam);
5.48.2 Arguments
Table 5-61. GFLIB_Lut2D_F16 arguments
Type
tFrac16
Name
f16In1
Direction
input
Description
First input variable for which 2D interpolation is performed.
Table continues on the next page...
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Function GFLIB_Lut2D_F16
Table 5-61. GFLIB_Lut2D_F16 arguments (continued)
Type
Name
Direction
Description
tFrac16
f16In2
input
Second input variable for which 2D interpolation is performed.
const
GFLIB_LUT2D_T_F16
*const
pParam
input
Pointer to the parameters structure with parameters of the two
dimensional look-up table function.
5.48.3 Return
The interpolated value from the look-up table.
5.48.4 Description
The GFLIB_Lut2D_F16 function performs two dimensional linear interpolation over a
2D table of data.
The following interpolation formulas are used:
Equation GFLIB_Lut2D_Eq1
Equation GFLIB_Lut2D_Eq2
Equation GFLIB_Lut2D_Eq3
where:
• f[x,y] is the interpolated value
• f[x,y 1] and f[x,y 2] are the ordinate values at, respectively, the beginning and the end
of the final interpolating interval
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• x 1, x 2, y 1 and y 2 are the area values, respectively, the interpolated area
• the x, y are the input values provided to the function in the f16In1 and f16In2
arguments
The interpolating intervals are defined in the table provided by the pf16Table member of
the parameters structure. The table contains ordinate values consecutively over the whole
interpolating range. The abscissa values are assumed to be defined implicitly by a single
interpolating interval length and a table index while the interpolating index zero is the
table element pointed to by the pf16Table parameter. The abscissa value is equal to the
multiplication of the interpolating index and the interpolating interval length. For
example let's consider the following interpolating table:
Table 5-62. GFLIB_Lut2D example table
ordinate (f[x,y])
interpolating index
abscissa (x)
-1)
abscissa (y)
-1*(2 -1)
-0.5
-1
-1*(2
pf16Table{rarrow} 0.0
0
0*(2 -1)
0*(2 -1)
0.5
1
1*(2 -1)
1*(2 -1)
1.0
N/A
2*(2 -1)
2*(2 -1)
The Table 5-62 contains 4 interpolating points (note four rows). Interpolating interval
length in this example is equal to 2 -1 . The pf16Table parameter points to the second
row, defining also the interpolating index 0. The x-coordinates of the interpolating points
are calculated in the right column. It should be noticed that the pf16Table pointer does
not have to point to the start of the memory area with ordinate values. Therefore the
interpolating index can be positive or negative or, even, does not have to have zero in its
range.
Special algorithm is used to make the computation efficient, however under some
additional assumptions as provided below:
• the values of the interpolated function are 16-bit long
• the length of each interpolating interval is equal to 2 -n, where n is an integer in the
range of 1, 2, ... 13
• the provided abscissa for interpolation is 16-bit long
The algorithm performs the following steps:
1. Compute the index representing the interval, in which the bilinear interpolation will
be performed in each axis:
Equation GFLIB_Lut2D_Eq4
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Function GFLIB_Lut2D_F16
Equation GFLIB_Lut2D_Eq5
where I x and I y is the interval index and the s IntervalX and s IntervalY are the shift
amounts provided in the parameters structure as a member u16ShamOffset1 or
u16ShamOffset2. The operator >> represents the binary arithmetic right shift.
2. Compute the abscissas offset for both axis within an interpolating intervals:
Equation GFLIB_Lut2D_Eq6
Equation GFLIB_Lut2D_Eq7
where Δ{x} and Δ{y} are the abscissas offset within an Xinterval and Yinterval. The
s Offset1 and s Offset2 are the shift amounts provided in the parameters structure. The
operators << and & represent the binary left shift and the bitwise logical conjunction.
It should be noted that the computation represents extraction of some least significant
bits of the x and y with the sign bit cleared.
3. Compute the interpolated value by the linear interpolation in X-axis by y 1 value
between the ordinates x1 and x 2 readed from the table at the start and the end of the
computed interval in X-axis way. The computed abscissa offset is used for the linear
interpolation:
Equation GFLIB_Lut2D_Eq8
Equation GFLIB_Lut2D_Eq9
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Equation GFLIB_Lut2D_Eq10
where f[x,y 1] is interpolated value, f[x 1,y 1] and f[x 2,y 1] are, the ordinate at the
start of the interpolating interval and the ordinate at the end of the interpolating
interval. The pTable} is the address provided in the parameters structure pParam>f16Table.
4. The same computation as shown above in X-axis by y 2 value. Interpolation formulas
are the same as paragraph 3:
Equation GFLIB_Lut2D_Eq11
Equation GFLIB_Lut2D_Eq12
Equation GFLIB_Lut2D_Eq13
5. Final linear interpolation in Y-axis way Interpolation formulas are the same as
paragraph 3 or 4:
Equation GFLIB_Lut2D_Eq14
Equation GFLIB_Lut2D_Eq15
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Function GFLIB_Lut2D_F16
Equation GFLIB_Lut2D_Eq16
It should be noted that due to assumption of the equidistant data points, the division
by the interval length is avoided.
It should be noted that the computations are performed with the 16-bit accuracy. In
particular the 16 least significant bits are ignored in all multiplications.
The shift amounts shall be provided in the parameters structure (pParam>u16ShamOffset1 and pParam->u16ShamOffset2). The address of the table with the
data, the pTable}, shall be defined by the parameter structure member pParam>pf16Table.
The shift amounts, the s Interval1,2 and s Offset1,2, can be computed with the following
formulas:
Equation GFLIB_Lut2D_Eq17
where n is the integer defining the length of the interpolating interval in the range of -1,
-2, ... -29.
The computation of the abscissa offset and the interval index can be viewed also in the
following way. The input abscissa value can be divided into two parts. The first n most
significant bits of the 16-bit halfword, after the sign bit, compose the interval index, in
which interpolation is performed. The rest of the bits form the abscissa offset within the
interpolating interval. This simple way to calculate the interpolating interval index and
the abscissa offset is the consequence of assumption of all interpolating interval lengths
equal 2 -n.
It should be noted that the input abscissa value can be positive or negative. If it is positive
then the ordinate values are read as in the ordinary data array, that is at or after the data
pointer provided in the parameters structure (pParam->pf16Table). However, if it is
negative, then the ordinate values are read from the memory, which is located behind the
pParam->pf16Table pointer.
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Note
The input pointer must contain a valid address and the range of
the input values must fall within the range of the interpolating
data table otherwise an exception may occur (Data TLB Error,
Data Storage, Alignment, Machine Check).
The function performs the bilinear interpolation.
CAUTION
The function does not check whether the input values are within
a range allowed by the interpolating data table pParam>pf16Table. If the computed interval index points to data
outside the provided data table then the interpolation will be
computed with invalid data. The range of the input abscissa
value depends on the position of the pointer in the interpolating
data table. Sum of the absolute values of the lower and upper
border values is equal to the SFRACT_MAX. For a better
understanding, please, see the extended code example.
5.48.5 Re-entrancy
The function is re-entrant.
5.48.6 Code Example
#include "gflib.h"
(0.03), FRAC16
(0.13), FRAC16
(0.23), FRAC16
(0.33), FRAC16
(0.43), FRAC16
(0.53), FRAC16
(0.63), FRAC16
(0.73), FRAC16
(0.83), FRAC16
tFrac16 f16In1;
tFrac16 f16In2;
tFrac16 f16Out;
GFLIB_LUT2D_T_F16 tr16tMyLut2D = GFLIB_LUT2D_DEFAULT_F16;
tFrac16 pf16Table2D[81] = {FRAC16 (0.9), FRAC16 (0.01), FRAC16 (0.02),
(0.04), FRAC16 (0.05), FRAC16 (0.06), FRAC16 (0.07), FRAC16 (0.08),
FRAC16 (0.1), FRAC16 (0.11), FRAC16 (0.12),
(0.14), FRAC16 (0.15), FRAC16 (0.16), FRAC16 (0.17), FRAC16 (0.18),
FRAC16 (0.2), FRAC16 (0.21), FRAC16 (0.22),
(0.24), FRAC16 (0.25), FRAC16 (0.26), FRAC16 (0.27), FRAC16 (0.28),
FRAC16 (0.3), FRAC16 (0.31), FRAC16 (0.32),
(0.34), FRAC16 (0.35), FRAC16 (0.36), FRAC16 (0.37), FRAC16 (0.38),
FRAC16 (0.4), FRAC16 (0.41), FRAC16 (0.42),
(0.44), FRAC16 (0.45), FRAC16 (0.46), FRAC16 (0.47), FRAC16 (0.48),
FRAC16 (0.5), FRAC16 (0.51), FRAC16 (0.52),
(0.54), FRAC16 (0.55), FRAC16 (0.56), FRAC16 (0.57), FRAC16 (0.58),
FRAC16 (0.6), FRAC16 (0.61), FRAC16 (0.62),
(0.64), FRAC16 (0.65), FRAC16 (0.66), FRAC16 (0.67), FRAC16 (0.68),
FRAC16 (0.7), FRAC16 (0.71), FRAC16 (0.72),
(0.74), FRAC16 (0.75), FRAC16 (0.76), FRAC16 (0.77), FRAC16 (0.78),
FRAC16 (0.8), FRAC16 (0.81), FRAC16 (0.82),
(0.84), FRAC16 (0.85), FRAC16 (0.86), FRAC16 (0.87), FRAC16 (0.88)};
FRAC16
FRAC16
FRAC16
FRAC16
FRAC16
FRAC16
FRAC16
FRAC16
FRAC16
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Function GFLIB_Lut2D_F16
void main(void)
{
// ####################################################################
// Pointer is located in the middle of the interpolating data table.
// ####################################################################
// setting parameters for Lut2D function
tr16tMyLut2D.u16ShamOffset1 = (tU16)3;
tr16tMyLut2D.u16ShamOffset2 = (tU16)3;
tr16tMyLut2D.pf16Table = &(pf16Table2D[40]);
// input vector
f16In1 = FRAC16 (-0.5);
f16In2 = FRAC16 (-0.5);
// output should be 0x7333 ~ FRAC16(0.9)
f16Out = GFLIB_Lut2D_F16 (f16In1,f16In2,&tr16tMyLut2D);
// output should be 0x7333 ~ FRAC16(0.9)
f16Out = GFLIB_Lut2D (f16In1,f16In2,&tr16tMyLut2D,F16);
// available only if 16-bit fractional implementation selected as default
// output should be 0x7333 ~ FRAC16(0.9)
f16Out = GFLIB_Lut2D (f16In1,f16In2,&tr16tMyLut2D);
// ####################################################################
// Pointer is located at the beginning of the interpolating data table.
// ####################################################################
// setting parameters for Lut2D function
tr16tMyLut2D.u16ShamOffset1 = (tU16)3;
tr16tMyLut2D.u16ShamOffset2 = (tU16)3;
tr16tMyLut2D.pf16Table = &(pf16Table2D[0]);
// input vector
f16In1 = FRAC16 (0);
f16In2 = FRAC16 (0);
// output should be 0x7333 ~ FRAC16(0.9)
f16Out = GFLIB_Lut2D_F16 (f16In1,f16In2,&tr16tMyLut2D);
// output should be 0x7333 ~ FRAC16(0.9)
f16Out = GFLIB_Lut2D (f16In1,f16In2,&tr16tMyLut2D,F16);
// available only if 16-bit fractional implementation selected as default
// output should be 0x7333 ~ FRAC16(0.9)
f16Out = GFLIB_Lut2D (f16In1,f16In2,&tr16tMyLut2D);
// ####################################################################
// Pointer is located at the end of the interpolating data table.
// ####################################################################
// setting parameters for Lut2D function
tr16tMyLut2D.u16ShamOffset1 = (tU16)3;
tr16tMyLut2D.u16ShamOffset2 = (tU16)3;
tr16tMyLut2D.pf16Table = &(pf16Table2D[80]);
// input vector
f16In1 = FRAC16 (-1);
f16In2 = FRAC16 (-1);
// output should be 0x7333 ~ FRAC16(0.9)
f16Out = GFLIB_Lut2D_F16 (f16In1,f16In2,&tr16tMyLut2D);
// output should be 0x7333 ~ FRAC16(0.9)
f16Out = GFLIB_Lut2D (f16In1,f16In2,&tr16tMyLut2D,F16);
}
// available only if 16-bit fractional implementation selected as default
// output should be 0x7333 ~ FRAC16(0.9)
f16Out = GFLIB_Lut2D (f16In1,f16In2,&tr16tMyLut2D);
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5.49 Function GFLIB_Ramp_F32
The function calculates the up/down ramp with the step increment/decrement defined in
the pParam structure.
5.49.1 Declaration
tFrac32 GFLIB_Ramp_F32(tFrac32 f32In, GFLIB_RAMP_T_F32 *const pParam);
5.49.2 Arguments
Table 5-63. GFLIB_Ramp_F32 arguments
Type
Name
Direction
Description
tFrac32
f32In
input
Input argument representing the desired output value.
GFLIB_RAMP_T_F32
*const
pParam
input,
output
Pointer to the ramp parameters structure.
5.49.3 Return
The function returns a 32-bit value in format Q1.31, which represents the actual ramp
output value. This, in time, is approaching the desired (input) value by step increments
defined in the pParam structure.
5.49.4 Description
The GFLIB_Ramp function, denoting ANSI-C compatible source code implementation,
can be called via the function alias GFLIB_Ramp.
If the desired (input) value is greater than the ramp output value, the function adds the
f32RampUp value to the actual output value. The output cannot be greater than the
desired value.
If the desired value is lower than the actual value, the function subtracts the
f32RampDown value from the actual value. The output cannot be lower than the desired
value.
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Function GFLIB_Ramp_F32
Functionality of the implemented ramp algorithm can be explained with use of Figure
5-21
Figure 5-21. GFLIB_Ramp functionality
Note
The input pointer must contain a valid address otherwise an
exception may occur (Data TLB Error, Data Storage,
Alignment, Machine Check).
All parameters and states used by the function can be reset
during declaration using the #GFLIB_RAMP_DEFAULT
macro.
5.49.5 Re-entrancy
The function is re-entrant.
5.49.6 Code Example
#include "gflib.h"
tFrac32 f32In;
tFrac32 f32Out;
GFLIB_RAMP_T_F32 f32trMyRamp = GFLIB_RAMP_DEFAULT_F32;
void main(void)
{
// increment/decrement coefficients
f32trMyRamp.f32RampUp = FRAC32 (0.1);
f32trMyRamp.f32RampDown = FRAC32 (0.03333333);
// input value = 0.5
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f32In
= FRAC32 (0.5);
// output should be 0x0CCCCCCC ~ FRAC32(0.1)
f32Out = GFLIB_Ramp_F32 (f32In, &f32trMyRamp);
// clearing of the internal states
f32trMyRamp.f32State = (tFrac32)0;
// output should be 0x0CCCCCCC ~ FRAC32(0.1)
f32Out = GFLIB_Ramp (f32In, &f32trMyRamp, F32);
//
//
//
//
}
##############################################################
Available only if 32-bit fractional implementation selected
as default
##############################################################
// clearing of the internal states
f32trMyRamp.f32State = (tFrac32)0;
// output should be 0x0CCCCCCC ~ FRAC32(0.1)
f32Out = GFLIB_Ramp (f32In, &f32trMyRamp);
5.50 Function GFLIB_Ramp_F16
The function calculates the up/down ramp with the step increment/decrement defined in
the pParam structure.
5.50.1 Declaration
tFrac16 GFLIB_Ramp_F16(tFrac16 f16In, GFLIB_RAMP_T_F16 *const pParam);
5.50.2 Arguments
Table 5-64. GFLIB_Ramp_F16 arguments
Type
Name
Direction
Description
tFrac16
f16In
input
Input argument representing the desired output value.
GFLIB_RAMP_T_F16
*const
pParam
input,
output
Pointer to the ramp parameters structure.
5.50.3 Return
The function returns a 16-bit value in format Q1.15, which represents the actual ramp
output value. This, in time, is approaching the desired (input) value by step increments
defined in the pParam structure.
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Function GFLIB_Ramp_F16
5.50.4 Description
The GFLIB_Ramp function, denoting ANSI-C compatible source code implementation,
can be called via the function alias GFLIB_Ramp.
If the desired (input) value is greater than the ramp output value, the function adds the
f16RampUp value to the actual output value. The output cannot be greater than the
desired value.
If the desired value is lower than the actual value, the function subtracts the
f16RampDown value from the actual value. The output cannot be lower than the desired
value.
Functionality of the implemented ramp algorithm can be explained with use of Figure
5-22
Figure 5-22. GFLIB_Ramp functionality
Note
The input pointer must contain a valid address otherwise an
exception may occur (Data TLB Error, Data Storage,
Alignment, Machine Check).
All parameters and states used by the function can be reset
during declaration using the #GFLIB_RAMP_DEFAULT
macro.
5.50.5 Re-entrancy
The function is re-entrant.
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5.50.6 Code Example
#include "gflib.h"
tFrac16 f16In;
tFrac16 f16Out;
GFLIB_RAMP_T_F16 f16trMyRamp = GFLIB_RAMP_DEFAULT_F16;
void main(void)
{
// increment/decrement coefficients
f16trMyRamp.f16RampUp = FRAC16 (0.1);
f16trMyRamp.f16RampDown = FRAC16 (0.03333333);
// input value = 0.5
f16In = FRAC16 (0.5);
// output should be 0x0CCC ~ FRAC16(0.1)
f16Out = GFLIB_Ramp_F16 (f16In, &f16trMyRamp);
// clearing of the internal states
f16trMyRamp.f16State = (tFrac16)0;
// output should be 0x0CCC ~ FRAC16(0.1)
f16Out = GFLIB_Ramp (f16In, &f16trMyRamp, F16);
//
//
//
//
}
##############################################################
Available only if 16-bit fractional implementation selected
as default
##############################################################
// clearing of the internal states
f16trMyRamp.f16State = (tFrac16)0;
// output should be 0x0CCC ~ FRAC16(0.1)
f16Out = GFLIB_Ramp (f16In, &f16trMyRamp);
5.51 Function GFLIB_Sign_F32
This function returns the signum of input value.
5.51.1 Declaration
tFrac32 GFLIB_Sign_F32(tFrac32 f32In);
5.51.2 Arguments
Table 5-65. GFLIB_Sign_F32 arguments
Type
tFrac32
Name
f32In
Direction
input
Description
Input argument.
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Function GFLIB_Sign_F32
5.51.3 Return
The function returns the sign of the input argument.
5.51.4 Description
The GFLIB_Sign function calculates the sign of the input argument. The function return
value is computed as follows. If the input value is negative, then the return value will be
set to "-1" (0x80000000 hex), if the input value is zero, then the function returns "0" (0x0
hex), otherwise if the input value is greater than zero, the return value will be "1"
(0x7fffffff hex).
In mathematical terms, the function works according to the equation below:
Equation GFLIB_Sign_Eq1
where:
• y out is the return value
• x in is the input value provided as the f32In parameter
Note
The input and the output values are in the 32-bit fixed point
fractional data format.
5.51.5 Re-entrancy
The function is re-entrant.
5.51.6 Code Example
#include "gflib.h"
tFrac32 f32In;
tFrac32 f32Out;
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void main(void)
{
// input value = 0.5
f32In = FRAC32 (0.5);
// output should be 0x7FFFFFFF ~ FRAC32(1-(2^-31))
f32Out = GFLIB_Sign_F32 (f32In);
// output should be 0x7FFFFFFF ~ FRAC32(1-(2^-31))
f32Out = GFLIB_Sign (f32In,F32);
//
//
//
//
}
##############################################################
Available only if 32-bit fractional implementation selected
as default
##############################################################
// output should be 0x7FFFFFFF ~ FRAC32(1-(2^-31))
f32Out = GFLIB_Sign (f32In);
5.52 Function GFLIB_Sign_F16
This function returns the signum of input value.
5.52.1 Declaration
tFrac16 GFLIB_Sign_F16(tFrac16 f16In);
5.52.2 Arguments
Table 5-66. GFLIB_Sign_F16 arguments
Type
tFrac16
Name
f16In
Direction
input
Description
Input argument.
5.52.3 Return
The function returns the sign of the input argument.
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Function GFLIB_Sign_F16
5.52.4 Description
The GFLIB_Sign function calculates the sign of the input argument. The function return
value is computed as follows. If the input value is negative, then the return value will be
set to "-1" (0x8000 hex), if the input value is zero, then the function returns "0" (0x0
hex), otherwise if the input value is greater than zero, the return value will be "1" (0x7fff
hex).
In mathematical terms, the function works according to the equation below:
Equation GFLIB_Sign_Eq1
where:
• y out is the return value
• x in is the input value provided as the f16In parameter
Note
The input and the output values are in the 16-bit fixed point
fractional data format.
5.52.5 Re-entrancy
The function is re-entrant.
5.52.6 Code Example
#include "gflib.h"
tFrac16 f16In;
tFrac16 f16Out;
void main(void)
{
// input value = 0.5
f16In = FRAC16 (0.5);
// output should be 0x7FFF ~ FRAC16(1-(2^-15))
f16Out = GFLIB_Sign_F16 (f16In);
// output should be 0x7FFF ~ FRAC16(1-(2^-15))
f16Out = GFLIB_Sign (f16In,F16);
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//
//
//
//
}
##############################################################
Available only if 16-bit fractional implementation selected
as default
##############################################################
// output should be 0x7FFF ~ FRAC16(1-(2^-15))
f16Out = GFLIB_Sign (f16In);
5.53 Function GFLIB_Sin_F32
This function implements polynomial approximation of sine function.
5.53.1 Declaration
tFrac32 GFLIB_Sin_F32(tFrac32 f32In, const GFLIB_SIN_T_F32 *const pParam);
5.53.2 Arguments
Table 5-67. GFLIB_Sin_F32 arguments
Type
Name
Direction
Description
tFrac32
f32In
input
Input argument is a 32-bit number that contains an angle in
radians between [- π, π) normalized between [-1, 1).
const
GFLIB_SIN_T_F32
*const
pParam
input
Pointer to an array of Taylor coefficients.
5.53.3 Return
The function returns the sin of the input argument as a fixed point 32-bit number,
normalized between [-1, 1).
5.53.4 Description
The GFLIB_Sin_F32 function provides a computational method for calculation of a
standard trigonometric sine function sin(x), using the 9th order Taylor polynomial
approximation. The Taylor polynomial approximation of a sine function is described as
follows:
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Function GFLIB_Sin_F32
Equation GFLIB_Sin_Eq1
where x is the input angle.
The 9th order polynomial approximation is chosen as sufficient an order to achieve the
best ratio between calculation accuracy and speed of calculation. Because the
GFLIB_Sin_F32 function is implemented with consideration to fixed point fractional
arithmetic, all variables are normalized to fit into the [-1, 1) range. Therefore, in order to
cast the fractional value of the input angle f32In [-1, 1) into the correct range [- π, π), the
input f32In must be multiplied by π. So the fixed point fractional implementation of the
GFLIB_Sin_F32 function, using optimized 9th order Taylor approximation, is given as
follows:
Equation GFLIB_Sin_Eq2
The 9th order polynomial approximation of the sine function has a very good accuracy in
the range [- π/2, π/2) of the argument, but in wider ranges the calculation error quickly
increases. To minimize the error without having to use a higher order polynomial, the
symmetry of the sine function sin(x) = sin( π - x) is utilized. Therefore, the input
argument is transferred to be always in the range [- π/2, π/2) and the Taylor polynomial is
calculated only in the range of the argument [- π/2, π/2).
To make calculations more precise, the given argument value f32In (that is to be
transferred into the range [-0.5, 0.5) due to the sine function symmetry) is shifted by 1 bit
to the left (multiplied by 2). Then, the value of f32In 2, used in the calculations, is in the
range [-1, 1) instead of [-0.25, 0.25). Shifting the input value by 1 bit to the left will
increase the accuracy of the calculated sin( π * f32In) function. Implementing such a
scale on the approximation function described by equation GFLIB_Sin_Eq2, results in
the following:
Equation GFLIB_Sin_Eq3
Equation GFLIB_Sin_Eq3 can be further rewritten into the following form:
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Equation GFLIB_Sin_Eq4
where a 1 ... a 5 are coefficients of the approximation polynomial, which are calculated as
follows (represented as 32-bit signed fractional numbers):
Equation GFLIB_Sin_Eq5
Therefore, the resulting equation has the following form:
Equation GFLIB_Sin_Eq6
Figure 5-23 depicts a floating point sine function generated from Matlab and the
approximated value of the sine function obtained from GFLIB_Sin_F32, plus their
difference. The course of calculation accuracy as a function of the input angle can be
observed from this figure.
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Function GFLIB_Sin_F32
Figure 5-23. sin(x) vs. GFLIB_Sin_F32(f32In)
Note
The input pointer must contain a valid address otherwise an
exception may occur (Data TLB Error, Data Storage,
Alignment, Machine Check).
The input angle (f32In) is normalized into the range [-1, 1). The
function call is slightly different from common approach in the
library set. The function can be called in three different ways:
• With implementation postfix (i.e. GFLIB_Sin_F32(f32In,
&pParam)), where the &pParam is pointer to
approximation coefficients. In case the default
approximation coefficients are used, the &pParam must be
replaced with GFLIB_SIN_DEFAULT_F32 symbol. The
&pParam parameter is mandatory.
• With additional implementation parameter (i.e.
GFLIB_Sin(f32In, &pParam, F32), where the &pParam is
pointer to approximation coefficients. In case the default
approximation coefficients are used, the &pParam must be
replaced with GFLIB_SIN_DEFAULT_F32 symbol. The
&pParam parameter is mandatory.
• With preselected default implementation (i.e.
GFLIB_Sin(f32In, &pParam), where the &pParam is
pointer to approximation coefficients. The &pParam
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parameter is optional and in case it is not used, the default
GFLIB_SIN_DEFAULT_F32 approximation coefficients
are used.
5.53.5 Re-entrancy
The function is re-entrant.
5.53.6 Code Example
#include "gflib.h"
tFrac32 f32Angle;
tFrac32 f32Output;
void main(void)
{
// input angle = 0.5 => pi/2
f32Angle = FRAC32 (0.5);
// output should be 0x7FFFFFFF
f32Output = GFLIB_Sin_F32 (f32Angle, GFLIB_SIN_DEFAULT_F32);
// output should be 0x7FFFFFFF
f32Output = GFLIB_Sin (f32Angle, GFLIB_SIN_DEFAULT_F32, F32);
//
//
//
//
}
##############################################################
Available only if 32-bit fractional implementation selected
as default
##############################################################
// output should be 0x7FFFFFFF
f32Output = GFLIB_Sin (f32Angle);
5.54 Function GFLIB_Sin_F16
This function implements polynomial approximation of sine function.
5.54.1 Declaration
tFrac16 GFLIB_Sin_F16(tFrac16 f16In, const GFLIB_SIN_T_F16 *const pParam);
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Function GFLIB_Sin_F16
5.54.2 Arguments
Table 5-68. GFLIB_Sin_F16 arguments
Type
Name
Direction
Description
tFrac16
f16In
input
Input argument is a 16-bit number that contains an angle in
radians between [- π, π) normalized between [-1, 1).
const
GFLIB_SIN_T_F16
*const
pParam
input
Pointer to an array of Taylor coefficients.
5.54.3 Return
The function returns the sin of the input argument as a fixed point 16-bit number,
normalized between [-1, 1).
5.54.4 Description
The GFLIB_Sin_F16 function provides a computational method for calculation of a
standard trigonometric sine function sin(x), using the 7th order Taylor polynomial
approximation. The Taylor polynomial approximation of a sine function is described as
follows:
Equation GFLIB_Sin_Eq1
where x is the input angle.
The 7th order polynomial approximation is chosen as sufficient an order to achieve the
best ratio between calculation accuracy and speed of calculation. Because the
GFLIB_Sin_F16 function is implemented with consideration to fixed point fractional
arithmetic, all variables are normalized to fit into the [-1, 1) range. Therefore, in order to
cast the fractional value of the input angle f16In [-1, 1) into the correct range [- π, π), the
input f16In must be multiplied by π. So the fixed point fractional implementation of the
GFLIB_Sin_F16 function, using 7th order Taylor approximation, is given as follows:
Equation GFLIB_Sin_Eq2
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The 7th order polynomial approximation of the sine function has a very good accuracy in
the range [- π/2, π/2) of the argument, but in wider ranges the calculation error quickly
increases. To minimize the error without having to use a higher order polynomial, the
symmetry of the sine function sin(x) = sin( π - x) is utilized. Therefore, the input
argument is transferred to be always in the range [- π/2, π/2) and the Taylor polynomial is
calculated only in the range of the argument [- π/2, π/2).
To make calculations more precise, the given argument value f16In (that is to be
transferred into the range [-0.5, 0.5) due to the sine function symmetry) is shifted by 1 bit
to the left (multiplied by 2). Then, the value of f16In 2, used in the calculations, is in the
range [-1, 1) instead of [-0.25, 0.25). Shifting the input value by 1 bit to the left will
increase the accuracy of the calculated sin( π * f16In) function. Implementing such a
scale on the approximation function described by equation GFLIB_Sin_Eq2, results in
the following:
Equation GFLIB_Sin_Eq3
Equation GFLIB_Sin_Eq3 can be further rewritten into the following form:
Equation GFLIB_Sin_Eq4
where a 1 ... a 4 are coefficients of the approximation polynomial, which are calculated as
follows (represented as 16-bit signed fractional numbers):
Equation GFLIB_Sin_Eq5
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Function GFLIB_Sin_F16
Therefore, the resulting equation has the following form:
Equation GFLIB_Sin_Eq6
Figure 5-24 depicts a floating point sine function generated from Matlab and the
approximated value of the sine function obtained from GFLIB_Sin_F16, plus their
difference. The course of calculation accuracy as a function of the input angle can be
observed from this figure.
Figure 5-24. sin(x) vs. GFLIB_Sin_F16(f16In)
Note
The input pointer must contain a valid address otherwise an
exception may occur (Data TLB Error, Data Storage,
Alignment, Machine Check).
The input angle (f16In) is normalized into the range [-1, 1). The
function call is slightly different from common approach in the
library set. The function can be called in three different ways:
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• With implementation postfix (i.e. GFLIB_Sin_F16(f16In,
&pParam)), where the &pParam is pointer to
approximation coefficients. In case the default
approximation coefficients are used, the &pParam must be
replaced with GFLIB_SIN_DEFAULT_F16 symbol. The
&pParam parameter is mandatory.
• With additional implementation parameter (i.e.
GFLIB_Sin(f16In, &pParam, F16), where the &pParam is
pointer to approximation coefficients. In case the default
approximation coefficients are used, the &pParam must be
replaced with GFLIB_SIN_DEFAULT_F16 symbol. The
&pParam parameter is mandatory.
• With preselected default implementation (i.e.
GFLIB_Sin(f16In, &pParam), where the &pParam is
pointer to approximation coefficients. The &pParam
parameter is optional and in case it is not used, the default
GFLIB_SIN_DEFAULT_F16 approximation coefficients
are used.
5.54.5 Re-entrancy
The function is re-entrant.
5.54.6 Code Example
#include "gflib.h"
tFrac16 f16Angle;
tFrac16 f16Output;
void main(void)
{
// input angle = 0.5 => pi/2
f16Angle = FRAC16 (0.5);
// output should be 0x7FFF
f16Output = GFLIB_Sin_F16 (f16Angle, GFLIB_SIN_DEFAULT_F16);
// output should be 0x7FFF
f16Output = GFLIB_Sin (f16Angle, GFLIB_SIN_DEFAULT_F16, F16);
//
//
//
//
##############################################################
Available only if 16-bit fractional implementation selected
as default
##############################################################
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Function GFLIB_SinCos_F32
}
// output should be 0x7FFF
f16Output = GFLIB_Sin (f16Angle);
5.55 Function GFLIB_SinCos_F32
This function implements polynomial approximation of sine and cosine function.
5.55.1 Declaration
void GFLIB_SinCos_F32(tFrac32 f32In, SWLIBS_2Syst_F32 *pOut, const GFLIB_SINCOS_T_F32 *const
pParam);
5.55.2 Arguments
Table 5-69. GFLIB_SinCos_F32 arguments
Type
Name
Direction
Description
tFrac32
f32In
input
Input argument is a 32-bit number that contains an angle in
radians between [- π, π) normalized between [-1, 1).
SWLIBS_2Syst_F32 *
pOut
output
Pointer to the structure where the values of the sine and
cosine of the input angle are stored. The function returns the
sine and cosine of the input argument as a fixed point 32-bit
number, normalized between [-1, 1). The sine of input angle is
returned in first item of the structure and the cosine of input
angle is returned in second item of the structure.
const
GFLIB_SINCOS_T_F3
2 *const
pParam
input
Pointer to an array of Taylor coefficients.
5.55.3 Return
void
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5.55.4 Description
The GFLIB_SinCos_F32 function provides a computational method for calculation of a
standard trigonometric sine function sin(x) and cosine function cos(x), using the 9th order
Taylor polynomial approximation. The Taylor polynomial approximation of a sine
function is used for both, sine and cosine function. The relation between cosine and sine
function of the same input angle is:
Equation GFLIB_SinCos_Eq1
Both results, sin(x) and cos(x), are calculated using the same approach, thus the
calculation steps will be discussed for sin(x) function only. The Taylor polynomial
approximation of sine function is described by the following equation:
Equation GFLIB_SinCos_Eq2
where x is the input angle.
The 9th order polynomial approximation is chosen as sufficient an order to achieve the
best ratio between calculation accuracy and speed of calculation. Because the
GFLIB_SinCos_F32 function is implemented with consideration to fixed point fractional
arithmetic, all variables are normalized to fit into the [-1, 1) range. Therefore, in order to
cast the fractional value of the input angle f32In [-1, 1) into the correct range [- π, π), the
input f32In must be multiplied by π. So the fixed point fractional implementation of the
GFLIB_SinCos_F32 function, using optimized 9th order Taylor approximation, is given
as follows:
Equation GFLIB_SinCos_Eq3
The 9th order polynomial approximation of the sine function has a very good accuracy in
the range [- π/2, π/2) of the argument, but in wider ranges the calculation error quickly
increases. To minimize the error without having to use a higher order polynomial, the
symmetry of the sine function sin(x) = sin( π - x) is utilized. Therefore, the input
argument is transferred to be always in the range [- π/2, π/2) and the Taylor polynomial is
calculated only in the range of the argument [- π/2, π/2).
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Function GFLIB_SinCos_F32
To make calculations more precise, the given argument value f32In (that is to be
transferred into the range [-0.5, 0.5) due to the sine function symmetry) is shifted by 1 bit
to the left (multiplied by 2). Then, the value of f32In 2, used in the calculations, is in the
range [-1, 1) instead of [-0.25, 0.25). Shifting the input value by 1 bit to the left will
increase the accuracy of the calculated sin( π * f32In) function. Implementing such a
scale on the approximation function described by equation GFLIB_SinCos_Eq3, results
in the following:
Equation GFLIB_SinCos_Eq4
Equation GFLIB_SinCos_Eq4 can be further rewritten into the following form:
Equation GFLIB_SinCos_Eq5
where a 1 ... a 5 are coefficients of the approximation polynomial, which are calculated as
follows (represented as 32-bit signed fractional numbers):
Equation GFLIB_SinCos_Eq6
Therefore, the resulting equation has the following form:
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Equation GFLIB_SinCos_Eq7
Figure 5-25 depicts a floating point sine function generated from Matlab and the
approximated value of the sine function obtained from GFLIB_SinCos_F32, plus their
difference. The course of calculation accuracy as a function of the input angle can be
observed from this figure.
Figure 5-25. sin(x) vs. GFLIB_SinCos_F32(f32In)
Figure 5-26 depicts a floating point cosine function generated from Matlab and the
approximated value of the cosine function obtained from GFLIB_SinCos_F32, plus their
difference. The course of calculation accuracy as a function of the input angle can be
observed from this figure.
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Function GFLIB_SinCos_F32
Figure 5-26. cos(x) vs. GFLIB_SinCos_F32(f32In)
Note
The input/output pointers must contain valid addresses
otherwise an exception may occur (Data TLB Error, Data
Storage, Alignment, Machine Check).
The input angle (f32In) is normalized into the range [-1, 1). The
function call is slightly different from common approach in the
library set. The function can be called in three different ways:
• With implementation postfix (i.e.
GFLIB_SinCos_F32(f32In, &pOut, &pParam)), where the
&pOut is the pointer to output values and &pParam is
pointer to approximation coefficients. In case the default
approximation coefficients are used, the &pParam must be
replaced with GFLIB_SINCOS_DEFAULT_F32 symbol.
The &pParam parameter is mandatory.
• With additional implementation parameter (i.e.
GFLIB_SinCos(f32In, &pOut, &pParam, F32)), where the
&pOut is the pointer to output values and &pParam is
pointer to approximation coefficients. In case the default
approximation coefficients are used, the &pParam must be
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replaced with GFLIB_SINCOS_DEFAULT_F32 symbol.
The &pParam parameter is mandatory.
• With preselected default implementation (i.e.
GFLIB_SinCos(f32In, &pOut, &pParam)), where the
&pOut is the pointer to output values and &pParam is
pointer to approximation coefficients. The &pParam
parameter is optional and in case it is not used, the default
GFLIB_SINCOS_DEFAULT_F32 approximation
coefficients are used.
5.55.5 Re-entrancy
The function is re-entrant.
5.55.6 Code Example
#include "gflib.h"
tFrac32 f32Angle;
SWLIBS_2Syst_F32 pf32Output;
void main(void)
{
// input angle = 0.5 => pi/2
f32Angle = FRAC32 (0.5);
// output should be:
// pf32Output.f32Arg1 ~ sin(f32Angle) = 0x7FFF0000
// pf32Output.f32Arg2 ~ cos(f32Angle) = 0x00000000
GFLIB_SinCos_F32 (f32Angle, &pf32Output, GFLIB_SINCOS_DEFAULT_F32);
// output should be:
// pf32Output.f32Arg1 ~ sin(f32Angle) = 0x7FFF0000
// pf32Output.f32Arg2 ~ cos(f32Angle) = 0x00000000
GFLIB_SinCos (f32Angle, &pf32Output, GFLIB_SINCOS_DEFAULT_F32, F32);
//
//
//
//
}
##############################################################
Available only if 32-bit fractional implementation selected
as default
##############################################################
// output should be:
// pf32Output.f32Arg1 ~ sin(f32Angle) = 0x7FFF0000
// pf32Output.f32Arg2 ~ cos(f32Angle) = 0x00000000
GFLIB_SinCos (f32Angle, &pf32Output);
5.56 Function GFLIB_SinCos_F16
This function implements polynomial approximation of sine and cosine function.
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Function GFLIB_SinCos_F16
5.56.1 Declaration
void GFLIB_SinCos_F16(tFrac16 f16In, SWLIBS_2Syst_F16 *pOut, const GFLIB_SINCOS_T_F16 *const
pParam);
5.56.2 Arguments
Table 5-70. GFLIB_SinCos_F16 arguments
Type
Name
Direction
Description
tFrac16
f16In
input
Input argument is a 16-bit number that contains an angle in
radians between [- π, π) normalized between [-1, 1).
SWLIBS_2Syst_F16 *
pOut
output
Pointer to the structure where the values of the sine and
cosine of the input angle are stored. The function returns the
sine and cosine of the input argument as a fixed point 16-bit
number, normalized between [-1, 1). The sine of input angle is
returned in first item of the structure and the cosine of input
angle is returned in second item of the structure.
const
GFLIB_SINCOS_T_F1
6 *const
pParam
input
Pointer to an array of Taylor coefficients.
5.56.3 Return
void
5.56.4 Description
The GFLIB_SinCos_F16 function provides a computational method for calculation of a
standard trigonometric sine function sin(x) and cosine function cos(x), using the 7th order
Taylor polynomial approximation. The Taylor polynomial approximation of a sine
function is used for both, sine and cosine function. The realation between cosine and sine
function of the same input angle is:
Equation GFLIB_SinCos_Eq1
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Both results, sin(x) and cos(x), are calculated using the same approach, thus the
calculation steps will be discussed for sin(x) function only. The Taylor polynomial
approximation of sine function is described by the following equation:
Equation GFLIB_SinCos_Eq2
where x is the input angle.
The 7th order polynomial approximation is chosen as sufficient an order to achieve the
best ratio between calculation accuracy and speed of calculation. Because the
GFLIB_SinCos_F16 function is implemented with consideration to fixed point fractional
arithmetic, all variables are normalized to fit into the [-1, 1) range. Therefore, in order to
cast the fractional value of the input angle f16In [-1, 1) into the correct range [- π, π), the
input f16In must be multiplied by π. So the fixed point fractional implementation of the
GFLIB_SinCos_F16 function, using 7th order Taylor approximation, is given as follows:
Equation GFLIB_SinCos_Eq3
The 7th order polynomial approximation of the sine function has a very good accuracy in
the range [- π/2, π/2) of the argument, but in wider ranges the calculation error quickly
increases. To minimize the error without having to use a higher order polynomial, the
symmetry of the sine function sin(x) = sin( π - x) is utilized. Therefore, the input
argument is transferred to be always in the range [- π/2, π/2) and the Taylor polynomial is
calculated only in the range of the argument [- π/2, π/2).
To make calculations more precise, the given argument value f16In (that is to be
transferred into the range [-0.5, 0.5) due to the sine function symmetry) is shifted by 1 bit
to the left (multiplied by 2). Then, the value of f16In 2, used in the calculations, is in the
range [-1, 1) instead of [-0.25, 0.25). Shifting the input value by 1 bit to the left will
increase the accuracy of the calculated sin( π * f16In) function. Implementing such a
scale on the approximation function described by equation GFLIB_SinCos_Eq3, results
in the following:
Equation GFLIB_SinCos_Eq4
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Function GFLIB_SinCos_F16
Equation GFLIB_SinCos_Eq4 can be further rewritten into the following form:
Equation GFLIB_SinCos_Eq5
where a 1 ... a 4 are coefficients of the approximation polynomial, which are calculated as
follows (represented as 16-bit signed fractional numbers):
Equation GFLIB_SinCos_Eq6
Therefore, the resulting equation has the following form:
Equation GFLIB_SinCos_Eq7
Figure 5-27 depicts a floating point sine function generated from Matlab and the
approximated value of the sine function obtained from GFLIB_SinCos_F16, plus their
difference. The course of calculation accuracy as a function of the input angle can be
observed from this figure.
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Figure 5-27. sin(x) vs. GFLIB_SinCos_F16(f16In)
Figure 5-28 depicts a floating point cosine function generated from Matlab and the
approximated value of the cosine function obtained from GFLIB_SinCos_F16, plus their
difference. The course of calculation accuracy as a function of the input angle can be
observed from this figure.
Figure 5-28. cos(x) vs. GFLIB_SinCos_F16(f16In)
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Function GFLIB_SinCos_F16
Note
The input/output pointers must contain valid addresses
otherwise an exception may occur (Data TLB Error, Data
Storage, Alignment, Machine Check).
The input angle (f16In) is normalized into the range [-1, 1). The
function call is slightly different from common approach in the
library set. The function can be called in three different ways:
• With implementation postfix (i.e.
GFLIB_SinCos_F16(f16In, &pOut, &pParam)), where the
&pOut is the pointer to output values and &pParam is
pointer to approximation coefficients. In case the default
approximation coefficients are used, the &pParam must be
replaced with GFLIB_SINCOS_DEFAULT_F16 symbol.
The &pParam parameter is mandatory.
• With additional implementation parameter (i.e.
GFLIB_SinCos(f16In, &pOut, &pParam, F16)), where the
&pOut is the pointer to output values and &pParam is
pointer to approximation coefficients. In case the default
approximation coefficients are used, the &pParam must be
replaced with GFLIB_SINCOS_DEFAULT_F16 symbol.
The &pParam parameter is mandatory.
• With preselected default implementation (i.e.
GFLIB_SinCos(f16In, &pOut, &pParam)), where the
&pOut is the pointer to output values and &pParam is
pointer to approximation coefficients. The &pParam
parameter is optional and in case it is not used, the default
GFLIB_SINCOS_DEFAULT_F16 approximation
coefficients are used.
5.56.5 Re-entrancy
The function is re-entrant.
5.56.6 Code Example
#include "gflib.h"
tFrac16 f16Angle;
SWLIBS_2Syst_F16 pf16Output;
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void main(void)
{
// input angle = 0.5 => pi/2
f16Angle = FRAC16 (0.5);
// output should be:
// pf16Output.f16Arg1 ~ sin(f16Angle) = 0x7FFF
// pf16Output.f16Arg2 ~ cos(f16Angle) = 0x0000
GFLIB_SinCos_F16 (f16Angle, &pf16Output, GFLIB_SINCOS_DEFAULT_F16);
// output should be:
// pf16Output.f16Arg1 ~ sin(f16Angle) = 0x7FFF
// pf16Output.f16Arg2 ~ cos(f16Angle) = 0x0000
GFLIB_SinCos (f16Angle, &pf16Output, GFLIB_SINCOS_DEFAULT_F16, F16);
//
//
//
//
}
##############################################################
Available only if 16-bit fractional implementation selected
as default
##############################################################
// output should be:
// pf16Output.f16Arg1 ~ sin(f16Angle) = 0x7FFF
// pf16Output.f16Arg2 ~ cos(f16Angle) = 0x0000
GFLIB_SinCos (f16Angle, &pf16Output);
5.57 Function GFLIB_Sqrt_F32
This function returns the square root of input value.
5.57.1 Declaration
tFrac32 GFLIB_Sqrt_F32(tFrac32 f32In);
5.57.2 Arguments
Table 5-71. GFLIB_Sqrt_F32 arguments
Type
tFrac32
Name
f32In
Direction
input
Description
The input value.
5.57.3 Return
The function returns the square root of the input value. The return value is within the [0,
1) fraction range.
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Function GFLIB_Sqrt_F32
5.57.4 Description
The GFLIB_Sqrt_F32 function computes the square root of the input value.
The computations are made by a simple iterative testing of each bit starting from the most
significant one. In total, 15 iterations are made, each performing the following steps:
1. Add to the tentative square root value a single testing bit.
2. Square the tentative square root value and test whether it is greater or lower than the
input value.
3. If greater, then clear the bit in the tentative square root value.
4. Shift the single testing bit right
Figure 5-29. real sqrt(x) vs. GFLIB_Sqrt(f32In)
Note
The input value is limited to the range [0, 1), if not within this
range the function returns zero.
5.57.5 Re-entrancy
The function is re-entrant.
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5.57.6 Code Example
#include "gflib.h"
tFrac32 f32In;
tFrac32 f32Out;
void main(void)
{
// input value = 0.5
f32In = FRAC32 (0.5);
// output should be 0x5A820000 ~ FRAC32(0.70710678)
f32Out = GFLIB_Sqrt_F32 (f32In);
// output should be 0x5A820000 ~ FRAC32(0.70710678)
f32Out = GFLIB_Sqrt (f32In,F32);
//
//
//
//
}
##############################################################
Available only if 32-bit fractional implementation selected
as default
##############################################################
// output should be 0x5A820000 ~ FRAC32(0.70710678)
f32Out = GFLIB_Sqrt (f32In);
5.58 Function GFLIB_Sqrt_F16
This function returns the square root of input value.
5.58.1 Declaration
tFrac16 GFLIB_Sqrt_F16(tFrac16 f16In);
5.58.2 Arguments
Table 5-72. GFLIB_Sqrt_F16 arguments
Type
tFrac16
Name
f16In
Direction
input
Description
The input value.
5.58.3 Return
The function returns the square root of the input value. The return value is within the [0,
1) fraction range.
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Function GFLIB_Sqrt_F16
5.58.4 Description
The GFLIB_Sqrt_F16 function computes the square root of the input value.
The computations are made by a simple iterative testing of each bit starting from the most
significant one. In total, 15 iterations are made, each performing the following steps:
1. Add to the tentative square root value a single testing bit.
2. Square the tentative square root value and test whether it is greater or lower than the
input value.
3. If greater, then clear the bit in the tentative square root value.
4. Shift the single testing bit right
Figure 5-30. real sqrt(x) vs. GFLIB_Sqrt(f16In)
Note
The input value is limited to the range [0, 1), if not within this
range the function returns zero.
5.58.5 Re-entrancy
The function is re-entrant.
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5.58.6 Code Example
#include "gflib.h"
tFrac16 f16In;
tFrac16 f16Out;
void main(void)
{
// input value = 0.5
f16In = FRAC16 (0.5);
// output should be 0x5A82 ~ FRAC16(0.70710678)
f16Out = GFLIB_Sqrt_F16 (f16In);
// output should be 0x5A82 ~ FRAC16(0.70710678)
f16Out = GFLIB_Sqrt (f16In,F16);
//
//
//
//
}
##############################################################
Available only if 16-bit fractional implementation selected
as default
##############################################################
// output should be 0x5A82 ~ FRAC16(0.70710678)
f16Out = GFLIB_Sqrt (f16In);
5.59 Function GFLIB_Tan_F32
This function implements polynomial approximation of tangent function.
5.59.1 Declaration
tFrac32 GFLIB_Tan_F32(tFrac32 f32In, const GFLIB_TAN_T_F32 *const pParam);
5.59.2 Arguments
Table 5-73. GFLIB_Tan_F32 arguments
Type
Name
Direction
Description
tFrac32
f32In
input
Input argument is a 32-bit number that contains an angle in
radians between [- π, π) normalized between [-1, 1).
const
GFLIB_TAN_T_F32
*const
pParam
input
Pointer to an array of Taylor coefficients.
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5.59.3 Return
The function returns tan( π * f32In) as a fixed point 32-bit number, normalized between
[-1, 1).
5.59.4 Description
The GFLIB_Tan_F32 function provides a computational method for calculation of a
standard trigonometric tangent function tan(x), using the piece-wise polynomial
approximation. Function tan(x) takes an angle and returns the ratio of two sides of a
right-angled triangle. The ratio is the length of the side opposite the angle divided by the
length of the side adjacent to the angle. Therefore, the tangent function is defined by:
Equation GFLIB_Tan_Eq1
Because both sin(x) and cos(x) are defined on interval [- π, π), function tan(x) is equal to
zero when sin(x)=0 and is equal to infinity when cos(x)=0. Therefore, the tangent
function has asymptotes at n*π/2 for n=1, 3, 5,... The graph of tan(x) is shown in Figure
5-31.
Figure 5-31. Course of the function GFLIB_Tan
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The GFLIB_Tan_F32 function is implemented with consideration to fixed point
fractional arithmetic, hence all tangent values falling beyond [-1, 1) are truncated to -1
and 1 respectively. This truncation is applied for angles in the ranges [-3 π/4, - π/4) and
[ π/4, 3 π/4). As can be further seen from Figure 5-31, tangent values are identical for
angles in the ranges:
1. [- π/4, 0) and [3 π/4, π)
2. [- π, -3 π/4) and [0, π/4)
Moreover, it can be observed from Figure 5-31 that the course of the tan(x) function
output for angles in interval 1. is identical, but with the opposite sign, to output for angles
in interval 2. Therefore, the approximation of the tangent function over the entire defined
range of input angles can be simplified to an approximation for angles in the range [0,
π/4), and then, depending on the input angle, the result will be negated. In order to
increase the accuracy of approximation without the need for a higher order polynomial,
the interval [0, π/4) is further divided into eight equally spaced sub intervals, and
polynomial approximation is done for each interval respectively. Such a division results
in eight sets of polynomial coefficients. Moreover, it allows using a polynomial of only
the 4th order to achieve an accuracy of less than 0.5LSB (on the upper 16 bits of 32-bit
results) across the full range of input angles.
The GFLIB_Tan_F32 function uses fixed point fractional arithmetic, so to cast the
fractional value of the input angle f32In [-1, 1) into the correct range [- π, π), the fixed
point input angle f32In must be multiplied by π. Then the fixed point fractional
implementation of the approximation polynomial, used for calculation of each sub sector,
is defined as follows:
Equation GFLIB_Tan_Eq2
Equation GFLIB_Tan_Eq3
The division of the [0, π/4) interval into eight sub-intervals, with polynomial coefficients
calculated for each sub-interval, is noted in Table 5-74. Polynomial coefficients were
obtained using the Matlab fitting function, where a polynomial of the 4th order was used
for the fitting of each respective sub-interval.
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Function GFLIB_Tan_F32
Table 5-74. Integer polynomial coefficients for each interval
Interval
a1
a2
a3
a4
<0, π/32)
688168
1024000
211337216
105498624
< π/32, 2 π/32)
737280
3145728
107732992
318550016
<2 π/32, 3 π/32)
851968
5521408
224055296
537917440
<3 π/32, 4 π/32)
1064960
8364032
237821952
768380928
<4 π/32, 5 π/32)
1392640
12001280
257990656
1015683072
<5 π/32, 6 π/32)
1916928
16900096
286568448
1287151616
<6 π/32, 7 π/32)
2785280
23855104
326795264
1592680448
<7 π/32, 8 π/32)
4292608
34275328
384016384
1946363904
Figure 5-32. tan(x) vs. GFLIB_Tan(f32In)
Figure 5-32 depicts a floating point tangent function generated from Matlab and the
approximated value of the tangent function obtained from GFLIB_Tan_F32, plus their
difference. The course of calculation accuracy as a function of the input angle can be
observed from this figure. The achieved accuracy with consideration to the 4th order
piece-wise polynomial approximation and described fixed point scaling is less than
0.5LSB on the upper 16 bits of the 32-bit result.
Note
The input pointer must contain a valid address otherwise an
exception may occur (Data TLB Error, Data Storage,
Alignment, Machine Check).
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The input angle (f32In) is normalized into the range [-1, 1). The
function call is slightly different from common approach in the
library set. The function can be called in three different ways:
• With implementation postfix (i.e. GFLIB_Tan_F32(f32In,
&pParam)), where the &pParam is pointer to
approximation coefficients. In case the default
approximation coefficients are used, the &pParam must be
replaced with GFLIB_TAN_DEFAULT_F32 symbol. The
&pParam parameter is mandatory.
• With additional implementation parameter (i.e.
GFLIB_Tan(f32In, &pParam, F32), where the &pParam is
pointer to approximation coefficients. In case the default
approximation coefficients are used, the &pParam must be
replaced with GFLIB_TAN_DEFAULT_F32 symbol. The
&pParam parameter is mandatory.
• With preselected default implementation (i.e.
GFLIB_Tan(f32In, &pParam), where the &pParam is
pointer to approximation coefficients. The &pParam
parameter is optional and in case it is not used, the default
GFLIB_TAN_DEFAULT_F32 approximation coefficients
are used.
5.59.5 Re-entrancy
The function is re-entrant.
5.59.6 Code Example
#include "gflib.h"
tFrac32 f32Angle;
tFrac32 f32Output;
void main(void)
{
// input angle = 0.25 => pi/4
f32Angle = FRAC32 (0.25);
// output should be 0x7FFFFFFF = 1
f32Output = GFLIB_Tan_F32 (f32Angle, GFLIB_TAN_DEFAULT_F32);
// output should be 0x7FFFFFFF = 1
f32Output = GFLIB_Tan (f32Angle, GFLIB_TAN_DEFAULT_F32, F32);
// ##############################################################
// Available only if 32-bit fractional implementation selected
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Function GFLIB_Tan_F16
// as default
// ##############################################################
}
// output should be 0x7FFFFFFF = 1
f32Output = GFLIB_Tan (f32Angle);
5.60 Function GFLIB_Tan_F16
This function implements polynomial approximation of tangent function.
5.60.1 Declaration
tFrac16 GFLIB_Tan_F16(tFrac16 f16In, const GFLIB_TAN_T_F16 *const pParam);
5.60.2 Arguments
Table 5-75. GFLIB_Tan_F16 arguments
Type
Name
Direction
Description
tFrac16
f16In
input
Input argument is a 16-bit number that contains an angle in
radians between [- π, π) normalized between [-1, 1).
const
GFLIB_TAN_T_F16
*const
pParam
input
Pointer to an array of Taylor coefficients.
5.60.3 Return
The function returns tan( π * f16In) as a fixed point 16-bit number, normalized between
[-1, 1).
5.60.4 Description
The GFLIB_Tan_F16 function provides a computational method for calculation of a
standard trigonometric tangent function tan(x), using the piece-wise polynomial
approximation. Function tan(x) takes an angle and returns the ratio of two sides of a
right-angled triangle. The ratio is the length of the side opposite the angle divided by the
length of the side adjacent to the angle. Therefore, the tangent function is defined by:
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Equation GFLIB_Tan_Eq1
Because both sin(x) and cos(x) are defined on interval [- π, π), function tan(x) is equal to
zero when sin(x)=0 and is equal to infinity when cos(x)=0. Therefore, the tangent
function has asymptotes at n*π/2 for n=1, 3, 5,... The graph of tan(x) is shown in Figure
5-33.
Figure 5-33. Course of the function GFLIB_Tan
The GFLIB_Tan_F16 function is implemented with consideration to fixed point
fractional arithmetic, hence all tangent values falling beyond [-1, 1) are truncated to -1
and 1 respectively. This truncation is applied for angles in the ranges [-3 π/4, - π/4) and
[ π/4, 3 π/4). As can be further seen from Figure 5-33, tangent values are identical for
angles in the ranges:
1. [- π/4, 0) and [3 π/4, π)
2. [- π,- 3 π/4) and [0, π/4)
Moreover, it can be observed from Figure 5-33 that the course of the tan(x) function
output for angles in interval 1. is identical, but with the opposite sign, to output for angles
in interval 2. Therefore, the approximation of the tangent function over the entire defined
range of input angles can be simplified to an approximation for angles in the range [0,
π/4), and then, depending on the input angle, the result will be negated. In order to
increase the accuracy of approximation without the need for a higher order polynomial,
the interval [0, π/4) is further divided into eight equally spaced sub intervals, and
polynomial approximation is done for each interval respectively. Such a division results
in eight sets of polynomial coefficients.
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Function GFLIB_Tan_F16
The GFLIB_Tan_F16 function uses fixed point fractional arithmetic, so to cast the
fractional value of the input angle f16In [-1, 1) into the correct range [- π, π), the fixed
point input angle f16In must be multiplied by π. Then the fixed point fractional
implementation of the approximation polynomial, used for calculation of each sub sector,
is defined as follows:
Equation GFLIB_Tan_Eq2
Equation GFLIB_Tan_Eq3
The division of the [0, π/4) interval into eight sub-intervals, with polynomial coefficients
calculated for each sub-interval, is noted in Table 5-76. Polynomial coefficients were
obtained using the Matlab fitting function, where a polynomial of the 4th order was used
for the fitting of each respective sub-interval.
Table 5-76. Integer polynomial coefficients for each interval
Interval
a1
a2
a3
a4
<0, π/32)
11
160
3225
1610
< π/32, 2 π/32)
11
48
3288
4861
<2 π/32, 3 π/32)
13
84
3419
8208
<3 π/32, 4 π/32)
16
128
3629
11725
<4 π/32, 5 π/32)
21
183
3937
15498
<5 π/32, 6 π/32)
29
258
4373
19640
<6 π/32, 7 π/32)
43
364
4987
24302
<7 π/32, 8 π/32)
66
523
5860
29699
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Figure 5-34. tan(x) vs. GFLIB_Tan(f16In)
Figure 5-34 depicts a floating point tangent function generated from Matlab and the
approximated value of the tangent function obtained from GFLIB_Tan_F16, plus their
difference. The course of calculation accuracy as a function of the input angle can be
observed from this figure.
Note
The input pointer must contain a valid address otherwise an
exception may occur (Data TLB Error, Data Storage,
Alignment, Machine Check).
The input angle (f16In) is normalized into the range [-1, 1). The
function call is slightly different from common approach in the
library set. The function can be called in three different ways:
• With implementation postfix (i.e. GFLIB_Tan_F16(f16In,
&pParam)), where the &pParam is pointer to
approximation coefficients. In case the default
approximation coefficients are used, the &pParam must be
replaced with GFLIB_TAN_DEFAULT_F16 symbol. The
&pParam parameter is , mandatory.
• With additional implementation parameter (i.e.
GFLIB_Tan(f16In, &pParam, F16), where the &pParam is
pointer to approximation coefficients. In case the default
approximation coefficients are used, the &pParam must be
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Function GFLIB_UpperLimit_F32
replaced with GFLIB_TAN_DEFAULT_F16 symbol. The
&pParam parameter is mandatory.
• With preselected default implementation (i.e.
GFLIB_Tan(f16In, &pParam), where the &pParam is
pointer to approximation coefficients. The &pParam
parameter is optional and in case it is not used, the default
GFLIB_TAN_DEFAULT_F16 approximation coefficients
are used.
5.60.5 Re-entrancy
The function is re-entrant.
5.60.6 Code Example
#include "gflib.h"
tFrac16 f16Angle;
tFrac16 f16Output;
void main(void)
{
// input angle = 0.25 => pi/4
f16Angle = FRAC16 (0.25);
// output should be 0x7FFF = 1
f16Output = GFLIB_Tan_F16 (f16Angle, GFLIB_TAN_DEFAULT_F16);
// output should be 0x7FFF = 1
f16Output = GFLIB_Tan (f16Angle, GFLIB_TAN_DEFAULT_F16, F16);
//
//
//
//
}
##############################################################
Available only if 16-bit fractional implementation selected
as default
##############################################################
// output should be 0x7FFF = 1
f16Output = GFLIB_Tan (f16Angle);
5.61 Function GFLIB_UpperLimit_F32
This function tests whether the input value is below the upper limit.
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5.61.1 Declaration
tFrac32 GFLIB_UpperLimit_F32(tFrac32 f32In, const GFLIB_UPPERLIMIT_T_F32 *const pParam);
5.61.2 Arguments
Table 5-77. GFLIB_UpperLimit_F32 arguments
Type
Name
tFrac32
f32In
const
pParam
GFLIB_UPPERLIMIT_T
_F32 *const
Direction
Description
input
Input value.
input
Pointer to the limits structure.
5.61.3 Return
The input value in case the input value is below the limit, or the upper limit if the input
value is above the limit.
5.61.4 Description
The GFLIB_UpperLimit function tests whether the input value is below the upper limit.
If so, the input value will be returned. Otherwise, if the input value is above the upper
limit, the upper limit will be returned.
The upper limit f32UpperLimit can be found in the parameters structure, supplied to the
function as a pointer pParam.
Note
The input pointer must contain a valid address otherwise an
exception may occur (Data TLB Error, Data Storage,
Alignment, Machine Check).
5.61.5 Re-entrancy
The function is re-entrant.
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Function GFLIB_UpperLimit_F16
5.61.6 Code Example
#include "gflib.h"
tFrac32 f32In;
tFrac32 f32Out;
GFLIB_UPPERLIMIT_T_F32 f32trMyUpperLimit = GFLIB_UPPERLIMIT_DEFAULT_F32;
void main(void)
{
// upper limit
f32trMyUpperLimit.f32UpperLimit = FRAC32 (0.5);
// input value = 0.75
f32In = FRAC32 (0.75);
// output should be 0x40000000 ~ FRAC32(0.5)
f32Out = GFLIB_UpperLimit_F32 (f32In,&f32trMyUpperLimit);
// output should be 0x40000000 ~ FRAC32(0.5)
f32Out = GFLIB_UpperLimit (f32In,&f32trMyUpperLimit,F32);
//
//
//
//
}
##############################################################
Available only if 32-bit fractional implementation selected
as default
##############################################################
// output should be 0x40000000 ~ FRAC32(0.5)
f32Out = GFLIB_UpperLimit (f32In,&f32trMyUpperLimit);
5.62 Function GFLIB_UpperLimit_F16
This function tests whether the input value is below the upper limit.
5.62.1 Declaration
tFrac16 GFLIB_UpperLimit_F16(tFrac16 f16In, const GFLIB_UPPERLIMIT_T_F16 *const pParam);
5.62.2 Arguments
Table 5-78. GFLIB_UpperLimit_F16 arguments
Type
tFrac16
Name
f16In
const
pParam
GFLIB_UPPERLIMIT_T
_F16 *const
Direction
Description
input
Input value.
input
Pointer to the limits structure.
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5.62.3 Return
The input value in case the input value is below the limit, or the upper limit if the input
value is above the limit.
5.62.4 Description
The GFLIB_UpperLimit function tests whether the input value is below the upper limit.
If so, the input value will be returned. Otherwise, if the input value is above the upper
limit, the upper limit will be returned.
The upper limit f16UpperLimit can be found in the parameters structure, supplied to the
function as a pointer pParam.
Note
The input pointer must contain a valid address otherwise an
exception may occur (Data TLB Error, Data Storage,
Alignment, Machine Check).
5.62.5 Re-entrancy
The function is re-entrant.
5.62.6 Code Example
#include "gflib.h"
tFrac16 f16In;
tFrac16 f16Out;
GFLIB_UPPERLIMIT_T_F16 f16trMyUpperLimit = GFLIB_UPPERLIMIT_DEFAULT_F16;
void main(void)
{
// upper limit
f16trMyUpperLimit.f16UpperLimit = FRAC16 (0.5);
// input value = 0.75
f16In = FRAC16 (0.75);
// output should be 0x4000 ~ FRAC16(0.5)
f16Out = GFLIB_UpperLimit_F16 (f16In,&f16trMyUpperLimit);
// output should be 0x4000 ~ FRAC16(0.5)
f16Out = GFLIB_UpperLimit (f16In,&f16trMyUpperLimit,F16);
//
//
//
//
##############################################################
Available only if 16-bit fractional implementation selected
as default
##############################################################
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Function GFLIB_VectorLimit_F32
}
// output should be 0x4000 ~ FRAC16(0.5)
f16Out = GFLIB_UpperLimit (f16In,&f16trMyUpperLimit);
5.63 Function GFLIB_VectorLimit_F32
This function limits the magnitude of the input vector.
5.63.1 Declaration
tBool GFLIB_VectorLimit_F32(SWLIBS_2Syst_F32 *const pOut, const SWLIBS_2Syst_F32 *const pIn,
const GFLIB_VECTORLIMIT_T_F32 *const pParam);
5.63.2 Arguments
Table 5-79. GFLIB_VectorLimit_F32 arguments
Type
Name
Direction
Description
const
SWLIBS_2Syst_F32
*const
pIn
input
Pointer to the structure of the input vector.
SWLIBS_2Syst_F32
*const
pOut
output
Pointer to the structure of the limited output vector.
const
GFLIB_VECTORLIMIT
_T_F32 *const
pParam
input
Pointer to the parameters structure.
5.63.3 Return
The function will return true "TRUE" if the input vector is being limited, or false
"FALSE" otherwise.
5.63.4 Description
The GFLIB_VectorLimit function limits the magnitude of the input vector, keeping its
direction unchanged. Limitation is performed as follows:
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Equation GFLIB_VectorLimit_Eq1
Equation GFLIB_VectorLimit_Eq2
Where:
• x in, y in and x out, y out are the co-ordinates of the input and output vector,
respectively
• L is the maximum magnitude of the vector
The input vector co-ordinates are defined by the structure pointed to by the pIn
parameter, and the output vector co-ordinates be found in the structure pointed by the
pOut parameter. The maximum vector magnitude is defined in the parameters structure
pointed to by the pParam function parameter.
A graphical interpretation of the function can be seen in the figure below.
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Function GFLIB_VectorLimit_F32
Figure 5-35. Graphical interpretation of the GFLIB_VectorLimit function.
If an actual limitation occurs, the function will return the logical true (TRUE), otherwise
the logical false will be returned (FALSE).
For computational reasons, the output vector will be computed as zero if the input vector
magnitude is lower than 2 -15, regardless of the set maximum magnitude of the input
vector. The function returns the logical true (TRUE) in this case.
Also, the 16 least significant bits of the maximum vector magnitude in the parameters
structure, the pParam->f32Limit, are ignored. This means that the defined magnitude
must be equal to or greater than 2 -15, otherwise the result is undefined.
Note
The input/output pointers must contain valid addresses
otherwise an exception may occur (Data TLB Error, Data
Storage, Alignment, Machine Check).
The function calls the AMMCLIB square root routine
GFLIB_Sqrt.
CAUTION
The maximum vector magnitude in the parameters structure, the
pParam->f32Limit, must be positive and equal to or greater
than 2 -15, otherwise the result is undefined. The function does
not check for the valid range of pParam->f32Limit.
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5.63.5 Re-entrancy
The function is re-entrant.
5.63.6 Code Example
#include "gflib.h"
SWLIBS_2Syst_F32 f32pIn;
SWLIBS_2Syst_F32 f32pOut;
GFLIB_VECTORLIMIT_T_F32 f32trMyVectorLimit = GFLIB_VECTORLIMIT_DEFAULT_F32;
tBool bLim;
void main(void)
{
// desired magnitude of the input vector
f32trMyVectorLimit.f32Limit = FRAC32 (0.25);
// input vector
f32pIn.f32Arg1 = FRAC32 (0.25);
f32pIn.f32Arg2 = FRAC32 (0.25);
// output should be:
// bLim = TRUE;
// f32pOut.f32Arg1 = 0x16A08000 ~ FRAC32(0.17677)
// f32pOut.f32Arg2 = 0x16A08000 ~ FRAC32(0.17677)
bLim = GFLIB_VectorLimit_F32 (&f32pOut,&f32pIn,&f32trMyVectorLimit);
// output should be:
// bLim = TRUE;
// f32pOut.f32Arg1 = 0x16A08000 ~ FRAC32(0.17677)
// f32pOut.f32Arg2 = 0x16A08000 ~ FRAC32(0.17677)
bLim = GFLIB_VectorLimit (&f32pOut,&f32pIn,&f32trMyVectorLimit,F32);
//
//
//
//
}
##############################################################
Available only if 32-bit fractional implementation selected
as default
##############################################################
// output should be:
// bLim = TRUE;
// f32pOut.f32Arg1 = 0x16A08000 ~ FRAC32(0.17677)
// f32pOut.f32Arg2 = 0x16A08000 ~ FRAC32(0.17677)
bLim = GFLIB_VectorLimit (&f32pOut,&f32pIn,&f32trMyVectorLimit);
5.64 Function GFLIB_VectorLimit_F16
This function limits the magnitude of the input vector.
5.64.1 Declaration
tBool GFLIB_VectorLimit_F16(SWLIBS_2Syst_F16 *const pOut, const SWLIBS_2Syst_F16 *const pIn,
const GFLIB_VECTORLIMIT_T_F16 *const pParam);
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Function GFLIB_VectorLimit_F16
5.64.2 Arguments
Table 5-80. GFLIB_VectorLimit_F16 arguments
Type
Name
Direction
Description
const
SWLIBS_2Syst_F16
*const
pIn
input
Pointer to the structure of the input vector.
SWLIBS_2Syst_F16
*const
pOut
output
Pointer to the structure of the limited output vector.
const
GFLIB_VECTORLIMIT
_T_F16 *const
pParam
input
Pointer to the parameters structure.
5.64.3 Return
The function will return true "TRUE" if the input vector is being limited, or false
"FALSE" otherwise.
5.64.4 Description
The GFLIB_VectorLimit function limits the magnitude of the input vector, keeping its
direction unchanged. Limitation is performed as follows:
Equation GFLIB_VectorLimit_Eq1
Equation GFLIB_VectorLimit_Eq2
Where:
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• x in, y in and x out, y out are the co-ordinates of the input and output vector,
respectively
• L is the maximum magnitude of the vector
The input vector co-ordinates are defined by the structure pointed to by the pIn
parameter, and the output vector co-ordinates be found in the structure pointed by the
pOut parameter. The maximum vector magnitude is defined in the parameters structure
pointed to by the pParam function parameter.
A graphical interpretation of the function can be seen in the figure below.
Figure 5-36. Graphical interpretation of the GFLIB_VectorLimit function.
If an actual limitation occurs, the function will return the logical true (TRUE), otherwise
the logical false will be returned (FALSE).
Note
The input/output pointers must contain valid addresses
otherwise an exception may occur (Data TLB Error, Data
Storage, Alignment, Machine Check).
The function calls the AMMCLIB square root routine
GFLIB_Sqrt.
CAUTION
The maximum vector magnitude in the parameters structure, the
pParam->f16Limit, must be positive and equal to or greater
than "0", otherwise the result is undefined. The function does
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Function GMCLIB_Clark_F32
not check for the valid range of the parameter pParam>f16Limit.
5.64.5 Re-entrancy
The function is re-entrant.
5.64.6 Code Example
#include "gflib.h"
SWLIBS_2Syst_F16 f16pIn;
SWLIBS_2Syst_F16 f16pOut;
GFLIB_VECTORLIMIT_T_F16 f16trMyVectorLimit = GFLIB_VECTORLIMIT_DEFAULT_F16;
tBool bLim;
void main(void)
{
// desired magnitude of the input vector
f16trMyVectorLimit.f16Limit = FRAC16 (0.25);
// input vector
f16pIn.f16Arg1 = FRAC16 (0.25);
f16pIn.f16Arg2 = FRAC16 (0.25);
// output should be:
// bLim = TRUE;
// f16pOut.f16Arg1 = 0x16A0 ~ FRAC16(0.17677)
// f16pOut.f16Arg2 = 0x16A0 ~ FRAC16(0.17677)
bLim = GFLIB_VectorLimit_F16 (&f16pOut,&f16pIn,&f16trMyVectorLimit);
// output should be:
// bLim = TRUE;
// f16pOut.f16Arg1 = 0x16A0 ~ FRAC16(0.17677)
// f16pOut.f16Arg2 = 0x16A0 ~ FRAC16(0.17677)
bLim = GFLIB_VectorLimit (&f16pOut,&f16pIn,&f16trMyVectorLimit,F16);
//
//
//
//
}
##############################################################
Available only if 16-bit fractional implementation selected
as default
##############################################################
// output should be:
// bLim = TRUE;
// f16pOut.f16Arg1 = 0x16A0 ~ FRAC16(0.17677)
// f16pOut.f16Arg2 = 0x16A0 ~ FRAC16(0.17677)
bLim = GFLIB_VectorLimit (&f16pOut,&f16pIn,&f16trMyVectorLimit);
5.65 Function GMCLIB_Clark_F32
The function implements the Clarke transformation.
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5.65.1 Declaration
void GMCLIB_Clark_F32(SWLIBS_2Syst_F32 *const pOut, const SWLIBS_3Syst_F32 *const pIn);
5.65.2 Arguments
Table 5-81. GMCLIB_Clark_F32 arguments
Type
Name
Direction
Description
const
SWLIBS_3Syst_F32
*const
pIn
input
Pointer to the structure containing data of the three-phase
stationary system (f32A-f32B-f32C). Arguments of the
structure contain fixed point 32-bit values.
SWLIBS_2Syst_F32
*const
pOut
output
Pointer to the structure containing data of the two-phase
stationary orthogonal system ( α- β). Arguments of the
structure contain fixed point 32-bit values.
5.65.3 Return
Function returns no value.
5.65.4 Description
The Clarke Transformation is used to transform values from the three-phase (A-B-C)
coordinate system to the two-phase ( α- β) orthogonal coordinate system, according to
the following equations:
Equation GMCLIB_Clark_Eq1
Equation GMCLIB_Clark_Eq2
where it is assumed that the axis f32A (axis of the first phase) and the axis α are in the
same direction.
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Function GMCLIB_Clark_F16
Note
The input/output pointers must contain valid addresses
otherwise an exception may occur (Data TLB Error, Data
Storage, Alignment, Machine Check).
The inputs and the outputs are normalized to fit in the range [-1,
1).
5.65.5 Re-entrancy
The function is re-entrant.
5.65.6 Code Example
#include "gmclib.h"
SWLIBS_3Syst_F32 f32trAbc;
SWLIBS_2Syst_F32 f32trAlBe;
void main(void)
{
// input phase A
// input phase B
// input phase C
f32trAbc.f32Arg1
f32trAbc.f32Arg2
f32trAbc.f32Arg3
~
~
~
=
=
=
sin(45) ~ 0.707106781
sin(45 + 120) ~ 0.258819045
sin(45 - 120) ~ -0.965925826
FRAC32 (0.707106781);
FRAC32 (0.258819045);
FRAC32 (-0.965925826);
// output should be f32trAlBe.f32Arg1 = 0x5A827999 ~ FRAC32(0.707106781)
// output should be f32trAlBe.f32Arg2 = 0x5A827999 ~ FRAC32(0.707106781)
GMCLIB_Clark_F32 (&f32trAlBe,&f32trAbc);
// output should be f32trAlBe.f32Arg1 = 0x5A827999 ~ FRAC32(0.707106781)
// output should be f32trAlBe.f32Arg2 = 0x5A827999 ~ FRAC32(0.707106781)
GMCLIB_Clark (&f32trAlBe,&f32trAbc,F32);
//
//
//
//
}
##############################################################
Available only if 32-bit fractional implementation selected
as default
##############################################################
// output should be f32trAlBe.f32Arg1 = 0x5A827999 ~ FRAC32(0.707106781)
// output should be f32trAlBe.f32Arg2 = 0x5A827999 ~ FRAC32(0.707106781)
GMCLIB_Clark (&f32trAlBe,&f32trAbc);
5.66 Function GMCLIB_Clark_F16
The function implements the Clarke transformation.
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Chapter 5 API References
5.66.1 Declaration
void GMCLIB_Clark_F16(SWLIBS_2Syst_F16 *const pOut, const SWLIBS_3Syst_F16 *const pIn);
5.66.2 Arguments
Table 5-82. GMCLIB_Clark_F16 arguments
Type
Name
Direction
Description
const
SWLIBS_3Syst_F16
*const
pIn
input
Pointer to the structure containing data of the three-phase
stationary system (f16A-f16B-f16C). Arguments of the
structure contain fixed point 16-bit values.
SWLIBS_2Syst_F16
*const
pOut
output
Pointer to the structure containing data of the two-phase
stationary orthogonal system ( α- β). Arguments of the
structure contain fixed point 16-bit values.
5.66.3 Return
Function returns no value.
5.66.4 Description
The Clarke Transformation is used to transform values from the three-phase (A-B-C)
coordinate system to the two-phase ( α- β) orthogonal coordinate system, according to
the following equations:
Equation GMCLIB_Clark_Eq1
Equation GMCLIB_Clark_Eq2
where it is assumed that the axis f16A (axis of the first phase) and the axis α are in the
same direction.
Automotive Math and Motor Control Library Set for NXP MPC560xB devices, Rev. 7
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Function GMCLIB_ClarkInv_F32
Note
The input/output pointers must contain valid addresses
otherwise an exception may occur (Data TLB Error, Data
Storage, Alignment, Machine Check).
The inputs and the outputs are normalized to fit in the range [-1,
1).
5.66.5 Re-entrancy
The function is re-entrant.
5.66.6 Code Example
#include "gmclib.h"
SWLIBS_3Syst_F16 f16trAbc;
SWLIBS_2Syst_F16 f16trAlBe;
void main(void)
{
// input phase A
// input phase B
// input phase C
f16trAbc.f16Arg1
f16trAbc.f16Arg2
f16trAbc.f16Arg3
~
~
~
=
=
=
sin(45) ~ 0.707106781
sin(45 + 120) ~ 0.258819045
sin(45 - 120) ~ -0.965925826
FRAC16 (0.707106781);
FRAC16 (0.258819045);
FRAC16 (-0.965925826);
// output should be f16trAlBe.f16Arg1 = 0x5A82 ~ FRAC16(0.707106781)
// output should be f16trAlBe.f16Arg2 = 0x5A82 ~ FRAC16(0.707106781)
GMCLIB_Clark_F16 (&f16trAlBe,&f16trAbc);
// output should be f16trAlBe.f16Arg1 = 0x5A82 ~ FRAC16(0.707106781)
// output should be f16trAlBe.f16Arg2 = 0x5A82 ~ FRAC16(0.707106781)
GMCLIB_Clark (&f16trAlBe,&f16trAbc,F16);
//
//
//
//
}
##############################################################
Available only if 16-bit fractional implementation selected
as default
##############################################################
// output should be f16trAlBe.f16Arg1 = 0x5A82 ~ FRAC16(0.707106781)
// output should be f16trAlBe.f16Arg2 = 0x5A82 ~ FRAC16(0.707106781)
GMCLIB_Clark (&f16trAlBe,&f16trAbc);
5.67 Function GMCLIB_ClarkInv_F32
The function implements the inverse Clarke transformation.
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Chapter 5 API References
5.67.1 Declaration
void GMCLIB_ClarkInv_F32(SWLIBS_3Syst_F32 *const pOut, const SWLIBS_2Syst_F32 *const pIn);
5.67.2 Arguments
Table 5-83. GMCLIB_ClarkInv_F32 arguments
Type
Name
Direction
Description
const
SWLIBS_2Syst_F32
*const
pIn
input
Pointer to the structure containing data of the two-phase
stationary orthogonal system ( α- β). Arguments of the
structure contain fixed point 32-bit values.
SWLIBS_3Syst_F32
*const
pOut
output
Pointer to the structure containing data of the three-phase
stationary system (f32A-f32B-f32C). Arguments of the
structure contain fixed point 32-bit values.
5.67.3 Return
Function returns no value.
5.67.4 Description
The GMCLIB_ClarkInv function calculates the Inverse Clarke transformation, which is
used to transform values from the two-phase ( α- β) orthogonal coordinate system to the
three-phase (f32A-f32B-f32C) coordinate system, according to these equations:
Equation GMCLIB_ClarkInv_Eq1
Equation GMCLIB_ClarkInv_Eq2
Automotive Math and Motor Control Library Set for NXP MPC560xB devices, Rev. 7
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Function GMCLIB_ClarkInv_F16
Equation GMCLIB_ClarkInv_Eq3
Note
The input/output pointers must contain valid addresses
otherwise an exception may occur (Data TLB Error, Data
Storage, Alignment, Machine Check).
The inputs and the outputs are normalized to fit in the range [-1,
1).
5.67.5 Re-entrancy
The function is re-entrant.
5.67.6 Code Example
#include "gmclib.h"
SWLIBS_2Syst_F32 f32trAlBe;
SWLIBS_3Syst_F32 f32trAbc;
void main(void)
{
// input phase alpha ~ sin(45) ~ 0.707106781
// input phase beta ~ cos(45) ~ 0.707106781
f32trAlBe.f32Arg1 = FRAC32 (0.707106781);
f32trAlBe.f32Arg2 = FRAC32 (0.707106781);
// output should be
// output should be
// output should be
GMCLIB_ClarkInv_F32
f32trAbc.f32Arg1 = 0x5A827999 ~ FRAC32(0.707106781)
f32trAbc.f32Arg2 = 0x2120FB83 ~ FRAC32(0.258819045)
f32trAbc.f32Arg3 = 0x845C8AE5 ~ FRAC32(-0.965925826)
(&f32trAbc,&f32trAlBe);
// output should be f32trAbc.f32Arg1 = 0x5A827999 ~ FRAC32(0.707106781)
// output should be f32trAbc.f32Arg2 = 0x2120FB83 ~ FRAC32(0.258819045)
// output should be f32trAbc.f32Arg3 = 0x845C8AE5 ~ FRAC32(-0.965925826)
GMCLIB_ClarkInv (&f32trAbc,&f32trAlBe,F32);
//
//
//
//
}
##############################################################
Available only if 32-bit fractional implementation selected
as default
##############################################################
// output should be f32trAbc.f32Arg1 = 0x5A827999 ~ FRAC32(0.707106781)
// output should be f32trAbc.f32Arg2 = 0x2120FB83 ~ FRAC32(0.258819045)
// output should be f32trAbc.f32Arg3 = 0x845C8AE5 ~ FRAC32(-0.965925826)
GMCLIB_ClarkInv (&f32trAbc,&f32trAlBe);
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Chapter 5 API References
5.68 Function GMCLIB_ClarkInv_F16
The function implements the inverse Clarke transformation.
5.68.1 Declaration
void GMCLIB_ClarkInv_F16(SWLIBS_3Syst_F16 *const pOut, const SWLIBS_2Syst_F16 *const pIn);
5.68.2 Arguments
Table 5-84. GMCLIB_ClarkInv_F16 arguments
Type
Name
Direction
Description
const
SWLIBS_2Syst_F16
*const
pIn
input
Pointer to the structure containing data of the two-phase
stationary orthogonal system ( α- β). Arguments of the
structure contain fixed point 16-bit values.
SWLIBS_3Syst_F16
*const
pOut
output
Pointer to the structure containing data of the three-phase
stationary system (f16A-f16B-f16C). Arguments of the
structure contain fixed point 16-bit values.
5.68.3 Return
Function returns no value.
5.68.4 Description
The GMCLIB_ClarkInv function calculates the Inverse Clarke transformation, which is
used to transform values from the two-phase ( α- β) orthogonal coordinate system to the
three-phase (f16A-f16B-f16C) coordinate system, according to these equations:
Equation GMCLIB_ClarkInv_Eq1
Equation GMCLIB_ClarkInv_Eq2
Automotive Math and Motor Control Library Set for NXP MPC560xB devices, Rev. 7
NXP Semiconductors
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Function GMCLIB_ClarkInv_F16
Equation GMCLIB_ClarkInv_Eq3
Note
The input/output pointers must contain valid addresses
otherwise an exception may occur (Data TLB Error, Data
Storage, Alignment, Machine Check).
The inputs and the outputs are normalized to fit in the range [-1,
1).
5.68.5 Re-entrancy
The function is re-entrant.
5.68.6 Code Example
#include "gmclib.h"
SWLIBS_2Syst_F16 f16trAlBe;
SWLIBS_3Syst_F16 f16trAbc;
void main(void)
{
// input phase alpha ~ sin(45) ~ 0.707106781
// input phase beta ~ cos(45) ~ 0.707106781
f16trAlBe.f16Arg1 = FRAC16 (0.707106781);
f16trAlBe.f16Arg2 = FRAC16 (0.707106781);
// output should be
// output should be
// output should be
GMCLIB_ClarkInv_F16
f16trAbc.f16Arg1 = 0x5A82 ~ FRAC16(0.707106781)
f16trAbc.f16Arg2 = 0x2120 ~ FRAC16(0.258819045)
f16trAbc.f16Arg3 = 0x845C ~ FRAC16(-0.965925826)
(&f16trAbc,&f16trAlBe);
// output should be f16trAbc.f16Arg1 = 0x5A82 ~ FRAC16(0.707106781)
// output should be f16trAbc.f16Arg2 = 0x2120 ~ FRAC16(0.258819045)
// output should be f16trAbc.f16Arg3 = 0x845C ~ FRAC16(-0.965925826)
GMCLIB_ClarkInv (&f16trAbc,&f16trAlBe,F16);
//
//
//
//
}
##############################################################
Available only if 16-bit fractional implementation selected
as default
##############################################################
// output should be f16trAbc.f16Arg1 = 0x5A82 ~ FRAC16(0.707106781)
// output should be f16trAbc.f16Arg2 = 0x2120 ~ FRAC16(0.258819045)
// output should be f16trAbc.f16Arg3 = 0x845C ~ FRAC16(-0.965925826)
GMCLIB_ClarkInv (&f16trAbc,&f16trAlBe);
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NXP Semiconductors
Chapter 5 API References
5.69 Function GMCLIB_DecouplingPMSM_F32
This function calculates the cross-coupling voltages to eliminate the dq axis coupling
causing on-linearity of the field oriented control.
5.69.1 Declaration
void GMCLIB_DecouplingPMSM_F32(SWLIBS_2Syst_F32 *const pUdqDec, const SWLIBS_2Syst_F32 *const
pUdq, const SWLIBS_2Syst_F32 *const pIdq, tFrac32 f32AngularVel, const
GMCLIB_DECOUPLINGPMSM_T_F32 *const pParam);
5.69.2 Arguments
Table 5-85. GMCLIB_DecouplingPMSM_F32 arguments
Type
Name
Direction
Description
SWLIBS_2Syst_F32
*const
pUdqDec
output
Pointer to the structure containing direct (u df_dec) and
quadrature (u qf_dec) components of the decoupled stator
voltage vector to be applied on the motor terminals.
const
SWLIBS_2Syst_F32
*const
pUdq
input
Pointer to the structure containing direct (u df) and quadrature
(u qf) components of the stator voltage vector generated by
the current controllers.
const
SWLIBS_2Syst_F32
*const
pIdq
input
Pointer to the structure containing direct (i df) and quadrature
(i qf) components of the stator current vector measured on the
motor terminals.
tFrac32
f32AngularVel
input
Rotor angular velocity in rad/sec, referred to as ( ωef) in the
detailed section of the documentation.
input
Pointer to the structure containing k df and k qf coefficients
(see the detailed section of the documentation) and scale
parameters (k d_shift) and (k q_shift).
const
pParam
GMCLIB_DECOUPLIN
GPMSM_T_F32 *const
5.69.3 Return
Function returns no value.
Automotive Math and Motor Control Library Set for NXP MPC560xB devices, Rev. 7
NXP Semiconductors
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Function GMCLIB_DecouplingPMSM_F32
5.69.4 Description
The quadrature phase model of a PMSM motor, in a synchronous reference frame, is very
popular for field oriented control structures because both controllable quantities, current
and voltage, are DC values. This allows employing only simple controllers to force the
machine currents into the defined states.
The voltage equations of this model can be obtained by transforming the motor three
phase voltage equations into a quadrature phase rotational frame, which is aligned and
rotates synchronously with the rotor. Such a transformation, after some mathematical
corrections, yields the following set of equations, describing the quadrature phase model
of a PMSM motor, in a synchronous reference frame:
Equation GMCLIB_DecouplingPMSM_Eq1
It can be seen that GMCLIB_DecouplingPMSM_Eq1 represents a non-linear cross
dependent system. The linear voltage components cover the model of the phase winding,
which is simplified to a resistance in series with inductance (R-L circuit). The crosscoupling components represent the mutual coupling between the two phases of the
quadrature phase model, and the back-EMF component (visible only in q-axis voltage)
represents the generated back EMF voltage caused by rotor rotation.
In order to achieve dynamic torque, speed and positional control, the non-linear and
back-EMF components from GMCLIB_DecouplingPMSM_Eq1 must be compensated
for. This will result in a fully decoupled flux and torque control of the machine and
simplifies the PMSM motor model into two independent R-L circuit models as follows:
Equation GMCLIB_DecouplingPMSM_Eq2
Such a simplification of the PMSM model also greatly simplifies the design of both the
d-q current controllers.
Therefore, it is advantageous to compensate for the cross-coupling terms in
GMCLIB_DecouplingPMSM_Eq1, using the feed-forward voltages
overline{u_dq_comp} given from GMCLIB_DecouplingPMSM_Eq1 as follows:
Automotive Math and Motor Control Library Set for NXP MPC560xB devices, Rev. 7
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NXP Semiconductors
Chapter 5 API References
Equation GMCLIB_DecouplingPMSM_Eq3
The feed-forward voltages overline{u_dq_comp} are added to the voltages generated by
the current controllers overline{u_dq}, which cover the R-L model. The resulting
voltages represent the direct u q_dec and quadrature u q_decq components of the decoupled
voltage vector that is to be applied on the motor terminals (using a pulse width
modulator). The back EMF voltage component is already considered to be compensated
by an external function.
The function GMCLIB_DecouplingPMSM_F32 calculates the cross-coupling voltages
overline{u_dq_comp} and adds these to the input overline{u_dq} voltage vector.
Because the back EMF voltage component is considered compensated, this component is
equal to zero. Therefore, calculations performed by GMCLIB_DecouplingPMSM_F32
are derived from these two equations:
Equation GMCLIB_DecouplingPMSM_Eq4
where overline{u_dq} is the voltage vector calculated by the controllers (with the already
compensated back EMF component), overline{u_dq_comp} is the feed-forward
compensating voltage vector described in GMCLIB_DecouplingPMSM_Eq3, and
overline{u_dq_dec} is the resulting decoupled voltage vector to be applied on the motor
terminals. Substituting GMCLIB_DecouplingPMSM_Eq3 into
GMCLIB_DecouplingPMSM_Eq4, and normalizing GMCLIB_DecouplingPMSM_Eq4,
results in the following set of equations:
Equation GMCLIB_DecouplingPMSM_Eq5
where subscript f denotes the fractional representation of the respective quantity, and U
max, I max, Ωmax are the maximal values (scale values) for the voltage, current and angular
velocity respectively.
Automotive Math and Motor Control Library Set for NXP MPC560xB devices, Rev. 7
NXP Semiconductors
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Function GMCLIB_DecouplingPMSM_F32
Real quantities are converted to the fractional range [-1, 1) using the following equations:
Equation GMCLIB_DecouplingPMSM_Eq6
Further, rearranging GMCLIB_DecouplingPMSM_Eq5 results in:
Equation GMCLIB_DecouplingPMSM_Eq7
where k d and k q are coefficients calculated as:
Equation GMCLIB_DecouplingPMSM_Eq8
Because function GMCLIB_DecouplingPMSM_F32 is implemented using the fractional
arithmetic, both the k d and k q coefficients also have to be scaled to fit into the fractional
range [-1, 1). For that purpose, two additional scaling coefficients are defined as:
Equation GMCLIB_DecouplingPMSM_Eq9
Automotive Math and Motor Control Library Set for NXP MPC560xB devices, Rev. 7
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NXP Semiconductors
Chapter 5 API References
Using scaling coefficients GMCLIB_DecouplingPMSM_Eq9, the fractional
representation of coefficients k d and k q from GMCLIB_DecouplingPMSM_Eq8 are
derived as follows:
Equation GMCLIB_DecouplingPMSM_Eq10
Substituting GMCLIB_DecouplingPMSM_Eq8 - GMCLIB_DecouplingPMSM_Eq10
into GMCLIB_DecouplingPMSM_Eq7 results in the final form of the equation set,
actually implemented in the GMCLIB_DecouplingPMSM_F32 function:
Equation GMCLIB_DecouplingPMSM_Eq11
Scaling of both equations into the fractional range is done using a multiplication by 2
k_d_shift, 2 k_q_shift, respectively. Therefore, it is implemented as a simple left shift with
overflow protection.
Note
The input/output pointers must contain valid addresses
otherwise an exception may occur (Data TLB Error, Data
Storage, Alignment, Machine Check).
All parameters can be reset during declaration using the
GMCLIB_DECOUPLINGPMSM_DEFAULT_F32 macro.
5.69.5 Re-entrancy
The function is re-entrant.
Automotive Math and Motor Control Library Set for NXP MPC560xB devices, Rev. 7
NXP Semiconductors
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Function GMCLIB_DecouplingPMSM_F16
5.69.6 Code Example
#include "gmclib.h"
#define
#define
#define
#define
#define
L_D
L_Q
U_MAX
I_MAX
W_MAX
(50.0e-3)
(100.0e-3)
(50.0)
(10.0)
(2000.0)
//
//
//
//
//
Ld inductance = 50mH
Lq inductance = 100mH
scale for voltage = 50V
scale for current = 10A
scale for angular velocity = 2000rad/sec
GMCLIB_DECOUPLINGPMSM_T_F32 f32trDec = GMCLIB_DECOUPLINGPMSM_DEFAULT_F32;
SWLIBS_2Syst_F32 f32trUDQ;
SWLIBS_2Syst_F32 f32trIDQ;
SWLIBS_2Syst_F32 f32trUDecDQ;
tFrac32 f32We;
void main(void)
{
// input values - scaling coefficients of given decoupling algorithm
f32trDec.f32Kd = FRAC32 (0.625);
f32trDec.s16KdShift = (tS16)6;
f32trDec.f32Kq = FRAC32 (0.625);
f32trDec.s16KqShift = (tS16)5;
// d quantity of input voltage vector 5[V]
f32trUDQ.f32Arg1 = FRAC32 (5.0/U_MAX);
// q quantity of input voltage vector 10[V]
f32trUDQ.f32Arg2 = FRAC32 (10.0/U_MAX);
// d quantity of measured current vector 6[A]
f32trIDQ.f32Arg1 = FRAC32 (6.0/I_MAX);
// q quantity of measured current vector 4[A]
f32trIDQ.f32Arg2 = FRAC32 (4.0/I_MAX);
// rotor angular velocity
f32We = FRAC32 (100.0/W_MAX);
// output should be f32trUDecDQ.f32Arg1 ~ 0xA6666666 ~ FRAC32(-0.7)*50V
~=-35[V]
// output should be f32trUDecDQ.f32Arg2 ~ 0x66666666 ~ FRAC32(0.8)*50V
~=40[V]
GMCLIB_DecouplingPMSM_F32
(&f32trUDecDQ,&f32trUDQ,&f32trIDQ,f32We,&f32trDec);
// output should be f32trUDecDQ.f32Arg1 ~ 0xA6666666 ~ FRAC32(-0.7)*50V
~=-35[V]
// output should be f32trUDecDQ.f32Arg2 ~ 0x66666666 ~ FRAC32(0.8)*50V
~=40[V]
GMCLIB_DecouplingPMSM
(&f32trUDecDQ,&f32trUDQ,&f32trIDQ,f32We,&f32trDec,F32);
//
//
//
//
##############################################################
Available only if 32-bit fractional implementation selected
as default
##############################################################
// output should be f32trUDecDQ.f32Arg1 ~ 0xA6666666 ~ FRAC32(-0.7)*50V
~=-35[V]
// output should be f32trUDecDQ.f32Arg2 ~ 0x66666666 ~ FRAC32(0.8)*50V
~=40[V]
}
GMCLIB_DecouplingPMSM (&f32trUDecDQ,&f32trUDQ,&f32trIDQ,f32We,&f32trDec);
Automotive Math and Motor Control Library Set for NXP MPC560xB devices, Rev. 7
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NXP Semiconductors
Chapter 5 API References
5.70 Function GMCLIB_DecouplingPMSM_F16
This function calculates the cross-coupling voltages to eliminate the dq axis coupling
causing non-linearity of the field oriented control.
5.70.1 Declaration
void GMCLIB_DecouplingPMSM_F16(SWLIBS_2Syst_F16 *const pUdqDec, const SWLIBS_2Syst_F16 *const
pUdq, const SWLIBS_2Syst_F16 *const pIdq, tFrac16 f16AngularVel, const
GMCLIB_DECOUPLINGPMSM_T_F16 *const pParam);
5.70.2 Arguments
Table 5-86. GMCLIB_DecouplingPMSM_F16 arguments
Type
Name
Direction
Description
SWLIBS_2Syst_F16
*const
pUdqDec
output
Pointer to the structure containing direct (u df_dec) and
quadrature (u qf_dec) components of the decoupled stator
voltage vector to be applied on the motor terminals.
const
SWLIBS_2Syst_F16
*const
pUdq
input
Pointer to the structure containing direct (u df) and quadrature
(u qf) components of the stator voltage vector generated by
the current controllers.
const
SWLIBS_2Syst_F16
*const
pIdq
input
Pointer to the structure containing direct (i df) and quadrature
(i qf) components of the stator current vector measured on the
motor terminals.
tFrac16
f16AngularVel
input
Rotor angular velocity in rad/sec, referred to as ( omegaef) in
the detailed section of the documentation.
input
Pointer to the structure containing k df and k qf coefficients
(see the detailed section of the documentation) and scale
parameters (k d_shift) and (k q_shift).
const
pParam
GMCLIB_DECOUPLIN
GPMSM_T_F16 *const
5.70.3 Return
Function returns no value.
5.70.4 Description
The quadrature phase model of a PMSM motor, in a synchronous reference frame, is very
popular for field oriented control structures because both controllable quantities, current
and voltage, are DC values. This allows employing only simple controllers to force the
machine currents into the defined states.
Automotive Math and Motor Control Library Set for NXP MPC560xB devices, Rev. 7
NXP Semiconductors
363
Function GMCLIB_DecouplingPMSM_F16
The voltage equations of this model can be obtained by transforming the motor three
phase voltage equations into a quadrature phase rotational frame, which is aligned and
rotates synchronously with the rotor. Such a transformation, after some mathematical
corrections, yields the following set of equations, describing the quadrature phase model
of a PMSM motor, in a synchronous reference frame:
Equation GMCLIB_DecouplingPMSM_Eq1
It can be seen that GMCLIB_DecouplingPMSM_Eq1 represents a non-linear cross
dependent system. The linear voltage components cover the model of the phase winding,
which is simplified to a resistance in series with inductance (R-L circuit). The crosscoupling components represent the mutual coupling between the two phases of the
quadrature phase model, and the back-EMF component (visible only in q-axis voltage)
represents the generated back EMF voltage caused by rotor rotation.
In order to achieve dynamic torque, speed and positional control, the non-linear and
back-EMF components from GMCLIB_DecouplingPMSM_Eq1 must be compensated
for. This will result in a fully decoupled flux and torque control of the machine and
simplifies the PMSM motor model into two independent R-L circuit models as follows:
Equation GMCLIB_DecouplingPMSM_Eq2
Such a simplification of the PMSM model also greatly simplifies the design of both the
d-q current controllers.
Therefore, it is advantageous to compensate for the cross-coupling terms in
GMCLIB_DecouplingPMSM_Eq1, using the feed-forward voltages
overline{u_dq_comp} given from GMCLIB_DecouplingPMSM_Eq1 as follows:
Equation GMCLIB_DecouplingPMSM_Eq3
The feed-forward voltages overline{u_dq_comp} are added to the voltages generated by
the current controllers overline{u_dq}, which cover the R-L model. The resulting
voltages represent the direct u q_dec and quadrature u q_decq components of the decoupled
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voltage vector that is to be applied on the motor terminals (using a pulse width
modulator). The back EMF voltage component is already considered to be compensated
by an external function.
The function GMCLIB_DecouplingPMSM_F16 calculates the cross-coupling voltages
overline{u_dq_comp} and adds these to the input overline{u_dq} voltage vector.
Because the back EMF voltage component is considered compensated, this component is
equal to zero. Therefore, calculations performed by GMCLIB_DecouplingPMSM_F16
are derived from these two equations:
Equation GMCLIB_DecouplingPMSM_Eq4
where overline{u_dq} is the voltage vector calculated by the controllers (with the already
compensated back EMF component), overline{u_dq_comp} is the feed-forward
compensating voltage vector described in GMCLIB_DecouplingPMSM_Eq3, and
overline{u_dq_dec} is the resulting decoupled voltage vector to be applied on the motor
terminals. Substituting GMCLIB_DecouplingPMSM_Eq3 into
GMCLIB_DecouplingPMSM_Eq4, and normalizing GMCLIB_DecouplingPMSM_Eq4,
results in the following set of equations:
Equation GMCLIB_DecouplingPMSM_Eq5
where subscript f denotes the fractional representation of the respective quantity, and U
max, I max, Ωmax are the maximal values (scale values) for the voltage, current and angular
velocity respectively.
Real quantities are converted to the fractional range [-1, 1) using the following equations:
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Function GMCLIB_DecouplingPMSM_F16
Equation GMCLIB_DecouplingPMSM_Eq6
Further, rearranging GMCLIB_DecouplingPMSM_Eq5 results in:
Equation GMCLIB_DecouplingPMSM_Eq7
where k d and k q are coefficients calculated as:
Equation GMCLIB_DecouplingPMSM_Eq8
Because function GMCLIB_DecouplingPMSM_F16 is implemented using the fractional
arithmetic, both the k d and k q coefficients also have to be scaled to fit into the fractional
range [-1, 1). For that purpose, two additional scaling coefficients are defined as:
Equation GMCLIB_DecouplingPMSM_Eq9
Using scaling coefficients GMCLIB_DecouplingPMSM_Eq9, the fractional
representation of coefficients k d and k q from GMCLIB_DecouplingPMSM_Eq8 are
derived as follows:
Equation GMCLIB_DecouplingPMSM_Eq10
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Substituting GMCLIB_DecouplingPMSM_Eq8 - GMCLIB_DecouplingPMSM_Eq10
into GMCLIB_DecouplingPMSM_Eq7 results in the final form of the equation set,
actually implemented in the GMCLIB_DecouplingPMSM_F16 function:
Equation GMCLIB_DecouplingPMSM_Eq11
Scaling of both equations into the fractional range is done using a multiplication by 2
k_d_shift, 2 k_q_shift, respectively. Therefore, it is implemented as a simple left shift with
overflow protection.
Note
The input/output pointers must contain valid addresses
otherwise an exception may occur (Data TLB Error, Data
Storage, Alignment, Machine Check).
All parameters can be reset during declaration using the
GMCLIB_DECOUPLINGPMSM_DEFAULT_F16 macro.
5.70.5 Re-entrancy
The function is re-entrant.
5.70.6 Code Example
#include "gmclib.h"
#define
#define
#define
#define
#define
L_D
L_Q
U_MAX
I_MAX
W_MAX
(50.0e-3)
(100.0e-3)
(50.0)
(10.0)
(2000.0)
//
//
//
//
//
Ld inductance = 50mH
Lq inductance = 100mH
scale for voltage = 50V
scale for current = 10A
scale for angular velocity = 2000rad/sec
GMCLIB_DECOUPLINGPMSM_T_F16 f16trDec = GMCLIB_DECOUPLINGPMSM_DEFAULT_F16;
SWLIBS_2Syst_F16 f16trUDQ;
SWLIBS_2Syst_F16 f16trIDQ;
SWLIBS_2Syst_F16 f16trUDecDQ;
tFrac16 f16We;
void main(void)
{
// input values - scaling coefficients of given decoupling algorithm
f16trDec.f16Kd = FRAC16 (0.625);
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Function GMCLIB_ElimDcBusRip_F32
f16trDec.s16KdShift = (tS16)6;
f16trDec.f16Kq = FRAC16 (0.625);
f16trDec.s16KqShift = (tS16)5;
// d quantity of input voltage vector 5[V]
f16trUDQ.f16Arg1 = FRAC16 (5.0/U_MAX);
// q quantity of input voltage vector 10[V]
f16trUDQ.f16Arg2 = FRAC16 (10.0/U_MAX);
// d quantity of measured current vector 6[A]
f16trIDQ.f16Arg1 = FRAC16 (6.0/I_MAX);
// q quantity of measured current vector 4[A]
f16trIDQ.f16Arg2 = FRAC16 (4.0/I_MAX);
// rotor angular velocity
f16We = FRAC16 (100.0/W_MAX);
//output should be f16trUDecDQ.f16Arg1 ~ 0xA666 ~ FRAC16(-0.7)*50V ~=-35[V]
//output should be f16trUDecDQ.f16Arg2 ~ 0x6666 ~ FRAC16(0.8)*50V ~=40[V]
GMCLIB_DecouplingPMSM_F16
(&f16trUDecDQ,&f16trUDQ,&f16trIDQ,f16We,&f16trDec);
//output should be f16trUDecDQ.f16Arg1 ~ 0xA666 ~ FRAC16(-0.7)*50V ~=-35[V]
//output should be f16trUDecDQ.f16Arg2 ~ 0x6666 ~ FRAC16(0.8)*50V ~=40[V]
GMCLIB_DecouplingPMSM
(&f16trUDecDQ,&f16trUDQ,&f16trIDQ,f16We,&f16trDec,F16);
//
//
//
//
}
##############################################################
Available only if 16-bit fractional implementation selected
as default
##############################################################
//output should be f16trUDecDQ.f16Arg1 ~ 0xA666 ~ FRAC16(-0.7)*50V ~=-35[V]
//output should be f16trUDecDQ.f16Arg2 ~ 0x6666 ~ FRAC16(0.8)*50V ~=40[V]
GMCLIB_DecouplingPMSM (&f16trUDecDQ,&f16trUDQ,&f16trIDQ,f16We,&f16trDec);
5.71 Function GMCLIB_ElimDcBusRip_F32
This function implements the DC Bus voltage ripple elimination.
5.71.1 Declaration
void GMCLIB_ElimDcBusRip_F32(SWLIBS_2Syst_F32 *const pOut, const SWLIBS_2Syst_F32 *const pIn,
const GMCLIB_ELIMDCBUSRIP_T_F32 *const pParam);
5.71.2 Arguments
Table 5-87. GMCLIB_ElimDcBusRip_F32 arguments
Type
SWLIBS_2Syst_F32
*const
Name
pOut
Direction
output
Description
Pointer to the structure with direct ( α) and quadrature ( β)
components of the required stator voltage vector re-calculated
so as to compensate for voltage ripples on the DC bus.
Table continues on the next page...
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Table 5-87. GMCLIB_ElimDcBusRip_F32 arguments
(continued)
Type
const
SWLIBS_2Syst_F32
*const
Name
pIn
const
pParam
GMCLIB_ELIMDCBUS
RIP_T_F32 *const
Direction
Description
input
Pointer to the structure with direct ( α) and quadrature ( β)
components of the required stator voltage vector before
compensation of voltage ripples on the DC bus.
input
Pointer to the parameters structure.
5.71.3 Return
Function returns no value.
5.71.4 Description
The GMCLIB_ElimDcBusRip function provides a computational method for the
recalculation of the direct ( α) and quadrature ( β) components of the required stator
voltage vector, so as to compensate for voltage ripples on the DC bus of the power stage.
Considering a cascaded type structure of the control system in a standard motor control
application, the required voltage vector to be applied on motor terminals is generated by a
set of controllers (usually P, PI or PID) only with knowledge of the maximal value of the
DC bus voltage. The amplitude and phase of the required voltage vector are then used by
the pulse width modulator (PWM) for generation of appropriate duty-cycles for the
power inverter switches. Obviously, the amplitude of the generated phase voltage
(averaged across one switching period) does not only depend on the actual on/off times of
the given phase switches and the maximal value of the DC bus voltage. The actual
amplitude of the phase voltage is also directly affected by the actual value of the
available DC bus voltage. Therefore, any variations in amplitude of the actual DC bus
voltage must be accounted for by modifying the amplitude of the required voltage so that
the output phase voltage remains unaffected.
For a better understanding, let's consider the following two simple examples:
Example 1:
•
•
•
•
amplitude of the required phase voltage U reg=50[V]
maximal amplitude of the DC bus voltage U DC_BUS_MAX=100[V]
actual amplitude of the DC bus voltage U DC_BUS_ACTUAL=100[V]
voltage to be applied to the PWM modulator to generate U reg=50[V] on the inverter
phase output:
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Function GMCLIB_ElimDcBusRip_F32
Equation GMCLIB_ElimDcBusRip_Eq1
•
•
•
•
Example 2:
amplitude of the required phase voltage U reg=50[V]
maximal amplitude of the DC bus voltage U DC_BUS_MAX=100[V]
actual amplitude of the DC bus voltage U DC_BUS_ACTUAL=90[V]
voltage to be applied to the PWM modulator to generate U reg=50[V] on the inverter
phase output:
Equation GMCLIB_ElimDcBusRip_Eq2
The imperfections of the DC bus voltage are compensated for by the modification of
amplitudes of the direct- α and the quadrature- β components of the stator reference
voltage vector. The following formulas are used:
• for the α-component:
Equation GMCLIB_ElimDcBusRip_Eq3
• for the β-component:
Equation GMCLIB_ElimDcBusRip_Eq4
where: f32ModIndex is the inverse modulation index, f32ArgDcBusMsr is the measured
DC bus voltage, the u α and u β are the input voltages, and the u α* and u β* are the
output duty-cycle ratios.
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The f32ModIndex and f32ArgDcBusMsr are supplied to the function within the
parameters structure through its members. The u α, u β correspond respectively to the
f32Arg1 and f32Arg2 members of the input structure, and the u α* and u β* respectively
to the f32Arg1 and f32Arg2 members of the output structure.
It should be noted that although the modulation index (see the parameters structure, the
f32ModIndex member) is assumed to be equal to or greater than zero, the possible values
are restricted to those values resulting from the use of Space Vector Modulation
techniques.
In order to correctly handle the discontinuity at f32ArgDcBusMsr approaching 0, and for
efficiency reasons, the function will assign 0 to the output duty cycle ratios if the
f32ArgDcBusMsr is below the threshold of 2 -15. In other words, the 16 least significant
bits of the f32DcBusMsr are ignored. Also, the computed output of the u α* and u β*
components may have an inaccuracy in the 16 least significant bits.
Note
The input/output pointers must contain valid addresses
otherwise an exception may occur (Data TLB Error, Data
Storage, Alignment, Machine Check).
Both the inverse modulation index pIn->f32ModIndex and the
measured DC bus voltage pIn->f32DcBusMsr must be equal to
or greater than 0, otherwise the results are undefined.
5.71.5 Re-entrancy
The function is re-entrant.
5.71.6 Code Example
#include "gmclib.h"
#define U_MAX
(36.0) // voltage scale
SWLIBS_2Syst_F32 f32AB;
SWLIBS_2Syst_F32 f32OutAB;
GMCLIB_ELIMDCBUSRIP_T_F32 f32trMyElimDcBusRip =
GMCLIB_ELIMDCBUSRIP_DEFAULT_F32;
void main(void)
{
// inverse modulation coefficient for standard space vector modulation
f32trMyElimDcBusRip.f32ModIndex = FRAC32 (0.866025403784439);
// Input voltage vector 15V @ angle 30deg
// alpha component of input voltage vector = 12.99[V]
f32AB.f32Arg1 = FRAC32 (12.99/U_MAX);
// beta component of input voltage vector = 7.5[V]
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Function GMCLIB_ElimDcBusRip_F16
f32AB.f32Arg2 = FRAC32 (7.5/U_MAX);
// value of the measured DC bus voltage 17[V]
f32trMyElimDcBusRip.f32ArgDcBusMsr = FRAC32 (17.0/U_MAX);
~ 0x7FFFFFFF
// output alpha component of the output vector should be
// f32OutAB.f32Arg1 = (12.99/36)*0.8660/(17.0/36/2) = 1.3235 -> FRAC32(1.0)
// output beta component of the output vector should be
// f32OutAB.f32Arg2 = (7.5/36)*0.8660/(17.0/36/2) = 0.7641 ->
FRAC32(0.7641) ~ 0x61CF8000
GMCLIB_ElimDcBusRip_F32 (&f32OutAB,&f32AB,&f32trMyElimDcBusRip);
~ 0x7FFFFFFF
// output alpha component of the output vector should be
// f32OutAB.f32Arg1 = (12.99/36)*0.8660/(17.0/36/2) = 1.3235 -> FRAC32(1.0)
// output beta component of the output vector should be
// f32OutAB.f32Arg2 = (7.5/36)*0.8660/(17.0/36/2) = 0.7641 ->
FRAC32(0.7641) ~ 0x61CF8000
GMCLIB_ElimDcBusRip (&f32OutAB,&f32AB,&f32trMyElimDcBusRip,F32);
//
//
//
//
~ 0x7FFFFFFF
##############################################################
Available only if 32-bit fractional implementation selected
as default
##############################################################
// output alpha component of the output vector should be
// f32OutAB.f32Arg1 = (12.99/36)*0.8660/(17.0/36/2) = 1.3235 -> FRAC32(1.0)
// output beta component of the output vector should be
// f32OutAB.f32Arg2 = (7.5/36)*0.8660/(17.0/36/2) = 0.7641 ->
FRAC32(0.7641) ~ 0x61CF8000
GMCLIB_ElimDcBusRip (&f32OutAB,&f32AB,&f32trMyElimDcBusRip);
}
5.72 Function GMCLIB_ElimDcBusRip_F16
This function implements the DC Bus voltage ripple elimination.
5.72.1 Declaration
void GMCLIB_ElimDcBusRip_F16(SWLIBS_2Syst_F16 *const pOut, const SWLIBS_2Syst_F16 *const pIn,
const GMCLIB_ELIMDCBUSRIP_T_F16 *const pParam);
5.72.2 Arguments
Table 5-88. GMCLIB_ElimDcBusRip_F16 arguments
Type
SWLIBS_2Syst_F16
*const
Name
pOut
Direction
output
Description
Pointer to the structure with direct ( α) and quadrature ( β)
components of the required stator voltage vector re-calculated
so as to compensate for voltage ripples on the DC bus.
Table continues on the next page...
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Table 5-88. GMCLIB_ElimDcBusRip_F16 arguments
(continued)
Type
const
SWLIBS_2Syst_F16
*const
Name
pIn
const
pParam
GMCLIB_ELIMDCBUS
RIP_T_F16 *const
Direction
Description
input
Pointer to the structure with direct ( α) and quadrature ( β)
components of the required stator voltage vector before
compensation of voltage ripples on the DC bus.
input
Pointer to the parameters structure.
5.72.3 Return
Function returns no value.
5.72.4 Description
The GMCLIB_ElimDcBusRip function provides a computational method for the
recalculation of the direct ( α) and quadrature ( β) components of the required stator
voltage vector, so as to compensate for voltage ripples on the DC bus of the power stage.
Considering a cascaded type structure of the control system in a standard motor control
application, the required voltage vector to be applied on motor terminals is generated by a
set of controllers (usually P, PI or PID) only with knowledge of the maximal value of the
DC bus voltage. The amplitude and phase of the required voltage vector are then used by
the pulse width modulator (PWM) for generation of appropriate duty-cycles for the
power inverter switches. Obviously, the amplitude of the generated phase voltage
(averaged across one switching period) does not only depend on the actual on/off times of
the given phase switches and the maximal value of the DC bus voltage. The actual
amplitude of the phase voltage is also directly affected by the actual value of the
available DC bus voltage. Therefore, any variations in amplitude of the actual DC bus
voltage must be accounted for by modifying the amplitude of the required voltage so that
the output phase voltage remains unaffected.
For a better understanding, let's consider the following two simple examples:
Example 1:
•
•
•
•
amplitude of the required phase voltage U reg=50[V]
maximal amplitude of the DC bus voltage U DC_BUS_MAX=100[V]
actual amplitude of the DC bus voltage U DC_BUS_ACTUAL=100[V]
voltage to be applied to the PWM modulator to generate U reg=50[V] on the inverter
phase output:
Automotive Math and Motor Control Library Set for NXP MPC560xB devices, Rev. 7
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Function GMCLIB_ElimDcBusRip_F16
Equation GMCLIB_ElimDcBusRip_Eq1
•
•
•
•
amplitude of the required phase voltage U reg=50[V]
maximal amplitude of the DC bus voltage U DC_BUS_MAX=100[V]
actual amplitude of the DC bus voltage U DC_BUS_ACTUAL=90[V]
voltage to be applied to the PWM modulator to generate U reg=50[V] on the inverter
phase output:
Equation GMCLIB_ElimDcBusRip_Eq2
Equation GMCLIB_ElimDcBusRip_Eq3
• for the β-component:
Equation GMCLIB_ElimDcBusRip_Eq4
where: f16ModIndex is the inverse modulation index, f16ArgDcBusMsr is the measured
DC bus voltage, the u α and u β are the input voltages, and the u α* and u β* are the
output duty-cycle ratios.
The f16ModIndex and f16ArgDcBusMsr are supplied to the function within the
parameters structure through its members. The u α, u β correspond respectively to the
f16Arg1 and f16Arg2 members of the input structure, and the u α* and u β* respectively
to the f16Arg1 and f16Arg2 members of the output structure.
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It should be noted that although the modulation index (see the parameters structure, the
f16ModIndex member) is assumed to be equal to or greater than zero, the possible values
are restricted to those values resulting from the use of Space Vector Modulation
techniques.
In order to correctly handle the discontinuity at f16ArgDcBusMsr approaching 0, and for
efficiency reasons, the function will assign 0 to the output duty cycle ratios if the
f16ArgDcBusMsr is below the threshold of 2 -15. In other words, the 16 least significant
bits of the f16DcBusMsr are ignored. Also, the computed output of the u α* and u β*
components may have an inaccuracy in the 16 least significant bits.
Note
The input/output pointers must contain valid addresses
otherwise an exception may occur (Data TLB Error, Data
Storage, Alignment, Machine Check).
Both the inverse modulation index pIn->f16ModIndex and the
measured DC bus voltage pIn->f16DcBusMsr must be equal to
or greater than 0, otherwise the results are undefined.
5.72.5 Re-entrancy
The function is re-entrant.
5.72.6 Code Example
#include "gmclib.h"
#define U_MAX
(36.0) // voltage scale
SWLIBS_2Syst_F16 f16AB;
SWLIBS_2Syst_F16 f16OutAB;
GMCLIB_ELIMDCBUSRIP_T_F16 f16trMyElimDcBusRip =
GMCLIB_ELIMDCBUSRIP_DEFAULT_F16;
void main(void)
{
// inverse modulation coefficient for standard space vector modulation
f16trMyElimDcBusRip.f16ModIndex = FRAC16 (0.866025403784439);
// Input voltage vector 15V @ angle 30deg
// alpha component of input voltage vector = 12.99[V]
f16AB.f16Arg1 = FRAC16 (12.99/U_MAX);
// beta component of input voltage vector = 7.5[V]
f16AB.f16Arg2 = FRAC16 (7.5/U_MAX);
// value of the measured DC bus voltage 17[V]
f16trMyElimDcBusRip.f16ArgDcBusMsr = FRAC16 (17.0/U_MAX);
// output alpha component of the output vector should be
// f16OutAB.f16Arg1 = (12.99/36)*0.8660/(17.0/36/2) = 1.3235 -> FRAC16(1.0)
~ 0x7FFF
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Function GMCLIB_Park_F32
// output beta component of the output vector should be
// f16OutAB.f16Arg2 = (7.5/36)*0.8660/(17.0/36/2) = 0.7641 ->
FRAC16(0.7641) ~ 0x61CF
GMCLIB_ElimDcBusRip_F16 (&f16OutAB,&f16AB,&f16trMyElimDcBusRip);
// output alpha component of the output vector should be
// f16OutAB.f16Arg1 = (12.99/36)*0.8660/(17.0/36/2) = 1.3235 -> FRAC16(1.0)
~ 0x7FFF
// output beta component of the output vector should be
// f16OutAB.f16Arg2 = (7.5/36)*0.8660/(17.0/36/2) = 0.7641 ->
FRAC16(0.7641) ~ 0x61CF
GMCLIB_ElimDcBusRip (&f16OutAB,&f16AB,&f16trMyElimDcBusRip,F16);
//
//
//
//
##############################################################
Available only if 16-bit fractional implementation selected
as default
##############################################################
// output alpha component of the output vector should be
// f16OutAB.f16Arg1 = (12.99/36)*0.8660/(17.0/36/2) = 1.3235 -> FRAC16(1.0)
~ 0x7FFF
// output beta component of the output vector should be
// f16OutAB.f16Arg2 = (7.5/36)*0.8660/(17.0/36/2) = 0.7641 ->
FRAC16(0.7641) ~ 0x61CF
GMCLIB_ElimDcBusRip (&f16OutAB,&f16AB,&f16trMyElimDcBusRip);
}
5.73 Function GMCLIB_Park_F32
This function implements the calculation of Park transformation.
5.73.1 Declaration
void GMCLIB_Park_F32(SWLIBS_2Syst_F32 *pOut, const SWLIBS_2Syst_F32 *const pInAngle, const
SWLIBS_2Syst_F32 *const pIn);
5.73.2 Arguments
Table 5-89. GMCLIB_Park_F32 arguments
Type
Name
Direction
Description
SWLIBS_2Syst_F32 *
pOut
input,
output
Pointer to the structure containing data of the two-phase
rotational orthogonal system (d-q).
const
SWLIBS_2Syst_F32
*const
pInAngle
input
Pointer to the structure where the values of the sine and
cosine of the rotor position are stored.
const
SWLIBS_2Syst_F32
*const
pIn
input
Pointer to the structure containing data of the two-phase
stationary orthogonal system ( α- β).
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5.73.3 Return
void
5.73.4 Description
The GMCLIB_Park_F32 function calculates the Park Transformation, which transforms
values (flux, voltage, current) from the two-phase ( α- β) stationary orthogonal
coordinate system to the two-phase (d-q) rotational orthogonal coordinate system,
according to these equations:
Equation GMCLIB_Park_Eq1
Equation GMCLIB_Park_Eq2
where θe represents the electrical position of the rotor flux.
Note
The input/output pointers must contain valid addresses
otherwise an exception may occur (Data TLB Error, Data
Storage, Alignment, Machine Check).
The inputs and the outputs are normalized to fit in the range [-1,
1).
5.73.5 Re-entrancy
The function is re-entrant.
5.73.6 Code Example
#include "gmclib.h"
SWLIBS_2Syst_F32 tr32Angle;
SWLIBS_2Syst_F32 tr32AlBe;
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Function GMCLIB_Park_F16
SWLIBS_2Syst_F32 tr32Dq;
void main(void)
{
// input angle sin(60) = 0.866025403
// input angle cos(60) = 0.5
tr32Angle.f32Arg1 = FRAC32 (0.866025403);
tr32Angle.f32Arg2 = FRAC32 (0.5);
// input alpha = 0.123
// input beta = 0.654
tr32AlBe.f32Arg1 = FRAC32 (0.123);
tr32AlBe.f32Arg2 = FRAC32 (0.654);
// output should be
// tr32Dq.f32Arg1 ~ d = 0x505E6455
// tr32Dq.f32Arg2 ~ q = 0x1C38ABDC
GMCLIB_Park_F32 (&tr32Dq,&tr32Angle,&tr32AlBe);
// output should be
// tr32Dq.f32Arg1 ~ d = 0x505E6455
// tr32Dq.f32Arg2 ~ q = 0x1C38ABDC
GMCLIB_Park (&tr32Dq,&tr32Angle,&tr32AlBe,F32);
//
//
//
//
}
##############################################################
Available only if 32-bit fractional implementation selected
as default
##############################################################
// output should be
// tr32Dq.f32Arg1 ~ d = 0x505E6455
// tr32Dq.f32Arg2 ~ q = 0x1C38ABDC
GMCLIB_Park (&tr32Dq,&tr32Angle,&tr32AlBe);
5.74 Function GMCLIB_Park_F16
This function implements the calculation of Park transformation.
5.74.1 Declaration
void GMCLIB_Park_F16(SWLIBS_2Syst_F16 *pOut, const SWLIBS_2Syst_F16 *const pInAngle, const
SWLIBS_2Syst_F16 *const pIn);
5.74.2 Arguments
Table 5-90. GMCLIB_Park_F16 arguments
Type
SWLIBS_2Syst_F16 *
Name
pOut
Direction
input,
output
Description
Pointer to the structure containing data of the two-phase
rotational orthogonal system (d-q).
Table continues on the next page...
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Chapter 5 API References
Table 5-90. GMCLIB_Park_F16 arguments (continued)
Type
Name
Direction
Description
const
SWLIBS_2Syst_F16
*const
pInAngle
input
Pointer to the structure where the values of the sine and
cosine of the rotor position are stored.
const
SWLIBS_2Syst_F16
*const
pIn
input
Pointer to the structure containing data of the two-phase
stationary orthogonal system ( α- β).
5.74.3 Return
void
5.74.4 Description
The GMCLIB_Park_F16 function calculates the Park Transformation, which transforms
values (flux, voltage, current) from the two-phase ( α- β) stationary orthogonal
coordinate system to the two-phase (d-q) rotational orthogonal coordinate system,
according to these equations:
Equation GMCLIB_Park_Eq1
Equation GMCLIB_Park_Eq2
where θe represents the electrical position of the rotor flux.
Note
The input/output pointers must contain valid addresses
otherwise an exception may occur (Data TLB Error, Data
Storage, Alignment, Machine Check).
The inputs and the outputs are normalized to fit in the range [-1,
1).
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Function GMCLIB_ParkInv_F32
5.74.5 Re-entrancy
The function is re-entrant.
5.74.6 Code Example
#include "gmclib.h"
SWLIBS_2Syst_F16 tr16Angle;
SWLIBS_2Syst_F16 tr16AlBe;
SWLIBS_2Syst_F16 tr16Dq;
void main(void)
{
// input angle sin(60) = 0.866025403
// input angle cos(60) = 0.5
tr16Angle.f16Arg1 = FRAC16 (0.866025403);
tr16Angle.f16Arg2 = FRAC16 (0.5);
// input alpha = 0.123
// input beta = 0.654
tr16AlBe.f16Arg1 = FRAC16 (0.123);
tr16AlBe.f16Arg2 = FRAC16 (0.654);
// output should be
// tr16Dq.f16Arg1 ~ d = 0x505E
// tr16Dq.f16Arg2 ~ q = 0x1C38
GMCLIB_Park_F16 (&tr16Dq,&tr16Angle,&tr16AlBe);
// output should be
// tr16Dq.f16Arg1 ~ d = 0x505E
// tr16Dq.f16Arg2 ~ q = 0x1C38
GMCLIB_Park (&tr16Dq,&tr16Angle,&tr16AlBe,F16);
//
//
//
//
}
##############################################################
Available only if 16-bit fractional implementation selected
as default
##############################################################
// output should be
// tr16Dq.f16Arg1 ~ d = 0x505E
// tr16Dq.f16Arg2 ~ q = 0x1C38
GMCLIB_Park (&tr16Dq,&tr16Angle,&tr16AlBe);
5.75 Function GMCLIB_ParkInv_F32
This function implements the inverse Park transformation.
5.75.1 Declaration
void GMCLIB_ParkInv_F32(SWLIBS_2Syst_F32 *const pOut, const SWLIBS_2Syst_F32 *const pInAngle,
const SWLIBS_2Syst_F32 *const pIn);
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5.75.2 Arguments
Table 5-91. GMCLIB_ParkInv_F32 arguments
Type
Name
Direction
Description
SWLIBS_2Syst_F32
*const
pOut
input,
output
Pointer to the structure containing data of the two-phase
stationary orthogonal system ( α- β).
const
SWLIBS_2Syst_F32
*const
pInAngle
input
Pointer to the structure where the values of the sine and
cosine of the rotor position are stored.
const
SWLIBS_2Syst_F32
*const
pIn
input
Pointer to the structure containing data of the two-phase
rotational orthogonal system (d-q).
5.75.3 Return
void
5.75.4 Description
The GMCLIB_ParkInv_F32 function calculates the Inverse Park Transformation, which
transforms quantities (flux, voltage, current) from the two-phase (d-q) rotational
orthogonal coordinate system to the two-phase ( α- β) stationary orthogonal coordinate
system, according to these equations:
Equation GMCLIB_ParkInv_Eq1
Equation GMCLIB_ParkInv_Eq2
Note
The input/output pointers must contain valid addresses
otherwise an exception may occur (Data TLB Error, Data
Storage, Alignment, Machine Check).
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Function GMCLIB_ParkInv_F16
The inputs and the outputs are normalized to fit in the range [-1,
1).
5.75.5 Re-entrancy
The function is re-entrant.
5.75.6 Code Example
#include "gmclib.h"
SWLIBS_2Syst_F32 tr32Angle;
SWLIBS_2Syst_F32 tr32Dq;
SWLIBS_2Syst_F32 tr32AlBe;
void main(void)
{
// input angle sin(60) = 0.866025403
// input angle cos(60) = 0.5
tr32Angle.f32Arg1 = FRAC32 (0.866025403);
tr32Angle.f32Arg2 = FRAC32 (0.5);
// input d = 0.123
// input q = 0.654
tr32Dq.f32Arg1 = FRAC32 (0.123);
tr32Dq.f32Arg2 = FRAC32 (0.654);
// output should be
// tr32AlBe.f32Arg1 ~ alpha = 0xBF601273
// tr32AlBe.f32Arg2 ~ beta = 0x377D9EE4
GMCLIB_ParkInv_F32 (&tr32AlBe,&tr32Angle,&tr32Dq);
// output should be
// tr32AlBe.f32Arg1 ~ alpha = 0xBF601273
// tr32AlBe.f32Arg2 ~ beta = 0x377D9EE4
GMCLIB_ParkInv (&tr32AlBe,&tr32Angle,&tr32Dq,F32);
//
//
//
//
}
##############################################################
Available only if 32-bit fractional implementation selected
as default
##############################################################
// output should be
// tr32AlBe.f32Arg1 ~ alpha = 0xBF601273
// tr32AlBe.f32Arg2 ~ beta = 0x377D9EE4
GMCLIB_ParkInv (&tr32AlBe,&tr32Angle,&tr32Dq);
5.76 Function GMCLIB_ParkInv_F16
This function implements the inverse Park transformation.
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5.76.1 Declaration
void GMCLIB_ParkInv_F16(SWLIBS_2Syst_F16 *const pOut, const SWLIBS_2Syst_F16 *const pInAngle,
const SWLIBS_2Syst_F16 *const pIn);
5.76.2 Arguments
Table 5-92. GMCLIB_ParkInv_F16 arguments
Type
Name
Direction
Description
SWLIBS_2Syst_F16
*const
pOut
input,
output
Pointer to the structure containing data of the two-phase
stationary orthogonal system ( α- β).
const
SWLIBS_2Syst_F16
*const
pInAngle
input
Pointer to the structure where the values of the sine and
cosine of the rotor position are stored.
const
SWLIBS_2Syst_F16
*const
pIn
input
Pointer to the structure containing data of the two-phase
rotational orthogonal system (d-q).
5.76.3 Return
void
5.76.4 Description
The GMCLIB_ParkInv_F16 function calculates the Inverse Park Transformation, which
transforms quantities (flux, voltage, current) from the two-phase (d-q) rotational
orthogonal coordinate system to the two-phase ( α- β) stationary orthogonal coordinate
system, according to these equations:
Equation GMCLIB_ParkInv_Eq1
Equation GMCLIB_ParkInv_Eq2
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Function GMCLIB_ParkInv_F16
Note
The input/output pointers must contain valid addresses
otherwise an exception may occur (Data TLB Error, Data
Storage, Alignment, Machine Check).
The inputs and the outputs are normalized to fit in the range [-1,
1).
5.76.5 Re-entrancy
The function is re-entrant.
5.76.6 Code Example
#include "gmclib.h"
SWLIBS_2Syst_F16 tr16Angle;
SWLIBS_2Syst_F16 tr16Dq;
SWLIBS_2Syst_F16 tr16AlBe;
void main(void)
{
// input angle sin(60) = 0.866025403
// input angle cos(60) = 0.5
tr16Angle.f16Arg1 = FRAC16 (0.866025403);
tr16Angle.f16Arg2 = FRAC16 (0.5);
// input d = 0.123
// input q = 0.654
tr16Dq.f16Arg1 = FRAC16 (0.123);
tr16Dq.f16Arg2 = FRAC16 (0.654);
// output should be
// tr16AlBe.f16Arg1 ~ alpha = 0xBF61
// tr16AlBe.f16Arg2 ~ beta = 0x377C
GMCLIB_ParkInv_F16 (&tr16AlBe,&tr16Angle,&tr16Dq);
// output should be
// tr16AlBe.f16Arg1 ~ alpha = 0xBF61
// tr16AlBe.f16Arg2 ~ beta = 0x377C
GMCLIB_ParkInv (&tr16AlBe,&tr16Angle,&tr16Dq,F16);
//
//
//
//
}
##############################################################
Available only if 16-bit fractional implementation selected
as default
##############################################################
// output should be
// tr16AlBe.f16Arg1 ~ alpha = 0xBF61
// tr16AlBe.f16Arg2 ~ beta = 0x377C
GMCLIB_ParkInv (&tr16AlBe,&tr16Angle,&tr16Dq);
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Chapter 5 API References
5.77 Function GMCLIB_SvmStd_F32
This function calculates the duty-cycle ratios using the Standard Space Vector
Modulation technique.
5.77.1 Declaration
tU32 GMCLIB_SvmStd_F32(SWLIBS_3Syst_F32 *pOut, const SWLIBS_2Syst_F32 *const pIn);
5.77.2 Arguments
Table 5-93. GMCLIB_SvmStd_F32 arguments
Type
Name
Direction
Description
SWLIBS_3Syst_F32 *
pOut
input,
output
Pointer to the structure containing calculated duty-cycle ratios
of the 3-Phase system.
const
SWLIBS_2Syst_F32
*const
pIn
input
Pointer to the structure containing direct U α and quadrature U
β components of the stator voltage vector.
5.77.3 Return
The function returns a 32-bit value in format INT, representing the actual space sector
which contains the stator reference vector U s.
5.77.4 Description
The GMCLIB_SvmStd_F32 function for calculating duty-cycle ratios is widely-used in
the modern electric drive. This, function calculates appropriate duty-cycle ratios, which
are needed for generating the given stator reference voltage vector using a special Space
Vector Modulation technique, termed Standard Space Vector Modulation. The basic
principle of the Standard Space Vector Modulation Technique can be explained with the
help of the power stage diagram in Figure 5-37.
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Function GMCLIB_SvmStd_F32
Figure 5-37. Power stage schematic diagram
Top and bottom switches work in a complementary mode; i.e., if the top switch, S At, is
ON, then the corresponding bottom switch, S Ab, is OFF, and vice versa. Considering that
value 1 is assigned to the ON state of the top switch, and value 0 is assigned to the ON
state of the bottom switch, the switching vector, [a, b, c] T can be defined. Creating such
a vector allows a numerical definition of all possible switching states. In a three-phase
power stage configuration (as shown in Figure 5-37), eight possible switching states
(detailed in Figure 5-38) are feasible.
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Chapter 5 API References
Figure 5-38. Basic space vectors
These states, together with the resulting instantaneous output line-to-line and phase
voltages, are listed in Table 5-94.
Table 5-94. Switching patterns
a
b
c
Ua
Ub
Uc
U AB
U BC
U CA
Vector
0
0
0
0
0
0
0
0
0
O 000
1
0
0
U DCBus
0
-U DCBus
U0
0
U DCBus
-U DCBus
U 60
-U DCBus
U DCBus
0
U 120
-U DCBus
0
U DCBus
U 180
0
-U DCBus
U DCBus
U 240
U DCBus
-U DCBus
0
U 300
0
0
0
O 111
1
0
1
1
0
0
0
1
1
0
0
1
1
1
0
1
1
1
2/3*U
-1/3*U
-1/3*U
DCBus
DCBus
DCBus
1/3*U
1/3*U
-2/3*U
DCBus
DCBus
DCBus
-1/3*U
2/3*U
-1/3*U
DCBus
DCBus
DCBus
-2/3*U
1/3*U
1/3*U
DCBus
DCBus
DCBus
-1/3*U
-1/3*U
2/3*U
DCBus
DCBus
DCBus
1/3*U
-2/3*U
1/3*U
DCBus
DCBus
DCBus
0
0
0
The quantities of the direct-u α and the quadrature-u β components of the two-phase
orthogonal coordinate system, describing the three-phase stator voltages, are expressed
by the Clarke Transformation.
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Function GMCLIB_SvmStd_F32
Equation GMCLIB_SvmStd_Eq1
Equation GMCLIB_SvmStd_Eq2
The three-phase stator voltages, U a, U b, and U c, are transformed using the Clarke
Transformation into the U α and the U β components of the two-phase orthogonal
coordinate system. The transformation results are listed in Table 5-95.
Table 5-95. Switching patterns and space vectors
a
b
c
uα
uβ
Vector
0
0
0
0
0
O 000
1
0
0
2/3*U DCBus
0
U0
1
1
0
1/3*U DCBus
1/ √(3)*U DCBus
U 60
0
1
0
-1/3*U DCBus
1/ √(3)*U DCBus
U 120
0
1
1
-2/3*U DCBus
0
U 180
0
0
1
-1/3*U DCBus
-1/ √(3)*U DCBus
U 240
1
0
1
1/3*U DCBus
-1/ √(3)*U DCBus
U 300
1
1
1
0
0
O 111
Figure 5-38 graphically depicts some feasible basic switching states (vectors). It is clear
that there are six non-zero vectors U 0, U 60, U 120, U 180, U 240, U 300, and two zero
vectors O 111, O 000, usable for switching. Therefore, the principle of the Standard Space
Vector Modulation resides in applying appropriate switching states for a certain time and
thus generating a voltage vector identical to the reference one.
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Chapter 5 API References
Figure 5-39. Projection of reference voltage vector in sector I
Referring to that principle, an objective of the Standard Space Vector Modulation is an
approximation of the reference stator voltage vector U S with an appropriate combination
of the switching patterns composed of basic space vectors. The graphical explanation of
this objective is shown in Figure 5-39 and Figure 5-40.
Figure 5-40. Detail of the voltage vector projection in sector I
The stator reference voltage vector U S is phase-advanced by 30 ° from the axis- α and
thus might be generated with an appropriate combination of the adjacent basic switching
states U 0 and U60. These figures also indicate the resultant U α and U β components for
space vectors U 0 and U 60
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Function GMCLIB_SvmStd_F32
In this case, the reference stator voltage vector U S is located in Sector I and, as
previously mentioned, can be generated with the appropriate duty-cycle ratios of the
basic switching states U 60 and U 0. The principal equations concerning this vector
location are:
Equation GMCLIB_SvmStd_Eq3
Equation GMCLIB_SvmStd_Eq4
where T 60 and T 0 are the respective duty-cycle ratios for which the basic space vectors
U 60 and U 0 should be applied within the time period T. T null is the course of time for
which the null vectors O 000 and O 111 are applied. Those duty-cycle ratios can be
calculated using equations:
Equation GMCLIB_SvmStd_Eq5
Equation GMCLIB_SvmStd_Eq6
Considering that the normalized magnitudes of the basic space vectors are |U 60| = |U 0| =
2/ √(3) and by substitution of the trigonometric expressions sin(60 °) and tan(60 °) by
their quantities 2/ √(3) and √(3), respectively, equation GMCLIB_SvmStd_Eq5 and
equation GMCLIB_SvmStd_Eq6 can be rearranged for the unknown duty-cycle ratios T
60/T and T 0/T:
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Equation GMCLIB_SvmStd_Eq7
Equation GMCLIB_SvmStd_Eq8
Equation GMCLIB_SvmStd_Eq7
Equation GMCLIB_SvmStd_Eq8
Figure 5-41. Projection of the reference voltage vector in sector II
Sector II is depicted in Figure 5-41. In this particular case, the reference stator voltage
vector U S is generated by the appropriate duty-cycle ratios of the basic switching states
U 60 and U120 . The basic equations describing this sector are:
Equation GMCLIB_SvmStd_Eq9
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Function GMCLIB_SvmStd_F32
Equation GMCLIB_SvmStd_Eq10
where T 120 and T 60 are the respective duty-cycle ratios for which the basic space vectors
U 120 and U 60 should be applied within the time period T. These resultant duty-cycle
ratios are formed from the auxiliary components termed A and B. The graphical
representation of the auxiliary components is shown in Figure 5-42.
Figure 5-42. Detail of the voltage vector projection in sector II
The equations describing those auxiliary time-duration components are:
Equation GMCLIB_SvmStd_Eq11
Equation GMCLIB_SvmStd_Eq12
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Chapter 5 API References
Equation GMCLIB_SvmStd_Eq11 and equation GMCLIB_SvmStd_Eq12 have been
formed using the sine rule. These equations can be rearranged for the calculation of the
auxiliary time-duration components A and B. This is done simply by substitution of the
trigonometric terms sin(30 °), sin(120 °) and sin(60 °) by their numerical representations
1/2, √(3)/2 and 1/ √(3), respectively.
Equation GMCLIB_SvmStd_Eq13
Equation GMCLIB_SvmStd_Eq14
The resultant duty-cycle ratios, T 120/T and T 60/T, are then expressed in terms of the
auxiliary time-duration components defined by equation GMCLIB_SvmStd_Eq13 and
equation GMCLIB_SvmStd_Eq14, as follows:
Equation GMCLIB_SvmStd_Eq15
Equation GMCLIB_SvmStd_Eq16
With the help of these equations, and also considering the normalized magnitudes of the
basic space vectors to be |U 120| = |U 60| = 2/ √(3), the equations expressed for the
unknown duty-cycle ratios of basic space vectors T 120/T and T 60/T can be written:
Equation GMCLIB_SvmStd_Eq17
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Function GMCLIB_SvmStd_F32
Equation GMCLIB_SvmStd_Eq18
The duty-cycle ratios in remaining sectors can be derived using the same approach. The
resulting equations will be similar to those derived for Sector I and Sector II.
To depict duty-cycle ratios of the basic space vectors for all sectors, we define:
• Three auxiliary variables:
Equation GMCLIB_SvmStd_Eq19
Equation GMCLIB_SvmStd_Eq20
Equation GMCLIB_SvmStd_Eq21
Two expressions t_1 and t_2 generally represent duty-cycle ratios of the basic space
vectors in the respective sector; e.g., for the first sector, t_1 and t_2 represent duty-cycle
ratios of the basic space vectors U 60 and U 0; for the second sector, t_1 and t_2 represent
duty-cycle ratios of the basic space vectors U 120 and U 60, etc.
For each sector, the expressions t_1 and t_2, in terms of auxiliary variables X, Y and Z,
are listed in Table 5-96.
Table 5-96. Determination of t_1 and t_2 expressions
Sector
U 0, U 60
U 60, U 120
U 120, U 180
U 180, U 240
U 240, U 300
U 300, U 0
t_1
X
Y
-Y
Z
-Z
-X
t_2
-Z
Z
X
-X
-Y
Y
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For the determination of auxiliary variables X equation GMCLIB_SvmStd_Eq19, Y
equation GMCLIB_SvmStd_Eq20 and Z equation GMCLIB_SvmStd_Eq21, the sector
number is required. This information can be obtained by several approaches. One
approach discussed here requires the use of a modified Inverse Clark Transformation to
transform the direct- α and quadrature- β components into a balanced three-phase
quantity u ref1, u ref2 and u ref3, used for a straightforward calculation of the sector
number, to be shown later.
Equation GMCLIB_SvmStd_Eq22
Equation GMCLIB_SvmStd_Eq23
Equation GMCLIB_SvmStd_Eq24
The modified Inverse Clark Transformation projects the quadrature-u β component into u
ref1, as shown in Figure 5-43 and Figure 5-44, whereas voltages generated by the
conventional Inverse Clark Transformation project the u α component into u ref1.
Figure 5-43. Direct-ua and quadrature-ub components of stator reference voltage
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Function GMCLIB_SvmStd_F32
Figure 5-43 depicts the u α and u β components of the stator reference voltage vector U S
that were calculated by the equations u α = cos( θ) and u β = sin( θ), respectively.
Figure 5-44. Reference Voltages u_ref1, u_ref2 and u_ref3
The Sector Identification Tree, shown in Figure 5-45, can be a numerical solution of the
approach shown in Figure 5-44.
Figure 5-45. Identification of the sector number
It should be pointed out that, in the worst case, three simple comparisons are required to
precisely identify the sector of the stator reference voltage vector. For example, if the
stator reference voltage vector resides according to the one shown in Figure 5-39, the
stator reference voltage vector is phase-advanced by 30 ° from the α-axis, which results
in the positive quantities of u ref1 and u ref2 and the negative quantity of u ref3; refer to
Figure 5-44. If these quantities are used as the inputs to the Sector Identification Tree, the
product of those comparisons will be Sector I. Using the same approach identifies Sector
II, if the stator reference voltage vector is located according to the one shown in Figure
5-42. The variables t 1, t 2 and t 3, representing the switching duty-cycle ratios of the
respective three-phase system, are given by the following equations:
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Chapter 5 API References
Equation GMCLIB_SvmStd_Eq25
Equation GMCLIB_SvmStd_Eq26
Equation GMCLIB_SvmStd_Eq27
where T is the switching period, t_1 and t_2 are the duty-cycle ratios (see Table 5-96) of
the basic space vectors, given for the respective sector. Equation
GMCLIB_SvmStd_Eq25, equation GMCLIB_SvmStd_Eq26 and equation
GMCLIB_SvmStd_Eq27 are specific solely to the Standard Space Vector Modulation
technique; consequently, other Space Vector Modulation techniques discussed later will
require deriving different equations.
The next step is to assign the correct duty-cycle ratios, t 1, t 2 and t 3, to the respective
motor phases. This is a simple task, accomplished in view of the position of the stator
reference voltage vector as shown in Table 5-97.
Table 5-97. Assignment of the duty-cycle ratios to motor phases
Sector
U 0, U 60
U 60, U 120
U 120, U 180
U 180, U 240
U 240, U 300
U 300, U 0
pwm a
t3
t2
t1
t1
t2
t3
pwm b
t2
t3
t3
t2
t1
t1
pwm c
t1
t1
t2
t3
t3
t2
The principle of the Space Vector Modulation technique consists in applying the basic
voltage vectors U XXX and O XXX for the certain time in such a way that the mean vector,
generated by the Pulse Width Modulation approach for the period T, is equal to the
original stator reference voltage vector U S. This provides a great variability of the
arrangement of the basic vectors during the PWM period T. Those vectors might be
arranged either to lower switching losses or to achieve diverse results, such as centrealigned PWM, edge-aligned PWM or a minimal number of switching states. A brief
discussion of the widely-used centre-aligned PWM follows. Generating the centrealigned PWM pattern is accomplished practically by comparing the threshold levels,
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Function GMCLIB_SvmStd_F32
pwm a, pwm b and pwm c with a free-running up-down counter. The timer counts to 1
(0x7FFF) and then down to 0 (0x0000). It is supposed that when a threshold level is
larger than the timer value, the respective PWM output is active. Otherwise, it is inactive;
see Figure 5-46
Figure 5-46. Standard space vector modulation technique - centre-aligned PWM
Note
The input/output pointers must contain valid addresses
otherwise an exception may occur (Data TLB Error, Data
Storage, Alignment, Machine Check).
5.77.5 Re-entrancy
The function is re-entrant.
5.77.6 Code Example
#include "gmclib.h"
#define U_MAX 15
SWLIBS_2Syst_F32 tr32InVoltage;
SWLIBS_3Syst_F32 tr32PwmABC;
tU32
u32SvmSector;
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void main(void)
{
// Input voltage vector 15V @ angle 30deg
// alpha component of input voltage vector = 12.99[V]
// beta component of input voltage vector = 7.5[V]
tr32InVoltage.f32Arg1 = FRAC32 (12.99/U_MAX);
tr32InVoltage.f32Arg2 = FRAC32 (7.5/U_MAX);
// output pwm dutycycles stored in structure referenced by tr32PwmABC
// pwmA dutycycle = 0x7FFF A2C9 = FRAC32(0.9999888... )
// pwmb dutycycle = 0x4000 5D35 = FRAC32(0.5000111... )
// pwmc dutycycle = 0x0000 5D35 = FRAC32(0.0000111... )
// svmSector
= 0x1 [sector]
u32SvmSector = GMCLIB_SvmStd_F32 (&tr32PwmABC,&tr32InVoltage);
// output pwm dutycycles stored in structure referenced by tr32PwmABC
// pwmA dutycycle = 0x7FFF A2C9 = FRAC32(0.9999888... )
// pwmb dutycycle = 0x4000 5D35 = FRAC32(0.5000111... )
// pwmc dutycycle = 0x0000 5D35 = FRAC32(0.0000111... )
// svmSector
= 0x1 [sector]
u32SvmSector = GMCLIB_SvmStd (&tr32PwmABC,&tr32InVoltage,F32);
//
//
//
//
}
##############################################################
Available only if 32-bit fractional implementation selected
as default
##############################################################
// output pwm dutycycles stored in structure referenced by tr32PwmABC
// pwmA dutycycle = 0x7FFF A2C9 = FRAC32(0.9999888... )
// pwmb dutycycle = 0x4000 5D35 = FRAC32(0.5000111... )
// pwmc dutycycle = 0x0000 5D35 = FRAC32(0.0000111... )
// svmSector
= 0x1 [sector]
u32SvmSector = GMCLIB_SvmStd (&tr32PwmABC,&tr32InVoltage);
5.78 Function GMCLIB_SvmStd_F16
This function calculates the duty-cycle ratios using the Standard Space Vector
Modulation technique.
5.78.1 Declaration
tU16 GMCLIB_SvmStd_F16(SWLIBS_3Syst_F16 *pOut, const SWLIBS_2Syst_F16 *const pIn);
5.78.2 Arguments
Table 5-98. GMCLIB_SvmStd_F16 arguments
Type
SWLIBS_3Syst_F16 *
Name
pOut
Direction
input,
output
Description
Pointer to the structure containing calculated duty-cycle ratios
of the 3-Phase system.
Table continues on the next page...
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Function GMCLIB_SvmStd_F16
Table 5-98. GMCLIB_SvmStd_F16 arguments
(continued)
Type
const
SWLIBS_2Syst_F16
*const
Name
pIn
Direction
input
Description
Pointer to the structure containing direct U α and quadrature U
β components of the stator voltage vector.
5.78.3 Return
The function returns a 16-bit value in format INT, representing the actual space sector
which contains the stator reference vector U s.
5.78.4 Description
The GMCLIB_SvmStd_F16 function for calculating duty-cycle ratios is widely-used in
the modern electric drive. This, function calculates appropriate duty-cycle ratios, which
are needed for generating the given stator reference voltage vector using a special Space
Vector Modulation technique, termed Standard Space Vector Modulation. The basic
principle of the Standard Space Vector Modulation Technique can be explained with the
help of the power stage diagram in Figure 5-47.
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Figure 5-47. Power stage schematic diagram
Top and bottom switches work in a complementary mode; i.e., if the top switch, S At, is
ON, then the corresponding bottom switch, S Ab, is OFF, and vice versa. Considering that
value 1 is assigned to the ON state of the top switch, and value 0 is assigned to the ON
state of the bottom switch, the switching vector, [a, b, c] T can be defined. Creating such
a vector allows a numerical definition of all possible switching states. In a three-phase
power stage configuration (as shown in Figure 5-47), eight possible switching states
(detailed in Figure 5-48) are feasible.
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Function GMCLIB_SvmStd_F16
Figure 5-48. Basic space vectors
These states, together with the resulting instantaneous output line-to-line and phase
voltages, are listed in Table 5-99.
Table 5-99. Switching patterns
a
b
c
Ua
Ub
Uc
U AB
U BC
U CA
Vector
0
0
0
0
0
0
0
0
0
O 000
1
0
0
U DCBus
0
-U DCBus
U0
0
U DCBus
-U DCBus
U 60
-U DCBus
U DCBus
0
U 120
-U DCBus
0
U DCBus
U 180
0
-U DCBus
U DCBus
U 240
U DCBus
-U DCBus
0
U 300
0
0
0
O 111
1
0
1
1
0
0
0
1
1
0
0
1
1
1
0
1
1
1
2/3*U
-1/3*U
-1/3*U
DCBus
DCBus
DCBus
1/3*U
1/3*U
-2/3*U
DCBus
DCBus
DCBus
-1/3*U
2/3*U
-1/3*U
DCBus
DCBus
DCBus
-2/3*U
1/3*U
1/3*U
DCBus
DCBus
DCBus
-1/3*U
-1/3*U
2/3*U
DCBus
DCBus
DCBus
1/3*U
-2/3*U
1/3*U
DCBus
DCBus
DCBus
0
0
0
The quantities of the direct-u α and the quadrature-u β components of the two-phase
orthogonal coordinate system, describing the three-phase stator voltages, are expressed
by the Clarke Transformation.
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Chapter 5 API References
Equation GMCLIB_SvmStd_Eq1
Equation GMCLIB_SvmStd_Eq2
The three-phase stator voltages,U a, U b, and U c, are transformed using the Clarke
Transformation into the U α and the U β components of the two-phase orthogonal
coordinate system. The transformation results are listed in Table 5-100.
Table 5-100. Switching patterns and space vectors
a
b
c
uα
uβ
Vector
0
0
0
0
0
O 000
1
0
0
2/3*U DCBus
0
U0
1
1
0
1/3*U DCBus
1/ √(3)*U DCBus
U 60
0
1
0
-1/3*U DCBus
1/ √(3)*U DCBus
U 120
0
1
1
-2/3*U DCBus
0
U 180
0
0
1
-1/3*U DCBus
-1/ √(3)*U DCBus
U 240
1
0
1
1/3*U DCBus
-1/ √(3)*U DCBus
U 300
1
1
1
0
0
O 111
Figure 5-48 graphically depicts some feasible basic switching states (vectors). It is clear
that there are six non-zero vectors U 0, U 60, U 120, U 180, U 240, U 300, and two zero
vectors O 111, O 000, usable for switching. Therefore, the principle of the Standard Space
Vector Modulation resides in applying appropriate switching states for a certain time and
thus generating a voltage vector identical to the reference one.
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Function GMCLIB_SvmStd_F16
Figure 5-49. Projection of reference voltage vector in sector I
Referring to that principle, an objective of the Standard Space Vector Modulation is an
approximation of the reference stator voltage vector U S with an appropriate combination
of the switching patterns composed of basic space vectors. The graphical explanation of
this objective is shown in Figure 5-49 and Figure 5-50.
Figure 5-50. Detail of the voltage vector projection in sector I
The stator reference voltage vector U S is phase-advanced by 30 ° from the axis- α and
thus might be generated with an appropriate combination of the adjacent basic switching
states U 0 and U60. These figures also indicate the resultant U α and U β components for
space vectors U 0 and U 60
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In this case, the reference stator voltage vector U S is located in Sector I and, as
previously mentioned, can be generated with the appropriate duty-cycle ratios of the
basic switching states U 60 and U 0. The principal equations concerning this vector
location are:
Equation GMCLIB_SvmStd_Eq3
Equation GMCLIB_SvmStd_Eq4
where T 60 and T 0 are the respective duty-cycle ratios for which the basic space vectors
U 60 and U 0 should be applied within the time period T. T null is the course of time for
which the null vectors O 000 and O 111 are applied. Those duty-cycle ratios can be
calculated using equations:
Equation GMCLIB_SvmStd_Eq5
Equation GMCLIB_SvmStd_Eq6
Considering that the normalized magnitudes of the basic space vectors are |U 60| = |U 0| =
2/ √(3) and by substitution of the trigonometric expressions sin(60 °) and tan(60 °) by
their quantities 2/ √(3) and √(3), respectively, equation GMCLIB_SvmStd_Eq5 and
equation GMCLIB_SvmStd_Eq6 can be rearranged for the unknown duty-cycle ratios T
60/T and T 0/T:
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Function GMCLIB_SvmStd_F16
Equation GMCLIB_SvmStd_Eq7
Equation GMCLIB_SvmStd_Eq8
Equation GMCLIB_SvmStd_Eq7
Equation GMCLIB_SvmStd_Eq8
Figure 5-51. Projection of the reference voltage vector in sector II
Sector II is depicted in Figure 5-51. In this particular case, the reference stator voltage
vector U S is generated by the appropriate duty-cycle ratios of the basic switching states
U 60 and U 120. The basic equations describing this sector are:
Equation GMCLIB_SvmStd_Eq9
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Equation GMCLIB_SvmStd_Eq10
where T 120 and T 60 are the respective duty-cycle ratios for which the basic space vectors
U 120 and U 60 should be applied within the time period T. These resultant duty-cycle
ratios are formed from the auxiliary components termed A and B. The graphical
representation of the auxiliary components is shown in Figure 5-52.
Figure 5-52. Detail of the voltage vector projection in sector II
The equations describing those auxiliary time-duration components are:
Equation GMCLIB_SvmStd_Eq11
Equation GMCLIB_SvmStd_Eq12
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Function GMCLIB_SvmStd_F16
Equation GMCLIB_SvmStd_Eq11 and equation GMCLIB_SvmStd_Eq12 have been
formed using the sine rule. These equations can be rearranged for the calculation of the
auxiliary time-duration components A and B. This is done simply by substitution of the
trigonometric terms sin(30 °), sin(120 °) and sin(60 °) by their numerical representations
1/2, √(3)/2 and 1/ √(3), respectively.
Equation GMCLIB_SvmStd_Eq13
Equation GMCLIB_SvmStd_Eq14
The resultant duty-cycle ratios, T 120/T and T 60/T, are then expressed in terms of the
auxiliary time-duration components defined by equation GMCLIB_SvmStd_Eq13 and
equation GMCLIB_SvmStd_Eq14, as follows:
Equation GMCLIB_SvmStd_Eq15
Equation GMCLIB_SvmStd_Eq16
With the help of these equations, and also considering the normalized magnitudes of the
basic space vectors to be |U 120| = |U 60| = 2/ √(3), the equations expressed for the
unknown duty-cycle ratios of basic space vectors T 120/T and T 60/T can be written:
Equation GMCLIB_SvmStd_Eq17
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Equation GMCLIB_SvmStd_Eq18
The duty-cycle ratios in remaining sectors can be derived using the same approach. The
resulting equations will be similar to those derived for Sector I and Sector II.
To depict duty-cycle ratios of the basic space vectors for all sectors, we define:
• Three auxiliary variables:
Equation GMCLIB_SvmStd_Eq19
Equation GMCLIB_SvmStd_Eq20
Equation GMCLIB_SvmStd_Eq21
Two expressions t_1 and t_2 generally represent duty-cycle ratios of the basic space
vectors in the respective sector; e.g., for the first sector, t_1 and t_2 represent duty-cycle
ratios of the basic space vectors U 60 and U 0; for the second sector, t_1 and t_2 represent
duty-cycle ratios of the basic space vectors U 120 and U 60, etc.
For each sector, the expressions t_1 and t_2, in terms of auxiliary variables X, Y and Z,
are listed in Table 5-101.
Table 5-101. Determination of t_1 and t_2 expressions
Sector
U 0, U 60
U 60, U 120
U 120, U 180
U 180, U 240
U 240, U 300
U 300, U 0
t_1
X
Y
-Y
Z
-Z
-X
t_2
-Z
Z
X
-X
-Y
Y
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Function GMCLIB_SvmStd_F16
For the determination of auxiliary variables X equation GMCLIB_SvmStd_Eq19, Y
equation GMCLIB_SvmStd_Eq20 and Z equation GMCLIB_SvmStd_Eq21, the sector
number is required. This information can be obtained by several approaches. One
approach discussed here requires the use of a modified Inverse Clark Transformation to
transform the direct- α and quadrature- β components into a balanced three-phase
quantity u ref1, u ref2 and u ref3, used for a straightforward calculation of the sector
number, to be shown later.
Equation GMCLIB_SvmStd_Eq22
Equation GMCLIB_SvmStd_Eq23
Equation GMCLIB_SvmStd_Eq24
The modified Inverse Clark Transformation projects the quadrature-u β component into u
ref1, as shown in Figure 5-53 and Figure 5-54, whereas voltages generated by the
conventional Inverse Clark Transformation project the u α component into u ref1.
Figure 5-53. Direct-ua and quadrature-ub components of stator reference voltage
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Figure 5-53 depicts the u α and u β components of the stator reference voltage vector U S
that were calculated by the equations u α = cos( θ) and u β = sin( θ), respectively.
Figure 5-54. Reference voltages u_ref1, u_ref2 and u_ref3
The Sector Identification Tree, shown in Figure 5-55, can be a numerical solution of the
approach shown in Figure 5-54.
Figure 5-55. Identification of the sector number
It should be pointed out that, in the worst case, three simple comparisons are required to
precisely identify the sector of the stator reference voltage vector. For example, if the
stator reference voltage vector resides according to the one shown in Figure 5-49, the
stator reference voltage vector is phase-advanced by 30 ° from the α-axis, which results
in the positive quantities of u ref1 and u ref2 and the negative quantity of u ref3; refer to
Figure 5-54. If these quantities are used as the inputs to the Sector Identification Tree, the
product of those comparisons will be Sector I. Using the same approach identifies Sector
II, if the stator reference voltage vector is located according to the one shown in Figure
5-52. The variables t 1, t 2 and t 3, representing the switching duty-cycle ratios of the
respective three-phase system, are given by the following equations:
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Function GMCLIB_SvmStd_F16
Equation GMCLIB_SvmStd_Eq25
Equation GMCLIB_SvmStd_Eq26
Equation GMCLIB_SvmStd_Eq27
where T is the switching period, t_1 and t_2 are the duty-cycle ratios (see Table 5-101) of
the basic space vectors, given for the respective sector. Equation
GMCLIB_SvmStd_Eq25, equation GMCLIB_SvmStd_Eq26 and equation
GMCLIB_SvmStd_Eq27 are specific solely to the Standard Space Vector Modulation
technique; consequently, other Space Vector Modulation techniques discussed later will
require deriving different equations.
The next step is to assign the correct duty-cycle ratios, t 1, t 2 and t 3, to the respective
motor phases. This is a simple task, accomplished in view of the position of the stator
reference voltage vector as shown in Table 5-102.
Table 5-102. Assignment of the duty-cycle ratios to motor phases
Sector
U 0, U 60
U 60, U 120
U 120, U 180
U 180, U 240
U 240, U 300
U 300, U 0
pwm a
t3
t2
t1
t1
t2
t3
pwm b
t2
t3
t3
t2
t1
t1
pwm c
t1
t1
t2
t3
t3
t2
The principle of the Space Vector Modulation technique consists in applying the basic
voltage vectors U XXX and O XXX for the certain time in such a way that the mean vector,
generated by the Pulse Width Modulation approach for the period T, is equal to the
original stator reference voltage vector U S. This provides a great variability of the
arrangement of the basic vectors during the PWM period T. Those vectors might be
arranged either to lower switching losses or to achieve diverse results, such as centrealigned PWM, edge-aligned PWM or a minimal number of switching states. A brief
discussion of the widely-used centre-aligned PWM follows. Generating the centrealigned PWM pattern is accomplished practically by comparing the threshold levels,
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Chapter 5 API References
pwm a, pwm b and pwm c with a free-running up-down counter. The timer counts to 1
(0x7FFF) and then down to 0 (0x0000). It is supposed that when a threshold level is
larger than the timer value, the respective PWM output is active. Otherwise, it is inactive;
see Figure 5-56
Figure 5-56. Standard space vector modulation technique - centre-aligned PWM
Note
The input/output pointers must contain valid addresses
otherwise an exception may occur (Data TLB Error, Data
Storage, Alignment, Machine Check).
5.78.5 Re-entrancy
The function is re-entrant.
5.78.6 Code Example
#include "gmclib.h"
#define U_MAX 15
SWLIBS_2Syst_F16 tr16InVoltage;
SWLIBS_3Syst_F16 tr16PwmABC;
tU16
u16SvmSector;
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Function MLIB_Abs_F32
void main(void)
{
// Input voltage vector 15V @ angle 30deg
// alpha component of input voltage vector = 12.99[V]
// beta component of input voltage vector = 7.5[V]
tr16InVoltage.f16Arg1 = FRAC16 (12.99/U_MAX);
tr16InVoltage.f16Arg2 = FRAC16 (7.5/U_MAX);
// output pwm dutycycles stored in structure referenced by tr16PwmABC
// pwmA dutycycle = 0x7FFF = FRAC16(0.9999... )
// pwmb dutycycle = 0x4000 = FRAC16(0.5000... )
// pwmc dutycycle = 0x0000 = FRAC16(0.0000... )
// svmSector
= 0x1 [sector]
u16SvmSector = GMCLIB_SvmStd_F16 (&tr16PwmABC,&tr16InVoltage);
// output pwm dutycycles stored in structure referenced by tr16PwmABC
// pwmA dutycycle = 0x7FFF = FRAC16(0.9999... )
// pwmb dutycycle = 0x4000 = FRAC16(0.5000... )
// pwmc dutycycle = 0x0000 = FRAC16(0.0000... )
// svmSector
= 0x1 [sector]
u16SvmSector = GMCLIB_SvmStd (&tr16PwmABC,&tr16InVoltage,F16);
//
//
//
//
}
##############################################################
Available only if 16-bit fractional implementation selected
as default
##############################################################
// output pwm dutycycles stored in structure referenced by tr16PwmABC
// pwmA dutycycle = 0x7FFF = FRAC16(0.9999... )
// pwmb dutycycle = 0x4000 = FRAC16(0.5000... )
// pwmc dutycycle = 0x0000 = FRAC16(0.0000... )
// svmSector
= 0x1 [sector]
u16SvmSector = GMCLIB_SvmStd (&tr16PwmABC,&tr16InVoltage);
5.79 Function MLIB_Abs_F32
This function returns absolute value of input parameter.
5.79.1 Declaration
tFrac32 MLIB_Abs_F32(register tFrac32 f32In);
5.79.2 Arguments
Table 5-103. MLIB_Abs_F32 arguments
Type
register tFrac32
Name
f32In
Direction
input
Description
Input value.
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Chapter 5 API References
5.79.3 Return
Absolute value of input parameter.
5.79.4 Description
This inline function returns the absolute value of input parameter. The input value as well
as output value is considered as 32-bit fractional data type. The output saturation is not
implemented in this function, thus in case the absolute value of input parameter is outside
the (-1, 1) interval, the output value will overflow without any detection.
The output of the function is defined by the following simple equation:
Equation MLIB_Abs_Eq1
Note
Due to effectivity reason this function is implemented as inline,
and thus is not ANSI-C compliant.
5.79.5 Re-entrancy
The function is re-entrant.
5.79.6 Code Example
#include "mlib.h"
tFrac32 f32In;
tFrac32 f32Out;
void main(void)
{
// input value = -0.25
f32In = FRAC32 (-0.25);
// output should be FRAC32(0.25)
f32Out = MLIB_Abs_F32(f32In);
// output should be FRAC32(0.25)
f32Out = MLIB_Abs (f32In, F32);
// ##############################################################
// Available only if 32-bit fractional implementation selected
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Function MLIB_Abs_F16
// as default
// ##############################################################
}
// output should be FRAC32(0.25)
f32Out = MLIB_Abs (f32In);
5.80 Function MLIB_Abs_F16
This function returns absolute value of input parameter.
5.80.1 Declaration
tFrac16 MLIB_Abs_F16(register tFrac16 f16In);
5.80.2 Arguments
Table 5-104. MLIB_Abs_F16 arguments
Type
register tFrac16
Name
Direction
input
f16In
Description
Input value.
5.80.3 Return
Absolute value of input parameter.
5.80.4 Description
This inline function returns the absolute value of input parameter. The input value as well
as output value is considered as 16-bit fractional data type. The output saturation is not
implemented in this function, thus in case the absolute value of input parameter is outside
the (-1, 1) interval, the output value will overflow without any detection.
The output of the function is defined by the following simple equation:
Equation MLIB_Abs_Eq1
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Chapter 5 API References
Note
Due to effectivity reason this function is implemented as inline,
and thus is not ANSI-C compliant.
5.80.5 Re-entrancy
The function is re-entrant.
5.80.6 Code Example
#include "mlib.h"
tFrac16 f16In;
tFrac16 f16Out;
void main(void)
{
// input value = -0.25
f16In = FRAC16 (-0.25);
// output should be FRAC16(0.25)
f16Out = MLIB_Abs_F16(f16In);
// output should be FRAC16(0.25)
f16Out = MLIB_Abs (f16In, F16);
//
//
//
//
}
##############################################################
Available only if 16-bit fractional implementation selected
as default
##############################################################
// output should be FRAC16(0.25)
f16Out = MLIB_Abs (f16In);
5.81 Function MLIB_AbsSat_F32
This function returns absolute value of input parameter and saturate if necessary.
5.81.1 Declaration
tFrac32 MLIB_AbsSat_F32(register tFrac32 f32In);
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Function MLIB_AbsSat_F32
5.81.2 Arguments
Table 5-105. MLIB_AbsSat_F32 arguments
Type
register tFrac32
Name
Direction
input
f32In
Description
Input value.
5.81.3 Return
Absolute value of input parameter, saturated if necessary.
5.81.4 Description
This inline function returns the absolute value of input parameter. The input values as
well as output value is considered as 32-bit fractional data type. The output saturation is
implemented in this function, thus in case the absolute value of input parameter is outside
the (-1, 1) interval, the output value is limited to the boundary value.
The output of the function is defined by the following simple equation:
Equation MLIB_AbsSat_Eq1
Note
Due to effectivity reason this function is implemented as inline,
and thus is not ANSI-C compliant. The overflow is detected in
this function. The functions saturates the return value if it
cannot fit into the return type.
5.81.5 Re-entrancy
The function is re-entrant.
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Chapter 5 API References
5.81.6 Code Example
#include "mlib.h"
tFrac32 f32In;
tFrac32 f32Out;
void main(void)
{
// input value = -0.25
f32In = FRAC32 (-0.25);
// output should be FRAC32(0.25)
f32Out = MLIB_AbsSat_F32(f32In);
// output should be FRAC32(0.25)
f32Out = MLIB_AbsSat (f32In, F32);
//
//
//
//
}
##############################################################
Available only if 32-bit fractional implementation selected
as default
##############################################################
// output should be FRAC32(0.25)
f32Out = MLIB_AbsSat (f32In);
5.82 Function MLIB_AbsSat_F16
This function returns absolute value of input parameter and saturate if necessary.
5.82.1 Declaration
tFrac16 MLIB_AbsSat_F16(register tFrac16 f16In);
5.82.2 Arguments
Table 5-106. MLIB_AbsSat_F16 arguments
Type
register tFrac16
Name
f16In
Direction
input
Description
Input value.
5.82.3 Return
Absolute value of input parameter, saturated if necessary.
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Function MLIB_AbsSat_F16
5.82.4 Description
This inline function returns the absolute value of input parameter. The input values as
well as output value is considered as 16-bit fractional data type. The output saturation is
implemented in this function, thus in case the absolute value of input parameter is outside
the (-1, 1) interval, the output value is limited to the boundary value.
The output of the function is defined by the following simple equation:
Equation MLIB_AbsSat_Eq1
Note
Due to effectivity reason this function is implemented as inline,
and thus is not ANSI-C compliant. The overflow is detected in
this function. The functions saturates the return value if it
cannot fit into the return type.
5.82.5 Re-entrancy
The function is re-entrant.
5.82.6 Code Example
#include "mlib.h"
tFrac16 f16In;
tFrac16 f16Out;
void main(void)
{
// input value = -0.25
f16In = FRAC16 (-0.25);
// output should be FRAC16(0.25)
f16Out = MLIB_AbsSat_F16(f16In);
// output should be FRAC16(0.25)
f16Out = MLIB_AbsSat (f16In, F16);
// ##############################################################
// Available only if 16-bit fractional implementation selected
// as default
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// ##############################################################
}
// output should be FRAC16(0.25)
f16Out = MLIB_AbsSat (f16In);
5.83 Function MLIB_Add_F32
This function returns sum of two input parameters.
5.83.1 Declaration
tFrac32 MLIB_Add_F32(register tFrac32 f32In1, register tFrac32 f32In2);
5.83.2 Arguments
Table 5-107. MLIB_Add_F32 arguments
Type
Name
Direction
Description
register tFrac32
f32In1
input
First value to be add.
register tFrac32
f32In2
input
Second value to be add.
5.83.3 Return
Sum of two input values.
5.83.4 Description
This inline function returns the sum of two input values. The input values as well as
output value is considered as 32-bit fractional data type. The output saturation is not
implemented in this function, thus in case the sum of input values is outside the (-1, 1)
interval, the output value will overflow without any detection.
The output of the function is defined by the following simple equation:
Equation MLIB_Add_Eq1
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Function MLIB_Add_F16
Note
Due to effectivity reason this function is implemented as inline
and thus is not ANSI-C compliant.
5.83.5 Re-entrancy:
The function is re-entrant.
5.83.6 Code Example:
#include "mlib.h"
tFrac32 f32In1, f32In2;
tFrac32 f32Out;
void main(void)
{
// input value 1 = 0.25
f32In1 = FRAC32 (0.25);
// input value 2 = 0.25
f32In2 = FRAC32 (0.25);
// output should be FRAC32(0.5) = 0x40000000
f32Out = MLIB_Add_F32(f32In1, f32In2);
// output should be FRAC32(0.5) = 0x40000000
f32Out = MLIB_Add (f32In1, f32In2, F32);
//
//
//
//
}
##############################################################
Available only if 32-bit fractional implementation selected
as default
##############################################################
// output should be FRAC32(0.5) = 0x40000000
f32Out = MLIB_Add (f32In1, f32In2);
5.84 Function MLIB_Add_F16
This function returns sum of two input parameters.
5.84.1 Declaration
tFrac16 MLIB_Add_F16(register tFrac16 f16In1, register tFrac16 f16In2);
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5.84.2 Arguments
Table 5-108. MLIB_Add_F16 arguments
Type
Name
Direction
Description
register tFrac16
f16In1
input
First value to be add.
register tFrac16
f16In2
input
Second value to be add.
5.84.3 Return
Sum of two input values.
5.84.4 Description
This inline function returns the sum of two input values. The input values as well as
output value is considered as 16-bit fractional values. The output saturation is not
implemented in this function, thus in case the sum of input values is outside the (-1, 1)
interval, the output value will overflow without any detection.
The output of the function is defined by the following simple equation:
Equation MLIB_Add_Eq1
Note
Due to effectivity reason this function is implemented as inline
and thus is not ANSI-C compliant.
5.84.5 Re-entrancy
The function is re-entrant.
5.84.6 Code Example
#include "mlib.h"
tFrac16 f16In1, f16In2;
tFrac16 f16Out;
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Function MLIB_AddSat_F32
void main(void)
{
// input value 1 = 0.25
f16In1 = FRAC16 (0.25);
// input value 2 = 0.25
f16In2 = FRAC16 (0.25);
// output should be FRAC16(0.5) = 0x4000
f16Out = MLIB_Add_F16(f16In1, f16In2);
// output should be FRAC16(0.5) = 0x4000
f16Out = MLIB_Add (f16In1, f16In2, F16);
//
//
//
//
}
##############################################################
Available only if 16-bit fractional implementation selected
as default
##############################################################
// output should be FRAC16(0.5) = 0x4000
f16Out = MLIB_Add (f16In1, f16In2);
5.85 Function MLIB_AddSat_F32
This function returns sum of two input parameters and saturate if necessary.
5.85.1 Declaration
tFrac32 MLIB_AddSat_F32(register tFrac32 f32In1, register tFrac32 f32In2);
5.85.2 Arguments
Table 5-109. MLIB_AddSat_F32 arguments
Type
Name
Direction
Description
register tFrac32
f32In1
input
First value to be add.
register tFrac32
f32In2
input
Second value to be add.
5.85.3 Return
Sum of two input values, saturated if necessary.
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5.85.4 Description
This inline function returns the sum of two input values. The input values as well as
output value is considered as 32-bit fractional data type. The output saturation is
implemented in this function, thus in case the sum of input values is outside the (-1, 1)
interval, the output value is limited to the boundary value.
The output of the function is defined by the following simple equation:
Equation MLIB_AddSat_Eq1
Note
Due to effectivity reason this function is implemented as inline,
and thus is not ANSI-C compliant. The overflow is detected in
this function. The functions saturates the return value if it
cannot fit into the return type.
5.85.5 Re-entrancy
The function is re-entrant.
5.85.6 Code Example
#include "mlib.h"
tFrac32 f32In1, f32In2;
tFrac32 f32Out;
void main(void)
{
// input value 1 = 0.25
f32In1 = FRAC32 (0.25);
// input value 2 = 0.25
f32In2 = FRAC32 (0.25);
// output should be FRAC32(0.5) = 0x40000000
f32Out = MLIB_AddSat_F32(f32In1, f32In2);
// output should be FRAC32(0.5) = 0x40000000
f32Out = MLIB_AddSat (f32In1, f32In2, F32);
// ##############################################################
// Available only if 32-bit fractional implementation selected
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Function MLIB_AddSat_F16
// as default
// ##############################################################
}
// output should be FRAC32(0.5) = 0x40000000
f32Out = MLIB_AddSat (f32In1, f32In2);
5.86 Function MLIB_AddSat_F16
This function returns sum of two input parameters and saturate if necessary.
5.86.1 Declaration
tFrac16 MLIB_AddSat_F16(register tFrac16 f16In1, register tFrac16 f16In2);
5.86.2 Arguments
Table 5-110. MLIB_AddSat_F16 arguments
Type
Name
Direction
Description
register tFrac16
f16In1
input
First value to be add.
register tFrac16
f16In2
input
Second value to be add.
5.86.3 Return
Sum of two input values, saturated if necessary.
5.86.4 Description
This inline function returns the sum of two input values. The input values as well as
output value is considered as 16-bit fractional data type. The output saturation is
implemented in this function, thus in case the sum of input values is outside the (-1, 1)
interval, the output value is limited to the boundary value.
The output of the function is defined by the following simple equation:
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Equation MLIB_AddSat_Eq1
Note
Due to effectivity reason this function is implemented as inline,
and thus is not ANSI-C compliant. The overflow is detected in
this function. The functions saturates the return value if it
cannot fit into the return type.
5.86.5 Re-entrancy
The function is re-entrant.
5.86.6 Code Example
#include "mlib.h"
tFrac16 f16In1, f16In2;
tFrac16 f16Out;
void main(void)
{
// input value 1 = 0.25
f16In1 = FRAC16 (0.25);
// input value 2 = 0.25
f16In2 = FRAC16 (0.25);
// output should be FRAC16(0.5) = 0x4000
f16Out = MLIB_AddSat_F16(f16In1, f16In2);
// output should be FRAC16(0.5) = 0x4000
f16Out = MLIB_AddSat (f16In1, f16In2, F16);
//
//
//
//
}
##############################################################
Available only if 16-bit fractional implementation selected
as default
##############################################################
// output should be FRAC16(0.5) = 0x4000
f16Out = MLIB_AddSat (f16In1, f16In2);
5.87 Function MLIB_Convert_F32F16
This function converts the input value to different representation with scale.
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Function MLIB_Convert_F32F16
5.87.1 Declaration
tFrac32 MLIB_Convert_F32F16(register tFrac16 f16In1, register tFrac16 f16In2);
5.87.2 Arguments
Table 5-111. MLIB_Convert_F32F16 arguments
Type
Name
Direction
Description
register tFrac16
f16In1
input
Input value in 16-bit fractional format to be converted.
register tFrac16
f16In2
input
Scale factor in 16-bit fractional format.
5.87.3 Return
Converted input value in 32-bit fractional format.
5.87.4 Description
This inline function returns converted input value. The input value is considered as 16-bit
fractional data type and output value is considered as 32-bit fractional data type thus both
values represent the values in unity model. The second value represents the scale factor
and is considered as 16-bit fractional data type. The sign of the second value represents
the scale mechanism. In case the second value is positive the first input value is
multiplied with the second one and converted to the output format. In case the second
value is negative, the first input value is divided by absolute value of second input value
and converted to the output format. The output saturation is not implemented in this
function, thus in case the input value is outside the (-1, 1) interval, the output value will
overflow without any detection.
The output of the function is defined by the following simple equation:
Equation MLIB_Convert_Eq1
Note
Due to effectivity reason this function is implemented as inline
and thus is not ANSI-C compliant.
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5.87.5 Re-entrancy
The function is re-entrant.
5.87.6 Code Example
#include "mlib.h"
tFrac16 f16In1, f16In2;
tFrac32 f32Out;
void main(void)
{
// input value = 0.25 = 0x2000
f16In1 = FRAC16 (0.25);
// scale value = 0.5 = 0x4000
f16In2 = FRAC16 (0.5);
// output should be FRAC32(0.125) = 0x10000000
f32Out = MLIB_Convert_F32F16(f16In1, f16In2);
// output should be FRAC32(0.125) = 0x10000000
f32Out = MLIB_Convert (f16In1, f16In2, F32F16);
// scale value = -0.5 = 0xC000
f16In2 = FRAC16 (-0.5);
// output should be FRAC32(0.5) = 0x40000000
f32Out = MLIB_Convert_F32F16(f16In1, f16In2);
}
// output should be FRAC32(0.5) = 0x40000000
f32Out = MLIB_Convert (f16In1, f16In2, F32F16);
5.88 Function MLIB_Convert_F16F32
This function converts the input value to different representation with scale.
5.88.1 Declaration
tFrac16 MLIB_Convert_F16F32(register tFrac32 f32In1, register tFrac32 f32In2);
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Function MLIB_Convert_F16F32
5.88.2 Arguments
Table 5-112. MLIB_Convert_F16F32 arguments
Type
Name
Direction
Description
register tFrac32
f32In1
input
Input value in 32-bit fractional format to be converted.
register tFrac32
f32In2
input
Scale factor in 32-bit fractional format.
5.88.3 Return
Converted input value in 16-bit fractional format.
5.88.4 Description
This inline function returns converted input value. The input value is considered as 32-bit
fractional data type and output value is considered as 16-bit fractional data type thus both
values represent the values in unity model. The second value represents the scale factor
and is considered as 32-bit fractional data type. The sign of the second value represents
the scale mechanism. In case the second value is positive the first input value is
multiplied with the second one and converted to the output format. In case the second
value is negative, the first input value is divided by absolute value of second input value
and converted to the output format. The output saturation is not implemented in this
function, thus in case the input value is outside the (-1, 1) interval, the output value will
overflow without any detection.
The output of the function is defined by the following simple equation:
Equation MLIB_Convert_Eq1
Note
Due to effectivity reason this function is implemented as inline
and thus is not ANSI-C compliant.
5.88.5 Re-entrancy
The function is re-entrant.
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5.88.6 Code Example
#include "mlib.h"
tFrac32 f32In1, f32In2;
tFrac16 f16Out;
void main(void)
{
// input value = 0.25 = 0x20000000
f32In1 = FRAC32 (0.25);
// scale value = 0.5 = 0x40000000
f32In2 = FRAC32 (0.5);
// output should be FRAC16(0.125) = 0x1000
f16Out = MLIB_Convert_F16F32(f32In1, f32In2);
// output should be FRAC16(0.125) = 0x1000
f16Out = MLIB_Convert (f32In1, f32In2, F16F32);
// scale value = -0.5 = 0xC0000000
f32In2 = FRAC32 (-0.5);
// output should be FRAC16(0.5) = 0x4000
f16Out = MLIB_Convert_F16F32(f32In1, f32In2);
}
// output should be FRAC16(0.5) = 0x4000
f16Out = MLIB_Convert (f32In1, f32In2, F16F32);
5.89 Function MLIB_ConvertPU_F32F16
This function converts the input value to different representation without scale.
5.89.1 Declaration
tFrac32 MLIB_ConvertPU_F32F16(register tFrac16 f16In);
5.89.2 Arguments
Table 5-113. MLIB_ConvertPU_F32F16 arguments
Type
register tFrac16
Name
f16In
Direction
input
Description
Input value in 16-bit fractional format to be converted.
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Function MLIB_ConvertPU_F32F16
5.89.3 Return
Converted input value in 32-bit fractional format.
5.89.4 Description
This inline function returns converted input value. The input value is considered as 16-bit
fractional data type and output value is considered as 32-bit fractional data type thus both
values represent the values in unity model. The output saturation is not implemented in
this function, thus in case the input value is outside the (-1, 1) interval, the output value
will overflow without any detection.
The output of the function is defined by the following simple equation:
Equation MLIB_ConvertPU_Eq1
Note
Due to effectivity reason this function is implemented as inline,
and thus is not ANSI-C compliant.
5.89.5 Re-entrancy
The function is re-entrant.
5.89.6 Code Example
#include "mlib.h"
tFrac16 f16In;
tFrac32 f32Out;
void main(void)
{
// input value = 0.25 = 0x2000
f16In = FRAC16 (0.25);
// output should be FRAC32(0.25) = 0x20000000
f32Out = MLIB_ConvertPU_F32F16(f16In);
}
// output should be FRAC32(0.25) = 0x20000000
f32Out = MLIB_ConvertPU (f16In, F32F16);
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5.90 Function MLIB_ConvertPU_F16F32
This function converts the input value to different representation without scale.
5.90.1 Declaration
tFrac16 MLIB_ConvertPU_F16F32(register tFrac32 f32In);
5.90.2 Arguments
Table 5-114. MLIB_ConvertPU_F16F32 arguments
Type
Name
register tFrac32
Direction
input
f32In
Description
Input value in 32-bit fractional format to be converted.
5.90.3 Return
Converted input value in 16-bit fractional format.
5.90.4 Description
This inline function returns converted input value. The input value is considered as 32-bit
fractional data type and output value is considered as 16-bit fractional data type thus both
values represent the values in unity model. The output saturation is not implemented in
this function, thus in case the input value is outside the (-1, 1) interval, the output value
will overflow without any detection.
The output of the function is defined by the following simple equation:
Equation MLIB_ConvertPU_Eq1
Note
Due to effectivity reason this function is implemented as inline,
and thus is not ANSI-C compliant.
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Function MLIB_Div_F32
5.90.5 Re-entrancy
The function is re-entrant.
5.90.6 Code Example
#include "mlib.h"
tFrac32 f32In;
tFrac16 f16Out;
void main(void)
{
// input value = 0.25 = 0x2000 0000
f32In = FRAC32 (0.25);
// output should be FRAC16(0.25) = 0x2000
f16Out = MLIB_ConvertPU_F16F32(f32In);
}
// output should be FRAC16(0.25) = 0x2000
f16Out = MLIB_ConvertPU (f32In, F16F32);
5.91 Function MLIB_Div_F32
This function divides the first parameter by the second one.
5.91.1 Declaration
tFrac32 MLIB_Div_F32(register tFrac32 f32In1, register tFrac32 f32In2);
5.91.2 Arguments
Table 5-115. MLIB_Div_F32 arguments
Type
Name
Direction
Description
register tFrac32
f32In1
input
Numerator of division.
register tFrac32
f32In2
input
Denominator of division.
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5.91.3 Return
Division of two input values.
5.91.4 Description
This inline function returns the division of two input values. The first input value is
numerator and the second input value is denominator. The input values as well as output
value is considered as 32-bit fractional data type. The output saturation is not
implemented in this function, thus in case the numerator is greater or equal to
denominator, the output value is undefined. The function will never cause division by
zero exception.
The output of the function is defined by the following simple equation:
Equation MLIB_Div_Eq1
Note
Due to effectivity reason this function is implemented as inline,
and thus is not ANSI-C compliant. The overflow is not detected
in this function.
CAUTION
Due to effectivity reason the division is held in 16-bit precision.
5.91.5 Re-entrancy
The function is re-entrant.
5.91.6 Code Example
#include "mlib.h"
tFrac32 f32In1,f32In2;
tFrac32 f32Out;
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Function MLIB_Div_F16
void main(void)
{
// input value 1 = 0.25
f32In1 = FRAC32 (0.25);
// input value 2 = 0.5
f32In2 = FRAC32 (0.5);
// output should be FRAC32(0.5) = 0x40000000
f32Out = MLIB_Div_F32(f32In1,f32In2);
// output should be FRAC32(0.5) = 0x40000000
f32Out = MLIB_Div (f32In1,f32In2,F32);
//
//
//
//
}
##############################################################
Available only if 32-bit fractional implementation selected
as default
##############################################################
// output should be FRAC32(0.5) = 0x40000000
f32Out = MLIB_Div (f32In1,f32In2);
5.92 Function MLIB_Div_F16
This function divides the first parameter by the second one.
5.92.1 Declaration
tFrac16 MLIB_Div_F16(register tFrac16 f16In1, register tFrac16 f16In2);
5.92.2 Arguments
Table 5-116. MLIB_Div_F16 arguments
Type
Name
Direction
Description
register tFrac16
f16In1
input
Numerator of division.
register tFrac16
f16In2
input
Denominator of division.
5.92.3 Return
Division of two input values.
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5.92.4 Description
This inline function returns the division of two input values. The first input value is
numerator and the second input value is denominator. The input values as well as output
value is considered as 16-bit fractional data type. The output saturation is not
implemented in this function, thus in case the numerator is greater or equal to
denominator, the output value is undefined. The function will never cause division by
zero exception.
The output of the function is defined by the following simple equation:
Equation MLIB_Div_Eq1
Note
Due to effectivity reason this function is implemented as inline,
and thus is not ANSI-C compliant. The overflow is not detected
in this function.
5.92.5 Re-entrancy
The function is re-entrant.
5.92.6 Code Example
#include "mlib.h"
tFrac16 f16In1,f16In2;
tFrac16 f16Out;
void main(void)
{
// input value 1 = 0.25
f16In1 = FRAC16 (0.25);
// input value 2 = 0.5
f16In2 = FRAC16 (0.5);
// output should be FRAC16(0.5) = 0x4000
f16Out = MLIB_Div_F16(f16In1,f16In2);
// output should be FRAC16(0.5) = 0x4000
f16Out = MLIB_Div (f16In1,f16In2,F16);
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Function MLIB_DivSat_F32
//
//
//
//
}
##############################################################
Available only if 16-bit fractional implementation selected
as default
##############################################################
// output should be FRAC16(0.5) = 0x4000
f16Out = MLIB_Div (f16In1,f16In2);
5.93 Function MLIB_DivSat_F32
This function divides the first parameter by the second one as saturate.
5.93.1 Declaration
tFrac32 MLIB_DivSat_F32(register tFrac32 f32In1, register tFrac32 f32In2);
5.93.2 Arguments
Table 5-117. MLIB_DivSat_F32 arguments
Type
Name
Direction
Description
register tFrac32
f32In1
input
Numerator of division.
register tFrac32
f32In2
input
Denominator of division.
5.93.3 Return
Division of two input values, saturated if necessary.
5.93.4 Description
This inline function returns the division of two input values. The first input value is
numerator and the second input value is denominator. The input values as well as output
value is considered as 32-bit fractional data type. The output saturation is implemented in
this function, thus in case the sum of input values is outside the (-1, 1) interval, the output
value is limited to the boundary value.
The output of the function is defined by the following simple equation:
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Equation MLIB_DivSat_Eq1
Note
Due to effectivity reason this function is implemented as inline
and thus is not ANSI-C compliant.
5.93.5 Re-entrancy
The function is re-entrant.
5.93.6 Code Example
#include "mlib.h"
tFrac32 f32In1, f32In2;
tFrac32 f32Out;
void main(void)
{
// input value 1 = 0.25
f32In1 = FRAC32 (0.25);
// input value 2 = 0.5
f32In2 = FRAC32 (0.5);
// output should be FRAC32(0.5) = 0x40000000
f32Out = MLIB_DivSat_F32(f32In1, f32In2);
// output should be FRAC32(0.5) = 0x40000000
f32Out = MLIB_DivSat (f32In1, f32In2, F32);
//
//
//
//
}
##############################################################
Available only if 32-bit fractional implementation selected
as default
##############################################################
// output should be FRAC32(0.5) = 0x40000000
f32Out = MLIB_DivSat (f32In1, f32In2);
5.94 Function MLIB_DivSat_F16
This function divides the first parameter by the second one as saturate.
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Function MLIB_DivSat_F16
5.94.1 Declaration
tFrac16 MLIB_DivSat_F16(register tFrac16 f16In1, register tFrac16 f16In2);
5.94.2 Arguments
Table 5-118. MLIB_DivSat_F16 arguments
Type
Name
Direction
Description
register tFrac16
f16In1
input
Numerator of division.
register tFrac16
f16In2
input
Denominator of division.
5.94.3 Return
Division of two input values, saturated if necessary.
5.94.4 Description
This inline function returns the division of two input values. The first input value is
numerator and the second input value is denominator. The input values as well as output
value is considered as 16-bit fractional data type. The output saturation is implemented in
this function, thus in case the sum of input values is outside the (-1, 1) interval, the output
value is limited to the boundary value.
The output of the function is defined by the following simple equation:
Equation MLIB_DivSat_Eq1
Note
Due to effectivity reason this function is implemented as inline
and thus is not ANSI-C compliant.
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5.94.5 Re-entrancy
The function is re-entrant.
5.94.6 Code Example
#include "mlib.h"
tFrac16 f16In1, f16In2;
tFrac16 f16Out;
void main(void)
{
// input value 1 = 0.25
f16In1 = FRAC16 (0.25);
// input value 2 = 0.5
f16In2 = FRAC16 (0.5);
// output should be FRAC16(0.5) = 0x4000
f16Out = MLIB_DivSat_F16(f16In1, f16In2);
// output should be FRAC16(0.5) = 0x4000
f16Out = MLIB_DivSat (f16In1, f16In2, F16);
//
//
//
//
}
##############################################################
Available only if 16-bit fractional implementation selected
as default
##############################################################
// output should be FRAC16(0.5) = 0x4000
f16Out = MLIB_DivSat (f16In1, f16In2);
5.95 Function MLIB_Mac_F32
This function implements the multiply accumulate function.
5.95.1 Declaration
tFrac32 MLIB_Mac_F32(register tFrac32 f32In1, register tFrac32 f32In2, register tFrac32
f32In3);
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Function MLIB_Mac_F32
5.95.2 Arguments
Table 5-119. MLIB_Mac_F32 arguments
Type
Name
Direction
Description
register tFrac32
f32In1
input
Input value to be add.
register tFrac32
f32In2
input
First value to be multiplied.
register tFrac32
f32In3
input
Second value to be multiplied.
5.95.3 Return
Multiplied second and third input value with adding of first input value.
5.95.4 Description
This inline function returns the multiplied second and third input value with adding of
first input value. The input values as well as output value is considered as 32-bit
fractional values. The output saturation is not implemented in this function, thus in case
the output value is outside the (-1, 1) interval, the output value will overflow without any
detection.
The output of the function is defined by the following simple equation:
Equation MLIB_Mac_Eq1
Note
Due to effectivity reason this function is implemented as inline,
and thus is not ANSI-C compliant. The overflow is not detected
in this function.
5.95.5 Re-entrancy
The function is re-entrant.
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5.95.6 Code Example
#include "mlib.h"
tFrac32
tFrac32
tFrac32
tFrac32
f32In1;
f32In2;
f32In3;
f32Out;
void main(void)
{
// input1 value = 0.25
f32In1 = FRAC32 (0.25);
// input2 value = 0.15
f32In2 = FRAC32 (0.15);
// input3 value = 0.35
f32In3 = FRAC32 (0.35);
// output should be FRAC32(0.3025) = 0x26B851EB
f32Out = MLIB_Mac_F32(f32In1, f32In2, f32In3);
// output should be FRAC32(0.3025) = 0x26B851EB
f32Out = MLIB_Mac (f32In1, f32In2, f32In3, F32);
//
//
//
//
}
##############################################################
Available only if 32-bit fractional implementation selected
as default
##############################################################
// output should be FRAC32(0.3025) = 0x26B851EB
f32Out = MLIB_Mac (f32In1, f32In2, f32In3);
5.96 Function MLIB_Mac_F32F16F16
This function implements the multiply accumulate function.
5.96.1 Declaration
tFrac32 MLIB_Mac_F32F16F16(register tFrac32 f32In1, register tFrac16 f16In2, register tFrac16
f16In3);
5.96.2 Arguments
Table 5-120. MLIB_Mac_F32F16F16 arguments
Type
register tFrac32
Name
f32In1
Direction
input
Description
Input value to be add.
Table continues on the next page...
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Function MLIB_Mac_F32F16F16
Table 5-120. MLIB_Mac_F32F16F16 arguments (continued)
Type
Name
Direction
Description
register tFrac16
f16In2
input
First value to be multiplied.
register tFrac16
f16In3
input
Second value to be multiplied.
5.96.3 Return
Multiplied second and third input value with adding of first input value.
5.96.4 Description
This inline function returns the multiplied second and third input value with adding of
first input value. The first input value as well as output value is considered as 32-bit
fractional values. The second and third input values are considered as 16-bit fractional
values. The output saturation is not implemented in this function, thus in case the output
value is outside the (-1, 1) interval, the output value will overflow without any detection.
The output of the function is defined by the following simple equation:
Equation MLIB_Mac_Eq1
This implementation is available if 32-bit fractional implementations are enabled.
However it is not possible to use the default implementation based function call, thus the
implementation post-fix or additional parameter function call shall be used.
Note
Due to effectivity reason this function is implemented as inline,
and thus is not ANSI-C compliant. The overflow is not detected
in this function.
5.96.5 Re-entrancy
The function is re-entrant.
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5.96.6 Code Example
#include "mlib.h"
tFrac32
tFrac16
tFrac16
tFrac32
f32In1;
f16In2;
f16In3;
f32Out;
void main(void)
{
// input1 value = 0.25
f32In1 = FRAC32 (0.25);
// input2 value = 0.15
f16In2 = FRAC16 (0.15);
// input3 value = 0.35
f16In3 = FRAC16 (0.35);
// output should be FRAC32(0.3025) = 0x26B851EB
f32Out = MLIB_Mac_F32F16F16(f32In1, f16In2, f16In3);
// output should be FRAC32(0.3025) = 0x26B851EB
f32Out = MLIB_Mac (f32In1, f32In2, f32In3, F32F16F16);
}
5.97 Function MLIB_Mac_F16
This function implements the multiply accumulate function.
5.97.1 Declaration
tFrac16 MLIB_Mac_F16(register tFrac16 f16In1, register tFrac16 f16In2, register tFrac16
f16In3);
5.97.2 Arguments
Table 5-121. MLIB_Mac_F16 arguments
Type
Name
Direction
Description
register tFrac16
f16In1
input
Input value to be add.
register tFrac16
f16In2
input
First value to be multiplied.
register tFrac16
f16In3
input
Second value to be multiplied.
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Function MLIB_Mac_F16
5.97.3 Return
Multiplied second and third input value with adding of first input value.
5.97.4 Description
This inline function returns the multiplied second and third input value with adding of
first input value. The input values as well as output value is considered as 16-bit
fractional values. The output saturation is not implemented in this function, thus in case
the output value is outside the (-1, 1) interval, the output value will overflow without any
detection.
The output of the function is defined by the following simple equation:
Equation MLIB_Mac_Eq1
Note
Due to effectivity reason this function is implemented as inline,
and thus is not ANSI-C compliant. The overflow is not detected
in this function.
5.97.5 Re-entrancy
The function is re-entrant.
5.97.6 Code Example
#include "mlib.h"
tFrac16
tFrac16
tFrac16
tFrac16
f16In1;
f16In2;
f16In3;
f16Out;
void main(void)
{
// input1 value = 0.25
f16In1 = FRAC16 (0.25);
// input2 value = 0.15
f16In2 = FRAC16 (0.15);
// input3 value = 0.35
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f16In3 = FRAC16 (0.35);
// output should be FRAC16(0.3025) = 0x26B8
f16Out = MLIB_Mac_F16(f16In1, f16In2, f16In3);
// output should be FRAC16(0.3025) = 0x26B8
f16Out = MLIB_Mac (f16In1, f16In2, f16In3, F16);
//
//
//
//
}
##############################################################
Available only if 16-bit fractional implementation selected
as default
##############################################################
// output should be FRAC16(0.3025) = 0x26B8
f16Out = MLIB_Mac (f16In1, f16In2, f16In3);
5.98 Function MLIB_MacSat_F32
This function implements the multiply accumulate function saturated if necessary.
5.98.1 Declaration
tFrac32 MLIB_MacSat_F32(register tFrac32 f32In1, register tFrac32 f32In2, register tFrac32
f32In3);
5.98.2 Arguments
Table 5-122. MLIB_MacSat_F32 arguments
Type
Name
Direction
Description
register tFrac32
f32In1
input
Input value to be add.
register tFrac32
f32In2
input
First value to be multiplied.
register tFrac32
f32In3
input
Second value to be multiplied.
5.98.3 Return
Multiplied second and third input value with adding of first input value. The output value
is saturated if necessary.
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Function MLIB_MacSat_F32
5.98.4 Description
This inline function returns the multiplied second and third input value with adding of
first input value. The input values as well as output value is considered as 32-bit
fractional values. The output saturation is implemented in this function, thus in case the
output value is outside the (-1, 1) interval, the output value is limited to the boundary
value.
The output of the function is defined by the following simple equation:
Equation MLIB_MacSat_Eq1
Note
Due to effectivity reason this function is implemented as inline
and thus is not ANSI-C compliant. The overflow is detected in
this function. The functions saturates the return value if it
cannot fit into the return type.
5.98.5 Re-entrancy
The function is re-entrant.
5.98.6 Code Example
#include "mlib.h"
tFrac32
tFrac32
tFrac32
tFrac32
f32In1;
f32In2;
f32In3;
f32Out;
void main(void)
{
// input1 value = 0.25
f32In1 = FRAC32 (0.25);
// input2 value = 0.15
f32In2 = FRAC32 (0.15);
// input3 value = 0.35
f32In3 = FRAC32 (0.35);
// output should be FRAC32(0.3025) = 0x26B851EB
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f32Out = MLIB_MacSat_F32(f32In1, f32In2, f32In3);
// output should be FRAC32(0.3025) = 0x26B851EB
f32Out = MLIB_MacSat (f32In1, f32In2, f32In3, F32);
//
//
//
//
}
##############################################################
Available only if 32-bit fractional implementation selected
as default
##############################################################
// output should be FRAC32(0.3025) = 0x26B851EB
f32Out = MLIB_MacSat (f32In1, f32In2, f32In3);
5.99 Function MLIB_MacSat_F32F16F16
This function implements the multiply accumulate function saturated if necessary.
5.99.1 Declaration
tFrac32 MLIB_MacSat_F32F16F16(register tFrac32 f32In1, register tFrac16 f16In2, register
tFrac16 f16In3);
5.99.2 Arguments
Table 5-123. MLIB_MacSat_F32F16F16 arguments
Type
Name
Direction
Description
register tFrac32
f32In1
input
Input value to be add.
register tFrac16
f16In2
input
First value to be multiplied.
register tFrac16
f16In3
input
Second value to be multiplied.
5.99.3 Return
Multiplied second and third input value with adding of first input value. The output value
is saturated if necessary.
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Function MLIB_MacSat_F32F16F16
5.99.4 Description
This inline function returns the multiplied second and third input value with adding of
first input value. The first input values as well as output value is considered as 32-bit
fractional values, second and third input values are considered as 16-bit fractional values.
The output saturation is implemented in this function, thus in case the output value is
outside the (-1, 1) interval, the output value is limited to the boundary value.
The output of the function is defined by the following simple equation:
Equation MLIB_MacSat_Eq1
Note
Due to effectivity reason this function is implemented as inline
and thus is not ANSI-C compliant. The overflow is detected in
this function. The functions saturates the return value if it
cannot fit into the return type.
5.99.5 Re-entrancy
The function is re-entrant.
5.99.6 Code Example
#include "mlib.h"
tFrac32
tFrac16
tFrac16
tFrac32
f32In1;
f16In2;
f16In3;
f32Out;
void main(void)
{
// input1 value = 0.25
f32In1 = FRAC32 (0.25);
// input2 value = 0.15
f16In2 = FRAC16 (0.15);
// input3 value = 0.35
f16In3 = FRAC16 (0.35);
// output should be FRAC32(0.3025) = 0x26B851EB
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f32Out = MLIB_MacSat_F32F16F16(f32In1, f16In2, f16In3);
}
// output should be FRAC32(0.3025) = 0x26B851EB
f32Out = MLIB_MacSat (f32In1, f16In2, f16In3, F32F16F16);
5.100 Function MLIB_MacSat_F16
This function implements the multiply accumulate function saturated if necessary.
5.100.1 Declaration
tFrac16 MLIB_MacSat_F16(register tFrac16 f16In1, register tFrac16 f16In2, register tFrac16
f16In3);
5.100.2 Arguments
Table 5-124. MLIB_MacSat_F16 arguments
Type
Name
Direction
Description
register tFrac16
f16In1
input
Input value to be add.
register tFrac16
f16In2
input
First value to be multiplied.
register tFrac16
f16In3
input
Second value to be multiplied.
5.100.3 Return
Multiplied second and third input value with adding of first input value. The output value
is saturated if necessary.
5.100.4 Description
This inline function returns the multiplied second and third input value with adding of
first input value. The input values as well as output value is considered as 16-bit
fractional values. The output saturation is implemented in this function, thus in case the
output value is outside the (-1, 1) interval, the output value is limited to the boundary
value.
The output of the function is defined by the following simple equation:
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Function MLIB_MacSat_F16
Equation MLIB_MacSat_Eq1
Note
Due to effectivity reason this function is implemented as inline
and thus is not ANSI-C compliant. The overflow is detected in
this function. The functions saturates the return value if it
cannot fit into the return type.
5.100.5 Re-entrancy
The function is re-entrant.
5.100.6 Code Example
#include "mlib.h"
tFrac16
tFrac16
tFrac16
tFrac16
f16In1;
f16In2;
f16In3;
f16Out;
void main(void)
{
// input1 value = 0.25
f16In1 = FRAC16 (0.25);
// input2 value = 0.15
f16In2 = FRAC16 (0.15);
// input3 value = 0.35
f16In3 = FRAC16 (0.35);
// output should be FRAC16(0.3025) = 0x26B8
f16Out = MLIB_MacSat_F16(f16In1, f16In2, f16In3);
// output should be FRAC16(0.3025) = 0x26B8
f16Out = MLIB_MacSat (f16In1, f16In2, f16In3, F16);
//
//
//
//
}
##############################################################
Available only if 16-bit fractional implementation selected
as default
##############################################################
// output should be FRAC16(0.3025) = 0x26B8
f16Out = MLIB_MacSat (f16In1, f16In2, f16In3);
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5.101 Function MLIB_Mnac_F32
This function implements the multiply-subtract function.
5.101.1 Declaration
tFrac32 MLIB_Mnac_F32(register tFrac32 f32In1, register tFrac32 f32In2, register tFrac32
f32In3);
5.101.2 Arguments
Table 5-125. MLIB_Mnac_F32 arguments
Type
Name
Direction
Description
register tFrac32
f32In1
input
Input value to be subtracted.
register tFrac32
f32In2
input
First value to be multiplied.
register tFrac32
f32In3
input
Second value to be multiplied.
5.101.3 Return
Multiplied second and third input value with subtracted first input value.
5.101.4 Description
This inline function returns the multiplied second and third input value with subtracted
first input value. The input values as well as output value is considered as 32-bit
fractional values. The output saturation is not implemented in this function, thus in case
the output value is outside the (-1, 1) interval, the output value will overflow without any
detection.
The output of the function is defined by the following simple equation:
Equation MLIB_Mnac_Eq1
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Function MLIB_Mnac_F32F16F16
Note
Due to effectivity reason this function is implemented as inline,
and thus is not ANSI-C compliant. The overflow is not detected
in this function.
5.101.5 Re-entrancy
The function is re-entrant.
5.101.6 Code Example
#include "mlib.h"
tFrac32
tFrac32
tFrac32
tFrac32
f32In1;
f32In2;
f32In3;
f32Out;
void main(void)
{
// input1 value = 0.0625
f32In1 = FRAC32 (0.0625);
// input2 value = 0.5
f32In2 = FRAC32 (0.5);
// input3 value = 0.25
f32In3 = FRAC32 (0.25);
// output should be FRAC32(0.0625) = 0x08000000
f32Out = MLIB_Mnac_F32(f32In1, f32In2, f32In3);
// output should be FRAC32(0.0625) = 0x08000000
f32Out = MLIB_Mnac (f32In1, f32In2, f32In3, F32);
//
//
//
//
}
##############################################################
Available only if 32-bit fractional implementation selected
as default
##############################################################
// output should be FRAC32(0.0625) = 0x08000000
f32Out = MLIB_Mnac (f32In1, f32In2, f32In3);
5.102 Function MLIB_Mnac_F32F16F16
This function implements the multiply-subtract function.
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5.102.1 Declaration
tFrac32 MLIB_Mnac_F32F16F16(register tFrac32 f32In1, register tFrac16 f16In2, register
tFrac16 f16In3);
5.102.2 Arguments
Table 5-126. MLIB_Mnac_F32F16F16 arguments
Type
Name
Direction
Description
register tFrac32
f32In1
input
Input value to be subtracted.
register tFrac16
f16In2
input
First value to be multiplied.
register tFrac16
f16In3
input
Second value to be multiplied.
5.102.3 Return
Multiplied second and third input value with subtracted first input value.
5.102.4 Description
This inline function returns the multiplied second and third input value with subtracted
first input value. The first input value as well as output value is considered as 32-bit
fractional values. The second and third input values are considered as 16-bit fractional
values. The output saturation is not implemented in this function, thus in case the output
value is outside the (-1, 1) interval, the output value will overflow without any detection.
The output of the function is defined by the following simple equation:
Equation MLIB_Mnac_Eq1
This implementation is available if 32-bit fractional implementations are enabled.
However it is not possible to use the default implementation based function call, thus the
implementation post-fix or additional parameter function call shall be used.
Note
Due to effectivity reason this function is implemented as inline,
and thus is not ANSI-C compliant. The overflow is not detected
in this function.
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Function MLIB_Mnac_F16
5.102.5 Re-entrancy
The function is re-entrant.
5.102.6 Code Example
#include "mlib.h"
tFrac32
tFrac16
tFrac16
tFrac32
f32In1;
f16In2;
f16In3;
f32Out;
void main(void)
{
// input1 value = 0.0625
f32In1 = FRAC32 (0.0625);
// input2 value = 0.5
f16In2 = FRAC16 (0.5);
// input3 value = 0.25
f16In3 = FRAC16 (0.25);
// output should be FRAC32(0.0625) = 0x08000000
f32Out = MLIB_Mnac_F32F16F16(f32In1, f16In2, f16In3);
// output should be FRAC32(0.0625) = 0x08000000
f32Out = MLIB_Mnac (f32In1, f32In2, f32In3, F32F16F16);
}
5.103 Function MLIB_Mnac_F16
This function implements the multiply-subtract function.
5.103.1 Declaration
tFrac16 MLIB_Mnac_F16(register tFrac16 f16In1, register tFrac16 f16In2, register tFrac16
f16In3);
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5.103.2 Arguments
Table 5-127. MLIB_Mnac_F16 arguments
Type
Name
Direction
Description
register tFrac16
f16In1
input
Input value to be subtracted.
register tFrac16
f16In2
input
First value to be multiplied.
register tFrac16
f16In3
input
Second value to be multiplied.
5.103.3 Return
Multiplied second and third input value with subtracted first input value.
5.103.4 Description
This inline function returns the multiplied second and third input value with subtracted
first input value. The input values as well as output value is considered as 16-bit
fractional values. The output saturation is not implemented in this function, thus in case
the output value is outside the (-1, 1) interval, the output value will overflow without any
detection.
The output of the function is defined by the following simple equation:
Equation MLIB_Mnac_Eq1
Note
Due to effectivity reason this function is implemented as inline,
and thus is not ANSI-C compliant. The overflow is not detected
in this function.
5.103.5 Re-entrancy
The function is re-entrant.
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Function MLIB_Msu_F32
5.103.6 Code Example
#include "mlib.h"
tFrac16
tFrac16
tFrac16
tFrac16
f16In1;
f16In2;
f16In3;
f16Out;
void main(void)
{
// input1 value = 0.0625
f16In1 = FRAC16 (0.0625);
// input2 value = 0.5
f16In2 = FRAC16 (0.5);
// input3 value = 0.25
f16In3 = FRAC16 (0.25);
// output should be FRAC16(0.0625) = 0x0800
f16Out = MLIB_Mnac_F16(f16In1, f16In2, f16In3);
// output should be FRAC16(0.0625) = 0x0800
f16Out = MLIB_Mnac (f16In1, f16In2, f16In3, F16);
//
//
//
//
}
##############################################################
Available only if 16-bit fractional implementation selected
as default
##############################################################
// output should be FRAC16(0.0625) = 0x0800
f16Out = MLIB_Mnac (f16In1, f16In2, f16In3);
5.104 Function MLIB_Msu_F32
This function implements the multiply-subtract-from function.
5.104.1 Declaration
tFrac32 MLIB_Msu_F32(register tFrac32 f32In1, register tFrac32 f32In2, register tFrac32
f32In3);
5.104.2 Arguments
Table 5-128. MLIB_Msu_F32 arguments
Type
register tFrac32
Name
f32In1
Direction
input
Description
Input value from which to subtract.
Table continues on the next page...
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Table 5-128. MLIB_Msu_F32 arguments (continued)
Type
Name
Direction
Description
register tFrac32
f32In2
input
First value to be multiplied.
register tFrac32
f32In3
input
Second value to be multiplied.
5.104.3 Return
First input value from which the multiplication result of the second and third input values
is subtracted.
5.104.4 Description
This inline function returns the first input value from which the multiplication result of
the second and third input values is subtracted. The input values as well as output value is
considered as 32-bit fractional values. The output saturation is not implemented in this
function, thus in case the output value is outside the (-1, 1) interval, the output value will
overflow without any detection.
The output of the function is defined by the following simple equation:
Equation MLIB_Msu_Eq1
Note
Due to effectivity reason this function is implemented as inline,
and thus is not ANSI-C compliant. The overflow is not detected
in this function.
5.104.5 Re-entrancy
The function is re-entrant.
5.104.6 Code Example
#include "mlib.h"
tFrac32 f32In1;
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Function MLIB_Msu_F32F16F16
tFrac32 f32In2;
tFrac32 f32In3;
tFrac32 f32Out;
void main(void)
{
// input1 value = 0.25
f32In1 = FRAC32 (0.25);
// input2 value = 0.5
f32In2 = FRAC32 (0.5);
// input3 value = 0.125
f32In3 = FRAC32 (0.125);
// output should be FRAC32(0.1875) = 0x18000000
f32Out = MLIB_Msu_F32(f32In1, f32In2, f32In3);
// output should be FRAC32(0.1875) = 0x18000000
f32Out = MLIB_Msu (f32In1, f32In2, f32In3, F32);
//
//
//
//
}
##############################################################
Available only if 32-bit fractional implementation selected
as default
##############################################################
// output should be FRAC32(0.1875) = 0x18000000
f32Out = MLIB_Msu (f32In1, f32In2, f32In3);
5.105 Function MLIB_Msu_F32F16F16
This function implements the multiply-subtract-from function.
5.105.1 Declaration
tFrac32 MLIB_Msu_F32F16F16(register tFrac32 f32In1, register tFrac16 f16In2, register tFrac16
f16In3);
5.105.2 Arguments
Table 5-129. MLIB_Msu_F32F16F16 arguments
Type
Name
Direction
Description
register tFrac32
f32In1
input
Input value from which to subtract.
register tFrac16
f16In2
input
First value to be multiplied.
register tFrac16
f16In3
input
Second value to be multiplied.
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5.105.3 Return
First input value from which the multiplication result of the second and third input values
is subtracted.
5.105.4 Description
This inline function returns the first input value from which the multiplication result of
the second and third input values is subtracted. The first input value as well as output
value is considered as 32-bit fractional values. The second and third input values are
considered as 16-bit fractional values. The output saturation is not implemented in this
function, thus in case the output value is outside the (-1, 1) interval, the output value will
overflow without any detection.
The output of the function is defined by the following simple equation:
Equation MLIB_Msu_Eq1
This implementation is available if 32-bit fractional implementations are enabled.
However it is not possible to use the default implementation based function call, thus the
implementation post-fix or additional parameter function call shall be used.
Note
Due to effectivity reason this function is implemented as inline,
and thus is not ANSI-C compliant. The overflow is not detected
in this function.
5.105.5 Re-entrancy
The function is re-entrant.
5.105.6 Code Example
#include "mlib.h"
tFrac32
tFrac16
tFrac16
tFrac32
f32In1;
f16In2;
f16In3;
f32Out;
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Function MLIB_Msu_F16
void main(void)
{
// input1 value = 0.25
f32In1 = FRAC32 (0.25);
// input2 value = 0.5
f16In2 = FRAC16 (0.5);
// input3 value = 0.125
f16In3 = FRAC16 (0.125);
// output should be FRAC32(0.1875) = 0x18000000
f32Out = MLIB_Msu_F32F16F16(f32In1, f16In2, f16In3);
// output should be FRAC32(0.1875) = 0x18000000
f32Out = MLIB_Msu (f32In1, f32In2, f32In3, F32F16F16);
}
5.106 Function MLIB_Msu_F16
This function implements the multiply-subtract-from function.
5.106.1 Declaration
tFrac16 MLIB_Msu_F16(register tFrac16 f16In1, register tFrac16 f16In2, register tFrac16
f16In3);
5.106.2 Arguments
Table 5-130. MLIB_Msu_F16 arguments
Type
Name
Direction
Description
register tFrac16
f16In1
input
Input value from which to subtract.
register tFrac16
f16In2
input
First value to be multiplied.
register tFrac16
f16In3
input
Second value to be multiplied.
5.106.3 Return
First input value from which the multiplication result of the second and third input values
is subtracted.
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5.106.4 Description
This inline function returns the first input value from which the multiplication result of
the second and third input values is subtracted. The input values as well as output value is
considered as 16-bit fractional values. The output saturation is not implemented in this
function, thus in case the output value is outside the (-1, 1) interval, the output value will
overflow without any detection.
The output of the function is defined by the following simple equation:
Equation MLIB_Msu_Eq1
Note
Due to effectivity reason this function is implemented as inline,
and thus is not ANSI-C compliant. The overflow is not detected
in this function.
5.106.5 Re-entrancy
The function is re-entrant.
5.106.6 Code Example
#include "mlib.h"
tFrac16
tFrac16
tFrac16
tFrac16
f16In1;
f16In2;
f16In3;
f16Out;
void main(void)
{
// input1 value = 0.25
f16In1 = FRAC16 (0.25);
// input2 value = 0.5
f16In2 = FRAC16 (0.5);
// input3 value = 0.125
f16In3 = FRAC16 (0.125);
// output should be FRAC16(0.1875) = 0x1800
f16Out = MLIB_Msu_F16(f16In1, f16In2, f16In3);
// output should be FRAC16(0.1875) = 0x1800
f16Out = MLIB_Msu (f16In1, f16In2, f16In3, F16);
// ##############################################################
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Function MLIB_Mul_F32
// Available only if 16-bit fractional implementation selected
// as default
// ##############################################################
}
// output should be FRAC16(0.1875) = 0x1800
f16Out = MLIB_Msu (f16In1, f16In2, f16In3);
5.107 Function MLIB_Mul_F32
This function multiplies two input parameters.
5.107.1 Declaration
tFrac32 MLIB_Mul_F32(register tFrac32 f32In1, register tFrac32 f32In2);
5.107.2 Arguments
Table 5-131. MLIB_Mul_F32 arguments
Type
Name
Direction
Description
register tFrac32
f32In1
input
Operand is a 32-bit number normalized between [-1,1).
register tFrac32
f32In2
input
Operand is a 32-bit number normalized between [-1,1).
5.107.3 Return
Fractional multiplication of the input arguments.
5.107.4 Description
Fractional multiplication of two fractional 32-bit values. The input values as well as
output value is considered as 32-bit fractional values. The output saturation is not
implemented in this function, thus in case the multiplication of input values is outside the
(-1, 1) interval, the output value will overflow without any detection.
The output of the function is defined by the following simple equation:
Equation MLIB_Mul_Eq1
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Note
Due to effectivity reason this function is implemented as inline
and thus is not ANSI-C compliant.
5.107.5 Re-entrancy
The function is re-entrant.
5.107.6 Code Example
#include "mlib.h"
tFrac32 f32In1;
tFrac32 f32In2;
tFrac32 f32Out;
void main(void)
{
// first input = 0.5
f32In1 = FRAC32 (0.5);
// second input = 0.25
f32In2 = FRAC32 (0.25);
// output should be 0x10000000 = FRAC32(0.125)
f32Out = MLIB_Mul_F32(f32In1,f32In2);
// output should be 0x10000000 = FRAC32(0.125)
f32Out = MLIB_Mul (f32In1,f32In2,F32);
//
//
//
//
}
##############################################################
Available only if 32-bit fractional implementation selected
as default
##############################################################
// output should be 0x10000000 = FRAC32(0.125)
f32Out = MLIB_Mul (f32In1,f32In2);
5.108 Function MLIB_Mul_F32F16F16
This function multiplies two input parameters.
5.108.1 Declaration
tFrac32 MLIB_Mul_F32F16F16(register tFrac16 f16In1, register tFrac16 f16In2);
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Function MLIB_Mul_F32F16F16
5.108.2 Arguments
Table 5-132. MLIB_Mul_F32F16F16 arguments
Type
Name
Direction
Description
register tFrac16
f16In1
input
Operand is a 16-bit number normalized between [-1,1).
register tFrac16
f16In2
input
Operand is a 16-bit number normalized between [-1,1).
5.108.3 Return
Fractional multiplication of the input arguments.
5.108.4 Description
Fractional multiplication of two fractional 16-bit values. The input values are considered
as 16-bit fractional values and the output value is considered as 32-bit fractional value.
The output saturation is not implemented in this function, thus in case the multiplication
of input values is outside the (-1, 1) interval, the output value will overflow without any
detection.
The output of the function is defined by the following simple equation:
Equation MLIB_Mul_Eq1
Note
Due to effectivity reason this function is implemented as inline
and thus is not ANSI-C compliant.
5.108.5 Re-entrancy
The function is re-entrant.
5.108.6 Code Example
#include "mlib.h"
tFrac16 f16In1;
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tFrac16 f16In2;
tFrac32 f32Out;
void main(void)
{
// first input = 0.5
f16In1 = FRAC16 (0.5);
// second input = 0.25
f16In2 = FRAC16 (0.25);
// output should be 0x10000000 = FRAC32(0.125)
f32Out = MLIB_Mul_F32F16F16(f16In1, f16In2);
}
// output should be 0x10000000 = FRAC32(0.125)
f32Out = MLIB_Mul (f16In1, f16In2, F32F16F16);
5.109 Function MLIB_Mul_F16
This function multiplies two input parameters.
5.109.1 Declaration
tFrac16 MLIB_Mul_F16(register tFrac16 f16In1, register tFrac16 f16In2);
5.109.2 Arguments
Table 5-133. MLIB_Mul_F16 arguments
Type
Name
Direction
Description
register tFrac16
f16In1
input
Operand is a 16-bit number normalized between [-1,1).
register tFrac16
f16In2
input
Operand is a 16-bit number normalized between [-1,1).
5.109.3 Return
Fractional multiplication of the input arguments.
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Function MLIB_Mul_F16
5.109.4 Description
Fractional multiplication of two fractional 16-bit values. The input values as well as
output value is considered as 16-bit fractional values. The output saturation is not
implemented in this function, thus in case the multiplication of input values is outside the
(-1, 1) interval, the output value will overflow without any detection.
The output of the function is defined by the following simple equation:
Equation MLIB_Mul_Eq1
Note
Due to effectivity reason this function is implemented as inline
and thus is not ANSI-C compliant.
5.109.5 Re-entrancy
The function is re-entrant.
5.109.6 Code Example
#include "mlib.h"
tFrac16 f16In1;
tFrac16 f16In2;
tFrac16 f16Out;
void main(void)
{
// first input = 0.5
f16In1 = FRAC16 (0.5);
// second input = 0.25
f16In2 = FRAC16 (0.25);
// output should be 0x1000 = FRAC16(0.125)
f16Out = MLIB_Mul_F16(f16In1,f16In2);
// output should be 0x1000 = FRAC16(0.125)
f16Out = MLIB_Mul (f16In1,f16In2,F16);
//
//
//
//
##############################################################
Available only if 16-bit fractional implementation selected
as default
##############################################################
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}
// output should be 0x1000 = FRAC16(0.125)
f16Out = MLIB_Mul (f16In1,f16In2);
5.110 Function MLIB_MulSat_F32
This function multiplies two input parameters and saturate if necessary.
5.110.1 Declaration
tFrac32 MLIB_MulSat_F32(register tFrac32 f32In1, register tFrac32 f32In2);
5.110.2 Arguments
Table 5-134. MLIB_MulSat_F32 arguments
Type
Name
Direction
Description
register tFrac32
f32In1
input
Operand is a 32-bit number normalized between [-1,1).
register tFrac32
f32In2
input
Operand is a 32-bit number normalized between [-1,1).
5.110.3 Return
Fractional multiplication of the input arguments.
5.110.4 Description
Fractional multiplication of two fractional 32-bit values. The input values as well as
output value are considered as 32-bit fractional data type. The output saturation is
implemented in this function, thus in case the multiplication of input values is outside the
(-1, 1) interval, the output value is limited to the boundary value.
The output of the function is defined by the following simple equation:
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Function MLIB_MulSat_F32F16F16
Equation MLIB_MulSat_Eq1
Note
Due to effectivity reason this function is implemented as inline
and thus is not ANSI-C compliant. The overflow is detected in
this function. The functions saturates the return value if it
cannot fit into the return type.
5.110.5 Re-entrancy
The function is re-entrant.
5.110.6 Code Example
#include "mlib.h"
tFrac32 f32In1;
tFrac32 f32In2;
tFrac32 f32Out;
void main(void)
{
// first input = 0.8
f32In1 = FRAC32 (0.8);
// second input = 0.75
f32In2 = FRAC32 (0.75);
// output should be 0x4ccccccc = FRAC32(0.6)
f32Out = MLIB_MulSat_F32(f32In1,f32In2);
// output should be 0x4ccccccc = FRAC32(0.6)
f32Out = MLIB_MulSat (f32In1,f32In2,F32);
//
//
//
//
}
##############################################################
Available only if 32-bit fractional implementation selected
as default
##############################################################
// output should be 0x4ccccccc = FRAC32(0.6)
f32Out = MLIB_MulSat (f32In1,f32In2);
5.111 Function MLIB_MulSat_F32F16F16
This function multiplies two input parameters and saturate if necessary.
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5.111.1 Declaration
tFrac32 MLIB_MulSat_F32F16F16(register tFrac16 f16In1, register tFrac16 f16In2);
5.111.2 Arguments
Table 5-135. MLIB_MulSat_F32F16F16 arguments
Type
Name
Direction
Description
register tFrac16
f16In1
input
Operand is a 16-bit number normalized between [-1,1).
register tFrac16
f16In2
input
Operand is a 16-bit number normalized between [-1,1).
5.111.3 Return
Fractional multiplication of the input arguments.
5.111.4 Description
Fractional multiplication of two fractional 16-bit values. The input values are considered
as 16-bit fractional data type and the output value is considered as 32-bit fractional data
type. The output saturation is implemented in this function, thus in case the multiplication
of input values is outside the (-1, 1) interval, the output value is limited to the boundary
value.
The output of the function is defined by the following simple equation:
Equation MLIB_MulSat_Eq1
Note
Due to effectivity reason this function is implemented as inline
and thus is not ANSI-C compliant. The overflow is detected in
this function. The functions saturates the return value if it
cannot fit into the return type.
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Function MLIB_MulSat_F16
5.111.5 Re-entrancy
The function is re-entrant.
5.111.6 Code Example
#include "mlib.h"
tFrac16 f16In1;
tFrac16 f16In2;
tFrac32 f32Out;
void main(void)
{
// first input = 0.8
f16In1 = FRAC16 (0.8);
// second input = 0.75
f16In2 = FRAC16 (0.75);
// output should be 0x4ccccccc = FRAC32(0.6)
f32Out = MLIB_MulSat_F32F16F16(f16In1,f16In2);
}
// output should be 0x4ccccccc = FRAC32(0.6)
f32Out = MLIB_MulSat (f32In1,f32In2,F32F16f16);
5.112 Function MLIB_MulSat_F16
This function multiplies two input parameters and saturate if necessary.
5.112.1 Declaration
tFrac16 MLIB_MulSat_F16(register tFrac16 f16In1, register tFrac16 f16In2);
5.112.2 Arguments
Table 5-136. MLIB_MulSat_F16 arguments
Type
Name
Direction
Description
register tFrac16
f16In1
input
Operand is a 16-bit number normalized between [-1,1).
register tFrac16
f16In2
input
Operand is a 16-bit number normalized between [-1,1).
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5.112.3 Return
Fractional multiplication of the input arguments.
5.112.4 Description
Fractional multiplication of two fractional 16-bit values. The input values as well as
output value are considered as 16-bit fractional data type. The output saturation is
implemented in this function, thus in case the multiplication of input values is outside the
(-1, 1) interval, the output value is limited to the boundary value.
The output of the function is defined by the following simple equation:
Equation MLIB_MulSat_Eq1
Note
Due to effectivity reason this function is implemented as inline
and thus is not ANSI-C compliant. The overflow is detected in
this function. The functions saturates the return value if it
cannot fit into the return type.
5.112.5 Re-entrancy
The function is re-entrant.
5.112.6 Code Example
#include "mlib.h"
tFrac16 f16In1;
tFrac16 f16In2;
tFrac16 f16Out;
void main(void)
{
// first input = 0.8
f16In1 = FRAC16 (0.8);
// second input = 0.75
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Function MLIB_Neg_F32
f16In2 = FRAC16 (0.75);
// output should be 0x4ccc = FRAC16(0.6)
f16Out = MLIB_MulSat_F16(f16In1,f16In2);
// output should be 0x4ccc = FRAC16(0.6)
f16Out = MLIB_MulSat (f16In1,f16In2,F16);
//
//
//
//
}
##############################################################
Available only if 16-bit fractional implementation selected
as default
##############################################################
// output should be 0x4ccc = FRAC32(0.6)
f16Out = MLIB_MulSat (f16In1,f16In2);
5.113 Function MLIB_Neg_F32
This function returns negative value of input parameter.
5.113.1 Declaration
tFrac32 MLIB_Neg_F32(register tFrac32 f32In);
5.113.2 Arguments
Table 5-137. MLIB_Neg_F32 arguments
Type
register tFrac32
Name
f32In
Direction
input
Description
Input value which negative value should be returned.
5.113.3 Return
Negative value of input parameter.
5.113.4 Description
This inline function returns the negative value of input parameter. The input values as
well as output value is considered as 32-bit fractional values. The output saturation is not
implemented in this function, thus in case the negation of input values is outside the (-1,
1) interval, the output value will overflow without any detection.
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The output of the function is defined by the following simple equation:
Equation MLIB_Neg_Eq1
Note
Due to effectivity reason this function is implemented as inline,
and thus is not ANSI-C compliant. The overflow is not detected
in this function.
5.113.5 Re-entrancy
The function is re-entrant.
5.113.6 Code Example
#include "mlib.h"
tFrac32 f32In;
tFrac32 f32Out;
void main(void)
{
// input value = 0.25
f32In = FRAC32 (0.25);
// output should be FRAC32(-0.25) = 0xA0000000
f32Out = MLIB_Neg_F32(f32In);
// output should be FRAC32(-0.25) = 0xA0000000
f32Out = MLIB_Neg (f32In, F32);
//
//
//
//
}
##############################################################
Available only if 32-bit fractional implementation selected
as default
##############################################################
// output should be FRAC32(-0.25) = 0xA0000000
f32Out = MLIB_Neg (f32In);
5.114 Function MLIB_Neg_F16
This function returns negative value of input parameter.
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Function MLIB_Neg_F16
5.114.1 Declaration
tFrac16 MLIB_Neg_F16(register tFrac16 f16In);
5.114.2 Arguments
Table 5-138. MLIB_Neg_F16 arguments
Type
register tFrac16
Name
Direction
input
f16In
Description
Input value which negative value should be returned.
5.114.3 Return
Negative value of input parameter.
5.114.4 Description
This inline function returns the negative value of input parameter. The input values as
well as output value is considered as 16-bit fractional values. The output saturation is not
implemented in this function, thus in case the negation of input values is outside the (-1,
1) interval, the output value will overflow without any detection.
The output of the function is defined by the following simple equation:
Equation MLIB_Neg_Eq1
Note
Due to effectivity reason this function is implemented as inline,
and thus is not ANSI-C compliant. The overflow is not detected
in this function.
5.114.5 Re-entrancy
The function is re-entrant.
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5.114.6 Code Example
#include "mlib.h"
tFrac16 f16In;
tFrac16 f16Out;
void main(void)
{
// input value = 0.25
f16In = FRAC16 (0.25);
// output should be FRAC16(-0.25) = 0xA000
f16Out = MLIB_Neg_F16(f16In);
// output should be FRAC16(-0.25) = 0xA000
f16Out = MLIB_Neg (f16In, F16);
//
//
//
//
}
##############################################################
Available only if 16-bit fractional implementation selected
as default
##############################################################
// output should be FRAC16(-0.25) = 0xA000
f16Out = MLIB_Neg (f16In);
5.115 Function MLIB_NegSat_F32
This function returns negative value of input parameter and saturate if necessary.
5.115.1 Declaration
tFrac32 MLIB_NegSat_F32(register tFrac32 f32In);
5.115.2 Arguments
Table 5-139. MLIB_NegSat_F32 arguments
Type
register tFrac32
Name
f32In
Direction
input
Description
Input value which negative value should be returned.
5.115.3 Return
Negative value of input parameter.
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Function MLIB_NegSat_F32
5.115.4 Description
This inline function returns the negative value of input parameter. The input values as
well as output value is considered as 32-bit fractional data type. The output saturation is
implemented in this function, thus in case the negation of input values is outside the (-1,
1) interval, the output value is limited to the boundary value.
The output of the function is defined by the following simple equation:
Equation MLIB_NegSat_Eq1
Note
Due to effectivity reason this function is implemented as inline,
and thus is not ANSI-C compliant. The overflow is detected in
this function. The functions saturates the return value if it
cannot fit into the return type.
5.115.5 Re-entrancy
The function is re-entrant.
5.115.6 Code Example
#include "mlib.h"
tFrac32 f32In;
tFrac32 f32Out;
void main(void)
{
// input value = 0.25
f32In = FRAC32 (0.25);
// output should be FRAC32(-0.25) = 0xA0000000
f32Out = MLIB_NegSat_F32(f32In);
// output should be FRAC32(-0.25) = 0xA0000000
f32Out = MLIB_NegSat (f32In, F32);
// ##############################################################
// Available only if 32-bit fractional implementation selected
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// as default
// ##############################################################
}
// output should be FRAC32(-0.25) = 0xA0000000
f32Out = MLIB_NegSat (f32In);
5.116 Function MLIB_NegSat_F16
This function returns negative value of input parameter and saturate if necessary.
5.116.1 Declaration
tFrac16 MLIB_NegSat_F16(register tFrac16 f16In);
5.116.2 Arguments
Table 5-140. MLIB_NegSat_F16 arguments
Type
register tFrac16
Name
f16In
Direction
input
Description
Input value which negative value should be returned.
5.116.3 Return
Negative value of input parameter.
5.116.4 Description
This inline function returns the negative value of input parameter. The input values as
well as output value is considered as 16-bit fractional data type. The output saturation is
implemented in this function, thus in case the negation of input values is outside the (-1,
1) interval, the output value is limited to the boundary value.
The output of the function is defined by the following simple equation:
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Function MLIB_Norm_F32
Equation MLIB_NegSat_Eq1
Note
Due to effectivity reason this function is implemented as inline,
and thus is not ANSI-C compliant. The overflow is detected in
this function. The functions saturates the return value if it
cannot fit into the return type.
5.116.5 Re-entrancy
The function is re-entrant.
5.116.6 Code Example
#include "mlib.h"
tFrac16 f16In;
tFrac16 f16Out;
void main(void)
{
// input value = 0.25
f16In = FRAC16 (0.25);
// output should be FRAC16(-0.25) = 0xA000
f16Out = MLIB_NegSat_F16(f16In);
// output should be FRAC16(-0.25) = 0xA000
f16Out = MLIB_NegSat (f16In, F16);
//
//
//
//
}
##############################################################
Available only if 16-bit fractional implementation selected
as default
##############################################################
// output should be FRAC16(-0.25) = 0xA000
f16Out = MLIB_NegSat (f16In);
5.117 Function MLIB_Norm_F32
This function returns the number of left shifts needed to normalize the input parameter.
5.117.1 Declaration
tU16 MLIB_Norm_F32(register tFrac32 f32In);
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5.117.2 Arguments
Table 5-141. MLIB_Norm_F32 arguments
Type
Name
register tFrac32
f32In
Direction
input
Description
The first value to be normalized.
5.117.3 Return
The number of left shift needed to normalize the argument. For the input "0" returns "0".
5.117.4 Description
Depending on the sign of the input value the function counts and returns the number of
the left shift needed to get an equality between input value and the maximum fractional
values "1" or "-1".
Note
Due to effectivity reason this function is implemented as inline
and thus is not ANSI-C compliant.
5.117.5 Re-entrancy
The function is re-entrant.
5.117.6 Code Example
#include "mlib.h"
tFrac32 f32In;
tU16 u16Out;
void main(void)
{
// first input = 0.00005
f32In = FRAC32 (0.00005);
// output should be 14
u16Out = MLIB_Norm_F32(f32In);
// output should be 14
u16Out = MLIB_Norm (f32In,F32);
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Function MLIB_Norm_F16
//
//
//
//
}
##############################################################
Available only if 32-bit fractional implementation selected
as default
##############################################################
// output should be 14
u16Out = MLIB_Norm (f32In);
5.118 Function MLIB_Norm_F16
This function returns the number of left shifts needed to normalize the input parameter.
5.118.1 Declaration
tU16 MLIB_Norm_F16(register tFrac16 f16In);
5.118.2 Arguments
Table 5-142. MLIB_Norm_F16 arguments
Type
register tFrac16
Name
f16In
Direction
input
Description
The first value to be normalized.
5.118.3 Return
The number of left shift needed to normalize the argument. For the input "0" returns "0".
5.118.4 Description
Depending on the sign of the input value the function counts and returns the number of
the left shift needed to get an equality between input value and the maximum fractional
values "1" or "-1".
Note
Due to effectivity reason this function is implemented as inline
and thus is not ANSI-C compliant.
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5.118.5 Re-entrancy
The function is re-entrant.
5.118.6 Code Example
#include "mlib.h"
tFrac16 f16In;
tU16 u16Out;
void main(void)
{
// first input = 0.00005
f16In = FRAC16 (0.00005);
// output should be 14
u16Out = MLIB_Norm_F16(f16In);
// output should be 14
u16Out = MLIB_Norm (f16In,F16);
//
//
//
//
}
##############################################################
Available only if 16-bit fractional implementation selected
as default
##############################################################
// output should be 14
u16Out = MLIB_Norm (f16In);
5.119 Function MLIB_RndSat_F16F32
This function rounds the input value to the nearest saturated value in the output format.
5.119.1 Declaration
tFrac16 MLIB_RndSat_F16F32(register tFrac32 f32In);
5.119.2 Arguments
Table 5-143. MLIB_RndSat_F16F32 arguments
Type
register tFrac32
Name
f32In
Direction
input
Description
Input value.
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Function MLIB_Round_F32
5.119.3 Return
Rounded saturated value.
5.119.4 Description
This inline function rounds the input value to the nearest saturated value in the output
format. The input value is considered as 32-bit fractional data type and output value is
considered as 16-bit fractional data type.
5.119.5 Re-entrancy
The function is re-entrant.
5.119.6 Code Example
#include "mlib.h"
tFrac32 f32In;
tFrac16 f16Out;
void main(void)
{
// input value = 0.25 = 0x2000 0000
f32In = FRAC32 (0.25);
}
// output should be FRAC16(0.25) = 0x2000
f16Out = MLIB_RndSat_F16F32(f32In);
5.120 Function MLIB_Round_F32
The function rounds the input and saturates.
5.120.1 Declaration
tFrac32 MLIB_Round_F32(register tFrac32 f32In1, register tU16 u16In2);
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5.120.2 Arguments
Table 5-144. MLIB_Round_F32 arguments
Type
Name
Direction
Description
register tFrac32
f32In1
input
The value to be rounded.
register tU16
u16In2
input
The number of trailing zeros in the rounded result.
5.120.3 Return
Rounded 32-bit fractional value.
5.120.4 Description
The function rounds the first input argument to the nearest value (round half up). The
number of trailing zeros in the rounded result is equal to the second input argument, i.e.,
the number of significant digits is 32 - u16In2. The result is saturated to the fractional
range.
Note
The second input argument must not exceed 30 for positive and
31 for negative f32In1, respectively, otherwise the result is
undefined. Due to effectivity reason this function is
implemented as inline and thus is not ANSI-C compliant.
5.120.5 Re-entrancy
The function is re-entrant.
5.120.6 Code Example
#include "mlib.h"
tFrac32 f32In1;
tFrac32 f32Out;
tU16 u16In2;
void main(void)
{
// Example no. 1
// first input = 0.25
f32In1 = FRAC32 (0.25);
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Function MLIB_Round_F16
// second input = 29
u16In2 = (tU16)29;
// output should be 0x20000000 ~ FRAC32(0.25)
f32Out = MLIB_Round_F32(f32In1,u16In2);
// output should be 0x20000000 ~ FRAC32(0.25)
f32Out = MLIB_Round (f32In1,u16In2,F32);
//
//
//
//
##############################################################
Available only if 32-bit fractional implementation selected
as default
##############################################################
// output should be 0x20000000 ~ FRAC32(0.25)
f32Out = MLIB_Round (f32In1,u16In2);
// Example no. 2
// first input = 0.375
f32In1 = FRAC32 (0.375);
// second input = 29
u16In2 = (tU16)29;
// output should be 0x40000000 ~ FRAC32(0.5)
f32Out = MLIB_Round_F32(f32In1,u16In2);
// Example no. 3
// first input = -0.375
f32In1 = FRAC32 (-0.375);
// second input = 29
u16In2 = (tU16)29;
}
// output should be 0xE0000000 ~ FRAC32(-0.25)
f32Out = MLIB_Round_F32(f32In1,u16In2);
5.121 Function MLIB_Round_F16
The function rounds the input and saturates.
5.121.1 Declaration
tFrac16 MLIB_Round_F16(register tFrac16 f16In1, register tU16 u16In2);
5.121.2 Arguments
Table 5-145. MLIB_Round_F16 arguments
Type
Name
Direction
Description
register tFrac16
f16In1
input
The value to be rounded.
register tU16
u16In2
input
The number of trailing zeros in the rounded result.
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5.121.3 Return
Rounded 16-bit fractional value.
5.121.4 Description
The function rounds the first input argument to the nearest value (round half up). The
number of trailing zeros in the rounded result is equal to the second input argument, i.e.,
the number of significant digits is 16 - u16In2. The result is saturated to the fractional
range.
Note
The second input argument must not exceed 14 for positive and
15 for negative f16In1, respectively, otherwise the result is
undefined. Due to effectivity reason this function is
implemented as inline and thus is not ANSI-C compliant.
5.121.5 Re-entrancy
The function is re-entrant.
5.121.6 Code Example
#include "mlib.h"
tFrac16 f16In1;
tFrac16 f16Out;
tU16 u16In2;
void main(void)
{
// Example no. 1
// first input = 0.25
f16In1 = FRAC16 (0.25);
// second input = 13
u16In2 = (tU16)13;
// output should be 0x2000 ~ FRAC16(0.25)
f16Out = MLIB_Round_F16(f16In1,u16In2);
// output should be 0x2000 ~ FRAC16(0.25)
f16Out = MLIB_Round (f16In1,u16In2,F16);
//
//
//
//
##############################################################
Available only if 16-bit fractional implementation selected
as default
##############################################################
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Function MLIB_ShBi_F32
// output should be 0x2000 ~ FRAC16(0.25)
f16Out = MLIB_Round (f16In1,u16In2);
// Example no. 2
// first input = 0.375
f16In1 = FRAC16 (0.375);
// second input = 13
u16In2 = (tU16)13;
// output should be 0x4000 ~ FRAC16(0.5)
f16Out = MLIB_Round_F16(f16In1,u16In2);
// Example no. 3
// first input = -0.375
f16In1 = FRAC16 (-0.375);
// second input = 13
u16In2 = (tU16)13;
}
// output should be 0xE000 ~ FRAC16(-0.25)
f16Out = MLIB_Round_F16(f16In1,u16In2);
5.122 Function MLIB_ShBi_F32
This function shifts the first argument to left or right by number defined by second
argument.
5.122.1 Declaration
tFrac32 MLIB_ShBi_F32(register tFrac32 f32In1, register tS16 s16In2);
5.122.2 Arguments
Table 5-146. MLIB_ShBi_F32 arguments
Type
Name
Direction
Description
register tFrac32
f32In1
input
First value to be shift.
register tS16
s16In2
input
The shift amount value.
5.122.3 Return
32-bit fractional value shifted to left or right by the shift amount. The bits beyond the 32bit boundary are discarded.
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5.122.4 Description
Based on sign of second parameter this function shifts the first parameter to right or left.
If the sign of second parameter is negative, shift to right. Overflow is not detected.
Note
The shift amount cannot exceed in magnitude the bit-width of
the shift value, that means must be within the range -31...31.
Otherwise the result of the function is undefined. Due to
effectivity reason this function is implemented as inline, and
thus is not ANSI-C compliant.
5.122.5 Re-entrancy
The function is re-entrant.
5.122.6 Code Example
#include "mlib.h"
tFrac32 f32In1;
tFrac32 f32Out;
tS16 s16In2;
void main(void)
{
// first input = 0.25
f32In1 = FRAC32 (0.25);
// second input = -1
s16In2 = (tS16)-1;
// output should be 0x10000000 ~ FRAC32(0.125)
f32Out = MLIB_ShBi_F32(f32In1, s16In2);
// output should be 0x10000000 ~ FRAC32(0.125)
f32Out = MLIB_ShBi (f32In1, s16In2, F32);
//
//
//
//
}
##############################################################
Available only if 32-bit fractional implementation selected
as default
##############################################################
// output should be 0x10000000 ~ FRAC32(0.125)
f32Out = MLIB_ShBi (f32In1, s16In2);
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Function MLIB_ShBi_F16
5.123 Function MLIB_ShBi_F16
This function shifts the first argument to left or right by number defined by second
argument.
5.123.1 Declaration
tFrac16 MLIB_ShBi_F16(register tFrac16 f16In1, register tS16 s16In2);
5.123.2 Arguments
Table 5-147. MLIB_ShBi_F16 arguments
Type
Name
Direction
Description
register tFrac16
f16In1
input
First value to be left shift.
register tS16
s16In2
input
The shift amount value.
5.123.3 Return
16-bit fractional value shifted to left or right by the shift amount. The bits beyond the 16bit boundary are discarded.
5.123.4 Description
Based on sign of second parameter this function shifts the first parameter to right or left.
If the sign of second parameter is negative, shift to right. Overflow is not detected.
Note
The shift amount cannot exceed in magnitude the bit-width of
the shift value, that means must be within the range -15...15.
Otherwise the result of the function is undefined. Due to
effectivity reason this function is implemented as inline, and
thus is not ANSI-C compliant.
5.123.5 Re-entrancy
The function is re-entrant.
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5.123.6 Code Example
#include "mlib.h"
tFrac16 f16In1;
tFrac16 f16Out;
tS16 s16In2;
void main(void)
{
// first input = 0.25
f16In1 = FRAC16 (0.25);
// second input = -1
s16In2 = (tS16)-1;
// output should be 0x1000 ~ FRAC16(0.125)
f16Out = MLIB_ShBi_F16(f16In1, s16In2);
// output should be 0x1000 ~ FRAC16(0.125)
f16Out = MLIB_ShBi (f16In1, s16In2, F16);
//
//
//
//
}
##############################################################
Available only if 16-bit fractional implementation selected
as default
##############################################################
// output should be 0x1000 ~ FRAC16(0.125)
f16Out = MLIB_ShBi (f16In1, s16In2);
5.124 Function MLIB_ShBiSat_F32
This function shifts the first argument to left or right by number defined by second
argument and saturate if necessary.
5.124.1 Declaration
tFrac32 MLIB_ShBiSat_F32(register tFrac32 f32In1, register tS16 s16In2);
5.124.2 Arguments
Table 5-148. MLIB_ShBiSat_F32 arguments
Type
Name
Direction
Description
register tFrac32
f32In1
input
First value to be shift.
register tS16
s16In2
input
The shift amount value.
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Function MLIB_ShBiSat_F32
5.124.3 Return
32-bit fractional value shifted to left or right by the shift amount. The bits beyond the 32bit boundary are discarded.
5.124.4 Description
Based on sign of second parameter this function shifts the first parameter to right or left
and saturate if an overflow is detected. If the sign of second parameter is negative, shift to
right.
Note
The shift amount cannot exceed in magnitude the bit-width of
the shift value, that means must be within the range -31...31.
Otherwise the result of the function is undefined. Due to
effectivity reason this function is implemented as inline, and
thus is not ANSI-C compliant.
5.124.5 Re-entrancy
The function is re-entrant.
5.124.6 Code Example
#include "mlib.h"
tFrac32 f32In1;
tFrac32 f32Out;
tS16 s16In2;
void main(void)
{
// first input = 0.25
f32In1 = FRAC32 (0.25);
// second input = -1
s16In2 = (tS16)-1;
// output should be 0x10000000 ~ FRAC32(0.125)
f32Out = MLIB_ShBiSat_F32(f32In1, s16In2);
// output should be 0x10000000 ~ FRAC32(0.125)
f32Out = MLIB_ShBiSat (f32In1, s16In2, F32);
// ##############################################################
// Available only if 32-bit fractional implementation selected
// as default
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// ##############################################################
}
// output should be 0x10000000 ~ FRAC32(0.125)
f32Out = MLIB_ShBiSat (f32In1, s16In2);
5.125 Function MLIB_ShBiSat_F16
This function shifts the first argument to left or right by number defined by second
argument and saturate if necessary.
5.125.1 Declaration
tFrac16 MLIB_ShBiSat_F16(register tFrac16 f16In1, register tS16 s16In2);
5.125.2 Arguments
Table 5-149. MLIB_ShBiSat_F16 arguments
Type
Name
Direction
Description
register tFrac16
f16In1
input
First value to be left shift.
register tS16
s16In2
input
The shift amount value.
5.125.3 Return
16-bit fractional value shifted to left or right by the shift amount. The bits beyond the 16bit boundary are discarded.
5.125.4 Description
Based on sign of second parameter this function shifts the first parameter to right or left
and saturate if an overflow is detected. If the sign of second parameter is negative, shift to
right.
Note
The shift amount cannot exceed in magnitude the bit-width of
the shift value, that means must be within the range -15...15.
Otherwise the result of the function is undefined. Due to
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Function MLIB_ShL_F32
effectivity reason this function is implemented as inline, and
thus is not ANSI-C compliant.
5.125.5 Re-entrancy
The function is re-entrant.
5.125.6 Code Example
#include "mlib.h"
tFrac16 f16In1;
tFrac16 f16Out;
tS16 s16In2;
void main(void)
{
// first input = 0.25
f16In1 = FRAC16 (0.25);
// second input = -1
s16In2 = (tS16)-1;
// output should be 0x1000 ~ FRAC16(0.125)
f16Out = MLIB_ShBiSat_F16(f16In1, s16In2);
// output should be 0x1000 ~ FRAC16(0.125)
f16Out = MLIB_ShBiSat (f16In1, s16In2, F16);
//
//
//
//
}
##############################################################
Available only if 16-bit fractional implementation selected
as default
##############################################################
// output should be 0x1000 ~ FRAC16(0.125)
f16Out = MLIB_ShBiSat (f16In1, s16In2);
5.126 Function MLIB_ShL_F32
This function shifts the first parameter to left by number defined by second parameter.
5.126.1 Declaration
tFrac32 MLIB_ShL_F32(register tFrac32 f32In1, register tU16 u16In2);
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5.126.2 Arguments
Table 5-150. MLIB_ShL_F32 arguments
Type
Name
Direction
Description
register tFrac32
f32In1
input
First value to be left shift.
register tU16
u16In2
input
The shift amount value.
5.126.3 Return
32-bit fractional value shifted to left by the shift amount. The bits beyond the 32-bit
boundary are discarded.
5.126.4 Description
This function shifts the first argument to left by number defined by second argument.
Overflow is not detected.
Note
The shift amount cannot exceed in magnitude the bit-width of
the shift value, that means must be within the range 0...31.
Otherwise the result of the function is undefined. Due to
effectivity reason this function is implemented as inline, and
thus is not ANSI-C compliant.
5.126.5 Re-entrancy
The function is re-entrant.
5.126.6 Code Example
#include "mlib.h"
tFrac32 f32In1;
tFrac32 f32Out;
tU16 u16In2;
void main(void)
{
// first input = 0.25
f32In1 = FRAC32 (0.25);
// second input = 1
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Function MLIB_ShL_F16
u16In2 = (tU16)1;
// output should be 0x40000000 ~ FRAC32(0.5)
f32Out = MLIB_ShL_F32(f32In1, u16In2);
// output should be 0x40000000 ~ FRAC32(0.5)
f32Out = MLIB_ShL (f32In1, u16In2, F32);
//
//
//
//
}
##############################################################
Available only if 32-bit fractional implementation selected
as default
##############################################################
// output should be 0x40000000 ~ FRAC32(0.5)
f32Out = MLIB_ShL (f32In1, u16In2);
5.127 Function MLIB_ShL_F16
This function shifts the first parameter to left by number defined by second parameter.
5.127.1 Declaration
tFrac16 MLIB_ShL_F16(register tFrac16 f16In1, register tU16 u16In2);
5.127.2 Arguments
Table 5-151. MLIB_ShL_F16 arguments
Type
Name
Direction
Description
register tFrac16
f16In1
input
First value to be left shift.
register tU16
u16In2
input
The shift amount value.
5.127.3 Return
16-bit fractional value shifted to left by the shift amount. The bits beyond the 16-bit
boundary are discarded.
5.127.4 Description
This function shifts the first argument to left by number defined by second argument.
Overflow is not detected.
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Note
The shift amount cannot exceed in magnitude the bit-width of
the shift value, that means must be within the range 0...15.
Otherwise the result of the function is undefined. Due to
effectivity reason this function is implemented as inline, and
thus is not ANSI-C compliant.
5.127.5 Re-entrancy
The function is re-entrant.
5.127.6 Code Example
#include "mlib.h"
tFrac16 f16In1;
tFrac16 f16Out;
tU16 u16In2;
void main(void)
{
// first input = 0.25
f16In1 = FRAC16 (0.25);
// second input = 1
u16In2 = (tU16)1;
// output should be 0x4000 ~ FRAC16(0.5)
f16Out = MLIB_ShL_F16(f16In1, u16In2);
// output should be 0x4000 ~ FRAC16(0.5)
f16Out = MLIB_ShL (f16In1, u16In2, F16);
//
//
//
//
}
##############################################################
Available only if 16-bit fractional implementation selected
as default
##############################################################
// output should be 0x4000 ~ FRAC16(0.5)
f16Out = MLIB_ShL (f16In1, u16In2);
5.128 Function MLIB_ShLSat_F32
This function shifts the first parameter to left by number defined by second parameter and
saturate if necessary.
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Function MLIB_ShLSat_F32
5.128.1 Declaration
tFrac32 MLIB_ShLSat_F32(register tFrac32 f32In1, register tU16 u16In2);
5.128.2 Arguments
Table 5-152. MLIB_ShLSat_F32 arguments
Type
Name
Direction
Description
register tFrac32
f32In1
input
First value to be left shift.
register tU16
u16In2
input
The shift amount value.
5.128.3 Return
32-bit fractional value shifted to left by the shift amount. The bits beyond the 32-bit
boundary are discarded.
5.128.4 Description
This function shifts the first argument to left by number defined by second argument and
saturate if an overflow is detected. The function returns a saturated fractional value if the
return value cannot fit into the return type.
Note
The shift amount cannot exceed in magnitude the bit-width of
the shift value, that means must be within the range 0...31.
Otherwise the result of the function is undefined. Due to
effectivity reason this function is implemented as inline, and
thus is not ANSI-C compliant.
5.128.5 Re-entrancy
The function is re-entrant.
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5.128.6 Code Example
#include "mlib.h"
tFrac32 f32In1;
tFrac32 f32Out;
tU16 u16In2;
void main(void)
{
// first input = 0.25
f32In1 = FRAC32 (0.25);
// second input = 1
u16In2 = (tU16)1;
// output should be 0x40000000 ~ FRAC32(0.5)
f32Out = MLIB_ShLSat_F32(f32In1, u16In2);
// output should be 0x40000000 ~ FRAC32(0.5)
f32Out = MLIB_ShLSat (f32In1, u16In2, F32);
//
//
//
//
}
##############################################################
Available only if 32-bit fractional implementation selected
as default
##############################################################
// output should be 0x40000000 ~ FRAC32(0.5)
f32Out = MLIB_ShLSat (f32In1, u16In2);
5.129 Function MLIB_ShLSat_F16
This function shifts the first parameter to left by number defined by second parameter and
saturate if necessary.
5.129.1 Declaration
tFrac16 MLIB_ShLSat_F16(register tFrac16 f16In1, register tU16 u16In2);
5.129.2 Arguments
Table 5-153. MLIB_ShLSat_F16 arguments
Type
Name
Direction
Description
register tFrac16
f16In1
input
First value to be left shift.
register tU16
u16In2
input
The shift amount value.
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Function MLIB_ShLSat_F16
5.129.3 Return
16-bit fractional value shifted to left by the shift amount. The bits beyond the 16-bit
boundary are discarded.
5.129.4 Description
This function shifts the first argument to left by number defined by second argument and
saturate if an overflow is detected. The function returns a saturated fractional value if the
return value cannot fit into the return type.
Note
The shift amount cannot exceed in magnitude the bit-width of
the shift value, that means must be within the range 0...15.
Otherwise the result of the function is undefined. Due to
effectivity reason this function is implemented as inline, and
thus is not ANSI-C compliant.
5.129.5 Re-entrancy
The function is re-entrant.
5.129.6 Code Example
#include "mlib.h"
tFrac16 f16In1;
tFrac16 f16Out;
tU16 u16In2;
void main(void)
{
// first input = 0.25
f16In1 = FRAC16 (0.25);
// second input = 1
u16In2 = (tU16)1;
// output should be 0x4000 ~ FRAC16(0.5)
f16Out = MLIB_ShLSat_F16(f16In1, u16In2);
// output should be 0x4000 ~ FRAC16(0.5)
f16Out = MLIB_ShLSat (f16In1, u16In2, F16);
//
//
//
//
##############################################################
Available only if 16-bit fractional implementation selected
as default
##############################################################
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}
// output should be 0x4000 ~ FRAC16(0.5)
f16Out = MLIB_ShLSat (f16In1, u16In2);
5.130 Function MLIB_ShR_F32
This function shifts the first parameter to right by number defined by second parameter.
5.130.1 Declaration
tFrac32 MLIB_ShR_F32(register tFrac32 f32In1, register tU16 u16In2);
5.130.2 Arguments
Table 5-154. MLIB_ShR_F32 arguments
Type
Name
Direction
Description
register tFrac32
f32In1
input
First value to be right shift.
register tU16
u16In2
input
The shift amount value.
5.130.3 Return
32-bit fractional value shifted right by the shift amount. The bits beyond the 32-bit
boundary of the result are discarded.
5.130.4 Description
This function shifts the first argument to right by number defined by second argument.
Note
The shift amount cannot exceed in magnitude the bit-width of
the shifted value, that means it must be within the range 0...31.
Otherwise the result of the function is undefined. Due to
effectivity reason this function is implemented as inline, and
thus is not ANSI-C compliant.
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Function MLIB_ShR_F16
5.130.5 Re-entrancy
The function is re-entrant.
5.130.6 Code Example
#include "mlib.h"
tFrac32 f32In1;
tFrac32 f32Out;
tU16 u16In2;
void main(void)
{
// first input = 0.25
f32In1 = FRAC32 (0.25);
// second input = 1
u16In2 = (tU16)1;
// output should be 0x10000000 ~ FRAC32(0.125)
f32Out = MLIB_ShR_F32(f32In1, u16In2);
// output should be 0x10000000 ~ FRAC32(0.125)
f32Out = MLIB_ShR (f32In1, u16In2, F32);
//
//
//
//
}
##############################################################
Available only if 32-bit fractional implementation selected
as default
##############################################################
// output should be 0x10000000 ~ FRAC32(0.125)
f32Out = MLIB_ShR (f32In1, u16In2);
5.131 Function MLIB_ShR_F16
This function shifts the first parameter to right by number defined by second parameter.
5.131.1 Declaration
tFrac16 MLIB_ShR_F16(register tFrac16 f16In1, register tU16 u16In2);
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5.131.2 Arguments
Table 5-155. MLIB_ShR_F16 arguments
Type
Name
Direction
Description
register tFrac16
f16In1
input
First value to be right shift.
register tU16
u16In2
input
The shift amount value.
5.131.3 Return
16-bit fractional value shifted right by the shift amount. The bits beyond the 16-bit
boundary of the result are discarded.
5.131.4 Description
This function shifts the first argument to right by number defined by second argument.
Note
The shift amount cannot exceed in magnitude the bit-width of
the shifted value, that means it must be within the range 0...15.
Otherwise the result of the function is undefined. Due to
effectivity reason this function is implemented as inline, and
thus is not ANSI-C compliant.
5.131.5 Re-entrancy
The function is re-entrant.
5.131.6 Code Example
#include "mlib.h"
tFrac16 f16In1;
tFrac16 f16Out;
tU16 u16In2;
void main(void)
{
// first input = 0.25
f16In1 = FRAC16 (0.25);
// second input = 1
u16In2 = (tU16)1;
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Function MLIB_Sub_F32
// output should be 0x1000 ~ FRAC16(0.125)
f16Out = MLIB_ShR_F16(f16In1, u16In2);
// output should be 0x1000 ~ FRAC16(0.125)
f16Out = MLIB_ShR (f16In1, u16In2, F16);
//
//
//
//
}
##############################################################
Available only if 16-bit fractional implementation selected
as default
##############################################################
// output should be 0x1000 ~ FRAC16(0.125)
f16Out = MLIB_ShR (f16In1, u16In2);
5.132 Function MLIB_Sub_F32
This function subtracts the second parameter from the first one.
5.132.1 Declaration
tFrac32 MLIB_Sub_F32(register tFrac32 f32In1, register tFrac32 f32In2);
5.132.2 Arguments
Table 5-156. MLIB_Sub_F32 arguments
Type
Name
Direction
Description
register tFrac32
f32In1
input
Operand is a 32-bit number normalized between[-1,1).
register tFrac32
f32In2
input
Operand is a 32-bit number normalized between[-1,1).
5.132.3 Return
The subtraction of the second argument from the first argument.
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5.132.4 Description
Subtraction of two fractional 32-bit values. The second argument is subtracted from the
first one. The input values as well as output value are considered as 32-bit fractional data
type. The output saturation is not implemented in this function, thus in case the
subtraction of input parameters is outside the (-1, 1) interval, the output value will
overflow without any detection.
The output of the function is defined by the following simple equation:
Equation MLIB_Sub_Eq1
Note
Overflow is not detected. Due to effectivity reason this function
is implemented as inline and thus is not ANSI-C compliant.
5.132.5 Re-entrancy
The function is re-entrant.
5.132.6 Code Example
#include "mlib.h"
tFrac32 f32In1;
tFrac32 f32In2;
tFrac32 f32Out;
void main(void)
{
// first input = 0.5
f32In1 = FRAC32 (0.5);
// second input = 0.25
f32In2 = FRAC32 (0.25);
// output should be 0x20000000
f32Out = MLIB_Sub_F32(f32In1,f32In2);
// output should be 0x20000000
f32Out = MLIB_Sub (f32In1,f32In2,F32);
//
//
//
//
##############################################################
Available only if 32-bit fractional implementation selected
as default
##############################################################
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Function MLIB_Sub_F16
}
// output should be 0x20000000
f32Out = MLIB_Sub (f32In1,f32In2);
5.133 Function MLIB_Sub_F16
This function subtracts the second parameter from the first one.
5.133.1 Declaration
tFrac16 MLIB_Sub_F16(register tFrac16 f16In1, register tFrac16 f16In2);
5.133.2 Arguments
Table 5-157. MLIB_Sub_F16 arguments
Type
Name
Direction
Description
register tFrac16
f16In1
input
Operand is a 16-bit number normalized between [-1,1).
register tFrac16
f16In2
input
Operand is a 16-bit number normalized between [-1,1).
5.133.3 Return
The subtraction of the second argument from the first argument.
5.133.4 Description
Subtraction of two fractional 16-bit values. The second argument is subtracted from the
first one. The input values as well as output value are considered as 16-bit fractional data
type. The output saturation is not implemented in this function, thus in case the
subtraction of input parameters is outside the (-1, 1) interval, the output value will
overflow without any detection.
The output of the function is defined by the following simple equation:
Equation MLIB_Sub_Eq1
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Note
Overflow is not detected. Due to effectivity reason this function
is implemented as inline and thus is not ANSI-C compliant.
5.133.5 Re-entrancy
The function is re-entrant.
5.133.6 Code Example
#include "mlib.h"
tFrac16 f16In1;
tFrac16 f16In2;
tFrac16 f16Out;
void main(void)
{
// first input = 0.5
f16In1 = FRAC16 (0.5);
// second input = 0.25
f16In2 = FRAC16 (0.25);
// output should be 0x2000
f16Out = MLIB_Sub_F16(f16In1,f16In2);
// output should be 0x2000
f16Out = MLIB_Sub (f16In1,f16In2,F16);
//
//
//
//
}
##############################################################
Available only if 16-bit fractional implementation selected
as default
##############################################################
// output should be 0x20000000
f16Out = MLIB_Sub (f16In1,f16In2);
5.134 Function MLIB_SubSat_F32
This function subtracts the second parameter from the first one and saturate if necessary.
5.134.1 Declaration
tFrac32 MLIB_SubSat_F32(register tFrac32 f32In1, register tFrac32 f32In2);
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Function MLIB_SubSat_F32
5.134.2 Arguments
Table 5-158. MLIB_SubSat_F32 arguments
Type
Name
Direction
Description
register tFrac32
f32In1
input
Operand is a 32-bit number normalized between [-1,1).
register tFrac32
f32In2
input
Operand is a 32-bit number normalized between [-1,1).
5.134.3 Return
The subtraction of the second argument from the first argument.
5.134.4 Description
Subtraction with overflow control of two fractional 32-bit numbers. The second argument
is subtracted from the first one. The input values as well as output value are considered as
32-bit fractional data type. The output saturation is implemented in this function, thus in
case the subtraction of input parameters is outside the (-1, 1) interval, the output value is
limited to the boundary value.
The output of the function is defined by the following simple equation:
Equation MLIB_SubSat_Eq1
Note
Due to effectivity reason this function is implemented as inline
and thus is not ANSI-C compliant.
5.134.5 Re-entrancy
The function is re-entrant.
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5.134.6 Code Example
#include "mlib.h"
tFrac32 f32In1;
tFrac32 f32In2;
tFrac32 f32Out;
void main(void)
{
// first input = 0.5
f32In1 = FRAC32 (0.5);
// second input = 0.25
f32In2 = FRAC32 (0.25);
// output should be 0x20000000
f32Out = MLIB_SubSat_F32(f32In1,f32In2);
// output should be 0x20000000
f32Out = MLIB_SubSat (f32In1,f32In2,F32);
//
//
//
//
}
##############################################################
Available only if 32-bit fractional implementation selected
as default
##############################################################
// output should be 0x20000000
f32Out = MLIB_SubSat (f32In1,f32In2);
5.135 Function MLIB_SubSat_F16
This function subtracts the second parameter from the first one and saturate if necessary.
5.135.1 Declaration
tFrac16 MLIB_SubSat_F16(register tFrac16 f16In1, register tFrac16 f16In2);
5.135.2 Arguments
Table 5-159. MLIB_SubSat_F16 arguments
Type
Name
Direction
Description
register tFrac16
f16In1
input
Operand is a 16-bit number normalized between [-1,1).
register tFrac16
f16In2
input
Operand is a 16-bit number normalized between [-1,1).
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Function MLIB_SubSat_F16
5.135.3 Return
The subtraction of the second argument from the first argument.
5.135.4 Description
Subtraction with overflow control of two fractional 16-bit numbers. The second argument
is subtracted from the first one. The input values as well as output value are considered as
16-bit fractional data type. The output saturation is implemented in this function, thus in
case the subtraction of input parameters is outside the (-1, 1) interval, the output value is
limited to the boundary value.
The output of the function is defined by the following simple equation:
Equation MLIB_SubSat_Eq1
Note
Due to effectivity reason this function is implemented as inline
and thus is not ANSI-C compliant.
5.135.5 Re-entrancy
The function is re-entrant.
5.135.6 Code Example
#include "mlib.h"
tFrac16 f16In1;
tFrac16 f16In2;
tFrac16 f16Out;
void main(void)
{
// first input = 0.5
f16In1 = FRAC16 (0.5);
// second input = 0.25
f16In2 = FRAC16 (0.25);
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// output should be 0x2000
f16Out = MLIB_SubSat_F16(f16In1,f16In2);
// output should be 0x2000
f16Out = MLIB_SubSat (f16In1,f16In2,F16);
//
//
//
//
}
##############################################################
Available only if 16-bit fractional implementation selected
as default
##############################################################
// output should be 0x2000
f16Out = MLIB_SubSat (f16In1,f16In2);
5.136 Function MLIB_VMac_F32
This function implements the vector multiply accumulate function.
5.136.1 Declaration
tFrac32 MLIB_VMac_F32(register tFrac32 f32In1, register tFrac32 f32In2, register tFrac32
f32In3, register tFrac32 f32In4);
5.136.2 Arguments
Table 5-160. MLIB_VMac_F32 arguments
Type
Name
Direction
Description
register tFrac32
f32In1
input
First input value to first multiplication.
register tFrac32
f32In2
input
Second input value to first multiplication.
register tFrac32
f32In3
input
First input value to second multiplication.
register tFrac32
f32In4
input
Second input value to second multiplication.
5.136.3 Return
Vector multiplied input values with addition.
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Function MLIB_VMac_F32
5.136.4 Description
This inline function returns the vector multiply accumulate of input values. The input
values as well as output value is considered as 32-bit fractional values. The output
saturation is not implemented in this function, thus in case the vector multiply-add of
input values is outside the (-1, 1) interval, the output value will overflow without any
detection.
The output of the function is defined by the following simple equation:
Equation MLIB_VMac_Eq1
Note
Overflow is not detected. Due to effectivity reason this function
is implemented as inline and thus is not ANSI-C compliant.
5.136.5 Re-entrancy
The function is re-entrant.
5.136.6 Code Example
#include "mlib.h"
tFrac32
tFrac32
tFrac32
tFrac32
tFrac32
f32In1;
f32In2;
f32In3;
f32In4;
f32Out;
void main(void)
{
// input1 value = 0.25
f32In1 = FRAC32 (0.25);
// input2 value = 0.15
f32In2 = FRAC32 (0.15);
// input3 value = 0.35
f32In3 = FRAC32 (0.35);
// input4 value = 0.45
f32In4 = FRAC32 (0.45);
// output should be FRAC32(0.195) = 0x18F5C28F
f32Out = MLIB_VMac_F32(f32In1,f32In2,f32In3,f32In4);
// output should be FRAC32(0.195) = 0x18F5C28F
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f32Out = MLIB_VMac (f32In1,f32In2,f32In3,f32In4, F32);
//
//
//
//
}
##############################################################
Available only if 32-bit fractional implementation selected
as default
##############################################################
// output should be FRAC32(0.195) = 0x18F5C28F
f32Out = MLIB_VMac (f32In1,f32In2,f32In3,f32In4);
5.137 Function MLIB_VMac_F32F16F16
This function implements the vector multiply accumulate function.
5.137.1 Declaration
tFrac32 MLIB_VMac_F32F16F16(register tFrac16 f16In1, register tFrac16 f16In2, register
tFrac16 f16In3, register tFrac16 f16In4);
5.137.2 Arguments
Table 5-161. MLIB_VMac_F32F16F16 arguments
Type
Name
Direction
Description
register tFrac16
f16In1
input
First input value to first multiplication.
register tFrac16
f16In2
input
Second input value to first multiplication.
register tFrac16
f16In3
input
First input value to second multiplication.
register tFrac16
f16In4
input
Second input value to second multiplication.
5.137.3 Return
Vector multiplied input values with addition.
5.137.4 Description
This inline function returns the vector multiply accumulate of input values. The input
values are considered as 16-bit fractional values and the output value is considered as 32bit fractional value. The output saturation is not implemented in this function, thus in case
the vector multiply-add of input values is outside the (-1, 1) interval, the output value will
overflow without any detection.
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Function MLIB_VMac_F16
The output of the function is defined by the following simple equation:
Equation MLIB_VMac_Eq1
Note
Overflow is not detected. Due to effectivity reason this function
is implemented as inline and thus is not ANSI-C compliant.
5.137.5 Re-entrancy
The function is re-entrant.
5.137.6 Code Example
#include "mlib.h"
tFrac16
tFrac16
tFrac16
tFrac16
tFrac32
f16In1;
f16In2;
f16In3;
f16In4;
f32Out;
void main(void)
{
// input1 value = 0.25
f16In1 = FRAC16 (0.25);
// input2 value = 0.15
f16In2 = FRAC16 (0.15);
// input3 value = 0.35
f16In3 = FRAC16 (0.35);
// input4 value = 0.45
f16In4 = FRAC16 (0.45);
// output should be FRAC32(0.195) = 0x18F5C28F
f32Out = MLIB_VMac_F32F16F16(f16In1,f16In2,f16In3,f16In4);
}
// output should be FRAC32(0.195) = 0x18F5C28F
f32Out = MLIB_VMac (f16In1,f16In2,f16In3,f16In4, F32F16F16);
5.138 Function MLIB_VMac_F16
This function implements the vector multiply accumulate function.
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5.138.1 Declaration
tFrac16 MLIB_VMac_F16(register tFrac16 f16In1, register tFrac16 f16In2, register tFrac16
f16In3, register tFrac16 f16In4);
5.138.2 Arguments
Table 5-162. MLIB_VMac_F16 arguments
Type
Name
Direction
Description
register tFrac16
f16In1
input
First input value to first multiplication.
register tFrac16
f16In2
input
Second input value to first multiplication.
register tFrac16
f16In3
input
First input value to second multiplication.
register tFrac16
f16In4
input
Second input value to second multiplication.
5.138.3 Return
Vector multiplied input values with addition.
5.138.4 Description
This inline function returns the vector multiply accumulate of input values. The input
values as well as output value is considered as 16-bit fractional values. The output
saturation is not implemented in this function, thus in case the vector multiply-add of
input values is outside the (-1, 1) interval, the output value will overflow without any
detection.
The output of the function is defined by the following simple equation:
Equation MLIB_VMac_Eq1
Note
Overflow is not detected. Due to effectivity reason this function
is implemented as inline and thus is not ANSI-C compliant.
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Function SWLIBS_GetVersion
5.138.5 Re-entrancy
The function is re-entrant.
5.138.6 Code Example
#include "mlib.h"
tFrac16
tFrac16
tFrac16
tFrac16
tFrac16
f16In1;
f16In2;
f16In3;
f16In4;
f16Out;
void main(void)
{
// input1 value = 0.25
f16In1 = FRAC16 (0.25);
// input2 value = 0.15
f16In2 = FRAC16 (0.15);
// input3 value = 0.35
f16In3 = FRAC16 (0.35);
// input4 value = 0.45
f16In4 = FRAC16 (0.45);
// output should be FRAC16(0.195) = 0x18F5
f16Out = MLIB_VMac_F16(f16In1,f16In2,f16In3,f16In4);
// output should be FRAC16(0.195) = 0x18F5
f16Out = MLIB_VMac (f16In1,f16In2,f16In3,f16In4, F16);
//
//
//
//
}
##############################################################
Available only if 16-bit fractional implementation selected
as default
##############################################################
// output should be FRAC16(0.195) = 0x18F5
f16Out = MLIB_VMac (f16In1,f16In2,f16In3,f16In4);
5.139 Function SWLIBS_GetVersion
This function returns the information about AMMCLIB version.
5.139.1 Declaration
const SWLIBS_VERSION_T * SWLIBS_GetVersion();
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5.139.2 Return
The function returns the information about the version of Motor Control Library Set.
5.139.3 Description
The function returns the information about the version of Motor Control Library Set. The
information are structured as follows:
• Motor Control Library Set identification code
• Motor Control Library Set version code
• Motor Control Library Set supported implementation code
5.139.4 Reentrancy
The function is reentrant.
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Function SWLIBS_GetVersion
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6.1 Typedefs Index
Table 6-1. Quick typedefs reference
Type
Name
Description
typedef unsigned char
tBool
basic boolean type
typedef double
tDouble
double precision float type
typedef float
tFloat
single precision float type
typedef tS16
tFrac16
16-bit signed fractional Q1.15 type
typedef tS32
tFrac32
32-bit Q1.31 type
typedef signed short
tS16
signed 16-bit integer type
typedef signed long
tS32
signed 32-bit integer type
typedef signed long long
tS64
signed 64-bit integer type
typedef signed char
tS8
signed 8-bit integer type
typedef unsigned short
tU16
unsigned 16-bit integer type
typedef unsigned long
tU32
unsigned 32-bit integer type
typedef unsigned char
tU8
unsigned 8-bit integer type
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Typedefs Index
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Compound Data Types
Table 7-1. Compound data types overview
Name
Description
GDFLIB_FILTER_IIR1_COEFF_T_F16
Sub-structure containing filter coefficients.
GDFLIB_FILTER_IIR1_COEFF_T_F32
Sub-structure containing filter coefficients.
GDFLIB_FILTER_IIR1_T_F16
Structure containing filter buffer and coefficients.
GDFLIB_FILTER_IIR1_T_F32
Structure containing filter buffer and coefficients.
GDFLIB_FILTER_IIR2_COEFF_T_F16
Sub-structure containing filter coefficients.
GDFLIB_FILTER_IIR2_COEFF_T_F32
Sub-structure containing filter coefficients.
GDFLIB_FILTER_IIR2_T_F16
Structure containing filter buffer and coefficients.
GDFLIB_FILTER_IIR2_T_F32
Structure containing filter buffer and coefficients.
GDFLIB_FILTER_MA_T_F16
Structure containing filter buffer and coefficients.
GDFLIB_FILTER_MA_T_F32
Structure containing filter buffer and coefficients.
GDFLIB_FILTERFIR_PARAM_T_F16
Structure containing parameters of the filter.
GDFLIB_FILTERFIR_PARAM_T_F32
Structure containing parameters of the filter.
GDFLIB_FILTERFIR_STATE_T_F16
Structure containing the current state of the filter.
GDFLIB_FILTERFIR_STATE_T_F32
Structure containing the current state of the filter.
GFLIB_ACOS_T_F16
Default approximation coefficients datatype for arccosine approximation.
GFLIB_ACOS_T_F32
Default approximation coefficients datatype for arccosine approximation.
GFLIB_ACOS_TAYLOR_COEF_T_F16
Array of approximation coefficients for piece-wise polynomial.
GFLIB_ACOS_TAYLOR_COEF_T_F32
Array of approximation coefficients for piece-wise polynomial.
GFLIB_ASIN_T_F16
Default approximation coefficients datatype for arcsine approximation.
GFLIB_ASIN_T_F32
Default approximation coefficients datatype for arcsine approximation.
GFLIB_ASIN_TAYLOR_COEF_T_F16
Array of approximation coefficients for piece-wise polynomial.
GFLIB_ASIN_TAYLOR_COEF_T_F32
Array of approximation coefficients for piece-wise polynomial.
GFLIB_ATAN_T_F16
Structure containing eight sub-structures with polynomial coefficients to
cover all sub-intervals.
GFLIB_ATAN_T_F32
Structure containing eight sub-structures with polynomial coefficients to
cover all sub-intervals.
GFLIB_ATAN_TAYLOR_COEF_T_F16
Array of polynomial approximation coefficients for one sub-interval.
GFLIB_ATAN_TAYLOR_COEF_T_F32
Array of minimax polynomial approximation coefficients for one sub-interval.
GFLIB_ATANYXSHIFTED_T_F16
Structure containing the parameter for the AtanYXShifted function.
GFLIB_ATANYXSHIFTED_T_F32
Structure containing the parameter for the AtanYXShifted function.
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Table 7-1. Compound data types overview (continued)
Name
Description
GFLIB_CONTROLLER_PI_P_T_F16
Structure containing parameters and states of the parallel form PI controller.
GFLIB_CONTROLLER_PI_P_T_F32
Structure containing parameters and states of the parallel form PI controller.
GFLIB_CONTROLLER_PI_R_T_F16
Structure containing parameters and states of the recurrent form PI
controller.
GFLIB_CONTROLLER_PI_R_T_F32
Structure containing parameters and states of the recurrent form PI
controller.
GFLIB_CONTROLLER_PIAW_P_T_F16
Structure containing parameters and states of the parallel form PI controller
with anti-windup.
GFLIB_CONTROLLER_PIAW_P_T_F32
Structure containing parameters and states of the parallel form PI controller
with anti-windup.
GFLIB_CONTROLLER_PIAW_R_T_F16
Structure containing parameters and states of the recurrent form PI
controller with anti-windup.
GFLIB_CONTROLLER_PIAW_R_T_F32
Structure containing parameters and states of the recurrent form PI
controller with anti-windup.
GFLIB_COS_T_F16
Array of four 16-bit elements for storing coefficients of the Taylor
polynomial.
GFLIB_COS_T_F32
Array of five 32-bit elements for storing coefficients of the Taylor polynomial.
GFLIB_HYST_T_F16
Structure containing parameters and states for the hysteresis function.
GFLIB_HYST_T_F32
Structure containing parameters and states for the hysteresis function.
GFLIB_INTEGRATOR_TR_T_F16
Structure containing integrator parameters and coefficients.
GFLIB_INTEGRATOR_TR_T_F32
Structure containing integrator parameters and coefficients.
GFLIB_LIMIT_T_F16
Structure containing the limits.
GFLIB_LIMIT_T_F32
Structure containing the limits.
GFLIB_LOWERLIMIT_T_F16
Structure containing the lower limit.
GFLIB_LOWERLIMIT_T_F32
Structure containing the lower limit.
GFLIB_LUT1D_T_F16
Structure containing 1D look-up table parameters.
GFLIB_LUT1D_T_F32
Structure containing 1D look-up table parameters.
GFLIB_LUT2D_T_F16
Structure containing 2D look-up table parameters.
GFLIB_LUT2D_T_F32
Structure containing 2D look-up table parameters.
GFLIB_RAMP_T_F16
Structure containing increment/decrement coefficients and state value for
the ramp function implemented in GFLIB_Ramp.
GFLIB_RAMP_T_F32
Structure containing increment/decrement coefficients and state value for
the ramp function implemented in GFLIB_Ramp.
GFLIB_SIN_T_F16
Array of four 16-bit elements for storing coefficients of the Taylor
polynomial.
GFLIB_SIN_T_F32
Array of five 32-bit elements for storing coefficients of the Taylor polynomial.
GFLIB_SINCOS_T_F16
Array of four 16-bit elements for storing coefficients of the Taylor
polynomial.
GFLIB_SINCOS_T_F32
Array of five 32-bit elements for storing coefficients of the Taylor polynomial.
GFLIB_TAN_T_F16
Output of tan(PI * f16In) for interval [0, PI/4) of the input angles is divided
into eight sub-sectors. Polynomial approximation is done using a 4th order
polynomial, for each sub-sector respectively. Eight arrays, each including
four polynomial coefficients for each sub-interval, are stored in this
(GFLIB_TAN_T_F16) structure.
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Table 7-1. Compound data types overview (continued)
Name
Description
GFLIB_TAN_T_F32
Output of tan(PI * f32In) for interval [0, PI/4) of the input angles is divided
into eight sub-sectors. Polynomial approximation is done using a 4th order
polynomial, for each sub-sector respectively. Eight arrays, each including
four polynomial coefficients for each sub-interval, are stored in this
(GFLIB_TAN_T_F32) structure.
GFLIB_TAN_TAYLOR_COEF_T_F16
Structure containing four polynomial coefficients for one sub-interval.
GFLIB_TAN_TAYLOR_COEF_T_F32
Structure containing four polynomial coefficients for one sub-interval.
GFLIB_UPPERLIMIT_T_F16
Structure containing the upper limit.
GFLIB_UPPERLIMIT_T_F32
Structure containing the upper limit.
GFLIB_VECTORLIMIT_T_F16
Structure containing the limit.
GFLIB_VECTORLIMIT_T_F32
Structure containing the limit.
GMCLIB_DECOUPLINGPMSM_T_F16
Structure containing coefficients for calculation of the decoupling.
GMCLIB_DECOUPLINGPMSM_T_F32
Structure containing coefficients for calculation of the decoupling.
GMCLIB_ELIMDCBUSRIP_T_F16
Structure containing the PWM modulation index and the measured value of
the DC bus voltage.
GMCLIB_ELIMDCBUSRIP_T_F32
Structure containing the PWM modulation index and the measured value of
the DC bus voltage.
SWLIBS_2Syst_F16
Array of two standard 16-bit fractional arguments.
SWLIBS_2Syst_F32
Array of two standard 32-bit fractional arguments.
SWLIBS_3Syst_F16
Array of three standard 16-bit fractional arguments.
SWLIBS_3Syst_F32
Array of three standard 32-bit fractional arguments.
SWLIBS_VERSION_T
Motor Control Library Set identification structure.
7.1 GDFLIB_FILTER_IIR1_COEFF_T_F16
#include <GDFLIB_FilterIIR1.h>
7.1.1 Description
Sub-structure containing filter coefficients.
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GDFLIB_FILTER_IIR1_COEFF_T_F32
7.1.2 Compound Type Members
Table 7-2. GDFLIB_FILTER_IIR1_COEFF_T_F16 members
description
Type
Name
Description
tFrac16
f16B0
B0 coefficient of an IIR1 filter, fractional
format normalized to fit into (-2 15, 2 15-1).
tFrac16
f16B1
B1 coefficient of an IIR1 filter, fractional
format normalized to fit into (-2 15, 2 15-1).
tFrac16
f16A1
A1 coefficient of an IIR1 filter, fractional
format normalized to fit into (-2 15, 2 15-1).
7.2 GDFLIB_FILTER_IIR1_COEFF_T_F32
#include <GDFLIB_FilterIIR1.h>
7.2.1 Description
Sub-structure containing filter coefficients.
7.2.2 Compound Type Members
Table 7-3. GDFLIB_FILTER_IIR1_COEFF_T_F32 members
description
Type
Name
Description
tFrac32
f32B0
B0 coefficient of an IIR1 filter, fractional
format normalized to fit into (-2 31, 2 31-1).
tFrac32
f32B1
B1 coefficient of an IIR1 filter, fractional
format normalized to fit into (-2 31, 2 31-1).
tFrac32
f32A1
A1 coefficient of an IIR1 filter, fractional
format normalized to fit into (-2 31, 2 31-1).
7.3 GDFLIB_FILTER_IIR1_T_F16
#include <GDFLIB_FilterIIR1.h>
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7.3.1 Description
Structure containing filter buffer and coefficients.
7.3.2 Compound Type Members
Table 7-4. GDFLIB_FILTER_IIR1_T_F16 members description
Type
Name
Description
GDFLIB_FILTER_IIR1_COEF trFiltCoeff
F_T_F16
Sub-structure containing filter coefficients.
tFrac16
f16FiltBufferX
Input buffer of an IIR1 filter, fractional format
normalized to fit into (-2 15, 2 15-1).
tFrac32
f32FiltBufferY
Internal accumulator buffer, fractional format
normalized to fit into (-2 15, 2 15-1).
7.4 GDFLIB_FILTER_IIR1_T_F32
#include <GDFLIB_FilterIIR1.h>
7.4.1 Description
Structure containing filter buffer and coefficients.
7.4.2 Compound Type Members
Table 7-5. GDFLIB_FILTER_IIR1_T_F32 members description
Type
Name
Description
GDFLIB_FILTER_IIR1_COEF trFiltCoeff
F_T_F32
Sub-structure containing filter coefficients.
tFrac32
f32FiltBufferX
Input buffer of an IIR1 filter, fractional format
normalized to fit into (-2 31, 2 31-1).
tFrac32
f32FiltBufferY
Internal accumulator buffer, fractional format
normalized to fit into (-2 31, 2 31-1).
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GDFLIB_FILTER_IIR2_COEFF_T_F32
7.5 GDFLIB_FILTER_IIR2_COEFF_T_F16
#include <GDFLIB_FilterIIR2.h>
7.5.1 Description
Sub-structure containing filter coefficients.
7.5.2 Compound Type Members
Table 7-6. GDFLIB_FILTER_IIR2_COEFF_T_F16 members
description
Type
Name
Description
tFrac16
f16B0
B0 coefficient of an IIR2 filter, fractional
format normalized to fit into (-2 15, 2 15-1).
tFrac16
f16B1
B1 coefficient of an IIR2 filter, fractional
format normalized to fit into (-2 15, 2 15-1).
tFrac16
f16B2
B2 coefficient of an IIR2 filter, fractional
format normalized to fit into (-2 15, 2 15-1).
tFrac16
f16A1
A1 coefficient of an IIR2 filter, fractional
format normalized to fit into (-2 15, 2 15-1).
tFrac16
f16A2
A2 coefficient of an IIR2 filter, fractional
format normalized to fit into (-2 15, 2 15-1).
7.6 GDFLIB_FILTER_IIR2_COEFF_T_F32
#include <GDFLIB_FilterIIR2.h>
7.6.1 Description
Sub-structure containing filter coefficients.
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7.6.2 Compound Type Members
Table 7-7. GDFLIB_FILTER_IIR2_COEFF_T_F32 members
description
Type
Name
Description
tFrac32
f32B0
B0 coefficient of an IIR2 filter, fractional
format normalized to fit into (-2 31, 2 31-1).
tFrac32
f32B1
B1 coefficient of an IIR2 filter, fractional
format normalized to fit into (-2 31, 2 31-1).
tFrac32
f32B2
B2 coefficient of an IIR2 filter, fractional
format normalized to fit into (-2 31, 2 31-1).
tFrac32
f32A1
A1 coefficient of an IIR2 filter, fractional
format normalized to fit into (-2 31, 2 31-1).
tFrac32
f32A2
A2 coefficient of an IIR2 filter, fractional
format normalized to fit into (-2 31, 2 31-1).
7.7 GDFLIB_FILTER_IIR2_T_F16
#include <GDFLIB_FilterIIR2.h>
7.7.1 Description
Structure containing filter buffer and coefficients.
7.7.2 Compound Type Members
Table 7-8. GDFLIB_FILTER_IIR2_T_F16 members description
Type
Name
Description
GDFLIB_FILTER_IIR2_COEF trFiltCoeff
F_T_F16
Sub-structure containing filter coefficients.
tFrac16
f16FiltBufferX
Input buffer of an IIR2 filter, fractional format
normalized to fit into (-2 15, 2 15-1).
tFrac32
f32FiltBufferY
Internal accumulator buffer, fractional format
normalized to fit into (-2 15, 2 15-1).
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GDFLIB_FILTER_MA_T_F16
7.8 GDFLIB_FILTER_IIR2_T_F32
#include <GDFLIB_FilterIIR2.h>
7.8.1 Description
Structure containing filter buffer and coefficients.
7.8.2 Compound Type Members
Table 7-9. GDFLIB_FILTER_IIR2_T_F32 members description
Type
Name
Description
GDFLIB_FILTER_IIR2_COEF trFiltCoeff
F_T_F32
Sub-structure containing filter coefficients.
tFrac32
f32FiltBufferX
Input buffer of an IIR2 filter, fractional format
normalized to fit into (-2 31, 2 31-1).
tFrac32
f32FiltBufferY
Internal accumulator buffer, fractional format
normalized to fit into (-2 31, 2 31-1).
7.9 GDFLIB_FILTER_MA_T_F16
#include <GDFLIB_FilterMA.h>
7.9.1 Description
Structure containing filter buffer and coefficients.
7.9.2 Compound Type Members
Table 7-10. GDFLIB_FILTER_MA_T_F16 members description
Type
Name
Description
tFrac32
f32Acc
Filter accumulator.
tU16
u16NSamples
Recalculated smoothing factor [0, 15].
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7.10 GDFLIB_FILTER_MA_T_F32
#include <GDFLIB_FilterMA.h>
7.10.1 Description
Structure containing filter buffer and coefficients.
7.10.2 Compound Type Members
Table 7-11. GDFLIB_FILTER_MA_T_F32 members description
Type
Name
Description
tFrac32
f32Acc
Filter accumulator.
tU16
u16NSamples
Recalculated smoothing factor [0, 31].
7.11 GDFLIB_FILTERFIR_PARAM_T_F16
#include <GDFLIB_FilterFIR.h>
7.11.1 Description
Structure containing parameters of the filter.
7.11.2 Compound Type Members
Table 7-12. GDFLIB_FILTERFIR_PARAM_T_F16 members
description
Type
Name
Description
tU16
u16Order
FIR filter order, must be 1 or more.
const tFrac16 *
pCoefBuf
FIR filter coefficients buffer.
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GDFLIB_FILTERFIR_STATE_T_F16
7.12 GDFLIB_FILTERFIR_PARAM_T_F32
#include <GDFLIB_FilterFIR.h>
7.12.1 Description
Structure containing parameters of the filter.
7.12.2 Compound Type Members
Table 7-13. GDFLIB_FILTERFIR_PARAM_T_F32 members
description
Type
Name
Description
tU32
u32Order
FIR filter order, must be 1 or more.
const tFrac32 *
pCoefBuf
FIR filter coefficients buffer.
7.13 GDFLIB_FILTERFIR_STATE_T_F16
#include <GDFLIB_FilterFIR.h>
7.13.1 Description
Structure containing the current state of the filter.
7.13.2 Compound Type Members
Table 7-14. GDFLIB_FILTERFIR_STATE_T_F16 members
description
Type
Name
Description
tU16
u16Idx
Input buffer index.
tFrac16 *
pInBuf
Pointer to the input buffer.
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7.14 GDFLIB_FILTERFIR_STATE_T_F32
#include <GDFLIB_FilterFIR.h>
7.14.1 Description
Structure containing the current state of the filter.
7.14.2 Compound Type Members
Table 7-15. GDFLIB_FILTERFIR_STATE_T_F32 members
description
Type
Name
Description
tU32
u32Idx
Input buffer index.
tFrac32 *
pInBuf
Pointer to the input buffer.
7.15 GFLIB_ACOS_T_F16
#include <GFLIB_Acos.h>
7.15.1 Description
Default approximation coefficients datatype for arccosine approximation.
7.15.2 Compound Type Members
Table 7-16. GFLIB_ACOS_T_F16 members description
Type
GFLIB_ACOS_TAYLOR_CO
EF_T_F16
Name
GFLIB_ACOS_SECTOR
Description
Array of two elements for storing two subarrays (each sub-array contains five 16-bit
coefficients) for all sub-intervals.
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GFLIB_ACOS_TAYLOR_COEF_T_F16
7.16 GFLIB_ACOS_T_F32
#include <GFLIB_Acos.h>
7.16.1 Description
Default approximation coefficients datatype for arccosine approximation.
7.16.2 Compound Type Members
Table 7-17. GFLIB_ACOS_T_F32 members description
Type
GFLIB_ACOS_TAYLOR_CO
EF_T_F32
Name
GFLIB_ACOS_SECTOR
Description
Array of two elements for storing three subarrays (each sub-array contains five 32-bit
coefficients) for all sub-intervals.
7.17 GFLIB_ACOS_TAYLOR_COEF_T_F16
#include <GFLIB_Acos.h>
7.17.1 Description
Array of approximation coefficients for piece-wise polynomial.
7.17.2 Compound Type Members
Table 7-18. GFLIB_ACOS_TAYLOR_COEF_T_F16 members
description
Type
const tFrac16
Name
f16A
Description
Array of five 16-bit elements for storing
coefficients of the piece-wise polynomial.
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7.18 GFLIB_ACOS_TAYLOR_COEF_T_F32
#include <GFLIB_Acos.h>
7.18.1 Description
Array of approximation coefficients for piece-wise polynomial.
7.18.2 Compound Type Members
Table 7-19. GFLIB_ACOS_TAYLOR_COEF_T_F32 members
description
Type
Name
const tFrac32
f32A
Description
Array of five 32-bit elements for storing
coefficients of the piece-wise polynomial.
7.19 GFLIB_ASIN_T_F16
#include <GFLIB_Asin.h>
7.19.1 Description
Default approximation coefficients datatype for arcsine approximation.
7.19.2 Compound Type Members
Table 7-20. GFLIB_ASIN_T_F16 members description
Type
Name
GFLIB_ASIN_TAYLOR_COE GFLIB_ASIN_SECTOR
F_T_F16
Description
Default approximation coefficients datatype
for arcsine approximation.
7.20 GFLIB_ASIN_T_F32
#include <GFLIB_Asin.h>
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GFLIB_ASIN_TAYLOR_COEF_T_F16
7.20.1 Description
Default approximation coefficients datatype for arcsine approximation.
7.20.2 Compound Type Members
Table 7-21. GFLIB_ASIN_T_F32 members description
Type
Name
GFLIB_ASIN_TAYLOR_COE GFLIB_ASIN_SECTOR
F_T_F32
Description
Default approximation coefficients datatype
for arcsine approximation.
7.21 GFLIB_ASIN_TAYLOR_COEF_T_F16
#include <GFLIB_Asin.h>
7.21.1 Description
Array of approximation coefficients for piece-wise polynomial.
7.21.2 Compound Type Members
Table 7-22. GFLIB_ASIN_TAYLOR_COEF_T_F16 members
description
Type
const tFrac16
Name
f16A
Description
Array of approximation coefficients for piecewise polynomial.
7.22 GFLIB_ASIN_TAYLOR_COEF_T_F32
#include <GFLIB_Asin.h>
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7.22.1 Description
Array of approximation coefficients for piece-wise polynomial.
7.22.2 Compound Type Members
Table 7-23. GFLIB_ASIN_TAYLOR_COEF_T_F32 members
description
Type
Name
const tFrac32
f32A
Description
Array of five 32-bit elements for storing
coefficients of the piece-wise polynomial.
7.23 GFLIB_ATAN_T_F16
#include <GFLIB_Atan.h>
7.23.1 Description
Structure containing eight sub-structures with polynomial coefficients to cover all subintervals.
7.23.2 Compound Type Members
Table 7-24. GFLIB_ATAN_T_F16 members description
Type
Name
const
GFLIB_ATAN_SECTOR
GFLIB_ATAN_TAYLOR_COE
F_T_F16
Description
Structure containing eight sub-structures with
polynomial coefficients to cover all subintervals.
7.24 GFLIB_ATAN_T_F32
#include <GFLIB_Atan.h>
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GFLIB_ATAN_TAYLOR_COEF_T_F16
7.24.1 Description
Structure containing eight sub-structures with polynomial coefficients to cover all subintervals.
7.24.2 Compound Type Members
Table 7-25. GFLIB_ATAN_T_F32 members description
Type
Name
const
GFLIB_ATAN_SECTOR
GFLIB_ATAN_TAYLOR_COE
F_T_F32
Description
Structure containing eight sub-structures with
polynomial coefficients to cover all subintervals.
7.25 GFLIB_ATAN_TAYLOR_COEF_T_F16
#include <GFLIB_Atan.h>
7.25.1 Description
Array of polynomial approximation coefficients for one sub-interval.
7.25.2 Compound Type Members
Table 7-26. GFLIB_ATAN_TAYLOR_COEF_T_F16 members
description
Type
const tFrac16
Name
f16A
Description
Array of polynomial approximation coefficients
for one sub-interval.
7.26 GFLIB_ATAN_TAYLOR_COEF_T_F32
#include <GFLIB_Atan.h>
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7.26.1 Description
Array of minimax polynomial approximation coefficients for one sub-interval.
7.26.2 Compound Type Members
Table 7-27. GFLIB_ATAN_TAYLOR_COEF_T_F32 members
description
Type
const tFrac32
Name
f32A
Description
Array of minimax polynomial approximation
coefficients for one sub-interval.
7.27 GFLIB_ATANYXSHIFTED_T_F16
#include <GFLIB_AtanYXShifted.h>
7.27.1 Description
Structure containing the parameter for the AtanYXShifted function.
7.27.2 Compound Type Members
Table 7-28. GFLIB_ATANYXSHIFTED_T_F16 members description
Type
Name
Description
tFrac16
f16Ky
Multiplication coefficient for the y-signal.
tFrac16
f16Kx
Multiplication coefficient for the x-signal.
tS16
s16Ny
Scaling coefficient for the y-signal.
tS16
s16Nx
Scaling coefficient for the x-signal.
tFrac16
f16ThetaAdj
Adjusting angle.
7.28 GFLIB_ATANYXSHIFTED_T_F32
#include <GFLIB_AtanYXShifted.h>
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537
GFLIB_CONTROLLER_PI_P_T_F16
7.28.1 Description
Structure containing the parameter for the AtanYXShifted function.
7.28.2 Compound Type Members
Table 7-29. GFLIB_ATANYXSHIFTED_T_F32 members description
Type
Name
Description
tFrac32
f32Ky
Multiplication coefficient for the y-signal.
tFrac32
f32Kx
Multiplication coefficient for the x-signal.
tS32
s32Ny
Scaling coefficient for the y-signal.
tS32
s32Nx
Scaling coefficient for the x-signal.
tFrac32
f32ThetaAdj
Adjusting angle.
7.29 GFLIB_CONTROLLER_PI_P_T_F16
#include <GFLIB_ControllerPIp.h>
7.29.1 Description
Structure containing parameters and states of the parallel form PI controller.
7.29.2 Compound Type Members
Table 7-30. GFLIB_CONTROLLER_PI_P_T_F16 members
description
Type
Name
Description
tFrac16
f16PropGain
Proportional Gain, fractional format
normalized to fit into (-2 15, 2 15-1).
tFrac16
f16IntegGain
Integral Gain, fractional format normalized to
fit into (-2 15, 2 15-1).
tS16
s16PropGainShift
Proportional Gain Shift, integer format [-15,
15].
tS16
s16IntegGainShift
Integral Gain Shift, integer format [-15, 15].
tFrac32
f32IntegPartK_1
State variable integral part at step k-1.
tFrac16
f16InK_1
State variable input error at step k-1.
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Chapter 7 Compound Data Types
7.30 GFLIB_CONTROLLER_PI_P_T_F32
#include <GFLIB_ControllerPIp.h>
7.30.1 Description
Structure containing parameters and states of the parallel form PI controller.
7.30.2 Compound Type Members
Table 7-31. GFLIB_CONTROLLER_PI_P_T_F32 members
description
Type
Name
Description
tFrac32
f32PropGain
Proportional Gain, fractional format
normalized to fit into (-2 31, 2 31-1).
tFrac32
f32IntegGain
Integral Gain, fractional format normalized to
fit into (-2 31, 2 31-1).
tS16
s16PropGainShift
Proportional Gain Shift, integer format [-31,
31].
tS16
s16IntegGainShift
Integral Gain Shift, integer format [-31, 31].
tFrac32
f32IntegPartK_1
State variable integral part at step k-1.
tFrac32
f32InK_1
State variable input error at step k-1.
7.31 GFLIB_CONTROLLER_PI_R_T_F16
#include <GFLIB_ControllerPIr.h>
7.31.1 Description
Structure containing parameters and states of the recurrent form PI controller.
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539
GFLIB_CONTROLLER_PI_R_T_F32
7.31.2 Compound Type Members
Table 7-32. GFLIB_CONTROLLER_PI_R_T_F16 members
description
Type
Name
Description
tFrac16
f16CC1sc
CC1 coefficient, fractional format normalized
to fit into (-2 15, 2 15-1).
tFrac16
f16CC2sc
CC2 coefficient, fractional format normalized
to fit into (-2 15, 2 15-1).
tFrac32
f32Acc
Internal controller accumulator.
tFrac16
f16InErrK1
Controller input from the previous calculation
step.
tU16
u16NShift
Scaling factor for the controller coefficients,
integer format [0, 15].
7.32 GFLIB_CONTROLLER_PI_R_T_F32
#include <GFLIB_ControllerPIr.h>
7.32.1 Description
Structure containing parameters and states of the recurrent form PI controller.
7.32.2 Compound Type Members
Table 7-33. GFLIB_CONTROLLER_PI_R_T_F32 members
description
Type
Name
Description
tFrac32
f32CC1sc
CC1 coefficient, fractional format normalized
to fit into (-2 31, 2 31-1).
tFrac32
f32CC2sc
CC2 coefficient, fractional format normalized
to fit into (-2 31, 2 31-1).
tFrac32
f32Acc
Internal controller accumulator.
tFrac32
f32InErrK1
Controller input from the previous calculation
step.
tU16
u16NShift
Scaling factor for the controller coefficients,
integer format [0, 31].
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NXP Semiconductors
Chapter 7 Compound Data Types
7.33 GFLIB_CONTROLLER_PIAW_P_T_F16
#include <GFLIB_ControllerPIpAW.h>
7.33.1 Description
Structure containing parameters and states of the parallel form PI controller with antiwindup.
7.33.2 Compound Type Members
Table 7-34. GFLIB_CONTROLLER_PIAW_P_T_F16 members
description
Type
Name
Description
tFrac16
f16PropGain
Proportional Gain, fractional format
normalized to fit into (-2 15, 2 15-1).
tFrac16
f16IntegGain
Integral Gain, fractional format normalized to
fit into (-2 15, 2 15-1).
tS16
s16PropGainShift
Proportional Gain Shift, integer format [-15,
15].
tS16
s16IntegGainShift
Integral Gain Shift, integer format [-15, 15].
tFrac16
f16LowerLimit
Lower Limit of the controller, fractional format
normalized to fit into (-2 15, 2 15-1).
tFrac16
f16UpperLimit
Upper Limit of the controller, fractional format
normalized to fit into (-2 15, 2 15-1).
tFrac32
f32IntegPartK_1
State variable integral part at step k-1.
tFrac16
f16InK_1
State variable input error at step k-1.
tU16
u16LimitFlag
Limitation flag, if set to 1, the controller output
has reached either the UpperLimit or
LowerLimit.
7.34 GFLIB_CONTROLLER_PIAW_P_T_F32
#include <GFLIB_ControllerPIpAW.h>
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GFLIB_CONTROLLER_PIAW_R_T_F16
7.34.1 Description
Structure containing parameters and states of the parallel form PI controller with antiwindup.
7.34.2 Compound Type Members
Table 7-35. GFLIB_CONTROLLER_PIAW_P_T_F32 members
description
Type
Name
Description
tFrac32
f32PropGain
Proportional Gain, fractional format
normalized to fit into (-2 31, 2 31-1).
tFrac32
f32IntegGain
Integral Gain, fractional format normalized to
fit into (-2 31, 2 31-1).
tS16
s16PropGainShift
Proportional Gain Shift, integer format [-31,
31].
tS16
s16IntegGainShift
Integral Gain Shift, integer format [-31, 31].
tFrac32
f32LowerLimit
Lower Limit of the controller, fractional format
normalized to fit into (-2 31, 2 31-1).
tFrac32
f32UpperLimit
Upper Limit of the controller, fractional format
normalized to fit into (-2 31, 2 31-1).
tFrac32
f32IntegPartK_1
State variable integral part at step k-1.
tFrac32
f32InK_1
State variable input error at step k-1.
tU16
u16LimitFlag
Limitation flag, if set to 1, the controller output
has reached either the UpperLimit or
LowerLimit.
7.35 GFLIB_CONTROLLER_PIAW_R_T_F16
#include <GFLIB_ControllerPIrAW.h>
7.35.1 Description
Structure containing parameters and states of the recurrent form PI controller with antiwindup.
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Chapter 7 Compound Data Types
7.35.2 Compound Type Members
Table 7-36. GFLIB_CONTROLLER_PIAW_R_T_F16 members
description
Type
Name
Description
tFrac16
f16CC1sc
CC1 coefficient, fractional format normalized
to fit into (-2 15, 2 15-1).
tFrac16
f16CC2sc
CC2 coefficient, fractional format normalized
to fit into (-2 15, 2 15-1).
tFrac32
f32Acc
Internal controller accumulator.
tFrac16
f16InErrK1
Controller input from the previous calculation
step.
tFrac16
f16UpperLimit
Upper Limit of the controller, fractional format
normalized to fit into (-2 15, 2 15-1).
tFrac16
f16LowerLimit
Lower Limit of the controller, fractional format
normalized to fit into (-2 15, 2 15-1).
tU16
u16NShift
Scaling factor for the controller coefficients,
integer format [0, 15].
7.36 GFLIB_CONTROLLER_PIAW_R_T_F32
#include <GFLIB_ControllerPIrAW.h>
7.36.1 Description
Structure containing parameters and states of the recurrent form PI controller with antiwindup.
7.36.2 Compound Type Members
Table 7-37. GFLIB_CONTROLLER_PIAW_R_T_F32 members
description
Type
Name
Description
tFrac32
f32CC1sc
CC1 coefficient, fractional format normalized
to fit into (-2 31, 2 31-1).
tFrac32
f32CC2sc
CC2 coefficient, fractional format normalized
to fit into (-2 31, 2 31-1).
tFrac32
f32Acc
Internal controller accumulator.
Table continues on the next page...
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543
GFLIB_COS_T_F16
Table 7-37. GFLIB_CONTROLLER_PIAW_R_T_F32 members description
(continued)
Type
Name
Description
tFrac32
f32InErrK1
Controller input from the previous calculation
step.
tFrac32
f32UpperLimit
Upper Limit of the controller, fractional format
normalized to fit into (-2 31, 2 31-1).
tFrac32
f32LowerLimit
Lower Limit of the controller, fractional format
normalized to fit into (-2 31, 2 31-1).
tU16
u16NShift
Scaling factor for the controller coefficients,
integer format [0, 31].
7.37 GFLIB_COS_T_F16
#include <GFLIB_Cos.h>
7.37.1 Description
Array of four 16-bit elements for storing coefficients of the Taylor polynomial.
7.37.2 Compound Type Members
Table 7-38. GFLIB_COS_T_F16 members description
Type
tFrac16
Name
f16A
Description
Array of four 16-bit elements for storing
coefficients of the Taylor polynomial.
7.38 GFLIB_COS_T_F32
#include <GFLIB_Cos.h>
7.38.1 Description
Array of five 32-bit elements for storing coefficients of the Taylor polynomial.
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NXP Semiconductors
Chapter 7 Compound Data Types
7.38.2 Compound Type Members
Table 7-39. GFLIB_COS_T_F32 members description
Type
Name
tFrac32
f32A
Description
Array of five 32-bit elements for storing
coefficients of the Taylor polynomial.
7.39 GFLIB_HYST_T_F16
#include <GFLIB_Hyst.h>
7.39.1 Description
Structure containing parameters and states for the hysteresis function.
7.39.2 Compound Type Members
Table 7-40. GFLIB_HYST_T_F16 members description
Type
Name
Description
tFrac16
f16HystOn
Value determining the upper threshold.
tFrac16
f16HystOff
Value determining the lower threshold.
tFrac16
f16OutValOn
Value of the output when input is higher than
the upper threshold.
tFrac16
f16OutValOff
Value of the output when input is higher than
the upper threshold.
tFrac16
f16OutState
Actual state of the output.
7.40 GFLIB_HYST_T_F32
#include <GFLIB_Hyst.h>
7.40.1 Description
Structure containing parameters and states for the hysteresis function.
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NXP Semiconductors
545
GFLIB_INTEGRATOR_TR_T_F16
7.40.2 Compound Type Members
Table 7-41. GFLIB_HYST_T_F32 members description
Type
Name
Description
tFrac32
f32HystOn
Value determining the upper threshold.
tFrac32
f32HystOff
Value determining the lower threshold.
tFrac32
f32OutValOn
Value of the output when input is higher than
the upper threshold.
tFrac32
f32OutValOff
Value of the output when input is higher than
the upper threshold.
tFrac32
f32OutState
Actual state of the output.
7.41 GFLIB_INTEGRATOR_TR_T_F16
#include <GFLIB_IntegratorTR.h>
7.41.1 Description
Structure containing integrator parameters and coefficients.
7.41.2 Compound Type Members
Table 7-42. GFLIB_INTEGRATOR_TR_T_F16 members description
Type
Name
Description
tFrac32
f32State
Integrator state value.
tFrac16
f16InK1
Input value in step k-1.
tFrac16
f16C1
Integrator coefficient = (E MAX/T s)(U MAX*2)*(2
-u16NShift).
tU16
u16NShift
Scaling factor for the integrator coefficient
f16C1, integer format [0, 15].
7.42 GFLIB_INTEGRATOR_TR_T_F32
#include <GFLIB_IntegratorTR.h>
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NXP Semiconductors
Chapter 7 Compound Data Types
7.42.1 Description
Structure containing integrator parameters and coefficients.
7.42.2 Compound Type Members
Table 7-43. GFLIB_INTEGRATOR_TR_T_F32 members description
Type
Name
Description
tFrac32
f32State
Integrator state value.
tFrac32
f32InK1
Input value in step k-1.
tFrac32
f32C1
Integrator coefficient = (E MAX/T s)(U MAX*2)*(2
-u16NShift).
tU16
u16NShift
Scaling factor for the integrator coefficient
f32C1, integer format [0, 15].
7.43 GFLIB_LIMIT_T_F16
#include <GFLIB_Limit.h>
7.43.1 Description
Structure containing the limits.
7.43.2 Compound Type Members
Table 7-44. GFLIB_LIMIT_T_F16 members description
Type
Name
Description
tFrac16
f16LowerLimit
Value determining the lower limit threshold.
tFrac16
f16UpperLimit
Value determining the upper limit threshold.
7.44 GFLIB_LIMIT_T_F32
#include <GFLIB_Limit.h>
Automotive Math and Motor Control Library Set for NXP MPC560xB devices, Rev. 7
NXP Semiconductors
547
GFLIB_LOWERLIMIT_T_F16
7.44.1 Description
Structure containing the limits.
7.44.2 Compound Type Members
Table 7-45. GFLIB_LIMIT_T_F32 members description
Type
Name
Description
tFrac32
f32LowerLimit
Value determining the lower limit threshold.
tFrac32
f32UpperLimit
Value determining the upper limit threshold.
7.45 GFLIB_LOWERLIMIT_T_F16
#include <GFLIB_LowerLimit.h>
7.45.1 Description
Structure containing the lower limit.
7.45.2 Compound Type Members
Table 7-46. GFLIB_LOWERLIMIT_T_F16 members description
Type
tFrac16
Name
f16LowerLimit
Description
Value determining the lower limit threshold.
7.46 GFLIB_LOWERLIMIT_T_F32
#include <GFLIB_LowerLimit.h>
7.46.1 Description
Structure containing the lower limit.
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NXP Semiconductors
Chapter 7 Compound Data Types
7.46.2 Compound Type Members
Table 7-47. GFLIB_LOWERLIMIT_T_F32 members description
Type
tFrac32
Name
f32LowerLimit
Description
Value determining the lower limit threshold.
7.47 GFLIB_LUT1D_T_F16
#include <GFLIB_Lut1D.h>
7.47.1 Description
Structure containing 1D look-up table parameters.
7.47.2 Compound Type Members
Table 7-48. GFLIB_LUT1D_T_F16 members description
Type
Name
Description
tU16
u16ShamOffset
Shift amount for extracting the fractional offset
within an interpolated interval.
const tFrac16 *
pf16Table
Table holding ordinate values of interpolating
intervals.
7.48 GFLIB_LUT1D_T_F32
#include <GFLIB_Lut1D.h>
7.48.1 Description
Structure containing 1D look-up table parameters.
Automotive Math and Motor Control Library Set for NXP MPC560xB devices, Rev. 7
NXP Semiconductors
549
GFLIB_LUT2D_T_F16
7.48.2 Compound Type Members
Table 7-49. GFLIB_LUT1D_T_F32 members description
Type
Name
Description
tU32
u32ShamOffset
Shift amount for extracting the fractional offset
within an interpolated interval.
const tFrac32 *
pf32Table
Table holding ordinate values of interpolating
intervals.
7.49 GFLIB_LUT2D_T_F16
#include <GFLIB_Lut2D.h>
7.49.1 Description
Structure containing 2D look-up table parameters.
7.49.2 Compound Type Members
Table 7-50. GFLIB_LUT2D_T_F16 members description
Type
Name
Description
tU16
u16ShamOffset1
Shift amount for extracting the fractional offset
within an interpolated interval.
tU16
u16ShamOffset2
Shift amount for extracting the fractional offset
within an interpolated interval.
const tFrac16 *
pf16Table
Table holding ordinate values of interpolating
intervals.
7.50 GFLIB_LUT2D_T_F32
#include <GFLIB_Lut2D.h>
7.50.1 Description
Structure containing 2D look-up table parameters.
Automotive Math and Motor Control Library Set for NXP MPC560xB devices, Rev. 7
550
NXP Semiconductors
Chapter 7 Compound Data Types
7.50.2 Compound Type Members
Table 7-51. GFLIB_LUT2D_T_F32 members description
Type
Name
Description
tU32
u32ShamOffset1
Shift amount for extracting the fractional offset
within an interpolated interval.
tU32
u32ShamOffset2
Shift amount for extracting the fractional offset
within an interpolated interval.
const tFrac32 *
pf32Table
Table holding ordinate values of interpolating
intervals.
7.51 GFLIB_RAMP_T_F16
#include <GFLIB_Ramp.h>
7.51.1 Description
Structure containing increment/decrement coefficients and state value for the ramp
function implemented in GFLIB_Ramp.
7.51.2 Compound Type Members
Table 7-52. GFLIB_RAMP_T_F16 members description
Type
Name
Description
tFrac16
f16State
Ramp state value.
tFrac16
f16RampUp
Ramp up increment coefficient.
tFrac16
f16RampDown
Ramp down increment (decrement)
coefficient.
7.52 GFLIB_RAMP_T_F32
#include <GFLIB_Ramp.h>
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NXP Semiconductors
551
GFLIB_SIN_T_F16
7.52.1 Description
Structure containing increment/decrement coefficients and state value for the ramp
function implemented in GFLIB_Ramp.
7.52.2 Compound Type Members
Table 7-53. GFLIB_RAMP_T_F32 members description
Type
Name
Description
tFrac32
f32State
Ramp state value.
tFrac32
f32RampUp
Ramp up increment coefficient.
tFrac32
f32RampDown
Ramp down increment (decrement)
coefficient.
7.53 GFLIB_SIN_T_F16
#include <GFLIB_Sin.h>
7.53.1 Description
Array of four 16-bit elements for storing coefficients of the Taylor polynomial.
7.53.2 Compound Type Members
Table 7-54. GFLIB_SIN_T_F16 members description
Type
tFrac16
Name
f16A
Description
Array of four 16-bit elements for storing
coefficients of the Taylor polynomial.
7.54 GFLIB_SIN_T_F32
#include <GFLIB_Sin.h>
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NXP Semiconductors
Chapter 7 Compound Data Types
7.54.1 Description
Array of five 32-bit elements for storing coefficients of the Taylor polynomial.
7.54.2 Compound Type Members
Table 7-55. GFLIB_SIN_T_F32 members description
Type
tFrac32
Name
f32A
Description
Array of five 32-bit elements for storing
coefficients of the Taylor polynomial.
7.55 GFLIB_SINCOS_T_F16
#include <GFLIB_SinCos.h>
7.55.1 Description
Array of four 16-bit elements for storing coefficients of the Taylor polynomial.
7.55.2 Compound Type Members
Table 7-56. GFLIB_SINCOS_T_F16 members description
Type
tFrac16
Name
f16A
Description
Array of four 16-bit elements for storing
coefficients of the Taylor polynomial.
7.56 GFLIB_SINCOS_T_F32
#include <GFLIB_SinCos.h>
7.56.1 Description
Array of five 32-bit elements for storing coefficients of the Taylor polynomial.
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NXP Semiconductors
553
GFLIB_TAN_T_F16
7.56.2 Compound Type Members
Table 7-57. GFLIB_SINCOS_T_F32 members description
Type
Name
tFrac32
f32A
Description
Array of five 32-bit elements for storing
coefficients of the Taylor polynomial.
7.57 GFLIB_TAN_T_F16
#include <GFLIB_Tan.h>
7.57.1 Description
Output of tan(PI * f16In) for interval [0, PI/4) of the input angles is divided into eight
sub-sectors. Polynomial approximation is done using a 4th order polynomial, for each
sub-sector respectively. Eight arrays, each including four polynomial coefficients for
each sub-interval, are stored in this (GFLIB_TAN_T_F16) structure.
7.57.2 Compound Type Members
Table 7-58. GFLIB_TAN_T_F16 members description
Type
Name
GFLIB_TAN_TAYLOR_COEF GFLIB_TAN_SECTOR
_T_F16
Description
Output of tan(PI * f16In) for interval [0, PI/4) of
the input angles is divided into eight subsectors. Polynomial approximation is done
using a 4th order polynomial, for each subsector respectively. Eight arrays, each
including four polynomial coefficients for each
sub-interval, are stored in this
(GFLIB_TAN_T_F16) structure.
7.58 GFLIB_TAN_T_F32
#include <GFLIB_Tan.h>
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Chapter 7 Compound Data Types
7.58.1 Description
Output of tan(PI * f32In) for interval [0, PI/4) of the input angles is divided into eight
sub-sectors. Polynomial approximation is done using a 4th order polynomial, for each
sub-sector respectively. Eight arrays, each including four polynomial coefficients for
each sub-interval, are stored in this (GFLIB_TAN_T_F32) structure.
7.58.2 Compound Type Members
Table 7-59. GFLIB_TAN_T_F32 members description
Type
Name
GFLIB_TAN_TAYLOR_COEF GFLIB_TAN_SECTOR
_T_F32
Description
Output of tan(PI * f32In) for interval [0, PI/4) of
the input angles is divided into eight subsectors. Polynomial approximation is done
using a 4th order polynomial, for each subsector respectively. Eight arrays, each
including four polynomial coefficients for each
sub-interval, are stored in this
(GFLIB_TAN_T_F32) structure.
7.59 GFLIB_TAN_TAYLOR_COEF_T_F16
#include <GFLIB_Tan.h>
7.59.1 Description
Structure containing four polynomial coefficients for one sub-interval.
7.59.2 Compound Type Members
Table 7-60. GFLIB_TAN_TAYLOR_COEF_T_F16 members description
Type
const tFrac16
Name
f16A
Description
Structure containing four polynomial
coefficients for one sub-interval.
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NXP Semiconductors
555
GFLIB_UPPERLIMIT_T_F16
7.60 GFLIB_TAN_TAYLOR_COEF_T_F32
#include <GFLIB_Tan.h>
7.60.1 Description
Structure containing four polynomial coefficients for one sub-interval.
7.60.2 Compound Type Members
Table 7-61. GFLIB_TAN_TAYLOR_COEF_T_F32 members description
Type
const tFrac32
Name
f32A
Description
Structure containing four polynomial
coefficients for one sub-interval.
7.61 GFLIB_UPPERLIMIT_T_F16
#include <GFLIB_UpperLimit.h>
7.61.1 Description
Structure containing the upper limit.
7.61.2 Compound Type Members
Table 7-62. GFLIB_UPPERLIMIT_T_F16 members description
Type
tFrac16
Name
f16UpperLimit
Description
Value determining the upper limit threshold.
7.62 GFLIB_UPPERLIMIT_T_F32
#include <GFLIB_UpperLimit.h>
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7.62.1 Description
Structure containing the upper limit.
7.62.2 Compound Type Members
Table 7-63. GFLIB_UPPERLIMIT_T_F32 members description
Type
Name
tFrac32
f32UpperLimit
Description
Value determining the upper limit threshold.
7.63 GFLIB_VECTORLIMIT_T_F16
#include <GFLIB_VectorLimit.h>
7.63.1 Description
Structure containing the limit.
7.63.2 Compound Type Members
Table 7-64. GFLIB_VECTORLIMIT_T_F16 members description
Type
tFrac16
Name
f16Limit
Description
The maximum magnitude of the input vector.
The defined magnitude must be positive and
equal to or greater than F16_MAX value.
7.64 GFLIB_VECTORLIMIT_T_F32
#include <GFLIB_VectorLimit.h>
7.64.1 Description
Structure containing the limit.
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GMCLIB_DECOUPLINGPMSM_T_F16
7.64.2 Compound Type Members
Table 7-65. GFLIB_VECTORLIMIT_T_F32 members description
Type
tFrac32
Name
f32Limit
Description
The maximum magnitude of the input vector.
The defined magnitude must be positive and
equal to or greater than F32_MAX value.
7.65 GMCLIB_DECOUPLINGPMSM_T_F16
#include <GMCLIB_DecouplingPMSM.h>
7.65.1 Description
Structure containing coefficients for calculation of the decoupling.
7.65.2 Compound Type Members
Table 7-66. GMCLIB_DECOUPLINGPMSM_T_F16 members description
Type
Name
Description
tFrac16
f16Kd
Coefficient k df.
tS16
s16KdShift
Scaling coefficient k d_shift.
tFrac16
f16Kq
Coefficient k qf.
tS16
s16KqShift
Scaling coefficient k q_shift.
7.66 GMCLIB_DECOUPLINGPMSM_T_F32
#include <GMCLIB_DecouplingPMSM.h>
7.66.1 Description
Structure containing coefficients for calculation of the decoupling.
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7.66.2 Compound Type Members
Table 7-67. GMCLIB_DECOUPLINGPMSM_T_F32 members description
Type
Name
Description
tFrac32
f32Kd
Coefficient k df.
tS16
s16KdShift
Scaling coefficient k d_shift.
tFrac32
f32Kq
Coefficient k qf.
tS16
s16KqShift
Scaling coefficient k q_shift.
7.67 GMCLIB_ELIMDCBUSRIP_T_F16
#include <GMCLIB_ElimDcBusRip.h>
7.67.1 Description
Structure containing the PWM modulation index and the measured value of the DC bus
voltage.
7.67.2 Compound Type Members
Table 7-68. GMCLIB_ELIMDCBUSRIP_T_F16 members
description
Type
Name
Description
tFrac16
f16ModIndex
Inverse Modulation Index.
tFrac16
f16ArgDcBusMsr
Measured DC bus voltage.
7.68 GMCLIB_ELIMDCBUSRIP_T_F32
#include <GMCLIB_ElimDcBusRip.h>
7.68.1 Description
Structure containing the PWM modulation index and the measured value of the DC bus
voltage.
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7.68.2 Compound Type Members
Table 7-69. GMCLIB_ELIMDCBUSRIP_T_F32 members
description
Type
Name
Description
tFrac32
f32ModIndex
Inverse Modulation Index.
tFrac32
f32ArgDcBusMsr
Measured DC bus voltage.
7.69 SWLIBS_2Syst_F16
#include <SWLIBS_Typedefs.h>
7.69.1 Description
Array of two standard 16-bit fractional arguments.
7.69.2 Compound Type Members
Table 7-70. SWLIBS_2Syst_F16 members description
Type
Name
Description
tFrac16
f16Arg1
First argument
tFrac16
f16Arg2
Second argument
7.70 SWLIBS_2Syst_F32
#include <SWLIBS_Typedefs.h>
7.70.1 Description
Array of two standard 32-bit fractional arguments.
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7.70.2 Compound Type Members
Table 7-71. SWLIBS_2Syst_F32 members description
Type
Name
Description
tFrac32
f32Arg1
First argument
tFrac32
f32Arg2
Second argument
7.71 SWLIBS_3Syst_F16
#include <SWLIBS_Typedefs.h>
7.71.1 Description
Array of three standard 16-bit fractional arguments.
7.71.2 Compound Type Members
Table 7-72. SWLIBS_3Syst_F16 members description
Type
Name
Description
tFrac16
f16Arg1
First argument
tFrac16
f16Arg2
Second argument
tFrac16
f16Arg3
Third argument
7.72 SWLIBS_3Syst_F32
#include <SWLIBS_Typedefs.h>
7.72.1 Description
Array of three standard 32-bit fractional arguments.
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7.72.2 Compound Type Members
Table 7-73. SWLIBS_3Syst_F32 members description
Type
Name
Description
tFrac32
f32Arg1
First argument
tFrac32
f32Arg2
Second argument
tFrac32
f32Arg3
Third argument
7.73 SWLIBS_VERSION_T
#include <SWLIBS_Version.h>
7.73.1 Description
Motor Control Library Set identification structure.
7.73.2 Compound Type Members
Table 7-74. SWLIBS_VERSION_T members
description
Type
Name
Description
unsigned char
mcId
MCLIB identification code
unsigned char
mcVersion
MCLIB version code
unsigned char
mcImpl
MCLIB supported implementation code
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8.1 Macro Definitions
8.1.1 Macro Definitions Overview
#define F16
#define F16TOINT16
#define F16TOINT32
#define F16TOINT64
#define F16_1_DIVBY_SQRT3
#define F16_SQRT2_DIVBY_2
#define F16_SQRT3_DIVBY_2
#define F32
#define F32TOINT16
#define F32TOINT32
#define F32TOINT64
#define F32_1_DIVBY_SQRT3
#define F32_SQRT2_DIVBY_2
#define F32_SQRT3_DIVBY_2
#define F64TOINT16
#define F64TOINT32
#define F64TOINT64
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#define FALSE
#define FLT
#define FRAC16
#define FRAC16_0_25
#define FRAC16_0_5
#define FRAC32
#define FRAC32_0_25
#define FRAC32_0_5
#define FRACT_MAX
#define FRACT_MIN
#define GDFLIB_FILTER_IIR1_DEFAULT_F16
#define GDFLIB_FILTER_IIR1_DEFAULT_F32
#define GDFLIB_FILTER_IIR2_DEFAULT_F16
#define GDFLIB_FILTER_IIR2_DEFAULT_F32
#define GDFLIB_FILTER_MA_DEFAULT_F16
#define GDFLIB_FILTER_MA_DEFAULT_F32
#define GDFLIB_FilterFIR
#define GDFLIB_FilterFIRInit
#define GDFLIB_FilterIIR1
#define GDFLIB_FilterIIR1Init
#define GDFLIB_FilterIIR2
#define GDFLIB_FilterIIR2Init
#define GDFLIB_FilterMA
#define GDFLIB_FilterMAInit
#define GFLIB_ACOS_DEFAULT_F16
#define GFLIB_ACOS_DEFAULT_F32
#define GFLIB_ASIN_DEFAULT_F16
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#define GFLIB_ASIN_DEFAULT_F32
#define GFLIB_ATAN_DEFAULT_F16
#define GFLIB_ATAN_DEFAULT_F32
#define GFLIB_Acos
#define GFLIB_Asin
#define GFLIB_Atan
#define GFLIB_AtanYX
#define GFLIB_AtanYXShifted
#define GFLIB_CONTROLLER_PIAW_P_DEFAULT_F16
#define GFLIB_CONTROLLER_PIAW_P_DEFAULT_F32
#define GFLIB_CONTROLLER_PIAW_R_DEFAULT_F16
#define GFLIB_CONTROLLER_PIAW_R_DEFAULT_F32
#define GFLIB_CONTROLLER_PI_P_DEFAULT_F16
#define GFLIB_CONTROLLER_PI_P_DEFAULT_F32
#define GFLIB_CONTROLLER_PI_R_DEFAULT_F16
#define GFLIB_CONTROLLER_PI_R_DEFAULT_F32
#define GFLIB_COS_DEFAULT_F16
#define GFLIB_COS_DEFAULT_F32
#define GFLIB_ControllerPIp
#define GFLIB_ControllerPIpAW
#define GFLIB_ControllerPIr
#define GFLIB_ControllerPIrAW
#define GFLIB_Cos
#define GFLIB_HYST_DEFAULT_F16
#define GFLIB_HYST_DEFAULT_F32
#define GFLIB_Hyst
#define GFLIB_INTEGRATOR_TR_DEFAULT_F16
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#define GFLIB_INTEGRATOR_TR_DEFAULT_F32
#define GFLIB_IntegratorTR
#define GFLIB_LIMIT_DEFAULT_F16
#define GFLIB_LIMIT_DEFAULT_F32
#define GFLIB_LOWERLIMIT_DEFAULT_F16
#define GFLIB_LOWERLIMIT_DEFAULT_F32
#define GFLIB_LUT1D_DEFAULT_F16
#define GFLIB_LUT1D_DEFAULT_F32
#define GFLIB_LUT2D_DEFAULT_F16
#define GFLIB_LUT2D_DEFAULT_F32
#define GFLIB_Limit
#define GFLIB_LowerLimit
#define GFLIB_Lut1D
#define GFLIB_Lut2D
#define GFLIB_RAMP_DEFAULT_F16
#define GFLIB_RAMP_DEFAULT_F32
#define GFLIB_Ramp
#define GFLIB_SINCOS_DEFAULT_F16
#define GFLIB_SINCOS_DEFAULT_F32
#define GFLIB_SIN_DEFAULT_F16
#define GFLIB_SIN_DEFAULT_F32
#define GFLIB_Sign
#define GFLIB_Sin
#define GFLIB_SinCos
#define GFLIB_Sqrt
#define GFLIB_TAN_DEFAULT_F16
#define GFLIB_TAN_DEFAULT_F32
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#define GFLIB_Tan
#define GFLIB_UPPERLIMIT_DEFAULT_F16
#define GFLIB_UPPERLIMIT_DEFAULT_F32
#define GFLIB_UpperLimit
#define GFLIB_VECTORLIMIT_DEFAULT_F16
#define GFLIB_VECTORLIMIT_DEFAULT_F32
#define GFLIB_VectorLimit
#define GMCLIB_Clark
#define GMCLIB_ClarkInv
#define GMCLIB_DECOUPLINGPMSM_DEFAULT_F16
#define GMCLIB_DECOUPLINGPMSM_DEFAULT_F32
#define GMCLIB_DecouplingPMSM
#define GMCLIB_ELIMDCBUSRIP_DEFAULT_F16
#define GMCLIB_ELIMDCBUSRIP_DEFAULT_F32
#define GMCLIB_ELIMDCBUSRIP_FLT_DNMAX
#define GMCLIB_ElimDcBusRip
#define GMCLIB_Park
#define GMCLIB_ParkInv
#define GMCLIB_SvmStd
#define INT16TOF16
#define INT16TOF32
#define INT16TOINT32
#define INT16_MAX
#define INT16_MIN
#define INT32TOF16
#define INT32TOF32
#define INT32TOINT16
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#define INT32TOINT64
#define INT32_MAX
#define INT32_MIN
#define INT64TOF16
#define INT64TOF32
#define INT64TOINT32
#define MLIB_Abs
#define MLIB_AbsSat
#define MLIB_Add
#define MLIB_AddSat
#define MLIB_Convert
#define MLIB_ConvertPU
#define MLIB_Div
#define MLIB_DivSat
#define MLIB_Mac
#define MLIB_MacSat
#define MLIB_Mnac
#define MLIB_Msu
#define MLIB_Mul
#define MLIB_MulSat
#define MLIB_Neg
#define MLIB_NegSat
#define MLIB_Norm
#define MLIB_Round
#define MLIB_ShBi
#define MLIB_ShBiSat
#define MLIB_ShL
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#define MLIB_ShLSat
#define MLIB_ShR
#define MLIB_Sub
#define MLIB_SubSat
#define MLIB_VMac
#define NULL
#define SFRACT_MAX
#define SFRACT_MIN
#define SWLIBS_2Syst
#define SWLIBS_2Syst
#define SWLIBS_2Syst
#define SWLIBS_3Syst
#define SWLIBS_3Syst
#define SWLIBS_3Syst
#define SWLIBS_DEFAULT_IMPLEMENTATION
#define SWLIBS_DEFAULT_IMPLEMENTATION_F16
#define SWLIBS_DEFAULT_IMPLEMENTATION_F32
#define SWLIBS_DEFAULT_IMPLEMENTATION_FLT
#define SWLIBS_ID
#define SWLIBS_MCID_SIZE
#define SWLIBS_MCIMPLEMENTATION_SIZE
#define SWLIBS_MCVERSION_SIZE
#define SWLIBS_STD_OFF
#define SWLIBS_STD_ON
#define SWLIBS_SUPPORTED_IMPLEMENTATION
#define SWLIBS_SUPPORT_F16
#define SWLIBS_SUPPORT_F32
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#define SWLIBS_SUPPORT_FLT
#define SWLIBS_VERSION
#define SWLIBS_VERSION_DEFAULT
#define TRUE
#define UINT16_MAX
#define UINT32_MAX
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Macro References
This section describes in details the macro definitions available in Automotive Math and
Motor Control Library Set for NXP MPC560xB devices.
9.1 Define GDFLIB_FilterFIRInit
#include <GDFLIB_FilterFIR.h>
9.1.1 Macro Definition
#define GDFLIB_FilterFIRInit macro_dispatcher(GDFLIB_FilterFIRInit, __VA_ARGS__)(__VA_ARGS__)
9.1.2 Description
This function initializes the FIR filter buffers.
9.2 Define GDFLIB_FilterFIR
#include <GDFLIB_FilterFIR.h>
9.2.1 Macro Definition
#define GDFLIB_FilterFIR macro_dispatcher(GDFLIB_FilterFIR, __VA_ARGS__)(__VA_ARGS__)
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Define GDFLIB_FilterIIR1Init
9.2.2 Description
The function performs a single iteration of an FIR filter.
9.3 Define GDFLIB_FilterIIR1Init
#include <GDFLIB_FilterIIR1.h>
9.3.1 Macro Definition
#define GDFLIB_FilterIIR1Init macro_dispatcher(GDFLIB_FilterIIR1Init, __VA_ARGS__)
(__VA_ARGS__)
9.3.2 Description
This function initializes the first order IIR filter buffers.
9.4 Define GDFLIB_FilterIIR1
#include <GDFLIB_FilterIIR1.h>
9.4.1 Macro Definition
#define GDFLIB_FilterIIR1 macro_dispatcher(GDFLIB_FilterIIR1, __VA_ARGS__)(__VA_ARGS__)
9.4.2 Description
This function implements the first order IIR filter.
9.5 Define GDFLIB_FILTER_IIR1_DEFAULT_F32
#include <GDFLIB_FilterIIR1.h>
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9.5.1 Macro Definition
#define GDFLIB_FILTER_IIR1_DEFAULT_F32 {{(tFrac32)0,(tFrac32)0,(tFrac32)0},{(tFrac32)0},
{(tFrac32)0}}
9.5.2 Description
Default value for GDFLIB_FILTER_IIR1_T_F32.
9.6 Define GDFLIB_FILTER_IIR1_DEFAULT_F16
#include <GDFLIB_FilterIIR1.h>
9.6.1 Macro Definition
#define GDFLIB_FILTER_IIR1_DEFAULT_F16 {{(tFrac16)0,(tFrac16)0,(tFrac16)0},{(tFrac16)0},
{(tFrac16)0}}
9.6.2 Description
Default value for GDFLIB_FILTER_IIR1_T_F16.
9.7 Define GDFLIB_FilterIIR2Init
#include <GDFLIB_FilterIIR2.h>
9.7.1 Macro Definition
#define GDFLIB_FilterIIR2Init macro_dispatcher(GDFLIB_FilterIIR2Init, __VA_ARGS__)
(__VA_ARGS__)
9.7.2 Description
This function initializes the second order IIR filter buffers.
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Define GDFLIB_FilterIIR2
9.8 Define GDFLIB_FilterIIR2
#include <GDFLIB_FilterIIR2.h>
9.8.1 Macro Definition
#define GDFLIB_FilterIIR2 macro_dispatcher(GDFLIB_FilterIIR2, __VA_ARGS__)(__VA_ARGS__)
9.8.2 Description
This function implements the second order IIR filter.
9.9 Define GDFLIB_FILTER_IIR2_DEFAULT_F32
#include <GDFLIB_FilterIIR2.h>
9.9.1 Macro Definition
#define GDFLIB_FILTER_IIR2_DEFAULT_F32 {{(tFrac32)0,(tFrac32)0,(tFrac32)0,(tFrac32)0,
(tFrac32)0},{(tFrac32)0,(tFrac32)0},{(tFrac32)0,(tFrac32)0}}
9.9.2 Description
Default value for GDFLIB_FILTER_IIR2_T_F32.
9.10 Define GDFLIB_FILTER_IIR2_DEFAULT_F16
#include <GDFLIB_FilterIIR2.h>
9.10.1 Macro Definition
#define GDFLIB_FILTER_IIR2_DEFAULT_F16 {{(tFrac16)0,(tFrac16)0,(tFrac16)0,(tFrac16)0,
(tFrac16)0},{(tFrac16)0,(tFrac16)0},{(tFrac16)0,(tFrac16)0}}
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9.10.2 Description
Default value for GDFLIB_FILTER_IIR2_T_F16.
9.11 Define GDFLIB_FilterMAInit
#include <GDFLIB_FilterMA.h>
9.11.1 Macro Definition
#define GDFLIB_FilterMAInit macro_dispatcher(GDFLIB_FilterMAInit, __VA_ARGS__)(__VA_ARGS__)
9.11.2 Description
This function clears the internal filter accumulator.
9.12 Define GDFLIB_FilterMA
#include <GDFLIB_FilterMA.h>
9.12.1 Macro Definition
#define GDFLIB_FilterMA macro_dispatcher(GDFLIB_FilterMA, __VA_ARGS__)(__VA_ARGS__)
9.12.2 Description
This function implements a moving average recursive filter.
9.13 Define GDFLIB_FILTER_MA_DEFAULT_F32
#include <GDFLIB_FilterMA.h>
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Define GDFLIB_FILTER_MA_DEFAULT_F16
9.13.1 Macro Definition
#define GDFLIB_FILTER_MA_DEFAULT_F32 {0,0}
9.13.2 Description
Default value for GDFLIB_FILTER_MA_T_F32.
9.14 Define GDFLIB_FILTER_MA_DEFAULT_F16
#include <GDFLIB_FilterMA.h>
9.14.1 Macro Definition
#define GDFLIB_FILTER_MA_DEFAULT_F16 {0,0}
9.14.2 Description
Default value for GDFLIB_FILTER_MA_T_F16.
9.15 Define GFLIB_Acos
#include <GFLIB_Acos.h>
9.15.1 Macro Definition
#define GFLIB_Acos macro_dispatcher(GFLIB_Acos, __VA_ARGS__)(__VA_ARGS__)
9.15.2 Description
This function implements polynomial approximation of arccosine function.
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9.16 Define GFLIB_ACOS_DEFAULT_F32
#include <GFLIB_Acos.h>
9.16.1 Macro Definition
#define GFLIB_ACOS_DEFAULT_F32 &f32gflibAcosCoef
9.16.2 Description
Default approximation coefficients for GFLIB_Acos_F32 function.
9.17 Define GFLIB_ACOS_DEFAULT_F16
#include <GFLIB_Acos.h>
9.17.1 Macro Definition
#define GFLIB_ACOS_DEFAULT_F16 &f16gflibAcosCoef
9.17.2 Description
Default approximation coefficients for GFLIB_Acos_F16 function.
9.18 Define GFLIB_Asin
#include <GFLIB_Asin.h>
9.18.1 Macro Definition
#define GFLIB_Asin macro_dispatcher(GFLIB_Asin, __VA_ARGS__)(__VA_ARGS__)
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Define GFLIB_ASIN_DEFAULT_F32
9.18.2 Description
This function implements polynomial approximation of arcsine function.
9.19 Define GFLIB_ASIN_DEFAULT_F32
#include <GFLIB_Asin.h>
9.19.1 Macro Definition
#define GFLIB_ASIN_DEFAULT_F32 &f32gflibAsinCoef
9.19.2 Description
Default approximation coefficients for GFLIB_Asin_F32 function.
9.20 Define GFLIB_ASIN_DEFAULT_F16
#include <GFLIB_Asin.h>
9.20.1 Macro Definition
#define GFLIB_ASIN_DEFAULT_F16 &f16gflibAsinCoef
9.20.2 Description
Default approximation coefficients for GFLIB_Asin_F16 function.
9.21 Define GFLIB_Atan
#include <GFLIB_Atan.h>
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9.21.1 Macro Definition
#define GFLIB_Atan macro_dispatcher(GFLIB_Atan, __VA_ARGS__)(__VA_ARGS__)
9.21.2 Description
This function implements polynomial approximation of arctangent function.
9.22 Define GFLIB_ATAN_DEFAULT_F32
#include <GFLIB_Atan.h>
9.22.1 Macro Definition
#define GFLIB_ATAN_DEFAULT_F32 &f32gflibAtanCoef
9.22.2 Description
Default approximation coefficients for GFLIB_Atan_F32 function.
9.23 Define GFLIB_ATAN_DEFAULT_F16
#include <GFLIB_Atan.h>
9.23.1 Macro Definition
#define GFLIB_ATAN_DEFAULT_F16 &f16gflibAtanCoef
9.23.2 Description
Default approximation coefficients for GFLIB_Atan_F16 function.
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Define GFLIB_AtanYXShifted
9.24 Define GFLIB_AtanYX
#include <GFLIB_AtanYX.h>
9.24.1 Macro Definition
#define GFLIB_AtanYX macro_dispatcher(GFLIB_AtanYX, __VA_ARGS__)(__VA_ARGS__)
9.24.2 Description
This function calculate the angle between the positive x-axis and the direction of a vector
given by the (x, y) coordinates.
9.25 Define GFLIB_AtanYXShifted
#include <GFLIB_AtanYXShifted.h>
9.25.1 Macro Definition
#define GFLIB_AtanYXShifted macro_dispatcher(GFLIB_AtanYXShifted, __VA_ARGS__)(__VA_ARGS__)
9.25.2 Description
This function calculates the angle of two sine waves shifted in phase to each other.
9.26 Define GFLIB_ControllerPIp
#include <GFLIB_ControllerPIp.h>
9.26.1 Macro Definition
#define GFLIB_ControllerPIp macro_dispatcher(GFLIB_ControllerPIp, __VA_ARGS__)(__VA_ARGS__)
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9.26.2 Description
This function calculates a parallel form of the Proportional- Integral controller, without
integral anti-windup.
9.27 Define GFLIB_CONTROLLER_PI_P_DEFAULT_F32
#include <GFLIB_ControllerPIp.h>
9.27.1 Macro Definition
#define GFLIB_CONTROLLER_PI_P_DEFAULT_F32 {(tFrac32)0,(tFrac32)0,(tS16)0,(tS16)0,(tFrac32)0,
(tFrac32)0}
9.27.2 Description
Default value for GFLIB_CONTROLLER_PI_P_T_F32.
9.28 Define GFLIB_CONTROLLER_PI_P_DEFAULT_F16
#include <GFLIB_ControllerPIp.h>
9.28.1 Macro Definition
#define GFLIB_CONTROLLER_PI_P_DEFAULT_F16 {(tFrac16)0,(tFrac16)0,(tS16)0,(tS16)0,(tFrac32)0,
(tFrac16)0}
9.28.2 Description
Default value for GFLIB_CONTROLLER_PI_P_T_F16.
9.29 Define GFLIB_ControllerPIpAW
#include <GFLIB_ControllerPIpAW.h>
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Define GFLIB_CONTROLLER_PIAW_P_DEFAULT_F32
9.29.1 Macro Definition
#define GFLIB_ControllerPIpAW macro_dispatcher(GFLIB_ControllerPIpAW, __VA_ARGS__)
(__VA_ARGS__)
9.29.2 Description
This function calculates a standard recurrent form of the Proportional- Integral controller,
with integral anti-windup.
9.30 Define GFLIB_CONTROLLER_PIAW_P_DEFAULT_F32
#include <GFLIB_ControllerPIpAW.h>
9.30.1 Macro Definition
#define GFLIB_CONTROLLER_PIAW_P_DEFAULT_F32 {(tFrac32)0,(tFrac32)0,(tS32)0,
(tS32)0,INT32_MIN,INT32_MAX,(tFrac32)0,(tFrac32)0,(tU16)0}
9.30.2 Description
Default value for GFLIB_CONTROLLER_PIAW_P_T_F32.
9.31 Define GFLIB_CONTROLLER_PIAW_P_DEFAULT_F16
#include <GFLIB_ControllerPIpAW.h>
9.31.1 Macro Definition
#define GFLIB_CONTROLLER_PIAW_P_DEFAULT_F16 {(tFrac16)0,(tFrac16)0,(tS16)0,
(tS16)0,INT16_MIN,INT16_MAX,(tFrac32)0,(tFrac16)0,(tU16)0}
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9.31.2 Description
Default value for GFLIB_CONTROLLER_PIAW_P_T_F16.
9.32 Define GFLIB_ControllerPIr
#include <GFLIB_ControllerPIr.h>
9.32.1 Macro Definition
#define GFLIB_ControllerPIr macro_dispatcher(GFLIB_ControllerPIr, __VA_ARGS__)(__VA_ARGS__)
9.32.2 Description
This function calculates a standard recurrent form of the Proportional- Integral controller,
without integral anti-windup.
9.33 Define GFLIB_CONTROLLER_PI_R_DEFAULT_F32
#include <GFLIB_ControllerPIr.h>
9.33.1 Macro Definition
#define GFLIB_CONTROLLER_PI_R_DEFAULT_F32 {(tFrac32)0,(tFrac32)0,(tFrac32)0,(tFrac32)0,
(tU16)0}
9.33.2 Description
Default value for GFLIB_CONTROLLER_PI_R_T_F32.
9.34 Define GFLIB_CONTROLLER_PI_R_DEFAULT_F16
#include <GFLIB_ControllerPIr.h>
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Define GFLIB_ControllerPIrAW
9.34.1 Macro Definition
#define GFLIB_CONTROLLER_PI_R_DEFAULT_F16 {(tFrac16)0,(tFrac16)0,(tFrac32)0,(tFrac16)0,
(tU16)0}
9.34.2 Description
Default value for GFLIB_CONTROLLER_PI_R_T_F16.
9.35 Define GFLIB_ControllerPIrAW
#include <GFLIB_ControllerPIrAW.h>
9.35.1 Macro Definition
#define GFLIB_ControllerPIrAW macro_dispatcher(GFLIB_ControllerPIrAW, __VA_ARGS__)
(__VA_ARGS__)
9.35.2 Description
This function calculates a standard recurrent form of the Proportional-Integral controller,
with integral anti-windup.
9.36 Define GFLIB_CONTROLLER_PIAW_R_DEFAULT_F32
#include <GFLIB_ControllerPIrAW.h>
9.36.1 Macro Definition
#define GFLIB_CONTROLLER_PIAW_R_DEFAULT_F32 {(tFrac32)0,(tFrac32)0,(tFrac32)0,
(tFrac32)0,INT32_MIN,INT32_MAX,(tU16)0}
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9.36.2 Description
Default value for GFLIB_CONTROLLER_PIAW_R_T_F32.
9.37 Define GFLIB_CONTROLLER_PIAW_R_DEFAULT_F16
#include <GFLIB_ControllerPIrAW.h>
9.37.1 Macro Definition
#define GFLIB_CONTROLLER_PIAW_R_DEFAULT_F16 {(tFrac16)0,(tFrac16)0,(tFrac32)0,
(tFrac16)0,INT16_MIN,INT16_MAX,(tU16)0}
9.37.2 Description
Default value for GFLIB_CONTROLLER_PIAW_R_T_F16.
9.38 Define GFLIB_Cos
#include <GFLIB_Cos.h>
9.38.1 Macro Definition
#define GFLIB_Cos macro_dispatcher(GFLIB_Cos, __VA_ARGS__)(__VA_ARGS__)
9.38.2 Description
This function implements polynomial approximation of cosine function.
9.39 Define GFLIB_COS_DEFAULT_F32
#include <GFLIB_Cos.h>
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Define GFLIB_COS_DEFAULT_F16
9.39.1 Macro Definition
#define GFLIB_COS_DEFAULT_F32 &f32gflibCosCoef
9.39.2 Description
Default approximation coefficients for GFLIB_Cos_F32 function.
9.40 Define GFLIB_COS_DEFAULT_F16
#include <GFLIB_Cos.h>
9.40.1 Macro Definition
#define GFLIB_COS_DEFAULT_F16 &f16gflibCosCoef
9.40.2 Description
Default approximation coefficients for GFLIB_Cos_F32 function.
9.41 Define GFLIB_Hyst
#include <GFLIB_Hyst.h>
9.41.1 Macro Definition
#define GFLIB_Hyst macro_dispatcher(GFLIB_Hyst, __VA_ARGS__)(__VA_ARGS__)
9.41.2 Description
The function implements the hysteresis functionality.
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9.42 Define GFLIB_HYST_DEFAULT_F32
#include <GFLIB_Hyst.h>
9.42.1 Macro Definition
#define GFLIB_HYST_DEFAULT_F32 {(tFrac32)0,(tFrac32)0,(tFrac32)0,(tFrac32)0,(tFrac32)0}
9.42.2 Description
Default value for GFLIB_HYST_T_F32.
9.43 Define GFLIB_HYST_DEFAULT_F16
#include <GFLIB_Hyst.h>
9.43.1 Macro Definition
#define GFLIB_HYST_DEFAULT_F16 {(tFrac16)0,(tFrac16)0,(tFrac16)0,(tFrac16)0,(tFrac16)0}
9.43.2 Description
Default value for GFLIB_HYST_T_F16.
9.44 Define GFLIB_IntegratorTR
#include <GFLIB_IntegratorTR.h>
9.44.1 Macro Definition
#define GFLIB_IntegratorTR macro_dispatcher(GFLIB_IntegratorTR, __VA_ARGS__)(__VA_ARGS__)
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Define GFLIB_INTEGRATOR_TR_DEFAULT_F32
9.44.2 Description
The function calculates a discrete implementation of the integrator (sum), discretized
using a trapezoidal (Bilinear) transformation.
9.45 Define GFLIB_INTEGRATOR_TR_DEFAULT_F32
#include <GFLIB_IntegratorTR.h>
9.45.1 Macro Definition
#define GFLIB_INTEGRATOR_TR_DEFAULT_F32 {(tFrac32)0,(tFrac32)0,(tFrac32)0,(tU16)0}
9.45.2 Description
Default value for GFLIB_INTEGRATOR_TR_T_F32.
9.46 Define GFLIB_INTEGRATOR_TR_DEFAULT_F16
#include <GFLIB_IntegratorTR.h>
9.46.1 Macro Definition
#define GFLIB_INTEGRATOR_TR_DEFAULT_F16 {(tFrac32)0,(tFrac16)0,(tFrac16)0,(tU16)0}
9.46.2 Description
Default value for GFLIB_INTEGRATOR_TR_T_F16.
9.47 Define GFLIB_Limit
#include <GFLIB_Limit.h>
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9.47.1 Macro Definition
#define GFLIB_Limit macro_dispatcher(GFLIB_Limit, __VA_ARGS__)(__VA_ARGS__)
9.47.2 Description
This function tests whether the input value is within the upper and lower limits.
9.48 Define GFLIB_LIMIT_DEFAULT_F32
#include <GFLIB_Limit.h>
9.48.1 Macro Definition
#define GFLIB_LIMIT_DEFAULT_F32 {INT32_MIN,INT32_MAX }
9.48.2 Description
Default value for GFLIB_LIMIT_T_F32.
9.49 Define GFLIB_LIMIT_DEFAULT_F16
#include <GFLIB_Limit.h>
9.49.1 Macro Definition
#define GFLIB_LIMIT_DEFAULT_F16 {INT16_MIN,INT16_MAX }
9.49.2 Description
Default value for GFLIB_LIMIT_T_F16.
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Define GFLIB_LOWERLIMIT_DEFAULT_F32
9.50 Define GFLIB_LowerLimit
#include <GFLIB_LowerLimit.h>
9.50.1 Macro Definition
#define GFLIB_LowerLimit macro_dispatcher(GFLIB_LowerLimit, __VA_ARGS__)(__VA_ARGS__)
9.50.2 Description
This function tests whether the input value is above the lower limit.
9.51 Define GFLIB_LOWERLIMIT_DEFAULT_F32
#include <GFLIB_LowerLimit.h>
9.51.1 Macro Definition
#define GFLIB_LOWERLIMIT_DEFAULT_F32 {INT32_MIN }
9.51.2 Description
Default value for GFLIB_LOWERLIMIT_T_F32.
9.52 Define GFLIB_LOWERLIMIT_DEFAULT_F16
#include <GFLIB_LowerLimit.h>
9.52.1 Macro Definition
#define GFLIB_LOWERLIMIT_DEFAULT_F16 {INT16_MIN }
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9.52.2 Description
Default value for GFLIB_LOWERLIMIT_T_F16.
9.53 Define GFLIB_Lut1D
#include <GFLIB_Lut1D.h>
9.53.1 Macro Definition
#define GFLIB_Lut1D macro_dispatcher(GFLIB_Lut1D, __VA_ARGS__)(__VA_ARGS__)
9.53.2 Description
This function implements the one-dimensional look-up table.
9.54 Define GFLIB_LUT1D_DEFAULT_F32
#include <GFLIB_Lut1D.h>
9.54.1 Macro Definition
#define GFLIB_LUT1D_DEFAULT_F32 {(tU32)0,(tFrac32 *)0}
9.54.2 Description
Default value for GFLIB_LUT1D_T_F32.
9.55 Define GFLIB_LUT1D_DEFAULT_F16
#include <GFLIB_Lut1D.h>
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Define GFLIB_Lut2D
9.55.1 Macro Definition
#define GFLIB_LUT1D_DEFAULT_F16 {(tU16)0,(tFrac16 *)0}
9.55.2 Description
Default value for GFLIB_LUT1D_T_F16.
9.56 Define GFLIB_Lut2D
#include <GFLIB_Lut2D.h>
9.56.1 Macro Definition
#define GFLIB_Lut2D macro_dispatcher(GFLIB_Lut2D, __VA_ARGS__)(__VA_ARGS__)
9.56.2 Description
This function implements the two-dimensional look-up table.
9.57 Define GFLIB_LUT2D_DEFAULT_F32
#include <GFLIB_Lut2D.h>
9.57.1 Macro Definition
#define GFLIB_LUT2D_DEFAULT_F32 {(tU32)0,(tU32)0,(tFrac32 *)0}
9.57.2 Description
Default value for GFLIB_LUT2D_T_F32.
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9.58 Define GFLIB_LUT2D_DEFAULT_F16
#include <GFLIB_Lut2D.h>
9.58.1 Macro Definition
#define GFLIB_LUT2D_DEFAULT_F16 {(tU16)0,(tU16)0,(tFrac16 *)0}
9.58.2 Description
Default value for GFLIB_LUT2D_T_F16.
9.59 Define GFLIB_Ramp
#include <GFLIB_Ramp.h>
9.59.1 Macro Definition
#define GFLIB_Ramp macro_dispatcher(GFLIB_Ramp, __VA_ARGS__)(__VA_ARGS__)
9.59.2 Description
The function calculates the up/down ramp with the step increment/decrement defined in
the pParam structure.
9.60 Define GFLIB_RAMP_DEFAULT_F32
#include <GFLIB_Ramp.h>
9.60.1 Macro Definition
#define GFLIB_RAMP_DEFAULT_F32 {(tFrac32)0,(tFrac32)0,(tFrac32)0}
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Define GFLIB_RAMP_DEFAULT_F16
9.60.2 Description
Default value for GFLIB_RAMP_T_F32.
9.61 Define GFLIB_RAMP_DEFAULT_F16
#include <GFLIB_Ramp.h>
9.61.1 Macro Definition
#define GFLIB_RAMP_DEFAULT_F16 {(tFrac16)0,(tFrac16)0,(tFrac16)0}
9.61.2 Description
Default value for GFLIB_RAMP_T_F16.
9.62 Define GFLIB_Sign
#include <GFLIB_Sign.h>
9.62.1 Macro Definition
#define GFLIB_Sign macro_dispatcher(GFLIB_Sign, __VA_ARGS__)(__VA_ARGS__)
9.62.2 Description
This function returns the signum of input value.
9.63 Define GFLIB_Sin
#include <GFLIB_Sin.h>
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9.63.1 Macro Definition
#define GFLIB_Sin macro_dispatcher(GFLIB_Sin, __VA_ARGS__)(__VA_ARGS__)
9.63.2 Description
This function implements polynomial approximation of sine function.
9.64 Define GFLIB_SIN_DEFAULT_F32
#include <GFLIB_Sin.h>
9.64.1 Macro Definition
#define GFLIB_SIN_DEFAULT_F32 &f32gflibSinCoef
9.64.2 Description
Default approximation coefficients for GFLIB_Sin_F32 function.
9.65 Define GFLIB_SIN_DEFAULT_F16
#include <GFLIB_Sin.h>
9.65.1 Macro Definition
#define GFLIB_SIN_DEFAULT_F16 &f16gflibSinCoef
9.65.2 Description
Default approximation coefficients for GFLIB_Sin_F16 function.
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Define GFLIB_SINCOS_DEFAULT_F32
9.66 Define GFLIB_SinCos
#include <GFLIB_SinCos.h>
9.66.1 Macro Definition
#define GFLIB_SinCos macro_dispatcher(GFLIB_SinCos, __VA_ARGS__)(__VA_ARGS__)
9.66.2 Description
This function implements polynomial approximation of sine function.
9.67 Define GFLIB_SINCOS_DEFAULT_F32
#include <GFLIB_SinCos.h>
9.67.1 Macro Definition
#define GFLIB_SINCOS_DEFAULT_F32 &f32gflibSinCosCoef
9.67.2 Description
Default approximation coefficients for GFLIB_SinCos_F32 function.
9.68 Define GFLIB_SINCOS_DEFAULT_F16
#include <GFLIB_SinCos.h>
9.68.1 Macro Definition
#define GFLIB_SINCOS_DEFAULT_F16 &f16gflibSinCosCoef
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9.68.2 Description
Default approximation coefficients for GFLIB_SinCos_F16 function.
9.69 Define GFLIB_Sqrt
#include <GFLIB_Sqrt.h>
9.69.1 Macro Definition
#define GFLIB_Sqrt macro_dispatcher(GFLIB_Sqrt, __VA_ARGS__)(__VA_ARGS__)
9.69.2 Description
This function returns the square root of input value.
9.70 Define GFLIB_Tan
#include <GFLIB_Tan.h>
9.70.1 Macro Definition
#define GFLIB_Tan macro_dispatcher(GFLIB_Tan, __VA_ARGS__)(__VA_ARGS__)
9.70.2 Description
This function implements polynomial approximation of tangent function.
9.71 Define GFLIB_TAN_DEFAULT_F32
#include <GFLIB_Tan.h>
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Define GFLIB_TAN_DEFAULT_F16
9.71.1 Macro Definition
#define GFLIB_TAN_DEFAULT_F32 &f32gflibTanCoef
9.71.2 Description
Default approximation coefficients for GFLIB_Tan_F32 function.
9.72 Define GFLIB_TAN_DEFAULT_F16
#include <GFLIB_Tan.h>
9.72.1 Macro Definition
#define GFLIB_TAN_DEFAULT_F16 &f16gflibTanCoef
9.72.2 Description
Default approximation coefficients for GFLIB_Tan_F16 function.
9.73 Define GFLIB_UpperLimit
#include <GFLIB_UpperLimit.h>
9.73.1 Macro Definition
#define GFLIB_UpperLimit macro_dispatcher(GFLIB_UpperLimit, __VA_ARGS__)(__VA_ARGS__)
9.73.2 Description
This function tests whether the input value is below the upper limit.
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9.74 Define GFLIB_UPPERLIMIT_DEFAULT_F32
#include <GFLIB_UpperLimit.h>
9.74.1 Macro Definition
#define GFLIB_UPPERLIMIT_DEFAULT_F32 {INT32_MAX }
9.74.2 Description
Default value for GFLIB_UPPERLIMIT_T_F32.
9.75 Define GFLIB_UPPERLIMIT_DEFAULT_F16
#include <GFLIB_UpperLimit.h>
9.75.1 Macro Definition
#define GFLIB_UPPERLIMIT_DEFAULT_F16 {INT16_MAX }
9.75.2 Description
Default value for GFLIB_UPPERLIMIT_T_F16.
9.76 Define GFLIB_VectorLimit
#include <GFLIB_VectorLimit.h>
9.76.1 Macro Definition
#define GFLIB_VectorLimit macro_dispatcher(GFLIB_VectorLimit, __VA_ARGS__)(__VA_ARGS__)
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Define GFLIB_VECTORLIMIT_DEFAULT_F32
9.76.2 Description
This function limits the magnitude of the input vector.
9.77 Define GFLIB_VECTORLIMIT_DEFAULT_F32
#include <GFLIB_VectorLimit.h>
9.77.1 Macro Definition
#define GFLIB_VECTORLIMIT_DEFAULT_F32 {(tFrac32)0}
9.77.2 Description
Default value for GFLIB_VECTORLIMIT_T_F32.
9.78 Define GFLIB_VECTORLIMIT_DEFAULT_F16
#include <GFLIB_VectorLimit.h>
9.78.1 Macro Definition
#define GFLIB_VECTORLIMIT_DEFAULT_F16 {(tFrac16)0}
9.78.2 Description
Default value for GFLIBVECTORLIMIT_T_F16.
9.79 Define GMCLIB_Clark
#include <GMCLIB_Clark.h>
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9.79.1 Macro Definition
#define GMCLIB_Clark macro_dispatcher(GMCLIB_Clark, __VA_ARGS__)(__VA_ARGS__)
9.79.2 Description
This function implements the Clarke transformation.
9.80 Define GMCLIB_ClarkInv
#include <GMCLIB_ClarkInv.h>
9.80.1 Macro Definition
#define GMCLIB_ClarkInv macro_dispatcher(GMCLIB_ClarkInv, __VA_ARGS__)(__VA_ARGS__)
9.80.2 Description
This function implements the inverse Clarke transformation.
9.81 Define GMCLIB_DecouplingPMSM
#include <GMCLIB_DecouplingPMSM.h>
9.81.1 Macro Definition
#define GMCLIB_DecouplingPMSM macro_dispatcher(GMCLIB_DecouplingPMSM, __VA_ARGS__)
(__VA_ARGS__)
9.81.2 Description
This function calculates the cross-coupling voltages to eliminate the dq axis coupling
causing non-linearity of the field oriented control.
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Define GMCLIB_DECOUPLINGPMSM_DEFAULT_F32
9.82 Define GMCLIB_DECOUPLINGPMSM_DEFAULT_F32
#include <GMCLIB_DecouplingPMSM.h>
9.82.1 Macro Definition
#define GMCLIB_DECOUPLINGPMSM_DEFAULT_F32 {(tFrac32)0,(tS16)0,(tFrac32)0,(tS16)0}
9.82.2 Description
Default value for GMCLIB_DECOUPLINGPMSM_T_F32.
9.83 Define GMCLIB_DECOUPLINGPMSM_DEFAULT_F16
#include <GMCLIB_DecouplingPMSM.h>
9.83.1 Macro Definition
#define GMCLIB_DECOUPLINGPMSM_DEFAULT_F16 {(tFrac16)0,(tS16)0,(tFrac16)0,(tS16)0}
9.83.2 Description
Default value for GMCLIB_DECOUPLINGPMSM_T_F16.
9.84 Define GMCLIB_ELIMDCBUSRIP_FLT_DNMAX
#include <GMCLIB_ElimDcBusRip.c>
9.84.1 Macro Definition
#define GMCLIB_ELIMDCBUSRIP_FLT_DNMAX ((tFloat)1.1754942106924411e-38)
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9.84.2 Description
Largest denormalized floating-point value.
9.85 Define GMCLIB_ElimDcBusRip
#include <GMCLIB_ElimDcBusRip.h>
9.85.1 Macro Definition
#define GMCLIB_ElimDcBusRip macro_dispatcher(GMCLIB_ElimDcBusRip, __VA_ARGS__)(__VA_ARGS__)
9.85.2 Description
This function implements the DC Bus voltage ripple elimination.
9.86 Define GMCLIB_ELIMDCBUSRIP_DEFAULT_F32
#include <GMCLIB_ElimDcBusRip.h>
9.86.1 Macro Definition
#define GMCLIB_ELIMDCBUSRIP_DEFAULT_F32 {(tFrac32)0,(tFrac32)0}
9.86.2 Description
Default value for GMCLIB_ELIMDCBUSRIP_T_F32.
9.87 Define GMCLIB_ELIMDCBUSRIP_DEFAULT_F16
#include <GMCLIB_ElimDcBusRip.h>
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Define GMCLIB_Park
9.87.1 Macro Definition
#define GMCLIB_ELIMDCBUSRIP_DEFAULT_F16 {(tFrac16)0,(tFrac16)0}
9.87.2 Description
Default value for GMCLIB_ELIMDCBUSRIP_T_F16.
9.88 Define GMCLIB_Park
#include <GMCLIB_Park.h>
9.88.1 Macro Definition
#define GMCLIB_Park macro_dispatcher(GMCLIB_Park, __VA_ARGS__)(__VA_ARGS__)
9.88.2 Description
This function implements the calculates Park transformation.
9.89 Define GMCLIB_ParkInv
#include <GMCLIB_ParkInv.h>
9.89.1 Macro Definition
#define GMCLIB_ParkInv macro_dispatcher(GMCLIB_ParkInv, __VA_ARGS__)(__VA_ARGS__)
9.89.2 Description
This function implements the inverse Park transformation.
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9.90 Define GMCLIB_SvmStd
#include <GMCLIB_SvmStd.h>
9.90.1 Macro Definition
#define GMCLIB_SvmStd macro_dispatcher(GMCLIB_SvmStd, __VA_ARGS__)(__VA_ARGS__)
9.90.2 Description
This function calculates the duty-cycle ratios using the Standard Space Vector
Modulation technique.
9.91 Define MLIB_Abs
#include <MLIB_Abs.h>
9.91.1 Macro Definition
#define MLIB_Abs macro_dispatcher(MLIB_Abs, __VA_ARGS__)(__VA_ARGS__)
9.91.2 Description
This function returns absolute value of input parameter.
9.92 Define MLIB_AbsSat
#include <MLIB_AbsSat.h>
9.92.1 Macro Definition
#define MLIB_AbsSat macro_dispatcher(MLIB_AbsSat, __VA_ARGS__)(__VA_ARGS__)
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Define MLIB_Add
9.92.2 Description
This function returns absolute value of input parameter and saturate if necessary.
9.93 Define MLIB_Add
#include <MLIB_Add.h>
9.93.1 Macro Definition
#define MLIB_Add macro_dispatcher(MLIB_Add, __VA_ARGS__)(__VA_ARGS__)
9.93.2 Description
This function returns sum of two input parameters.
9.94 Define MLIB_AddSat
#include <MLIB_AddSat.h>
9.94.1 Macro Definition
#define MLIB_AddSat macro_dispatcher(MLIB_AddSat, __VA_ARGS__)(__VA_ARGS__)
9.94.2 Description
This function returns sum of two input parameters and saturate if necessary.
9.95 Define MLIB_Convert
#include <MLIB_Convert.h>
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9.95.1 Macro Definition
#define MLIB_Convert macro_dispatcher(MLIB_Convert, __VA_ARGS__)(__VA_ARGS__)
9.95.2 Description
This function converts the input value to different representation.
9.96 Define MLIB_ConvertPU
#include <MLIB_ConvertPU.h>
9.96.1 Macro Definition
#define MLIB_ConvertPU macro_dispatcher(MLIB_ConvertPU, __VA_ARGS__)(__VA_ARGS__)
9.96.2 Description
This function converts the input value to different representation with scale.
9.97 Define MLIB_Div
#include <MLIB_Div.h>
9.97.1 Macro Definition
#define MLIB_Div macro_dispatcher(MLIB_Div,__VA_ARGS__)(__VA_ARGS__)
9.97.2 Description
This function divides the first parameter by the second one.
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Define MLIB_Mac
9.98 Define MLIB_DivSat
#include <MLIB_DivSat.h>
9.98.1 Macro Definition
#define MLIB_DivSat macro_dispatcher(MLIB_DivSat, __VA_ARGS__)(__VA_ARGS__)
9.98.2 Description
This function divides the first parameter by the second one as saturate.
9.99 Define MLIB_Mac
#include <MLIB_Mac.h>
9.99.1 Macro Definition
#define MLIB_Mac macro_dispatcher(MLIB_Mac, __VA_ARGS__)(__VA_ARGS__)
9.99.2 Description
This function implements the multiply accumulate function.
9.100 Define MLIB_MacSat
#include <MLIB_MacSat.h>
9.100.1 Macro Definition
#define MLIB_MacSat macro_dispatcher(MLIB_MacSat, __VA_ARGS__)(__VA_ARGS__)
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9.100.2 Description
This function implements the multiply accumulate function saturated if necessary.
9.101 Define MLIB_Mnac
#include <MLIB_Mnac.h>
9.101.1 Macro Definition
#define MLIB_Mnac macro_dispatcher(MLIB_Mnac, __VA_ARGS__)(__VA_ARGS__)
9.101.2 Description
This function implements the multiply-subtract function.
9.102 Define MLIB_Msu
#include <MLIB_Msu.h>
9.102.1 Macro Definition
#define MLIB_Msu macro_dispatcher(MLIB_Msu, __VA_ARGS__)(__VA_ARGS__)
9.102.2 Description
This function implements the multiply accumulate function.
9.103 Define MLIB_Mul
#include <MLIB_Mul.h>
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Define MLIB_MulSat
9.103.1 Macro Definition
#define MLIB_Mul macro_dispatcher(MLIB_Mul, __VA_ARGS__)(__VA_ARGS__)
9.103.2 Description
This function multiply two input parameters.
9.104 Define MLIB_MulSat
#include <MLIB_MulSat.h>
9.104.1 Macro Definition
#define MLIB_MulSat macro_dispatcher(MLIB_MulSat, __VA_ARGS__)(__VA_ARGS__)
9.104.2 Description
This function multiply two input parameters and saturate if necessary.
9.105 Define MLIB_Neg
#include <MLIB_Neg.h>
9.105.1 Macro Definition
#define MLIB_Neg macro_dispatcher(MLIB_Neg, __VA_ARGS__)(__VA_ARGS__)
9.105.2 Description
This function returns negative value of input parameter.
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9.106 Define MLIB_NegSat
#include <MLIB_NegSat.h>
9.106.1 Macro Definition
#define MLIB_NegSat macro_dispatcher(MLIB_NegSat, __VA_ARGS__)(__VA_ARGS__)
9.106.2 Description
This function returns negative value of input parameter and saturate if necessary.
9.107 Define MLIB_Norm
#include <MLIB_Norm.h>
9.107.1 Macro Definition
#define MLIB_Norm macro_dispatcher(MLIB_Norm, __VA_ARGS__)(__VA_ARGS__)
9.107.2 Description
This function returns the number of left shifts needed to normalize the input parameter.
9.108 Define MLIB_Round
#include <MLIB_Round.h>
9.108.1 Macro Definition
#define MLIB_Round macro_dispatcher(MLIB_Round, __VA_ARGS__)(__VA_ARGS__)
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Define MLIB_ShBi
9.108.2 Description
This function rounds the first input value for number of digits defined by second
parameter and saturate automatically.
9.109 Define MLIB_ShBi
#include <MLIB_ShBi.h>
9.109.1 Macro Definition
#define MLIB_ShBi macro_dispatcher(MLIB_ShBi, __VA_ARGS__)(__VA_ARGS__)
9.109.2 Description
Based on sign of second parameter this function shifts the first parameter to right or left.
If the sign of second parameter is negative, shift to right.
9.110 Define MLIB_ShBiSat
#include <MLIB_ShBiSat.h>
9.110.1 Macro Definition
#define MLIB_ShBiSat macro_dispatcher(MLIB_ShBiSat, __VA_ARGS__)(__VA_ARGS__)
9.110.2 Description
Based on sign of second parameter this function shifts the first parameter to right or left
and saturate if necessary. If the sign of second parameter is negative, shift to right.
9.111 Define MLIB_ShL
#include <MLIB_ShL.h>
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9.111.1 Macro Definition
#define MLIB_ShL macro_dispatcher(MLIB_ShL, __VA_ARGS__)(__VA_ARGS__)
9.111.2 Description
This function shifts the first parameter to left by number defined by second parameter.
9.112 Define MLIB_ShLSat
#include <MLIB_ShLSat.h>
9.112.1 Macro Definition
#define MLIB_ShLSat macro_dispatcher(MLIB_ShLSat, __VA_ARGS__)(__VA_ARGS__)
9.112.2 Description
This function shifts the first parameter to left by number defined by second parameter and
saturate if necessary.
9.113 Define MLIB_ShR
#include <MLIB_ShR.h>
9.113.1 Macro Definition
#define MLIB_ShR macro_dispatcher(MLIB_ShR, __VA_ARGS__)(__VA_ARGS__)
9.113.2 Description
This function shifts the first parameter to right by number defined by second parameter.
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Define MLIB_Sub
9.114 Define MLIB_Sub
#include <MLIB_Sub.h>
9.114.1 Macro Definition
#define MLIB_Sub macro_dispatcher(MLIB_Sub, __VA_ARGS__)(__VA_ARGS__)
9.114.2 Description
This function subtracts the second parameter from the first one.
9.115 Define MLIB_SubSat
#include <MLIB_SubSat.h>
9.115.1 Macro Definition
#define MLIB_SubSat macro_dispatcher(MLIB_SubSat, __VA_ARGS__)(__VA_ARGS__)
9.115.2 Description
This function subtracts the second parameter from the first one and saturate if necessary.
9.116 Define MLIB_VMac
#include <MLIB_VMac.h>
9.116.1 Macro Definition
#define MLIB_VMac macro_dispatcher(MLIB_VMac, __VA_ARGS__)(__VA_ARGS__)
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9.116.2 Description
This function implements the vector multiply accumulate function.
9.117 Define SWLIBS_VERSION
#include <SWLIBS_Config.h>
9.117.1 Macro Definition
#define SWLIBS_VERSION {(unsigned char)1U,(unsigned char)1U,(unsigned char)5U}
9.117.2 Description
9.118 Define SWLIBS_STD_ON
#include <SWLIBS_Config.h>
9.118.1 Macro Definition
#define SWLIBS_STD_ON 0x01U
9.118.2 Description
9.119 Define SWLIBS_STD_OFF
#include <SWLIBS_Config.h>
9.119.1 Macro Definition
#define SWLIBS_STD_OFF 0x00U
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Define F32
9.119.2 Description
9.120 Define F32
#include <SWLIBS_Config.h>
9.120.1 Macro Definition
#define F32 F32
9.120.2 Description
9.121 Define F16
#include <SWLIBS_Config.h>
9.121.1 Macro Definition
#define F16 F16
9.121.2 Description
9.122 Define FLT
#include <SWLIBS_Config.h>
9.122.1 Macro Definition
#define FLT FLT
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9.122.2 Description
9.123 Define SWLIBS_DEFAULT_IMPLEMENTATION_F32
#include <SWLIBS_Config.h>
9.123.1 Macro Definition
#define SWLIBS_DEFAULT_IMPLEMENTATION_F32 (1U)
9.123.2 Description
9.124 Define SWLIBS_DEFAULT_IMPLEMENTATION_F16
#include <SWLIBS_Config.h>
9.124.1 Macro Definition
#define SWLIBS_DEFAULT_IMPLEMENTATION_F16 (2U)
9.124.2 Description
9.125 Define SWLIBS_DEFAULT_IMPLEMENTATION_FLT
#include <SWLIBS_Config.h>
9.125.1 Macro Definition
#define SWLIBS_DEFAULT_IMPLEMENTATION_FLT (3U)
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Define SWLIBS_SUPPORT_F32
9.125.2 Description
9.126 Define SWLIBS_SUPPORT_F32
#include <SWLIBS_Config.h>
9.126.1 Macro Definition
#define SWLIBS_SUPPORT_F32 SWLIBS_STD_ON
9.126.2 Description
Enables/disables support of 32-bit fractional implementation.
9.127 Define SWLIBS_SUPPORT_F16
#include <SWLIBS_Config.h>
9.127.1 Macro Definition
#define SWLIBS_SUPPORT_F16 SWLIBS_STD_ON
9.127.2 Description
Enables/disables support of 16-bit fractional implementation.
9.128 Define SWLIBS_SUPPORT_FLT
#include <SWLIBS_Config.h>
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9.128.1 Macro Definition
#define SWLIBS_SUPPORT_FLT SWLIBS_STD_OFF
9.128.2 Description
Enables/disables support of single precision floating point implementation.
9.129 Define SWLIBS_SUPPORTED_IMPLEMENTATION
#include <SWLIBS_Config.h>
9.129.1 Macro Definition
#define SWLIBS_SUPPORTED_IMPLEMENTATION {SWLIBS_SUPPORT_F32,\ SWLIBS_SUPPORT_F16,\
SWLIBS_SUPPORT_FLT,\ 0,0,0,0,0,0}
9.129.2 Description
Array of supported implementations.
9.130 Define SWLIBS_DEFAULT_IMPLEMENTATION
#include <SWLIBS_Config.h>
9.130.1 Macro Definition
#define SWLIBS_DEFAULT_IMPLEMENTATION
9.130.2 Description
Selection of default implementation.
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Define SFRACT_MIN
9.131 Define SFRACT_MIN
#include <SWLIBS_Defines.h>
9.131.1 Macro Definition
#define SFRACT_MIN (-1.0)
9.131.2 Description
Definition of inline directive for all supported compilers.
Constant representing the maximal negative value of a signed 16-bit fixed point fractional
number, floating point representation.
9.132 Define SFRACT_MAX
#include <SWLIBS_Defines.h>
9.132.1 Macro Definition
#define SFRACT_MAX (0.999969482421875)
9.132.2 Description
Constant representing the maximal positive value of a signed 16-bit fixed point fractional
number, floating point representation.
9.133 Define FRACT_MIN
#include <SWLIBS_Defines.h>
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9.133.1 Macro Definition
#define FRACT_MIN (-1.0)
9.133.2 Description
Constant representing the maximal negative value of signed 32-bit fixed point fractional
number, floating point representation.
9.134 Define FRACT_MAX
#include <SWLIBS_Defines.h>
9.134.1 Macro Definition
#define FRACT_MAX (0.9999999995343387126922607421875)
9.134.2 Description
Constant representing the maximal positive value of a signed 32-bit fixed point fractional
number, floating point representation.
9.135 Define FRAC32_0_5
#include <SWLIBS_Defines.h>
9.135.1 Macro Definition
#define FRAC32_0_5 ((tFrac32) 0x40000000)
9.135.2 Description
Value 0.5 in 32-bit fixed point fractional format.
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Define FRAC16_0_5
9.136 Define FRAC16_0_5
#include <SWLIBS_Defines.h>
9.136.1 Macro Definition
#define FRAC16_0_5 ((tFrac16) 0x4000)
9.136.2 Description
Value 0.5 in 16-bit fixed point fractional format.
9.137 Define FRAC32_0_25
#include <SWLIBS_Defines.h>
9.137.1 Macro Definition
#define FRAC32_0_25 ((tFrac32) 0x20000000)
9.137.2 Description
Value 0.25 in 32-bit fixed point fractional format.
9.138 Define FRAC16_0_25
#include <SWLIBS_Defines.h>
9.138.1 Macro Definition
#define FRAC16_0_25 ((tFrac16) 0x2000)
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9.138.2 Description
Value 0.25 in 16-bit fixed point fractional format.
9.139 Define UINT16_MAX
#include <SWLIBS_Defines.h>
9.139.1 Macro Definition
#define UINT16_MAX ((tU16) 0x8000)
9.139.2 Description
Constant representing the maximal positive value of a unsigned 16-bit fixed point integer
number, equal to 2 15 = 0x8000.
9.140 Define INT16_MAX
#include <SWLIBS_Defines.h>
9.140.1 Macro Definition
#define INT16_MAX ((tS16) 0x7fff)
9.140.2 Description
Constant representing the maximal positive value of a signed 16-bit fixed point integer
number, equal to 2 15-1 = 0x7fff.
9.141 Define INT16_MIN
#include <SWLIBS_Defines.h>
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Define UINT32_MAX
9.141.1 Macro Definition
#define INT16_MIN ((tS16) 0x8000)
9.141.2 Description
Constant representing the maximal negative value of a signed 16-bit fixed point integer
number, equal to -2 15 = 0x8000.
9.142 Define UINT32_MAX
#include <SWLIBS_Defines.h>
9.142.1 Macro Definition
#define UINT32_MAX ((tU32) 0x80000000U)
9.142.2 Description
Constant representing the maximal positive value of a unsigned 32-bit fixed point integer
number, equal to 2 31 = 0x80000000.
9.143 Define INT32_MAX
#include <SWLIBS_Defines.h>
9.143.1 Macro Definition
#define INT32_MAX ((tS32) 0x7fffffff)
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9.143.2 Description
Constant representing the maximal positive value of a signed 32-bit fixed point integer
number, equal to 2 31-1 = 0x7fff ffff.
9.144 Define INT32_MIN
#include <SWLIBS_Defines.h>
9.144.1 Macro Definition
#define INT32_MIN ((tS32) 0x80000000U)
9.144.2 Description
Constant representing the maximal negative value of a signed 32-bit fixed point integer
number, equal to -2 31 = 0x8000 0000.
9.145 Define INT16TOINT32
#include <SWLIBS_Defines.h>
9.145.1 Macro Definition
#define INT16TOINT32 ((tS32) (x))
9.145.2 Description
Type casting - signed 16-bit integer value cast to a signed 32-bit integer.
9.146 Define INT32TOINT16
#include <SWLIBS_Defines.h>
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Define INT32TOINT64
9.146.1 Macro Definition
#define INT32TOINT16 ((tS16) (x))
9.146.2 Description
Type casting - signed 32-bit integer value cast to a signed 16-bit integer.
9.147 Define INT32TOINT64
#include <SWLIBS_Defines.h>
9.147.1 Macro Definition
#define INT32TOINT64 ((tS64) (x))
9.147.2 Description
Type casting - signed 32-bit integer value cast to a signed 64-bit integer.
9.148 Define INT64TOINT32
#include <SWLIBS_Defines.h>
9.148.1 Macro Definition
#define INT64TOINT32 ((tS32) (x))
9.148.2 Description
Type casting - signed 64-bit integer value cast to a signed 32-bit integer.
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9.149 Define F16TOINT16
#include <SWLIBS_Defines.h>
9.149.1 Macro Definition
#define F16TOINT16 ((tS16) (x))
9.149.2 Description
Type casting - signed 16-bit fractional value cast to a signed 16-bit integer.
9.150 Define F32TOINT16
#include <SWLIBS_Defines.h>
9.150.1 Macro Definition
#define F32TOINT16 ((tS16) (x))
9.150.2 Description
Type casting - lower 16 bits of a signed 32-bit fractional value cast to a signed 16-bit
integer.
9.151 Define F64TOINT16
#include <SWLIBS_Defines.h>
9.151.1 Macro Definition
#define F64TOINT16 ((tS16) (x))
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Define F16TOINT32
9.151.2 Description
Type casting - lower 16 bits of a signed 64-bit fractional value cast to a signed 16-bit
integer.
9.152 Define F16TOINT32
#include <SWLIBS_Defines.h>
9.152.1 Macro Definition
#define F16TOINT32 ((tS32) (x))
9.152.2 Description
Type casting - a signed 16-bit fractional value cast to a signed 32-bit integer, the value
placed at the lower 16-bits of the 32-bit result.
9.153 Define F32TOINT32
#include <SWLIBS_Defines.h>
9.153.1 Macro Definition
#define F32TOINT32 ((tS32) (x))
9.153.2 Description
Type casting - signed 32-bit fractional value cast to a signed 32-bit integer.
9.154 Define F64TOINT32
#include <SWLIBS_Defines.h>
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9.154.1 Macro Definition
#define F64TOINT32 ((tS32) (x))
9.154.2 Description
Type casting - lower 32 bits of a signed 64-bit fractional value cast to a signed 32-bit
integer.
9.155 Define F16TOINT64
#include <SWLIBS_Defines.h>
9.155.1 Macro Definition
#define F16TOINT64 ((tS64) (x))
9.155.2 Description
Type casting - signed 16-bit fractional value cast to a signed 64-bit integer, the value
placed at the lower 16-bits of the 64-bit result.
9.156 Define F32TOINT64
#include <SWLIBS_Defines.h>
9.156.1 Macro Definition
#define F32TOINT64 ((tS64) (x))
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Define F64TOINT64
9.156.2 Description
Type casting - signed 32-bit fractional value cast to a signed 64-bit integer, the value
placed at the lower 32-bits of the 64-bit result.
9.157 Define F64TOINT64
#include <SWLIBS_Defines.h>
9.157.1 Macro Definition
#define F64TOINT64 ((tS64) (x))
9.157.2 Description
Type casting - signed 64-bit fractional value cast to a signed 64-bit integer.
9.158 Define INT16TOF16
#include <SWLIBS_Defines.h>
9.158.1 Macro Definition
#define INT16TOF16 ((tFrac16) (x))
9.158.2 Description
Type casting - signed 16-bit integer value cast to a signed 16-bit fractional.
9.159 Define INT16TOF32
#include <SWLIBS_Defines.h>
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9.159.1 Macro Definition
#define INT16TOF32 ((tFrac32) (x))
9.159.2 Description
Type casting - signed 16-bit integer value cast to a signed 32-bit fractional, the value
placed at the lower 16 bits of the 32-bit result.
9.160 Define INT32TOF16
#include <SWLIBS_Defines.h>
9.160.1 Macro Definition
#define INT32TOF16 ((tFrac16) (x))
9.160.2 Description
Type casting - lower 16-bits of a signed 32-bit integer value cast to a signed 16-bit
fractional.
9.161 Define INT32TOF32
#include <SWLIBS_Defines.h>
9.161.1 Macro Definition
#define INT32TOF32 ((tFrac32) (x))
9.161.2 Description
Type casting - signed 32-bit integer value cast to a signed 32-bit fractional.
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Define INT64TOF16
9.162 Define INT64TOF16
#include <SWLIBS_Defines.h>
9.162.1 Macro Definition
#define INT64TOF16 ((tFrac16) (x))
9.162.2 Description
Type casting - lower 16-bits of a signed 64-bit integer value cast to a signed 16-bit
fractional.
9.163 Define INT64TOF32
#include <SWLIBS_Defines.h>
9.163.1 Macro Definition
#define INT64TOF32 ((tFrac32) (x))
9.163.2 Description
Type casting - lower 32-bits of a signed 64-bit integer value cast to a signed 32-bit
fractional.
9.164 Define F16_1_DIVBY_SQRT3
#include <SWLIBS_Defines.h>
9.164.1 Macro Definition
#define F16_1_DIVBY_SQRT3 ((tFrac16) 0x49E7)
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9.164.2 Description
One over sqrt(3) with a 16-bit result, the result rounded for a better precision, i.e.
round(1/ √(3)*2 15).
9.165 Define F32_1_DIVBY_SQRT3
#include <SWLIBS_Defines.h>
9.165.1 Macro Definition
#define F32_1_DIVBY_SQRT3 ((tFrac32) 0x49E69D16)
9.165.2 Description
One over sqrt(3) with a 32-bit result, the result rounded for a better precision, i.e.
round(1/ √(3)*2 31).
9.166 Define F16_SQRT3_DIVBY_2
#include <SWLIBS_Defines.h>
9.166.1 Macro Definition
#define F16_SQRT3_DIVBY_2 ((tFrac16) 0x6EDA)
9.166.2 Description
Sqrt(3) divided by two with a 16-bit result, the result rounded for a better precision, i.e.
round( √(3)/2*2 15).
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Define F16_SQRT2_DIVBY_2
9.167 Define F32_SQRT3_DIVBY_2
#include <SWLIBS_Defines.h>
9.167.1 Macro Definition
#define F32_SQRT3_DIVBY_2 ((tFrac32) 0x6ED9EBA1)
9.167.2 Description
Sqrt(3) divided by two with a 32-bit result, the result rounded for a better precision, i.e.
round( √(3)/2*2 31).
9.168 Define F16_SQRT2_DIVBY_2
#include <SWLIBS_Defines.h>
9.168.1 Macro Definition
#define F16_SQRT2_DIVBY_2 ((tFrac16) 0x5A82)
9.168.2 Description
Sqrt(2) divided by two with a 16-bit result, the result rounded for a better precision, i.e.
round( √(2)/2*2 15).
9.169 Define F32_SQRT2_DIVBY_2
#include <SWLIBS_Defines.h>
9.169.1 Macro Definition
#define F32_SQRT2_DIVBY_2 ((tFrac32) 0x5A82799A)
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9.169.2 Description
Sqrt(2) divided by two with a 32-bit result, the result rounded for a better precision, i.e.
round( √(2)/2*2 31).
9.170 Define FRAC16
#include <SWLIBS_Defines.h>
9.170.1 Macro Definition
#define FRAC16 ((tFrac16) ((x < SFRACT_MAX) ? ((x >= SFRACT_MIN) ? (x*32768.0) : INT16_MIN) :
INT16_MAX))
9.170.2 Description
Macro converting a signed fractional [-1,1) numbe