CIP-51 Performance for Standard Library Math Routines

Silicon Labs White Paper
CIP-51 Performance for Standard Library Math Routines
Introduction
This document summarizes a collection of profiling tests for fixed and floating point math routines
using Silicon Labs’ CIP-51 Microcontroller Core.
Code was developed using the Keil C51 Compiler
and Keil 8051 Library Routines, and executed on a
Silicon Labs C8051F005 device. Measurement was
performed using an on-chip timer configured to
count system clocks.
Floating-Point
Characterization
These tests measured the execution time requirements for various floating-point math functions
performed with the CIP-51 Microcontroller Core
on a C8051F005 device. A pseudo-random number
generator (based on the rand( ) function) was used
to generate input parameters; 10,000 samples were
taken for each function. Input parameters for the
Sin( ), Cos( ), and Tan( ) functions were restricted
to the input range -65535 to +65535; inputs for the
Sqrt( ), Log10( ) and Log( ) functions were
restricted to non-negative numbers; all other function inputs were limited to valid floating-point
numbers. Samples were only counted if the result
was a valid floating-point number (no overflows).
All times are given in system clocks, where one
system clock for the CIP-51 equals one oscillator
clock and is independent of oscillator frequency.
Floating-point routine execution times are inputdependent; the table below lists the minimum,
maximum, and mean execution times for the various routines. Each routine profile is detailed with
an execution time histogram in the following
pages. The x-axis represents each specific execution time; the y-axis represents the number of times
that execution time occurred (out of 10,000 input
samples).
Execution Times for Various Floating-Point Routines (in Oscillator Clocks)
Function
Mean
Minimum
Maximum
Addition
Subtraction
Multiplication
Division
Comparison
Square Root
173
179
225
877
113
2650
156
160
98
111
112
2433
320
347
307
1279
162
3004
Rev. 2.1 12/03
Standard 8051
(Mean)†
1284
1356
1368
8244
648
23232
Copyright © 2003 by Silicon Laboratories
Speed Increase Factor vs.
Standard 8051 (Mean)
7.4
7.6
6.1
9.4
5.7
8.8
Execution Times for Various Floating-Point Routines (in Oscillator Clocks)
Standard 8051 Speed Increase Factor vs.
Standard 8051 (Mean)
(Mean)†
Sin
2033
823
5558
35136
17.3
Cos
1852
786
5587
35052
18.9
Tan
3707
1280
8001
59592
16.1
ArcSin
4461
3941
9847
83892
18.8
ArcCos
6513
5832
9883
90936
14.0
ArcTan
1810
734
6126
39840
22.0
Exponential
4245
295
6646
39768
9.4
Natural Log
4692
4208
5175
41184
8.8
Common Log
4931
4448
5376
43284
8.8
†Based on data taken from the Keil C51 User’s Guide v1.97. Statistics in the Keil book are given in CPU
machine cycles; the numbers presented here are adjusted to represent the number of oscillator clocks required
(1 CPU machine cycle = 12 oscillator clocks for a Standard 8051).
Function
Mean
Minimum
Maximum
Addition
Mean:
Min:
Max:
173
156
320
Add
4500
4000
Samples (out of 10,000)
3500
3000
2500
2000
1500
1000
500
0
140
2
160
180
200
220
240
260
System Clock Cycles
Rev. 2.1
280
300
320
Subtraction
179
160
347
Subtract
4500
4000
3500
Samples (out of 10,000)
Mean:
Min:
Max:
3000
2500
2000
1500
1000
500
0
160
180
200
220
240
260
280
System Clock Cycles
Rev. 2.1
300
320
340
360
3
Multiplication
Mean:
Min:
Max:
225
98
307
Multiply
2000
1800
Samples (out of 10,000)
1600
1400
1200
1000
800
600
400
200
0
50
4
100
150
200
250
System Clock Cycles
Rev. 2.1
300
350
Division
877
111
1279
Divide
1800
1600
1400
Samples (out of 10,000)
Mean:
Min:
Max:
1200
1000
800
600
400
200
0
0
200
400
600
800
System Clock Cycles
Rev. 2.1
1000
1200
1400
5
Comparison (a == b)
Mean:
Min:
Max:
113
112
162
Compare
9000
8000
Samples (out of 10,000)
7000
6000
5000
4000
3000
2000
1000
0
110
6
120
130
140
150
System Clock Cycles
Rev. 2.1
160
170
Square Root
2650
2433
3004
SquareRoot
160
140
120
Samples (out of 10,000)
Mean:
Min:
Max:
100
80
60
40
20
0
2400
2500
2600
2700
2800
System Clock Cycles
Rev. 2.1
2900
3000
3100
7
Sin
Mean:
Min:
Max:
2033
823
5558
Sin
3500
Samples (out of 10,000)
3000
2500
2000
1500
1000
500
0
8
0
1000
2000
3000
4000
System Clock Cycles
Rev. 2.1
5000
6000
Cos
1852
786
5587
Cos
1600
1400
1200
Samples (out of 10,000)
Mean:
Min:
Max:
1000
800
600
400
200
0
0
1000
2000
3000
4000
System Clock Cycles
Rev. 2.1
5000
6000
9
Tan
Mean:
Min:
Max:
3707
1280
8001
Tan
1000
900
Samples (out of 10,000)
800
700
600
500
400
300
200
100
0
1000
10
2000
3000
4000
5000
6000
System Clock Cycles
Rev. 2.1
7000
8000
9000
ArcSin
4461
3941
9847
Arcsin
7000
6000
Samples (out of 10,000)
Mean:
Min:
Max:
5000
4000
3000
2000
1000
0
3000
4000
5000
6000
7000
System Clock Cycles
Rev. 2.1
8000
9000
10000
11
ArcCos
Mean:
Min:
Max:
6513
5832
9883
Arccos
160
140
Samples (out of 10,000)
120
100
80
60
40
20
0
5500
12
6000
6500
7000
7500
8000
8500
System Clock Cycles
Rev. 2.1
9000
9500
10000
ArcTan
1810
734
6126
Arctan
4000
3500
3000
Samples (out of 10,000)
Mean:
Min:
Max:
2500
2000
1500
1000
500
0
0
1000
2000
3000
4000
System Clock Cycles
Rev. 2.1
5000
6000
7000
13
Exponential
Mean:
Min:
Max:
4245
295
6646
Exponent
600
Samples (out of 10,000)
500
400
300
200
100
0
14
0
1000
2000
3000
4000
System Clock Cycles
Rev. 2.1
5000
6000
7000
Natural Log
4692
4208
5175
NaturalLog
70
60
Samples (out of 10,000)
Mean:
Min:
Max:
50
40
30
20
10
0
4200
4300
4400
4500
4600 4700 4800 4900
System Clock Cycles
Rev. 2.1
5000
5100
5200
15
Log (Base 10)
Mean:
Min:
Max:
4931
4448
5376
Log10
70
Samples (out of 10,000)
60
50
40
30
20
10
0
4400
16
4500
4600
4700
4800 4900 5000 5100
System Clock Cycles
Rev. 2.1
5200
5300
5400
Fixed-Point Characterization
These tests measured the execution time requirements for various fixed-point math functions performed
with the CIP-51 Microcontroller Core on a C8051F005 device. A pseudo-random number generator
(based on the rand( ) function) was used to generate input parameters; 10,000 samples were taken for
each function. All times are given in system clocks, where one system clock for the CIP-51 equals one
oscillator clock and is independent of oscillator frequency. Note: all 16-bit routines produced a 16-bit
result; all 32-bit routines produced a 32-bit result.
16- and 32-bit division routine execution times are input-dependent; the tables below list the minimum,
maximum, and mean execution times for each division routine. Each division routine profile is detailed
with an execution time histogram in the following pages. The x-axis represents each specific execution
time; the y-axis represents the number of times that execution time occurred (out of 10,000 input samples).
Execution Times for 16-bit Fixed Math Routines (in Oscillator Clocks)
Function
Mean
Minimum
Maximum
Standard 8051
(Mean)†
Speed Increase Factor vs.
Standard 8051 (Mean)
Addition
12
12
12
72
6
(signed/unsigned)
Subtraction
13
13
13
84
6.4
(signed/unsigned)
Multiplication
47
47
47
348
7.4
(signed/unsigned)
Division
221
66
252
1692
7.6
(signed)
Division
194
41
217
1536
7.9
(unsigned)
†
Based on data taken from the Keil C51 User’s Guide v1.97. Statistics in the Keil book are given in CPU machine
cycles; the numbers presented here are adjusted to represent the number of oscillator clocks required (1 CPU
machine cycle = 12 oscillator clocks for a Standard 8051).
Execution Times for 32-bit Fixed Point Math Routines (in Oscillator Clocks)
Function
Mean
Minimum
Maximum
Standard 8051
(Mean)†
Speed Increase Factor vs.
Standard 8051 (Mean)
Addition
24
24
24
144
6
(signed/unsigned)
Subtraction
25
25
25
156
6.2
(signed/unsigned)
Multiplication
141
141
141
1272
9.0
(signed/unsigned)
Division
359
334
795
6768
18.8
(signed)
Division
331
309
770
5964
18.0
(unsigned)
†Based on data taken from the Keil C51 User’s Guide 1.97. Statistics in the Keil book are given in CPU machine
cycles; the numbers presented here are adjusted to represent the number of oscillator clocks required (1 CPU
machine cycle = 12 oscillator clocks for a Standard 8051).
Rev. 2.1
17
Signed 16-bit Division
Mean:
Min:
Max:
221
66
252
Division,16x16->16
4500
4000
Samples (out of 10,000)
3500
3000
2500
2000
1500
1000
500
0
60
18
80
100
120
140
160
180
System Clock Cycles
Rev. 2.1
200
220
240
260
Unsigned 16-bit Division
194
41
217
Division,16x16->16
5000
4500
4000
Samples (out of 10,000)
Mean:
Min:
Max:
3500
3000
2500
2000
1500
1000
500
0
40
60
80
100
120
140
160
System Clock Cycles
Rev. 2.1
180
200
220
19
Signed 32-bit Division
Mean:
Min:
Max:
359
334
795
Division,32x32->32
5000
4500
Samples (out of 10,000)
4000
3500
3000
2500
2000
1500
1000
500
0
300
20
350
400
450
500
550
600
System Clock Cycles
Rev. 2.1
650
700
750
800
Unsigned 32-bit Division
331
309
770
Division,32x32->32
5000
4500
4000
Samples (out of 10,000)
Mean:
Min:
Max:
3500
3000
2500
2000
1500
1000
500
0
300
350
400
450
500
550
600
System Clock Cycles
Rev. 2.1
650
700
750
800
21
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22
Rev. 2.1
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