AP32307 - XMC1000 - Math Coprocessor(MATH)

XMC 1000
32-bit Microcontroller Series for Industrial Applications
Math Coprocessor (MA TH)
AP32307
Application Note
About this document
Scope and purpose
This document describes how to use the MATH Coprocessor for the XMC 32-bit Microcontroller. The
document includes code snippets and examples for a variety of use cases.
Intended audience
This document is intended for engineers who are developing applications that require math-intensive
computations with the XMC Microcontroller series.
Applicable Products

XMC130x

XMC140x

DAVE ™
References
Infineon: Example code: http://www.infineon.com/XMC1000 Tab: Documents
Infineon: XMC Lib, http://www.infineon.com/DAVE
Infineon: DAVE™, http://www.infineon.com/DAVE
Infineon: XMC Reference Manual, http://www.infineon.com/XMC1000 Tab: Documents
Infineon: XMC Data Sheet, http://www.infineon.com/XMC1000 Tab: Documents
V1.0
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2015-07
Math Coprocessor (MATH)
AP32307
Table of Contents
Table of Contents
About this document .....................................................................................................................1
Table of Contents ..........................................................................................................................2
1
1.1
1.2
MATH Coprocessor Overview .........................................................................................3
Features ............................................................................................................................................... 3
MATH Library ....................................................................................................................................... 3
2
2.1
2.2
2.3
2.4
2.5
2.6
2.7
Division Operation ........................................................................................................4
Configuration for Signed or Unsigned division operation ................................................................. 4
Configuration for starting the division operation .............................................................................. 4
Poll for the result to be ready ............................................................................................................. 5
Generate an Interrupt when result is ready ....................................................................................... 5
Divide by Zero Error ............................................................................................................................ 5
Using XMC Lib for DIV operations ....................................................................................................... 6
DIVS Benchmarking Results ................................................................................................................ 7
3
3.1
3.2
3.3
3.4
3.5
3.5.1
3.6
3.6.1
3.6.2
3.6.3
3.7
CORDIC ........................................................................................................................9
Configuration for CORDIC operation .................................................................................................. 9
Configuration for starting CORDIC operation .................................................................................. 10
Poll for the result to be ready ........................................................................................................... 11
Generate an Interrupt on completion .............................................................................................. 11
Using XMC Lib for CORDIC calculation.............................................................................................. 11
Calculating exp(z)........................................................................................................................ 13
CORDIC Examples .............................................................................................................................. 13
Calculating Vector Magnitude and Angle ................................................................................... 13
Calculating ln(x) .......................................................................................................................... 14
Calculating sqrt(x) ....................................................................................................................... 15
CORDIC Benchmarking Results ........................................................................................................ 16
4
4.1
4.2
4.3
4.4
4.5
Result Chaining........................................................................................................... 17
Data Compatibility between 32-bit DIV and 24-bit CORDIC............................................................. 17
Transfer of data from DIV to CORDIC ................................................................................................ 18
Transfer of data from CORDIC to DIV ................................................................................................ 18
Handling Busy Flags during Result Chaining ................................................................................... 18
Result Chaining Example .................................................................................................................. 18
5
Appendix .................................................................................................................... 20
6
Revision History .......................................................................................................... 21
Application Note
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Math Coprocessor (MATH)
AP32307
MATH Coprocessor Overview
1
MATH Coprocessor Overview
The Math Coprocessor (MATH) module provides assistance for math-intensive computations. The module
comprises of two independent sub-blocks which are executed in parallel to the CPU core. The two subblocks are:

A 32-bit Divider Unit (DIV) for signed and unsigned division functions

A 24-bit CORDIC (COrdinate Rotation DIgital Computer) for trigonometric, linear and hyperbolic
functions
1.1
Features
The MATH module includes the following features:

Divide function with operand pre-processing and result post-processing

CORDIC Coprocessor for computation of trigonometric, hyperbolic and linear functions

Support kernel clock to interface clock ratio 2:1 for faster execution

Support result chaining between the Divider Unit and CORDIC Coprocessor
1.2
MATH Library
The MATH library is a collection of Application Programming Interfaces (APIs) to compute common
mathematical operations such as division, modulus and trigonometric functions. The APIs configure the
respective registers of the MATH sub-blocks to perform the requested calculations. The library is provided as
part of the XMC Library (XMC Lib) from Infineon.
The APIs provided in the MATH library can be categorized as Blocking and Non-blocking. The blocking APIs
poll for the result by reading the result register. This adds wait states to the bus until the result is ready.
While waiting for the result, all other operations are blocked, hence the name.
The non-blocking APIs start the desired calculations and then control is returned to the calling thread. This
allows other operations to continue. The user can check if a calculation has ended by polling the busy flag of
the MATH Coprocessor. When the busy flag is cleared, the user can read the calculation result by calling the
GetResult APIs.
Note: The occurence of interrupts during the execution of non-blocking APIs may lead to erroneous results.
For example, the execution of a divide instruction ( ‘/’ ) in an interrupt service routine during the
execution of a non-blocking API may give erroneous results.
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Division Operation
2
Division Operation
DIVS supports the truncated division operation, which is the ISO C99 standard and the most popular choice
among modern processors:

q = D divide by d

r = D modulus by d
“D” is the dividend
(DVD register)
“d” is the divisor
(DVS register)
“q” is the quotient
(QUOT register)
“r” is the remainder
(RMD register)
2.1
Configuration for Signed or Unsigned division operation
Configuration is via the DIVCON.USIGN bit:

DIVCON.USIGN = 0
Signed division

DIVCON.USIGN = 1
Unsigned division
2.2
Configuration for starting the division operation
There are two methods for starting the division operation. Either:
1. Set the ST bit
2. Or have the division operation start automatically by loading a value into the DVS register
Starting the division operation by setting the ST bit
MATH->DIVCON = (1<<MATH_CON_ST_MODE_Pos);
// DIVCON.STMODE = 1
// Calculation start when ST bit is set
MATH->DVD = 0x12345678;
// Load the dividend value
MATH->DVS = 0x11223344;
// Load the divisor value
MATH->DIVCON |= (1<<MATH_CON_ST_Pos); // DIVCON.ST = 1
// ST bit is set. The division begins
Starting the division operation automatically
MATH->DIVCON = (0<<MATH_CON_ST_MODE_Pos);
// DIVCON.STMODE = 0
// Calculation start when write to DVS register
MATH->DVD = 0x12345678;
// Load the dividend value
MATH->DVS = 0x11223344;
// Load the divisor value, the division begin
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Division Operation
2.3
Poll for the result to be ready
The division operation takes 35 kernel clock cycles. The BSY flag is set to 1 when the division operation
starts.
On completion, the quotient and remainder values are available in the QUOT and RMD registers, and the BSY
flag is cleared.

DIVST.BSY = 0
DIV is not running any division operation

DIVST.BSY = 1
DIV is still running a division operation
// Insert code for division operation to start
while(MATH->DIVST);
// Wait until DIV is ready (Not busy)
// Insert code to read out result
2.4
Generate an Interrupt when result is ready
When the division is finished, the Divider event flag EVFR.DIVEOC is set. This can trigger an interrupt request
to the NVIC by enabling the EVIER.DIVEOCIEN bit. This event flag can only be cleared by a software write to
the EVFCR.DIVEOCC bit:
MATH->EVIER = (1<<MATH_EVIER_DIVEOCIEN_Pos); // EVIER.DIVEOCIEN = 1
// End of divider calculation interrupt generation is enabled
NVIC_EnableIRQ(7);
// Enabled MATH interrupt node
// Insert code for division operation to start
……………………………………………………………………………………………
// Inside the MATH ISR
MATH->EVFCR = (1<<MATH_EVFCR_DIVEOCC_Pos);
// EVFCR.DIVEOCC = 1
// Clear Divider end of calculation flag in EVFR
2.5
Divide by Zero Error
If a division operation is started with the divisor value equal to 0, the EVFR.DIVERR flag is set. The interrupt
request to the NVIC can be generated by enabling it with EVIER.DIVERRIEN. This event flag can only be
cleared by a software write to the EVFCR.DIVERRC bit.
MATH->EVIER = (1<<MATH_EVIER_DIVERRIEN_Pos); // EVIER.DIVERRIEN = 1
// Divider error interrupt generation is enabled
NVIC_EnableIRQ(7);
// Enabled MATH interrupt node
// Insert code for division operation to start
……………………………………………………………………………………………
// Inside the DIV_ERROR ISR
MATH->EVFCR = (1<<MATH_EVFCR_DIVERRC_Pos);
// EVFCR.DIVERRC = 1
// Clear the Divider error event flag in EVFR
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Division Operation
2.6
Using XMC Lib for DIV operations
The MATH Library provides alternate implementations of the ARM Embedded Application Binary Interface
(AEABI) functions for division and modulus operations. These alternate implementations use the DIV subblock to perform the operations. The following examples demonstrate their usage:
Blocking division operation
uint32_t a = 5000;
uint32_t b = 250;
uint32_t c = a / b;
Blocking modulus operation
uint32_t a = 5000;
uint32_t b = 240;
uint32_t c = a % b;
In both examples above, the ‘/’ and ‘%’ operators are automatically recognized and the respective AEABI
functions are called to perform the operations using the DIV sub-block.
Note: Only signed and unsigned integer division and modulus operations are supported by the MATH Library.
Non-blocking division operation
/* variable initialization */
uint32_t calculation_dividend = 5000;
uint32_t calculation_divisor = 250;
uint32_t calculation_result;
/* unsigned division calculation */
XMC_MATH_DIV_UnsignedDivNB(calculation_dividend,calculation_divisor);
while(XMC_MATH_DIV_IsBusy()); // wait for calculation to end
calculation_result = XMC_MATH_DIV_GetUnsignedDivResult();
In the example above, the XMC_MATH_DIV_IsBusy() API is used to check for the end of calculation.
Alternatively, the user can also perform other operations and read the CORDIC calculation result only after a
determined number of clock cycles or use an interrupt. The following example demonstrates the usage of an
interrupt.
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Division Operation
Non-blocking modulus operation
/* variable initialization */
uint32_t calculation_dividend = 5000;
uint32_t calculation_divisor = 240;
uint32_t calculation_result;
/* configure DIV end-of-calculation interrupt */
XMC_MATH_EnableEvent(XMC_MATH_EVENT_DIV_END_OF_CALC);
NVIC_SetPriority(MATH0_0_IRQn,3);
NVIC_EnableIRQ(MATH0_0_IRQn);
/* unsigned modulus calculation */
XMC_MATH_DIV_UnsignedModNB(calculation_dividend,calculation_divisor);
/* MATH Interrupt Handler */
void MATH0_0_IRQHandler(void)
{
uint32_t calculation_result;
XMC_MATH_ClearEvent(XMC_MATH_EVENT_DIV_END_OF_CALC);
calculation_result = XMC_MATH_DIV_GetUnsignedModResult();
}
2.7
DIVS Benchmarking Results
The performance of the Divider is evaluated by benchmarking the execution time of a division operation
running on the MATH Library against that of a similar operation running on a standard C library. The
execution time is measured in terms of the number of MCLK cycles.
The conditions for the benchmarking are as follows:

Execution time refers to complete function execution, inclusive of co-processor configuration, writing of
operands and state checking.

The ratio of PCLK to MCLK is 2:1.

Compilers from Infineon, Keil™ and IAR were used.
Application Note
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Division Operation
Table 1
Benchmarking results for division operation
Compiler
Number of MCLK cycles
With MATH Library
With Standard C Library
IAR EWARM v7.10
99
712
Keil™ Vision v5.10
95
230
114
415
TM
DAVE v3.1.10
From the benchmarking results, a division operation with the MATH library can be up to 7 times faster than a
similar operation with the standard C library.
Application Note
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CORDIC
3
CORDIC
The CORDIC algorithm is a useful convergence method for 24-bit computation of trigonometric (circular),
linear (multiply-add), hyperbolic and related functions. It allows performance of vector rotation not only in
the Euclidian plane, but also in the Linear and Hyperbolic planes.
CORDX, CORDY, and CORDZ are Data registers which are used to initialize the X, Y and Z parameters.
Figure 1
CORDIC data register structure
CORRX, CORRY, and CORRZ are Result registers from the CORDIC calculation.
Figure 2
CORDIC result register structure
3.1
Configuration for CORDIC operation
Table 2 gives an overview of the different CORDIC operating modes.
X, Y and Z represent the initial data and Xfinal, Yfinal & Zfinal represent the final result data when the CORDIC
computation is completed.
Table 2
Operating Modes of CORDIC
Function
Circular
Linear
Application Note
Rotation Mode
Xfinal = K[X cos(Z) - Y sin(Z)] / MPS
Vectoring Mode
Yfinal = K[Y cos(Z) + X sin(Z)] / MPS
Yfinal = 0
Zfinal = 0
Zfinal = Z + atan(Y / X)
K ≈ 1.646760258121
K ≈ 1.646760258121
Xfinal = X / MPS
Xfinal = X / MPS
Yfinal = [Y + X Z] / MPS
Yfinal = 0
Zfinal = 0
Zfinal = Z + Y / X
9
Xfinal = K sqrt(X2+Y2) / MPS
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CORDIC
Function
Hyperbolic
Rotation Mode
Xfinal = k[X cosh(Z) + Y sinh(Z)] / MPS
Vectoring Mode
Yfinal = k[Y cosh(Z) + X sinh(Z)] / MPS
Yfinal = 0
Zfinal = 0
Zfinal = Z + atanh(Y / X)
k ≈ 0.828159360960
k ≈ 0.828159360960
Xfinal = k sqrt(X2-Y2) / MPS
The different modes are configured via the ROTVEC and MODE fields in the CON control register.

CON.ROTVEC = 0
Vectoring Mode

CON.ROTVEC = 1
Rotation Mode

CON.MODE = 00b
Linear Mode

CON.MODE = 01b
Circular Mode

CON.MODE = 11b
Hyperbolic Mode
The X and Y Magnitude Prescaler (MPS) prevents the result data from overflowing. At the end of calculation,
the computed values of X and Y are each divided by the MPS factor to yield the final result.
Note: Refer to the appendix for other mathematical calculations supported by CORDIC.
3.2
Configuration for starting CORDIC operation
There are two methods to start the CORDIC operation:

Set the ST bit

Or have the operation automatically start by loading a value into the CORDX register
Starting the CORDIC operation by setting the ST bit
MATH->CON = (1<<MATH_CON_ST_MODE_Pos); // CON.STMODE = 1;
// Calculation start when ST bit is set to 1
MATH->CORDZ = 0x12345600;
MATH->CORDY = 0x11223300;
MATH->CORDX = 0x33221100;
MATH->CON |= (1<<MATH_CON_ST_Pos);
// CON.ST = 1;
// Start the CORDIC operation
Starting the CORDIC operation automatically
MATH->CON = (0<<MATH_CON_ST_MODE_Pos); // CON.STMODE = 0;
// Calculation start with a write to CORDX
MATH->CORDZ = 0x12345600;
MATH->CORDY = 0x11223300;
MATH->CORDX = 0x33221100; // Load CORDX value and start CORDIC operation
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CORDIC
3.3
Poll for the result to be ready
The CORDIC operation takes 62 kernel clock cycles. The BSY flag is set when operation starts.
On completion, the BSY flag is cleared.

STATC.BSY = 0
CORDIC is not computing any calculation

STATC.BSY = 1
CORDIC is still computing a calculation
// Insert code for CORDIC to start
while((MATH->STATC)&(1<<MATH_STATC_BSY_Pos));
// wait until CORDIC is ready (Not busy)
// Insert code to read out result
3.4
Generate an Interrupt on completion
At the end of the CORDIC computation, the event flag EVFR.CDEOC is set. An interrupt request to the NVIC
can be triggered by enabling the EVIER.CDEOCIEN bit. This event flag can only be cleared by a software write
to the EVFCR.CDEOCC bit.
MATH->EVIER = (1<<MATH_EVIER_CDEOCIEN_Pos);
// EVIER.CDEOCIEN = 1
// End of CORDIC calculation interrupt generation is enabled
NVIC_EnableIRQ(7);
// Enable MATH interrupt node
// Insert code for CORDIC to start
………………………………………………………………………………………..
// Inside the MATH ISR
MATH->EVFCR = (1<<MATH_EVFCR_CDEOCC_Pos);
// EVFCR.CDEOCC = 1
// Clear CORDIC end of calculation event flag in EVFR
3.5
Using XMC Lib for CORDIC calculation
The MATH Library supports the following CORDIC calculations:

Trigonometric: Sin, Cos, Tan, Atan

Hyperbolic: Sinh, Cosh, Tanh
When using the XMC Lib APIs for calculations where the input data is an angle, it is essential that the input
angle is converted using the following equation:
Input_angle = (angle_in_rad) * 8388608 / π
For example, to calculate cos(π/6), the input angle is:
Input_angle = (π/6) * 8388608 / π = 1398101 or 0x155555
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CORDIC
Example using Blocking APIs
/* variable initialization */
XMC_MATH_Q0_23_t angle = 0x2AAAAA; // (pi/3)*8388608/pi
XMC_MATH_Q0_23_t calculation_result;
/* cosine of angle calculation */
calculation_result = XMC_MATH_CORDIC_Cos(angle);
Example using Non-Blocking APIs
/* variable initialization */
XMC_MATH_Q0_23_t angle = 0x155555; // (pi/6)*8388608/pi
XMC_MATH_Q0_23_t calculation_result;
/* cosine of angle calculation */
XMC_MATH_CORDIC_CosNB(angle);
while(XMC_MATH_CORDIC_IsBusy()); // wait for calculation to end
calculation_result = XMC_MATH_CORDIC_GetCosResult();
In the non-blocking API example above, the XMC_MATH_CORDIC_IsBusy() API is used to check for the end
of the calculation. The user can instead perform other operations and read the CORDIC calculation result
only after a determined number of clock cycles or use an interrupt. The following example demonstrates the
use of an interrupt.
Example using Non-Blocking API and Interrupt
/* variable initialization */
XMC_MATH_Q0_23_t angle = 0x860A91; // (pi/3)*8388608/pi
/* configure CORDIC end-of-calculation interrupt */
XMC_MATH_EnableEvent(XMC_MATH_EVENT_CORDIC_END_OF_CALC);
NVIC_SetPriority(MATH0_0_IRQn,3);
NVIC_EnableIRQ(MATH0_0_IRQn);
/* cosine of angle calculation */
XMC_MATH_CORDIC_CosNB(angle);
/* MATH Interrupt Handler */
void MATH0_0_IRQHandler(void)
{
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CORDIC
XMC_MATH_Q0_23_t calculation_result;
XMC_MATH_ClearEvent(XMC_MATH_EVENT_CORDIC_END_OF_CALC);
calculation_result = XMC_MATH_CORDIC_GetCosResult();
}
3.5.1
Calculating exp(z)
It is known that:
exp(z) = sinh(z) + cosh(z)
The following example demonstrates how exp(0.5) can be calculated using the XMC Lib.
/* variable initialization */
XMC_MATH_Q0_23_t angle = 0x145F30; // 0.5*8388608/pi
XMC_MATH_Q0_23_t calculation_result;
/* hyperbolic sine of angle calculation */
calculation_result = XMC_MATH_CORDIC_Sinh(angle);
/* hyperbolic cosine of angle calculation (also final result) */
calculation_result += XMC_MATH_CORDIC_Cosh(angle);
Although the MATH Library supports only the abovementioned calculations, the CORDIC sub-block is
capable of computing many other calculations. These calculations can be performed by manually
configuring the registers of CORDIC. Refer to Figure 6 for a more complete view on the different
computations that can be performed with CORDIC.
3.6
CORDIC Examples
This section provides some CORDIC use-cases.
3.6.1
Calculating Vector Magnitude and Angle
The following example illustrates the use of CORDIC in the Circular Vectoring Mode for the calculation of the
magnitude and angle of two vectors.
Table 3
CORDIC Circular Vectoring Mode
Function
Circular
Vectoring Mode
2
2
Xfinal = K sqrt(X +Y ) / MPS
Yfinal = 0
Zfinal = Z + atan(Y / X)
K ≈ 1.646760258121
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CORDIC
MATH->CON = 0x0002;
// MODE = 01b, Circular Mode
// ROTVEC = 0, Vectoring Mode
// ST_MODE = 0, Auto start when CORDX is written
MATH->CORDZ = 0;
// Load the initial angle value
MATH->CORDY = (vector2<<8);
// Load the magnitude of vector 2
MATH->CORDX = (vector1<<8);
// Load the magnitude of vector 1
// CORDIC will automatically start
while((MATH->STATC)&(1<<MATH_STATC_BSY_Pos));
// wait until CORDIC is ready (Not busy)
Result_Mag = MATH->CORRX;
// Read out the result
Result_Ang = MATH->CORRZ;
3.6.2
Calculating ln(x)
It is known that:
ln(x) = 2*atanh[(x-1)/(x+1)]
CORDIC can be used in the Hyperbolic Vectoring mode for the calculation above by setting the initial input
data as follows:
X=x+1
Y=x-1
The following example illustrates the calculation of ln(variable_x) using CORDIC.
MATH->CON = 0x0006;
// MODE = 11b, Hyperbolic Mode
// ROTVEC = 0, Vectoring Mode
// ST_MODE = 0, Auto start when CORDX is written
MATH->CORDZ = 0;
// Load the initial angle value
MATH->CORDY = ((variable_x-1)<<8);
// Load (x-1)
MATH->CORDX = ((variable_x+1)<<8);
// Load (x+1)
// CORDIC will automatically start
while((MATH->STATC)&(1<<MATH_STATC_BSY_Pos));
// wait until CORDIC is ready (Not busy)
Result = (MATH->CORRZ>>8);
Application Note
// Read out the result of atanh
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CORDIC
Result = 2*Result;
// final result is scaled by 8388608/pi
Note: The result of this calculation has a scaling of 8388608/π.
3.6.3
Calculating sqrt(x)
It is known that:
sqrt(x) = sqrt[(x+0.25)2-(x-0.25)2]
CORDIC can be used in the Hyperbolic Vectoring mode for the calculation above by setting the initial input
data as follows:
X = (x + 0.25) / k
Y = (x - 0.25) / k
where k = 0.82815936960
The user should ensure that the input data lie within the domain of convergence, meaning atanh|Y/X| ≤ 1.11
radians.
The following example demonstrates the square root calculation of a Q1.8 number. The calculated result is a
Q5.12 number.
#define GAIN 0x0135
// (2^8)/0.82815936960
uint32_t number = 0x01C0;
MATH->CON = 0x0006;
// MODE = 11b, Hyperbolic Mode
// ROTVEC = 0, Vectoring Mode
// ST_MODE = 0, Auto start when CORDX is written
MATH->CORDZ = 0;
// Load the initial angle value
MATH->CORDY = ((GAIN*(number-0x40))<<8);
// Load (x-0.25)/k
MATH->CORDX = ((GAIN*(number+0x40))<<8);
// Load (x+0.25)/k
// CORDIC will automatically start
while((MATH->STATC)&(1<<MATH_STATC_BSY_Pos));
// wait until CORDIC is ready (Not busy)
Result = (MATH->CORRX>>8);
Application Note
// Read out the result
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CORDIC
3.7
CORDIC Benchmarking Results
The performance of the CORDIC co-processor is evaluated by benchmarking the execution time of a cosine
calculation running on the MATH Library against that of a similar operation running on a standard C library.
The execution time is measured in terms of the number of MCLK cycles.
The conditions for the benchmarking are as follows:

Execution time refers to complete function execution, inclusive of co-processor configuration, writing of
operands and state checking.

The ratio of PCLK to MCLK is 2:1.

Compilers from Infineon, Keil™ and IAR were used.
Table 4
Benchmarking results for cosine calculation
Compiler
Number of MCLK cycles
With MATH Library
With Standard C Library
IAR EWARM v7.10
234
4574
Keil Vision v5.10
238
6514
258
9832
TM
DAVE v3.1.10
From the benchmarking results, a cosine calculation with the MATH library can be up to 38 times faster than
a similar operation with the standard C library.
Application Note
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Result Chaining
4
Result Chaining
The MATH Coprocessor supports result chaining between the DIV and CORDIC modules. The DIV result can
be passed to the input of the CORDIC data register. Similarly, the CORDIC result can also be passed to the
input of the DIV DVD and DVS registers.
GLBCON.DVDRC and GLBCON.DVSRC

000b
No result chaining

001b
QUOT register is the input to DIV

010b
RMD register is the input to DIV

011b
CORRX register is the input to DIV

100b
CORRY register is the input to DIV

101b
CORRZ register is the input to DIV
GLBCON.CORDXRC, GLBCON.CORDYRC and GLBCON.CORDZRC

00b
No result chaining

01b
QUOT register is the input to DIV

10b
RMD register is the input to DIV
4.1
Data Compatibility between 32-bit DIV and 24-bit CORDIC
The data and result register for the DIV are assigned to bits[0 to 31].
Figure 3
DIV data and result register structure
The data and result register for the CORDIC are assigned to bits[8 to 31].
Figure 4
CORDIC data and result register structure
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Result Chaining
4.2
Transfer of data from DIV to CORDIC
The DIV’s quotient final value can be left-shifted by 8 to fit into the CORDIC data register format.

DIVCON.QSCNT
Number of bits the quotient is shifted after the division

DIV.QSDIR = 0
Left shift

DIV.QSDIR = 1
Right shift
4.3
Transfer of data from CORDIC to DIV
The DIV’s final divisor value can be right-shifted by 8 when it is updated by the CORDIC result register.

DIVCON.DVSSRC
Number of bits the divisor is shifted right before the division

DIV.QSDIR = 0
Left-shift
4.4
Handling Busy Flags during Result Chaining
When the DIV result is chained to the CORDIC’s CORDX, if CON.ST_MODE = 0 the start of the DIV calculation
sets the DIV’s busy flag and also sets the CORDIC’s busy flag.
After completion of the DIV operation, the result is written into the DIV’s register and CORDX. The DIV’s busy
flag is not immediately cleared. Instead, both the DIV and CORDIC busy flags are cleared after the CORDIC
calculation is completed.
Figure 5
Busy flags during Result Chaining
The rule described above is applied in the other direction when the CORDIC result is chained to DIV’s DVS
register and DIVCON.STMODE = 0.
4.5
Result Chaining Example
The following example illustrates the use of result chaining by updating the input data of DIV’s divisor using
the CORDIC’s CORRX output result.
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Result Chaining
/* DVSRC = 011b, DVS result will be updated when CORRX has new result */
MATH->GLBCON = XMC_MATH_DIV_DVSRC_CORRX_IS_SOURCE;
/* STMODE = 0, Auto start when DVS is written */
/* DVSSRC = 8, DVS value right shifted by 8 */
MATH->DIVCON = (0<<MATH_DIVCON_STMODE_Pos)+(8<<MATH_DIVCON_DVSSRC_Pos);
/* Preload the dividend value first */
MATH->DVD = 0x12345678;
/* MODE = 01b, Circular Mode */
/* ROTVEC = 0, Vectoring Mode */
/* ST_MODE = 0, Auto start when CORDX is written */
MATH->CON = XMC_MATH_CORDIC_OPERATING_MODE_CIRCULAR +
XMC_MATH_CORDIC_ROTVEC_MODE_VECTORING + (0<<MATH_CON_ST_MODE_Pos);
/* Load the initial angle value */
MATH->CORDZ = 0;
/* Load the magnitude of Vector2 */
MATH->CORDY = (0x123456<<8);
/* Load the magnitude of Vector1 */
MATH->CORDX = (0x112233<<8);
// CORDIC will automatically start
// …………………………………………………………………………………..
// CORDIC result to DVS will start DIV
while(XMC_MATH_DIV_IsBusy()); // wait until DIV is ready (Not busy)
Result = MATH->QUOT;
Application Note
// Read out the result
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Appendix
5
Appendix
Figure 6
CORDIC Coprocessor Operating Modes and Corresponding Result Data
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Revision History
6
Revision History
Current Version is V1.0, 2015-07
Page or Reference
Description of change
V1.0, 2015-07
Initial Version
Application Note
21
V1.0, 2015-07
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