Digital Sine-Wave Generation Using the TMS320C2xx … · Digital Sine-Wave Generation Using the TMS320C2xx iii ... 2.1 C- and Assembly-Compatible Functions 2 ... Digital Sine-Wave

��

ApplicationReport

1998 Digital Signal Processing Solutions

Printed in U.S.A., July 1998 SPRA179

1998

ReportApplication

��

��

Digital Sine-Wave GenerationUsing the TMS320C2xx

SPRA179July 1998

Printed on Recycled Paper

IMPORTANT NOTICE

Texas Instruments and its subsidiaries (TI) reserve the right to make changes to their productsor to discontinue any product or service without notice, and advise customers to obtain the latestversion of relevant information to verify, before placing orders, that information being relied onis current and complete. All products are sold subject to the terms and conditions of sale suppliedat the time of order acknowledgement, including those pertaining to warranty, patentinfringement, and limitation of liability.

TI warrants performance of its semiconductor products to the specifications applicable at thetime of sale in accordance with TI’s standard warranty. Testing and other quality controltechniques are utilized to the extent TI deems necessary to support this warranty. Specific testingof all parameters of each device is not necessarily performed, except those mandated bygovernment requirements.

CERTAIN APPLICATIONS USING SEMICONDUCTOR PRODUCTS MAY INVOLVEPOTENTIAL RISKS OF DEATH, PERSONAL INJURY, OR SEVERE PROPERTY ORENVIRONMENTAL DAMAGE (“CRITICAL APPLICATIONS”). TI SEMICONDUCTORPRODUCTS ARE NOT DESIGNED, AUTHORIZED, OR WARRANTED TO BE SUITABLE FORUSE IN LIFE-SUPPORT DEVICES OR SYSTEMS OR OTHER CRITICAL APPLICATIONS.INCLUSION OF TI PRODUCTS IN SUCH APPLICATIONS IS UNDERSTOOD TO BE FULLYAT THE CUSTOMER’S RISK.

In order to minimize risks associated with the customer’s applications, adequate design andoperating safeguards must be provided by the customer to minimize inherent or proceduralhazards.

TI assumes no liability for applications assistance or customer product design. TI does notwarrant or represent that any license, either express or implied, is granted under any patent right,copyright, mask work right, or other intellectual property right of TI covering or relating to anycombination, machine, or process in which such semiconductor products or services might beor are used. TI’s publication of information regarding any third party’s products or services doesnot constitute TI’s approval, warranty or endorsement thereof.

Copyright 1998, Texas Instruments Incorporated

iii Digital Sine-Wave Generation Using the TMS320C2xx

Contents1 Introduction 1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

2 Direct Look-Up and Linear Interpolation Method 2. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1 C- and Assembly-Compatible Functions 2. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

2.1.1 C-Compatible Functions 2. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1.2 Assembly-Compatible Functions 2. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

2.2 Interpolation 3. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3 Functions 3. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.4 System Utilization 3. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.5 Sine-Generation Precision 4. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

2.5.1 One-Sine-Period Analysis 4. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.5.2 Quarter-Sine-Period Analysis 7. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

3 Sine/Cosine With Mathematical Series 10. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1 C- and Assembly-Compatible Functions 10. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

3.1.1 C-Compatible Functions 10. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1.2 Assembly-Compatible Functions 10. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

3.2 Sine/Cosine Mathematical Series 11. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3 Functions 11. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4 System Utilization 11. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.5 Sine-Generation Precision 12. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

3.5.1 One-Sine-Period Analysis 13. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.5.2 Quarter-Sine-Period Analysis 14. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Appendix A Examples of a C Program and an Assembly Program Calling Sine andCosine Functions A-1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A.1 Main C Program to Call Sine or Cosine Functions A-1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A.2 Main Assembly Program to Call Sine or Cosine Functions A-2. . . . . . . . . . . . . . . . . . . . . . . A.3 COS Function With Direct Look-Up and Linear Interpolation for Assembly Program A-4. A.4 COS Function With Direct Look-Up and Linear Interpolation for C Program A-7. . . . . . . . A.5 SIN Function With Direct Look-Up and Linear Interpolation for

Assembly Program A-10. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A.6 SIN Function With Direct Look-Up and Linear Interpolation for C Program A-13. . . . . . . . A.7 Table for COS or SIN Function With Direct Look-Up A-16. . . . . . . . . . . . . . . . . . . . . . . . . . . . A.8 COS_SIN Function With Direct Look-Up and Linear Interpolation for

Assembly Program A-19. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A.9 Table for COS_SIN Function With Direct Look-Up A-23. . . . . . . . . . . . . . . . . . . . . . . . . . . . . A.10 SIN With Mathematical Series for Assembly Program A-27. . . . . . . . . . . . . . . . . . . . . . . . . A.11 SIN With Mathematical Series for C Program A-30. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A.12 COS With Mathematical Series for Assembly Program A-34. . . . . . . . . . . . . . . . . . . . . . . . A.13 COS With Mathematical Series for C Program A-38. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Figures

SPRA179iv

List of Figures

1 The Formula and the Resulting Graph for Calculating the Table InterpolationValue COS of an Angle 3. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

2 Direct Look-Up With Interpolation of Sine Calculation From 0 to 2*π With a 0.015-Radian Step 5. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

3 Error Between the C Floating-Point Result and Direct Look-Up Calculation From 0 to 2*π With a 0.015-Radian Step 6. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

4 Results of Direct Look-Up SIN From 0 to π/2 With a 0.0039-Radian Step 7. . . . . . . . . . . . . . .

5 Error Between the C Floating-Point Result and Direct Look-Up SINE Calculation From 0 to π/4 With a 0.0039-Radian Step in Q15 Format 8. . . . . . . . . . . . . . . . . . . . . . . . . . . . .

6 Error Between the C Floating-Point Result and the Direct Look-Up SINE Calculation From 0 to π/4 With a 0.0039-Radian Step in % 9. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

7 Formula for Calculating the Value SIN of an Angle 11. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

8 Formula for Calculating the Value COS of an Angle 11. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

9 Mathematical Series Sine Calculation From 0 to 2*π With a 0.015-Radian Step 13. . . . . . . .

10 Error Between the C Floating-Point Result and the Mathematical Series SINE Calculation From 0 to 2*π With a 0.015-Radian Step 14. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

11 Results of Mathematical Series Sine From 0 to π/2 With a 0.0039-Radian Step 15. . . . . . . . .

12 Error Between the C Floating-Point Result and a Mathematical Series SINE Calculation From 0 to π/4 With a 0.0039-Radian Step in Q15 Format 16. . . . . . . . . . . . . . . . .

13 Error Between the C Floating-Point Result and a Mathematical Series SINE Calculation From 0 to π/4 With a 0.0039-Radian Step in % 17. . . . . . . . . . . . . . . . . . . . . . . . . .

Tables

v Digital Sine-Wave Generation Using the TMS320C2xx

List of Tables1 Processor Utilization (Maximum) When Using Direct Look-up and Interpolation 4. . . . . . . . . 2 Memory Utilization When Using Direct Look-up and Interpolation 4. . . . . . . . . . . . . . . . . . . . . . 3 Processor Utilization (Maximum) When Using Mathematical Series 11. . . . . . . . . . . . . . . . . . . 4 Memory Utilization When Using Mathematical Series 12. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

SPRA179vi

1 Digital Sine-Wave Generation Using the TMS320C2xx

Digital Sine-Wave Generation Using the TMS320C2xx

ABSTRACTThis application report describes two methods for implementing a digital sine-wavegenerator using the TMS320C2xx: the use of a direct look-up table with linearinterpolation, and the use of mathematical series. Both methods are explained interms of C-compatible and assembly-compatible functions. Formulas used forcalculating and graphing the results are included for each method to demonstratethe differences.

1 IntroductionSine-wave generators are fundamental building blocks of signal processingsystems for use in control applications. The following two methodsdescribed in this application report are for implementing a digital sine-wavegenerator using the TMS320C2xx:

• Direct look-up with linear interpolation to provide sine waves with aminimum of harmonic distortion

• Realization of the sine/cosine functions with a mathematical series

The two methods respond to different constraints. The direct look-upmethod is fast with minimal errors and is significant in ROM programmingrequirements. The mathematical series method is fast and requiresminimum (ROM) programming but results in less precision.

Direct Look-Up and Linear Interpolation Method

SPRA1792

2 Direct Look-Up and Linear Interpolation MethodThis section describes the Direct Look-Up and Linear Interpolation methodof implementing a digital sine-wave generator using the TMS320C2xx.

2.1 C- and Assembly-Compatible Functions

The Direct Look-Up method, which uses 100 sine-period values in a table,reveals the sine/cosine functions. To provide minimum harmonic distortion,the method includes linear interpolation with a fixed-step table. An extendedtable is used for the cosine + sine function and is located in program memory.

Two versions of each function are presented:

• C-compatible functions

• Assembly-compatible functions

Examples of a C program and an assembly program (that call sine andcosine functions) are in the appendix.

2.1.1 C-Compatible Functions

Fully C-compatible functions employ C conventions to use the stack forparameters passed to the functions. Parameters returned by the functionsare passed by a pointer. Responsibilities of called functions are managedin a postfix expression called the function designator. Stack pointer AR1 iswell-positioned, and the return address of the hardware stack is popped(retrieved) in case of C-interrupt runtime events using C-function features(stack). The frame pointer is not modified and registers AR6 and AR7 arenot used.

2.1.2 Assembly-Compatible Functions

Assembly-compatible functions do not use their own variables, but instead,rely on variables in a software stack where arguments are passed. The AR1register points to the stack just after the last argument. After the return fromthe function, the results are placed in the stack. Registers AR0, AR6, andAR7 are not modified.



2.2 Interpolation

Figure 1 shows the formula and the resulting graph for calculating the tableinterpolation value COS(X) of an angle X.

ii+ 1x - x

Y = y + i+1 i

y - y )(

X – xi

i

r = ratiox x

i i+1

y

y

i

i+1

X

Y = ?

x

y

where:{xi} = {first coordinates of the table},{yi} = {second coordinates of the table},i chosen so that xi < X < xi+1.

Figure 1. The Formula and the Resulting Graph for Calculating the TableInterpolation Value COS of an Angle

Table interpolation is comprised of two steps:

1. Direct look-up: looking through the table to find the interval [xi, xi+1] atwhich the considered angle X is located, with xi < X < xi+1.

2. Interpolation: solving the above mentioned calculation to obtain Y.

2.3 Functions

Functions SINE, COSINE, and SINE + COSINE are illustrated by examplein the appendix. Conventions to interface with this function are:

• Input: ANGLE parameters are in the stack pointed by AR1. The valueof this angle is unsigned.

0° <-> 0000h

90° <-> 4000h

180° <-> 8000h

240° <-> C000h

• Output: COS(angle) or SIN(angle) are in ACCUMULATOR in Q15format (–1 to 1–215).

2.4 System Utilization

Table 1 shows processor utilization when using the direct look-up and linearinterpolation methods.


SPRA1794

Table 1. Processor Utilization (Maximum) When Using Direct Look-Up and Interpolation

FUNCTION CYCLES EXECUTION TIME

SIN assembly call 35 1.75 µs

COS assembly call 38 1.90 µs

SIN fully C-compatible 42 2.10 µs

COS fully C-compatible 45 2.25 µs

SIN + COS of an angle 58 2.90 µs

Table 2 shows memory utilization when using the direct look-up and linearinterpolation method.

Table 2. Memory Utilization When Using Direct Look-Up and Interpolation

FUNCTIONROM

(WORDS) STACKLEVELSREGISTERS

USEDRAM

(WORDS)

SIN assembly call 32 + 100 3 1 In stack

COS assembly call 34 + 100 3 1 In stack

COS and SIN assembly call 66 + 100 3 1 In stack

SIN Fully C compatible 42 + 100 5 1 In stack


COS + SIN in one function†

assembly call55 + 125 3 1 In stack

† In the case of Sine + Cosine, the same table is used.

2.5 Sine-Generation Precision

Figure 2 and Figure 3 are graphs that present the precision of the directlook-up and linear interpolation sine functions. The precision measurementis made by comparing the direct look-up and the floating-point C libraryresults.

2.5.1 One-Sine-Period Analysis

The sine period provides a general image of error calculation. In Figure 2and Figure 3, results of the sine calculation are in Q15 format.



Figure 2. Direct Look-Up With Interpolation of Sine Calculation From 0 to 2*π With a 0.015-Radian Step


SPRA1796

Figure 3. Error Between the C Floating-Point Result and Direct Look-Up CalculationFrom 0 to 2*π With a 0.015-Radian Step



2.5.2 Quarter-Sine-Period Analysis

Figure 4, Figure 5, and Figure 6 graph another precise analysis using aquarter of a half-sine period. In this case, the step is 0.0039 radian. Theinterpolation is made at 0.125-radian intervals. In this way, interpolationerror is exposed on the following graphs. Each interval (table approximation)is displayed with 32 pixels.

Figure 4. Results of Direct Look-Up SIN From 0 to π/2 With a 0.0039-Radian Step


SPRA1798

Figure 5. Error Between the C Floating-Point Result and the Direct Look-Up SINE Calculation From 0 to π/4 With a 0.0039-Radian Step in Q15 Format



Figure 6. Error Between the C Floating-Point Result and the Direct Look-Up SINE Calculation From 0 to π/4 With a 0.0039-Radian Step in %

Sine/Cosine With Mathematical Series

SPRA17910

3 Sine/Cosine With Mathematical SeriesThis section explains the second of two methods of implementing a digitalsine-wave generator using the TMS320C2xx.

3.1 C- and Assembly-Compatible Functions

The sine/cosine method calculates the sine/cosine functions with amathematical series for the sine period and a mathematical series forcosine. Calculations are made with fixed-point instructions to optimize thetime calculation. The dynamics used in the calculation fit with maximumprecision without overflow.

Two versions of each function are presented:




3.1.1 C-Compatible Functions

Fully C-compatible functions employ C conventions to use the stack forparameters passed to the functions. Parameters returned by functions arepassed by a pointer. Responsibilities of called functions are managed in apostfix expression called the function designator. Stack pointer AR1 iswell-positioned, and the return address of the hardware stack is popped(retrieved) in case of C-interrupt runtime events using C-function features(stack). The frame pointer is not modified and registers AR6 and AR7 arenot used.

3.1.2 Assembly-Compatible Functions




3.2 Sine/Cosine Mathematical Series

Figure 7 shows the formula for calculating the value SIN(X) of an angle X.

X in radian,If (X>=0.0)

SIN(X)=((((0.0372*X)–0.2338)*X+0.0544)*X+0.9826)*X+0.0013elseSIN(X)=((((0.0372*X)+0.2338)*X+0.0544)*X–0.9826)*X+0.0013

Figure 7. Formula for Calculating the Value SIN of an Angle

Figure 8 shows the formula for calculating the value COS(X) of an angle X.


COS(X)=(((((-0.0076*X)+0.0595)*X-0.0211)*X-0.4879)*X-0.0028)*X+1.0elseCOS(X)=(((((0.0076*X)+0.0595)*X+0.0211)*X-0.4879)*X+0.0028)*X+1.0

Figure 8. Formula for Calculating the Value COS of an Angle

3.3 Functions

Functions SINE and COSINE are illustrated by example in the appendix.Conventions to interface with these functions are:

• Input: ANGLE parameters are in the stack pointed to by AR1. The valueof this angle is unsigned.

0° <-> 0000h

90° <-> 4000h

180° <-> 8000h

240° or -90° <-> C000h


3.4 System Utilization

Table 3 shows processor utilization when using the mathematical seriesmethod.

Table 3. Processor Utilization (Maximum) When Using Mathematical Series


SIN assembly main 27 1.35 µs

COS assembly main 37 1.85 µs



SIN + COS of an angle – assembly main 64 3.20 µs


SPRA17912

Table 4 shows memory utilization when using the mathematical seriesmethod.

Table 4. Memory Utilization When Using Mathematical Series

FUNCTIONROM

(WORDS)STACKLEVELS REGISTERS USED

RAM(WORDS)

SIN 54 3 1 In stack

COS 67 3 1 In stack

SIN 64 5 1 In stack

COS 77 5 1 In stack

COS and SIN 121 3 1 In stack

3.5 Sine-Generation Precision

The following graphs present the precision of the mathematical series ofsine functions. The precision measurement is calculated by comparing themathematical series and floating-point C library results.



3.5.1 One-Sine-Period Analysis

The sine period provides a general image of error calculation. In Figure 9and Figure 10, results of the sine calculation are in Q15 format.

Figure 9. Mathematical Series Sine Calculation From 0 to 2*π With a 0.015-Radian Step


SPRA17914

Figure 10. Error Between the C Floating-Point Result and the Mathematical Series SINE Calculation From 0 to 2*π With a 0.015-Radian Step

3.5.2 Quarter-Sine-Period Analysis

Figure 11, Figure 12, and Figure 13 graph another precise analysis using aquarter of a half-sine period. In this case, the step is 0.0039 radian.



Figure 11. Results of Mathematical Series Sine From 0 to π/2 With a 0.0039-Radian Step


SPRA17916

Figure 12. Error Between the C Floating-Point Result and a Mathematical SeriesSINE Calculation From 0 to π/4 With a 0.0039-Radian Step in Q15 Format



Figure 13. Error Between the C Floating-Point Result and a Mathematical SeriesSINE Calculation From 0 to π/4 With a 0.0039-Radian Step in %

SPRA17918

Examples of a C Program and an Assembly Program Calling Sine and Cosine Functions

A-1 Digital Sine-Wave Generation Using the TMS320C2xx

Appendix A Examples of a C Program and an Assembly ProgramCalling Sine and Cosine Functions

A.1 Main C Program to Call Sine or Cosine Functions********************************************************************************

*File Name: Main_trig.c *

*Project: DMC Mathematical Library *

*Originator: Pascal DORSTER (Texas Instruments) *

*Description: Very simple main which calls COS or SIN function *

* *

* *

*Processor: C2xx *

* *

*Status: *

* *

*Last Update: 19 Oct 96 *

*______________________________________________________________________________*

*Date of Mod | DESCRIPTION *

*––––––––––––––|–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––*

* | *

********************************************************************************

extern ser_cos();

void main()

{

double rad;

double a;

int c;

.

.

.

if (rad!=0.0) /*–π < rad < +π*/ c=(int)(32767*rad/3.1415927);

else

c=0;

a=ser_cos(c);

.

}


SPRA179A-2

A.2 Main Assembly Program to Call Sine or Cosine Functions**********************************************************************************

*File Name: Main_trig.asm *



* *


* *

*Processor: C2xx *

*Status: *


*________________________________________________________________________________*


*––––––––––––––|–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––*

* | *

**********************************************************************************

.mmregs

.def _ser_sin

.sect “vectors”

b _c_int0

b $

*********************************************************************************** Main routine

**********************************************************************************

.text

_c_int0:

.

.

LAR AR1,#60h ;stack preparation

MAR *,AR1



LACC #4000h ;π/2

SACL *+ ;parameters in stack

CALL _ser_sin

. ;result in ACCU

.

.end


SPRA179A-4

A.3 COS Function With Direct Look-Up and Linear Interpolation for Assembly Program

**********************************************************************************

*Routine Name: COS *



* *

*Description: COS function with Direct Look–up and *

* Interpolation Assembly calling function, *

* variables in s/w stack. *

* *

*Status: *

* *

*Processor: C2xx *

* *

*Calling convention: *

* Input : Angle in stack value 0–360 degrees <=>0h–FFFFh *

* Output : COS(angle)*32767, Q15, in ACCU *

* Pointed register AR1 *

* *

*Stack commentary: *

* Position of current register in Caps *

* Stack at beginning : angle/X *

* *


*________________________________________________________________________________*


*––––––––––––––|–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––*

* *

**********************************************************************************

COS

MAR *–

LACC #4000h

ADDS * ;add 0.5 for COS

SACL *

LT *+ ;variable in size_sin

;*******stack : angle/X

LACC #64h



SACL *

;*******stack : angle/TEMP

MPYU * ;integer position in the table

PAC ;in High part of Acc

SACH *+ ;remainder

;*******stack : angle/indice/X

SACL * ;

;*******stack : angle/indice/REMAINDER

LACC *,15

AND #0ffffh,15

SACH *–

;*******stack : angle/INDICE/remainder

BCND equal_sin,EQ

LACC #Table_sin ;address of beginning of the table

ADD *– ;address of the nearest first indice

;*******stack : ANGLE/indice/remainder

TBLR *+

;*******stack : y1/INDICE/remainder

ADD #1h

TBLR * ;Load Y2 with the ordinate of the

;*******stack : y1/Y2/remainder

;nearest second indice

LACC *–

;*******stack : Y1/y2/remainder

SUB *+ ;difference between the two Y value


SACL *+

;*******stack : y1/temp/REMAINDER

LT *–

;*******stack : y1/TEMP/remainder

MPY *


SPH *– ;interpolation between Y1 and Y2

;*******stack : Y1/temp/remainder

LACC *+


ADD *,1 ;Y(Xdata) in ACCU

RET


SPRA179A-6

equal_sin


ADD *– ;address of the pointed indice

;*******stack : RESULT/

TBLR *

LACC *+

end_interp_sin

RET

**********************************************************************************

* Table

**********************************************************************************

Table_sin .include sine.tab

Table_sin_end

.word 0

.end



A.4 COS Function With Direct Look-Up and Linear Interpolation forC Program

**********************************************************************************

*Routine Name: _COS *



* *


* Interpolation C calling function, variables in C stack. *

* Fully C compatible *

* *

*Status: *

* *

*Processor: C2xx *

* *





* *




* *


* *

*________________________________________________________________________________*


*––––––––––––––|–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––*

* | *

* | *

**********************************************************************************

_COS

ADRK #2 ;C compatibility

POPD *+

SAR AR1,*

LAR AR2,*,AR2


SPRA179A-8

SBRK #3 ;C compatibility

SPM 0

LACC #4000h


SACL *



LACC #64h

SACL *




SACH *+ ;remainder


SACL * ;


LACC *,15

AND #0ffffh,15

SACH *–


BCND equal_sin,EQ




TBLR *+


ADD #1h




LACC *–




SACL *+


LT *–




MPY *




LACC *+


ADD *,1,AR1 ;Y(Xdata) in ACCU

MAR *– ;C compatibility

PSHD *–

SBRK #1

RET

equal_sin




TBLR *

LACC *+,0,AR1


PSHD *–

SBRK #1

RET

**********************************************************************************

* Table

**********************************************************************************


Table_sin_end

.word 0

.end


SPRA179A-10

A.5 SIN Function With Direct Look-Up and Linear Interpolation forAssembly Program

**********************************************************************************

*Routine Name: SIN *



* *

*Description: SIN function with Direct Look–up and Interpolation *

* Assembly calling function, variables in s/w stack. *

* *

*Status: *

* *

*Processor: C2xx *

* *



* Output : SIN(angle)*32767, Q15, in ACCU *


* *




* *

* *


*________________________________________________________________________________*


*––––––––––––––|–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––*

* | *

* | *

**********************************************************************************

SIN

MAR *+



LACC #64h

SACL *






SACH *+ ;remainder


SACL * ;


LACC *,15

AND #0ffffh,15

SACH *–


BCND equal_sin,EQ




TBLR *+


ADD #1h




LACC *–




SACL *+


LT *–


MPY *




LACC *+



RET

equal_sin


SPRA179A-12




TBLR *

LACC *+

;*******stack : result/X

end_interp_sin

RET

*********************************************************************************

* Table

*********************************************************************************


Table_sin_end

.word 0



A.6 SIN Function With Direct Look-Up and Linear Interpolation forC Program

**********************************************************************************

*Routine Name: _SIN *



* *

*Description: SIN function with Direct Look–up + Interpolation *

* C calling function, variables in C stack. *


* *

*Status: *

* *

*Processor: C2x *

* *





* *




* *

* *


* *

*________________________________________________________________________________*


*––––––––––––––|–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––*

* | *

* | *

**********************************************************************************

_SIN


POPD *+


SPRA179A-14

SAR AR1,*

LAR AR2,*,AR2


SPM 0



LACC #64h

SACL *




SACH *+ ;remainder


SACL * ;


LACC *,15

AND #0ffffh,15

SACH *–


BCND equal_sin,EQ




TBLR *+


ADD #1h




LACC *–




SACL *+


LT *–




MPY *




LACC *+




PSHD *–

SBRK #1

RET

equal_sin



;*******stack : RESULT/...

TBLR *

LACC *+,0,AR1



PSHD *–

SBRK #1

RET

**********************************************************************************

* Table

**********************************************************************************


Table_sin_end

.word 0


SPRA179A-16

A.7 Table for COS or SIN Function With Direct Look-Up**********************************************************************************

* TABLE Sine and Cosine for separate functions COS and SIN *

**********************************************************************************

.word 0

.word 2057

.word 4107

.word 6140

.word 8149

.word 10126

.word 12062

.word 13952

.word 15786

.word 17557

.word 19260

.word 20886

.word 22431

.word 23886

.word 25247

.word 26509

.word 27666

.word 28714

.word 29648

.word 30466

.word 31163

.word 31738

.word 32187

.word 32509

.word 32702

.word 32767

.word 32702

.word 32509

.word 32187

.word 31738

.word 31163

.word 30466

.word 29648

.word 28714



.word 27666

.word 26509

.word 25247

.word 23886

.word 22431

.word 20886

.word 19260

.word 17557

.word 15786

.word 13952

.word 12062

.word 10126

.word 8149

.word 6140

.word 4107

.word 2057

.word 0

.word –2057

.word –4107

.word –6140

.word –8149

.word –10126

.word –12062

.word –13952

.word –15786

.word –17557

.word –19260

.word –20886

.word –22431

.word –23886

.word –25247

.word –26509

.word –27666

.word –28714

.word –29648

.word –30466

.word –31163

.word –31738


SPRA179A-18

.word –32187

.word –32509

.word –32702

.word –32767

.word –32702

.word –32509

.word –32187

.word –31738

.word –31163

.word –30466

.word –29648

.word –28714

.word –27666

.word –26509

.word –25247

.word –23886

.word –22431

.word –20886

.word –19260

.word –17557

.word –15786

.word –13952

.word –12062

.word –10126

.word –8149

.word –6140

.word –4107

.word –2057



A.8 COS_SIN Function With Direct Look-Up and Linear Interpolation forAssembly Program

**********************************************************************************

*Routine Name: COS_SIN *



* *

*Description: COS+SIN function with Direct Look–up and Interpolation *


* *

*Status: *

* *

*Processor: C2xx *

* *



* Output: *

* SIN(angle)*32767, Q15, in stack pointed by AR1–1 *

* COS(angle)*32767,Q15, in stack pointed by AR1 *


* *




* *


*________________________________________________________________________________*


*––––––––––––––|–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––*

* | *

* | *

**********************************************************************************

size_tab .set 64h ;this is not an error

COS_SIN

MAR *+



SPRA179A-20

;*stack: angle/X

LACC #size_tab

SACL *

;*stack: angle/TEMP



SACH *+ ;remainder

;*stack: angle/indice/X

SACL * ;

;*stack: angle/indice/REMAINDER

LACC *,15

AND #0ffffh,15

SACH *–

;*stack: angle/INDICE/remainder

BCND equal_sin,EQ

LACC #Table_sin_cos ;address of beginning of the table


;*stack: ANGLE/indice/remainder

TBLR *+

;*stack: y1/INDICE/remainder

ADD #1h

TBLR *+ ;Load Y2 with the ordinate of the


;*stack: y1/y2/REMAINDER

ADRK #1

;*stack: y1/y2/remainder/X

ADD #18h

TBLR *+

;*stack: y1/y2/remainder/yy1/X

ADD #1h

TBLR * ;*stack: y1/y2/remainder/yy1/YY2

LACC *– ;calculate cos interpolate

;*stack: y1/y2/remainder/YY1/yy2


;*stack: y1/y2/remainder/yy1/YY2

SACL * ;*stack: y1/y2/remainder/yy1/TEMP

LT *–



;*stack: y1/y2/remainder/YY1

SBRK #1

;*stack: y1/y2/REMAINDER/yy1

MPY *


ADRK #2

;*stack: y1/y2/remainder/yy1/TEMP


;*stack: Y1/y2/remainder/YY1/temp

LACC *+


ADD *–,1 ;Y(Xdata) in ACCU


SACL *–

;*stack: y1/y2/REMAINDER/cos

;calculate sin interpolate

SBRK #1

;*stack: y1/Y2/remainder/cos

LACC *–

;*stack: Y1/y2/remainder



SACL *+

;*stack: y1/temp/REMAINDER/cos

LT *–

;*stack: y1/TEMP/remainder/cos

MPY *



;*stack: Y1/temp/remainder/cos

LACC *+



;*stack: y1/temp/remainder/cos

SACL * ;*stack: SIN/temp/remainder/cos

ADRK #3

;*stack: sin/temp/remainder/COS

LACC *


SPRA179A-22

SBRK #2

;*stack: sin/TEMP/remainder/cos

SACL *

;*stack: sin/COS

RET

equal_sin

LALK Table_sin_cos;address of beginning of the table



;*stack: ANGLE/indice

TBLR *+

;*stack: sin/INDICE/remainder

ADD #19h

TBLR *

;*stack: sin/COS

end_interp_sin

RET

**********************************************************************************

* Table

**********************************************************************************

Table_sin_cos .include sin_cos.tab

Table_sin_cos_end

.word 0



A.9 Table for COS_SIN Function With Direct Look-Up**********************************************************************************

* TABLE Sine + Cosine for functions COS_SIN *

**********************************************************************************

.word 0

.word 2057

.word 4107

.word 6140

.word 8149

.word 10126

.word 12062

.word 13952

.word 15786

.word 17557

.word 19260

.word 20886

.word 22431

.word 23886

.word 25247

.word 26509

.word 27666

.word 28714

.word 29648

.word 30466

.word 31163

.word 31738

.word 32187

.word 32509

.word 32702

.word 32767

.word 32702

.word 32509

.word 32187

.word 31738

.word 31163

.word 30466

.word 29648

.word 28714


SPRA179A-24

.word 27666

.word 26509

.word 25247

.word 23886

.word 22431

.word 20886

.word 19260

.word 17557

.word 15786

.word 13952

.word 12062

.word 10126

.word 8149

.word 6140

.word 4107

.word 2057

.word 0

.word –2057

.word –4107

.word –6140

.word –8149

.word –10126

.word –12062

.word –13952

.word –15786

.word –17557

.word –19260

.word –20886

.word –22431

.word –23886

.word –25247

.word –26509

.word –27666

.word –28714

.word –29648

.word –30466

.word –31163

.word –31738



.word –32187

.word –32509

.word –32702

.word –32767

.word –32702

.word –32509

.word –32187

.word –31738

.word –31163

.word –30466

.word –29648

.word –28714

.word –27666

.word –26509

.word –25247

.word –23886

.word –22431

.word –20886

.word –19260

.word –17557

.word –15786

.word –13952

.word –12062

.word –10126

.word –8149

.word –6140

.word –4107

.word –2057

.word 0

.word 2057

.word 4107

.word 6140

.word 8149

.word 10126

.word 12062

.word 13952

.word 15786

.word 17557


SPRA179A-26

.word 19260

.word 20886

.word 22431

.word 23886

.word 25247

.word 26509

.word 27666

.word 28714

.word 29648

.word 30466

.word 31163

.word 31738

.word 32187

.word 32509

.word 32702



A.10 SIN With Mathematical Series for Assembly Program**********************************************************************************

*Routine Name: sin_ser *



* *

*Description: SIN function with Mathematical Series *


* *

*Status: *

* *

*Processor: C2xx *

* *





* *




* *

* *


*________________________________________________________________________________*


*––––––––––––––|–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––*

* | *

* | *

**********************************************************************************

sin_ser

SETC SXM

MAR *–

LAC *

BCND angle_neg,LT

angle_pos


SPRA179A-28


;*stack : angle/X

MPY #0c90h ;abscissa scale modify degree –> rad

PAC

SACH *,4 ;angle in rad

;*stack : angle/RAD

LT *+

;*stack : angle/rad/X

MPY #985h ;0.0372

;

;PREG : angle * 0.0372

LACC #0C426h,13 ; in high ACCU

APAC ;ACCU : –0.2338 + angle * 0.0372

SACH * ,3 ;temporary value

;angle in TREG

MPY * ;multiply by temporary value

;temporary value

;*stack : angle/rad/TEMP

LACC #6f69h,10 ;0.0544

APAC ;ACCU: temp + 0.0544

SACH *,2 ;temp

;*stack : angle/RAD/temp

;angle in TREG


MPY * ;temp

LACC #7dc5h,13 ;0.9826

APAC ;ACCU=0.9826+temp

SACH *,3 ;treg = rad

;temp

MPY * ;rad * temp

;temp * angle

LACC #05532,4 ;0.0013

APAC

SACH * ,3 ;result

LACC *–

;*stack : angle/SIN

RET



angle_neg


;*stack : angle/X

MPY #0c90h ;abscisse scale modif degre –> rad

PAC


;*stack : angle/RAD

LT *+


MPY #985h ;0.0372

;


LACC #03bdah,13 ; in high ACCU

APAC ;ACCU : –0.2338 + angle * 0.0372


;angle in TREG


;temporary value


LACC #6f69h,10 ;0.0544


SACH *,2 ;temp


;angle in TREG


MPY * ;temp

LACC #7dc5h,13 ;0.9826

SPAC ;ACCU=0.9826+temp


MPY * ;rad * temp

;temp * angle

LACC #05532,4 ;0.0013

APAC

SACH *,3 ;result

LACC *–

;*stack : angle/SIN

RET


SPRA179A-30

A.11 SIN With Mathematical Series for C Program**********************************************************************************

*Routine Name: _sin_ser *



* *




* *

*Status: *

* *

*Processor: C2xx *

* *





* *




* *


* *

*________________________________________________________________________________*


*––––––––––––––|–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––*

* | *

* | *

**********************************************************************************

_sin_ser


POPD *+

SAR AR1,*

LAR AR2,*,AR2




SPM 0

SETC SXM

LACC *

BCND angle_neg,LT

angle_pos


;*stack : angle/X

MPY #0c90h ;abscissa scale modify degree –> rad

;in

PAC


;*stack : angle/RAD

LT *+


MPY #985h ;0.0372

;


LACC #0C426h,13 ; in high ACCU

APAC ;ACCU : –0.2338 + angle * 0.0372


;angle in TREG


;temporary value


LACC #6f69h,10 ;0.0544


SACH *,2 ;temp


;angle in TREG


MPY * ;temp

LACC #7dc5h,13 ;0.9826



;temp

MPY * ;rad * temp


SPRA179A-32

;temp * angle

LACC #05532,4 ;0.0013

APAC

SACH * ,3 ;result

LACC *–,0,AR1

;*stack : angle/SIN


PSHD *–

SBRK #1

RET

angle_neg


;*stack : angle/X


PAC


;*stack : angle/RAD

LT *+


MPY #985h ;0.0372

;


LACC #03bdah,13 ; in high ACCU

APAC ;ACCU : –0.2338 + angle * 0.0372


;angle in TREG


;temporary value


LACC #6f69h,10 ;0.0544


SACH *,2 ;temp


;angle in TREG


MPY * ;temp



LACC #7dc5h,13 ;0.9826



MPY * ;rad * temp

;temp * angle

LACC #05532,4 ;0.0013

APAC

SACH *,3 ;result

LACC *–,0,AR1

;*stack : angle/SIN


PSHD *–

SBRK #1

RET


SPRA179A-34

A.12 COS With Mathematical Series for Assembly Program**********************************************************************************

*Routine Name: cos_ser *



* *

*Description: COS function with Mathematical Series *


* *

*Status: *

* *

*Processor: C2xx *

* *

* *





* *




* *

* *


*________________________________________________________________________________*


*––––––––––––––|–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––*

* | *

* | *

**********************************************************************************

cos_ser

SETC SXM

MAR *–

LACC *

BCND angle_neg,LT



angle_pos


;*stack : angle/X


PAC


;*stack : angle/RAD

LT *+


MPY #1070h ;0.0076 neg

;


LACC #01e76h,15 ; in high ACCU

APAC ;ACCU : +0.0595 + angle * 0.0076


;angle in TREG


;temporary value


LACC #0f532h,15 ;0.0211


SACH * ;temp


;angle in TREG


MPY * ;temp

LACC #0e0c6h,15 ;0.4879



MPY * ;rad * temp

;temp * angle

LACC #0a440h,5 ;0.0028

APAC

SACH *,2 ;result

MPY * ;

LACC #1000h,15 ;1

APAC


SPRA179A-36

SETC OVM

SACH *,3

LACC *,16

ADD *,16

SACH *

LACC *–

;*stack : angle/SIN

RET

angle_neg


;*stack : angle/X


PAC


;*stack : angle/RAD

LT *+


MPY #0f90h ;0.0076 neg

;



APAC ;ACCU : +0.0595 + angle * 0.0076


;angle in TREG


;temporary value


LACC #00aceh,15 ;0.0211


SACH * ;temp


;angle in TREG


MPY * ;temp

LACC #0e0c6h,15 ;0.4879





;temp

MPY * ;rad * temp

;temp * angle

LACC #05bc0h,5 ;0.0028

APAC

SACH *,2 ;result

MPY * ;

LACC #1000h,15 ;1

APAC

SETC OVM

SACH *,3

LACC *,16

ADD *,16

SACH *

LACC *–

;*stack : angle/SIN

RET


SPRA179A-38

A.13 COS With Mathematical Series for C Program**********************************************************************************

*Routine Name: _cos_ser *



* *


* C calling function, *

* variables in C stack. Fully C compatible *

* *

*Status: *

* *

*Processor: C2xx *

* *





* *




* *


* *

*________________________________________________________________________________*


*––––––––––––––|–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––*

* | *

* | *

**********************************************************************************

_cos_ser


POPD *+

SAR AR1,*

LAR AR2,*,AR2




SPM 0

SETC SXM

LAC *

BCND angle_neg,LT

angle_pos


;*stack : angle/X


PAC


;*stack : angle/RAD

LT *+


MPY #1070h ;0.0076 neg

;



APAC ;ACCU : +0.0595 + angle * 0.0076


;angle in TREG


;temporary value


LACC #0f532h,15 ;0.0211


SACH * ;temp


;angle in TREG


MPY * ;temp

LACC #0e0c6h,15 ;0.4879



;temp


SPRA179A-40

MPY * ;rad * temp

;temp * angle

LACC #0a440h,5 ;0.0028

APAC

SACH *,2 ;result

MPY * ;

LACC #1000h,15 ;1

APAC

SETC OVM

SACH *,3

LACC *,16

ADD *,16

SACH *

LACC *–,0,AR1

;*stack : angle/SIN


PSHD *–

SBRK #1

RET

angle_neg


;*stack : angle/X


PAC


;*stack : angle/RAD

LT *+


MPY #0f90h ;0.0076 neg

;



APAC ;ACCU : +0.0595 + angle * 0.0076


;angle in TREG




;temporary value


LACC #00aceh,15 ;0.0211


SACH * ;temp


;angle in TREG


MPY * ;temp

LACC #0e0c6h,15 ;0.4879



MPY * ;rad * temp

;temp * angle in Q28

LACC #05bc0h,5 ;0.0028

SACH *,2 ;result

MPY * ;

LACC #1000h,15 ;1

APAC

SETC OVM

SACH *,3

LACC *,16

ADD *,16

SACH *

LACC *–,0,AR1

;*stack : angle/SIN


PSHD *–

SBRK #1

RET

SPRA179A-42


Digital Sine-Wave Generation Using the TMS320C2xx

ABSTRACTThis application report describes two methods for implementing a digital sine-wavegenerator using the TMS320C2xx: the use of a direct look-up table with linearinterpolation, and the use of mathematical series. Both methods are explained interms of C-compatible and assembly-compatible functions. Formulas used forcalculating and graphing the results are included for each method to demonstratethe differences.

B IntroductionSine-wave generators are fundamental building blocks of signal processingsystems for use in control applications. The following two methods aredescribed in this application report for implementing a digital sine-wavegenerator using the TMS320C2xx:

• Direct look-up with linear interpolation to provide sine waves with aminimum of harmonic distortion

• Realization of the sine/cosine functions with a mathematical series

The two methods respond to different constraints. The direct look-upmethod is fast with minimum errors and is significant in ROM programmingrequirements. The mathematical series method is fast and requiresminimum (ROM) programming but results in less precision.


STDZ001AA-2

C Direct Look-Up and Linear Interpolation MethodThis section describes the Direct Look- Up and Linear Interpolation methodof implementing a digital sine-wave generator using the TMS320C2xx.

C.1 C- and Assembly-Compatible Functions

The Direct Look-Up method, which uses 100 sine-period values in a table,reveals the sine/cosine functions. To provide minimum harmonic distortion,the method includes linear interpolation with a fixed-step table. An extendedtable is used for the cosine + sine function and is located in program memory.

Two versions of each function are presented :




C.1.1 C-Compatible Functions

Fully C-compatible functions employ C conventions to use the stack forparameters passed to the functions. Parameters returned by the functionsare passed by a pointer. Responsibilities of called functions are managedin a postfix expression called the function designator. Stack pointer AR1 iswell-positioned, and the return address of the hardware stack is popped(retrieved) in case of C-interrupt runtime events using C-function features(stack). The frame pointer is not modified and registers AR6 and AR7 arenot used.

C.1.2 Assembly-Compatible Functions




C.2 Interpolation

Figure B–1 shows the formula and the resulting graph for calculating thetable interpolation value COS(X) of an angle X.

ii+ 1x - x

Y = y + i+1 i

y - y )(

X – xi

i

r = ratiox x

i i+1

y

y

i

i+1

X

Y = ?

x

y

where:{xi} = {first coordinates of the table},{yi} = {second coordinates of the table},i chosen so that xi < X < xi+1.

Figure B–1. The Formula and the Resulting Graph for Calculating the TableInterpolation Value COS of an Angle

Table interpolation is comprised of two steps:

1. Direct look-up: looking through the table to find the interval [xi, xi+1] at which the considered angle X is located, with xi < X < xi+1.

• Interpolation: solving the above mentioned calculation to obtain Y.

C.3 Functions

Functions SINE, COSINE, and SINE + COSINE are illustrated by examplein the appendix. Conventions to interface with this function are:

• Input: ANGLE parameters are in the stack pointed by AR1. The valueof this angle is unsigned.

0° <-> 0000h

90° <-> 4000h

180° <-> 8000h

240° <-> C000h


C.4 System Utilization

Table E–1 shows processor utilization when using the direct look-up andlinear interpolation methods.


STDZ001AA-4

Table E–1. Processor Utilization (Maximum) When Using Table Look-Up and Interpolation


SIN assembly call 35 1.75 µs

COS assembly call 38 1.90 µs



SIN + COS of an angle 58 2.90 µs

Table E–2 shows memory utilization when using the direct look-up andlinear interpolation method.

Table E–2. Memory Utilization When Using Direct Look-Up and Interpolation

FUNCTIONROM

(WORDS) STACKLEVELSREGISTERS

USEDRAM

(WORDS)

SIN ssembly call 32 + 100 3 1 In stack


COS and SINassembly call 66 + 100 3 1 In stack

SIN Fully C compatible 42 + 100 5 1 In stack


COS + SIN in one function†

assembly call55 + 125 3 1 In stack

† In the case of Sine + Cosine, the same table is used.

C.5 Sine-Generation Precision

Figure B–2 and Figure B–3 are graphs that present the precision of thedirect look-up and linear interpolation sine functions. The precisionmeasurement is made by comparing the direct look-up and the floating-pointC library results.

C.5.1 One-Sine-Period Analysis

The sine period provides a general image of error calculation. In Figure B–2and Figure B–3, results of the sine calculation are in Q15 format.



Figure B–2. Direct Look-Up With Interpolation of Sine Calculation From 0 to 2*π With a 0.015-Radian Step


STDZ001AA-6

Figure B–3. Error Between the C Floating-Point Result and Direct Look-UpCalculation From 0 to 2*π With a 0.015-Radian Step



C.5.2 Quarter-Sine-Period Analysis

Figure B–4, Figure B–5, and Figure B–6 graph another precise analysisusing a quarter of a half-sine period. In this case, the step is 0.0039 radian.The interpolation is made at 0.125-radian intervals. In this way, interpolationerror is exposed on the following graphs. Each interval (table approximation)is displayed with 32 pixels.

Figure B–4. Results of Direct Look-Up SIN From 0 to π/2 With a 0.0039-RadianStep


STDZ001AA-8

Figure B–5. Error Between the C Floating-Point Result and Direct Look-Up SINE Calculation From 0 to π/4 With a 0.0039-Radian Step in Q15 Format



Figure B–6. Error Between the C Floating-Point Result and Direct Look-Up SINE Calculation From 0 to π/4 With a 0.0039-Radian Step in %


STDZ001AA-10

D Sine/Cosine With Mathematical SeriesThis section explains the second of two methods of implementing a digitalsine-wave generator using the TMS320C2xx.

D.1 C- and Assembly-Compatible Functions

The sine/cosine method calculates the sine/cosine functions with amathematical series for the sine period and a mathematical series forcosine. Calculations are made with fixed-point instructions to optimize thetime calculation. The dynamics used in the calculation fit with maximumprecision without overflow.

Two versions of each function are presented :




D.1.1 C-Compatible Functions

Fully C-compatible functions employ C conventions to use the stack forparameters passed to the functions. Parameters returned by functions arepassed by a pointer. Responsibilities of called functions are managed in apostfix expression called the function designator. Stack pointer AR1 iswell-positioned, and the return address of the hardware stack is popped(retrieved) in case of C-interrupt runtime events using C-function features(stack). The frame pointer is not modified and registers AR6 and AR7 arenot used.

D.1.2 Assembly-Compatible Functions




D.2 Sine/Cosine Mathematical SeriesFigure B–7 shows the formula for calculating the value SIN(X) of an angleX.


SIN(X)=((((0.0372*X)–0.2338)*X+0.0544)*X+0.9826)*X+0.0013elseSIN(X)=((((0.0372*X)+0.2338)*X+0.0544)*X–0.9826)*X+0.0013

Figure B–7. Formula for Calculating the Value SIN of an Angle

Figure B–8 shows the formula for calculating the value COS(X) of an angleX.


COS(X)=(((((-0.0076*X)+0.0595)*X-0.0211)*X-0.4879)*X-0.0028)*X+1.0elseCOS(X)=(((((0.0076*X)+0.0595)*X+0.0211)*X-0.4879)*X+0.0028)*X+1.0

Figure B–8. Formula for Calculating the Value COS of an Angle

D.3 FunctionsFunctions SINE and COSINE are illustrated by example in the appendix.Conventions to interface with these functions are:• Input: ANGLE parameters are in the stack pointed toby AR1. The value

of this angle is unsigned.0 º <-> 0000h90 º <-> 4000h180 º <-> 8000h240 º or -90º <-> C000h


D.4 System UtilizationTable E–3 shows processor utilization when using the mathematical seriesmethod.

Table E–3. Processor Utilization (Maximum) When Using Mathematical Series


SIN assembly main 27 1.35 µs

COS assembly main 37 1.85 µs



SIN + COS of an angle – assembly main 64 3.20 µs


STDZ001AA-12

Table E–4 shows memory utilization when using the mathematical seriesmethod.

Table E–4. Memory Utilization When Using Mathematical Series

FUNCTIONROM

(WORDS)STACKLEVELS REGISTERS USED

RAM(WORDS)

SIN 54 3 1 In stack

COS 67 3 1 In stack

SIN 64 5 1 In stack

COS 77 5 1 In stack

COS and SIN 121 3 1 In stack

D.5 Sine-Generation Precision

The following graphs present the precision of the mathematical series ofsine functions. The precision measurement is calculated by comparing themathematical series and floating-point C library results.



D.5.1 One-Sine-Period Analysis

The sine period provides a general image of error calculation. In Figure B–9and Figure B–10, results of the sine calculation are in Q15 format.

Figure B–9. Mathematical Series Sine Calculation From 0 to 2*π With a 0.015-Radian Step


STDZ001AA-14

Figure B–10. Error Between the C Floating-Point Result and the MathematicalSeries

SINE Calculation From 0 to 2*π With a 0.015-Radian Step

D.5.2 Quarter-Sine-Period Analysis

Figure B–11, Figure B–12, and Figure B–13 graph another precise analysisusing a quarter of a half-sine period. In this case, the step is 0.0039 radian.



Figure B–11. Results of Mathematical Series Sine From 0 to π/2 With a 0.0039-Radian Step


STDZ001AA-16

Figure B–12. Error Between the C Floating-Point Result and a MathematicalSeries Sine Calculation From 0 to π/4 With a 0.0039-Radian Step in Q15 Format



Figure B–13. Error Between the C Floating-Point Result and a MathematicalSeries Sine Calculation From 0 to π/4 With a 0.0039-Radian Step in %

A-1

********************************************************************************





* *

* *

*Processor: C2xx *

* *

*Status: *

* *


*______________________________________________________________________________*


*––––––––––––––|–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––*

* | *

********************************************************************************

extern ser_cos();

void main()

{

double rad;

double a;

int c;

.

.

.

if (rad!=0.0) /*–π < rad < +π*/

c=(int)(32767*rad/3.1415927);

else

c=0;

a=ser_cos(c);

.

}

**********************************************************************************




A-2

* *


* *

*Processor: C2xx *

*Status: *


*________________________________________________________________________________*


*––––––––––––––|–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––*

* | *

**********************************************************************************

.mmregs

.def _ser_sin

.sect “vectors”

b _c_int0

b $

*********************************************************************************** Main routine

**********************************************************************************

.text

_c_int0:

.

.


MAR *,AR1

A-3

LAC #4000h ;π/2


CALL _ser_sin

. ;result in ACCU

.

.end

**********************************************************************************




* *




* *

*Status: *

* *

*Processor: C2xx *

* *





* *




* *


*________________________________________________________________________________*


*––––––––––––––|–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––*

* *

**********************************************************************************

COS

MAR *–

LAC #4000h


A-4

SACL *



LAC #64h

SACL *




SACH *+ ;remainder


SACL * ;


LAC *,15

ANDK #0ffffh,15

SACH *–


BCND equal_sin,EQ

LALK Table_sin ;address of beginning of the table



TBLR *+


ADD #1h




LAC *–




SACL *+


LT *–


MPY *




A-5

LAC *+



RET

equal_sin




TBLR *

LAC *+

end_interp_sin

RET

**********************************************************************************

* Table

**********************************************************************************


Table_sin_end

.word 0

.end

**********************************************************************************




* *




* *

*Status: *

* *

*Processor: C2xx *

* *





A-6

* *




* *


* *

*________________________________________________________________________________*


*––––––––––––––|–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––*

* | *

* | *

**********************************************************************************

_COS

ADRK 2 ;C compatibility

POPD *+

SAR AR1,*

LAR AR2,*,AR2

SBRK 3 ;C compatibility

SPM 0

LAC #4000h


SACL *



LAC #64h

SACL *




SACH *+ ;remainder


SACL * ;


LAC *,15

ANDK #0ffffh,15

A-7

SACH *–


BCND equal_sin,EQ




TBLR *+


ADD #1h




LAC *–




SACL *+


LT *–


MPY *




LAC *+




PSHD *–

SBRK 1

RET

equal_sin




TBLR *

LAC *+,0,AR1

A-8


PSHD *–

SBRK 1

RET

**********************************************************************************

* Table

**********************************************************************************


Table_sin_end

.word 0

.end

**********************************************************************************




* *



* *

*Status: *

* *

*Processor: C2xx *

* *





* *




* *

* *


*________________________________________________________________________________*

A-9


*––––––––––––––|–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––*

* | *

* | *

**********************************************************************************

SIN

MAR *+



LAC #64h

SACL *




SACH *+ ;remainder


SACL * ;


LAC *,15

ANDK #0ffffh,15

SACH *–


BCND equal_sin,EQ




TBLR *+


ADD #1h




LAC *–




SACL *+

A-10


LT *–


MPY *




LAC *+



RET

equal_sin




TBLR *

LAC *+


end_interp_sin

RET

*********************************************************************************

* Table

*********************************************************************************


Table_sin_end

.word 0

**********************************************************************************




* *




A-11

* *

*Status: *

* *

*Processor: C2x *

* *





* *




* *

* *


* *

*________________________________________________________________________________*


*––––––––––––––|–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––*

* | *

* | *

**********************************************************************************

_SIN


POPD *+

SAR AR1,*

LAR AR2,*,AR2


SPM 0



LAC #64h

SACL *



A-12


SACH *+ ;remainder


SACL * ;


LAC *,15

ANDK #0ffffh,15

SACH *–


BCND equal_sin,EQ




TBLR *+


ADD #1h




LAC *–




SACL *+


LT *–


MPY *




LAC *+




PSHD *–

SBRK 1

RET

A-13

equal_sin




TBLR *

LAC *+,0,AR1



PSHD *–

SBRK 1

RET

**********************************************************************************

* Table

**********************************************************************************


Table_sin_end

.word 0

**********************************************************************************


**********************************************************************************

.word 0

.word 2057

.word 4107

.word 6140

.word 8149

.word 10126

.word 12062

.word 13952

.word 15786

.word 17557

.word 19260

.word 20886

.word 22431

.word 23886

.word 25247

.word 26509

.word 27666

.word 28714

A-14

.word 29648

.word 30466

.word 31163

.word 31738

.word 32187

.word 32509

.word 32702

.word 32767

.word 32702

.word 32509

.word 32187

.word 31738

.word 31163

.word 30466

.word 29648

.word 28714

.word 27666

.word 26509

.word 25247

.word 23886

.word 22431

.word 20886

.word 19260

.word 17557

.word 15786

.word 13952

.word 12062

.word 10126

.word 8149

.word 6140

.word 4107

.word 2057

.word 0

.word –2057

.word –4107

.word –6140

.word –8149

.word –10126

A-15

.word –12062

.word –13952

.word –15786

.word –17557

.word –19260

.word –20886

.word –22431

.word –23886

.word –25247

.word –26509

.word –27666

.word –28714

.word –29648

.word –30466

.word –31163

.word –31738

.word –32187

.word –32509

.word –32702

.word –32767

.word –32702

.word –32509

.word –32187

.word –31738

.word –31163

.word –30466

.word –29648

.word –28714

.word –27666

.word –26509

.word –25247

.word –23886

.word –22431

.word –20886

.word –19260

.word –17557

.word –15786

.word –13952

A-16

.word –12062

.word –10126

.word –8149

.word –6140

.word –4107

.word –2057

**********************************************************************************




* *



* *

*Status: *

* *

*Processor: C2xx *

* *



* Output: *




* *




* *


*________________________________________________________________________________*


*––––––––––––––|–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––*

* | *

* | *

**********************************************************************************


A-17

COS_SIN

MAR *+


;*stack: angle/X

LAC #size_tab

SACL *

;*stack: angle/TEMP



SACH *+ ;remainder


SACL * ;


LAC *,15

ANDK #0ffffh,15

SACH *–


BCND equal_sin,EQ




TBLR *+


ADD #1h




ADRK 1


ADD #18h

TBLR *+


ADD #1h


LAC *– ;calculate cos interpolate


A-18




LT *–


SBRK 1


MPY *


ADRK 2




LAC *+




SACL *–



SBRK 1


LAC *–




SACL *+


LT *–


MPY *




LAC *+




A-19


ADRK 3


LAC *

SBRK 2


SACL *

;*stack: sin/COS

RET

equal_sin





TBLR *+


ADDK 19h

TBLR *

;*stack: sin/COS

end_interp_sin

RET

**********************************************************************************

* Table

**********************************************************************************


Table_sin_cos_end

.word 0

**********************************************************************************


**********************************************************************************

.word 0

.word 2057

.word 4107

.word 6140

.word 8149

A-20

.word 10126

.word 12062

.word 13952

.word 15786

.word 17557

.word 19260

.word 20886

.word 22431

.word 23886

.word 25247

.word 26509

.word 27666

.word 28714

.word 29648

.word 30466

.word 31163

.word 31738

.word 32187

.word 32509

.word 32702

.word 32767

.word 32702

.word 32509

.word 32187

.word 31738

.word 31163

.word 30466

.word 29648

.word 28714

.word 27666

.word 26509

.word 25247

.word 23886

.word 22431

.word 20886

.word 19260

.word 17557

.word 15786

A-21

.word 13952

.word 12062

.word 10126

.word 8149

.word 6140

.word 4107

.word 2057

.word 0

.word –2057

.word –4107

.word –6140

.word –8149

.word –10126

.word –12062

.word –13952

.word –15786

.word –17557

.word –19260

.word –20886

.word –22431

.word –23886

.word –25247

.word –26509

.word –27666

.word –28714

.word –29648

.word –30466

.word –31163

.word –31738

.word –32187

.word –32509

.word –32702

.word –32767

.word –32702

.word –32509

.word –32187

.word –31738

.word –31163

A-22

.word –30466

.word –29648

.word –28714

.word –27666

.word –26509

.word –25247

.word –23886

.word –22431

.word –20886

.word –19260

.word –17557

.word –15786

.word –13952

.word –12062

.word –10126

.word –8149

.word –6140

.word –4107

.word –2057

.word 0

.word 2057

.word 4107

.word 6140

.word 8149

.word 10126

.word 12062

.word 13952

.word 15786

.word 17557

.word 19260

.word 20886

.word 22431

.word 23886

.word 25247

.word 26509

.word 27666

.word 28714

.word 29648

A-23

.word 30466

.word 31163

.word 31738

.word 32187

.word 32509

.word 32702

**********************************************************************************




* *



* *

*Status: *

* *

*Processor: C2xx *

* *





* *




* *

* *


*________________________________________________________________________________*


*––––––––––––––|–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––*

* | *

* | *

**********************************************************************************

sin_ser

SETC SXM

A-24

MAR *–

LAC *

BCND angle_neg,LT

angle_pos


;*stack : angle/X

MPYK 0c90h ;abscissa scale modify degree –> rad

PAC


;*stack : angle/RAD

LT *+


MPYK 985h ;0.0372

;


LAC #0C426h,13 ; in high ACCU

APAC ;ACCU : –0.2338 + angle * 0.0372


;angle in TREG


;temporary value


LAC #6f69h,10 ;0.0544


SACH *,2 ;temp


;angle in TREG


MPY * ;temp

LAC #7dc5h,13 ;0.9826



;temp

MPY * ;rad * temp

;temp * angle

LAC #05532,4 ;0.0013

APAC

A-25

SACH * ,3 ;result

LAC *–

;*stack : angle/SIN

RET

angle_neg


;*stack : angle/X

MPYK 0c90h ;abscisse scale modif degre –> rad

PAC


;*stack : angle/RAD

LT *+


MPYK 985h ;0.0372

;


LAC #03bdah,13 ; in high ACCU

APAC ;ACCU : –0.2338 + angle * 0.0372


;angle in TREG


;temporary value


LAC #6f69h,10 ;0.0544


SACH *,2 ;temp


;angle in TREG


MPY * ;temp

LAC #7dc5h,13 ;0.9826



MPY * ;rad * temp

;temp * angle

LAC #05532,4 ;0.0013

A-26

APAC

SACH *,3 ;result

LAC *–

;*stack : angle/SIN

RET

**********************************************************************************




* *




* *

*Status: *

* *

*Processor: C2xx *

* *





* *




* *


* *

*________________________________________________________________________________*


*––––––––––––––|–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––*

* | *

* | *

**********************************************************************************

_sin_ser


A-27

POPD *+

SAR AR1,*

LAR AR2,*,AR2


SPM 0

SETC SXM

LAC *

BCND angle_neg,LT

angle_pos


;*stack : angle/X


;in

PAC


;*stack : angle/RAD

LT *+


MPYK 985h ;0.0372

;



APAC ;ACCU : –0.2338 + angle * 0.0372


;angle in TREG


;temporary value


LAC #6f69h,10 ;0.0544


SACH *,2 ;temp


;angle in TREG


MPY * ;temp

LAC #7dc5h,13 ;0.9826

A-28



;temp

MPY * ;rad * temp

;temp * angle

LAC #05532,4 ;0.0013

APAC

SACH * ,3 ;result

LAC *–,0,AR1

;*stack : angle/SIN


PSHD *–

SBRK 1

RET

angle_neg


;*stack : angle/X


PAC


;*stack : angle/RAD

LT *+


MPYK 985h ;0.0372

;



APAC ;ACCU : –0.2338 + angle * 0.0372


;angle in TREG


;temporary value


LAC #6f69h,10 ;0.0544


SACH *,2 ;temp

A-29


;angle in TREG


MPY * ;temp

LAC #7dc5h,13 ;0.9826



MPY * ;rad * temp

;temp * angle

LAC #05532,4 ;0.0013

APAC

SACH *,3 ;result

LAC *–,0,AR1

;*stack : angle/SIN


PSHD *–

SBRK 1

RET

**********************************************************************************




* *



* *

*Status: *

* *

*Processor: C2xx *

* *

* *





A-30

* *




* *

* *


*________________________________________________________________________________*


*––––––––––––––|–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––*

* | *

* | *

**********************************************************************************

cos_ser

SETC SXM

MAR *–

LAC *

BCND angle_neg,LT

angle_pos


;*stack : angle/X


PAC


;*stack : angle/RAD

LT *+


MPYK 1070h ;0.0076 neg

;


LAC #01e76h,15 ; in high ACCU

APAC ;ACCU : +0.0595 + angle * 0.0076


;angle in TREG


;temporary value

A-31


LAC #0f532h,15 ;0.0211


SACH * ;temp


;angle in TREG


MPY * ;temp

LAC #0e0c6h,15 ;0.4879



MPY * ;rad * temp

;temp * angle

LAC #0a440h,5 ;0.0028

APAC

SACH *,2 ;result

MPY * ;

LAC #1000h,15 ;1

APAC

SETC OVM

SACH *,3

LAC *,16

ADD *,16

SACH *

LAC *–

;*stack : angle/SIN

RET

angle_neg


;*stack : angle/X


PAC


;*stack : angle/RAD

LT *+


A-32

MPYK 0f90h ;0.0076 neg

;



APAC ;ACCU : +0.0595 + angle * 0.0076


;angle in TREG


;temporary value


LAC #00aceh,15 ;0.0211


SACH * ;temp


;angle in TREG


MPY * ;temp

LAC #0e0c6h,15 ;0.4879



;temp

MPY * ;rad * temp

;temp * angle

LAC #05bc0h,5 ;0.0028

APAC

SACH *,2 ;result

MPY * ;

LAC #1000h,15 ;1

APAC

SETC OVM

SACH *,3

LAC *,16

ADD *,16

SACH *

LAC *–

;*stack : angle/SIN

RET

A-33

**********************************************************************************




* *




* *

*Status: *

* *

*Processor: C2xx *

* *





* *




* *


* *

*________________________________________________________________________________*


*––––––––––––––|–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––*

* | *

* | *

**********************************************************************************

_cos_ser


POPD *+

SAR AR1,*

LAR AR2,*,AR2


A-34

SPM 0

SETC SXM

LAC *

BCND angle_neg,LT

angle_pos


;*stack : angle/X


PAC


;*stack : angle/RAD

LT *+


MPYK 1070h ;0.0076 neg

;



APAC ;ACCU : +0.0595 + angle * 0.0076


;angle in TREG


;temporary value


LAC #0f532h,15 ;0.0211


SACH * ;temp


;angle in TREG


MPY * ;temp

LAC #0e0c6h,15 ;0.4879



;temp

MPY * ;rad * temp

A-35

;temp * angle

LAC #0a440h,5 ;0.0028

APAC

SACH *,2 ;result

MPY * ;

LAC #1000h,15 ;1

APAC

SETC OVM

SACH *,3

LAC *,16

ADD *,16

SACH *

LAC *–,0,AR1

;*stack : angle/SIN


PSHD *–

SBRK 1

RET

angle_neg


;*stack : angle/X


PAC


;*stack : angle/RAD

LT *+



;



APAC ;ACCU : +0.0595 + angle * 0.0076


;angle in TREG


;temporary value

A-36


LAC #00aceh,15 ;0.0211


SACH * ;temp


;angle in TREG


MPY * ;temp

LAC #0e0c6h,15 ;0.4879



MPY * ;rad * temp


LAC #05bc0h,5 ;0.0028

SACH *,2 ;result

MPY * ;

LAC #1000h,15 ;1

APAC

SETC OVM

SACH *,3

LAC *,16

ADD *,16

SACH *

LAC *–,0,AR1

;*stack : angle/SIN


PSHD *–

SBRK 1

RET

A-37

A-1

********************************************************************************





* *

* *

*Processor: C2xx *

* *

*Status: *

* *


*______________________________________________________________________________*


*––––––––––––––|–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––*

* | *

********************************************************************************

extern ser_cos();

void main()

{

double rad;

double a;

int c;

.

.

.

if (rad!=0.0) /*–π < rad < +π*/

c=(int)(32767*rad/3.1415927);

else

c=0;

a=ser_cos(c);

.

}

**********************************************************************************




A-2

* *


* *

*Processor: C2xx *

*Status: *


*________________________________________________________________________________*


*––––––––––––––|–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––*

* | *

**********************************************************************************

.mmregs

.def _ser_sin

.sect “vectors”

b _c_int0

b $

*********************************************************************************** Main routine

**********************************************************************************

.text

_c_int0:

.

.


MAR *,AR1

A-3

LAC #4000h ;π/2


CALL _ser_sin

. ;result in ACCU

.

.end

**********************************************************************************




* *




* *

*Status: *

* *

*Processor: C2xx *

* *





* *




* *


*________________________________________________________________________________*


*––––––––––––––|–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––*

* *

**********************************************************************************

COS

MAR *–

LAC #4000h


A-4

SACL *



LAC #64h

SACL *




SACH *+ ;remainder


SACL * ;


LAC *,15

ANDK #0ffffh,15

SACH *–


BCND equal_sin,EQ




TBLR *+


ADD #1h




LAC *–




SACL *+


LT *–


MPY *




A-5

LAC *+



RET

equal_sin




TBLR *

LAC *+

end_interp_sin

RET

**********************************************************************************

* Table

**********************************************************************************


Table_sin_end

.word 0

.end

**********************************************************************************




* *




* *

*Status: *

* *

*Processor: C2xx *

* *





A-6

* *




* *


* *

*________________________________________________________________________________*


*––––––––––––––|–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––*

* | *

* | *

**********************************************************************************

_COS


POPD *+

SAR AR1,*

LAR AR2,*,AR2


SPM 0

LAC #4000h


SACL *



LAC #64h

SACL *




SACH *+ ;remainder


SACL * ;


LAC *,15

ANDK #0ffffh,15

A-7

SACH *–


BCND equal_sin,EQ




TBLR *+


ADD #1h




LAC *–




SACL *+


LT *–


MPY *




LAC *+




PSHD *–

SBRK 1

RET

equal_sin




TBLR *

LAC *+,0,AR1

A-8


PSHD *–

SBRK 1

RET

**********************************************************************************

* Table

**********************************************************************************


Table_sin_end

.word 0

.end

**********************************************************************************




* *



* *

*Status: *

* *

*Processor: C2xx *

* *





* *




* *

* *


*________________________________________________________________________________*

A-9


*––––––––––––––|–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––*

* | *

* | *

**********************************************************************************

SIN

MAR *+



LAC #64h

SACL *




SACH *+ ;remainder


SACL * ;


LAC *,15

ANDK #0ffffh,15

SACH *–


BCND equal_sin,EQ




TBLR *+


ADD #1h




LAC *–




SACL *+

A-10


LT *–


MPY *




LAC *+



RET

equal_sin




TBLR *

LAC *+


end_interp_sin

RET

*********************************************************************************

* Table

*********************************************************************************


Table_sin_end

.word 0

**********************************************************************************




* *




A-11

* *

*Status: *

* *

*Processor: C2x *

* *





* *




* *

* *


* *

*________________________________________________________________________________*


*––––––––––––––|–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––*

* | *

* | *

**********************************************************************************

_SIN


POPD *+

SAR AR1,*

LAR AR2,*,AR2


SPM 0



LAC #64h

SACL *



A-12


SACH *+ ;remainder


SACL * ;


LAC *,15

ANDK #0ffffh,15

SACH *–


BCND equal_sin,EQ




TBLR *+


ADD #1h




LAC *–




SACL *+


LT *–


MPY *




LAC *+




PSHD *–

SBRK 1

RET

A-13

equal_sin




TBLR *

LAC *+,0,AR1



PSHD *–

SBRK 1

RET

**********************************************************************************

* Table

**********************************************************************************


Table_sin_end

.word 0

**********************************************************************************


**********************************************************************************

.word 0

.word 2057

.word 4107

.word 6140

.word 8149

.word 10126

.word 12062

.word 13952

.word 15786

.word 17557

.word 19260

.word 20886

.word 22431

.word 23886

.word 25247

.word 26509

.word 27666

.word 28714

A-14

.word 29648

.word 30466

.word 31163

.word 31738

.word 32187

.word 32509

.word 32702

.word 32767

.word 32702

.word 32509

.word 32187

.word 31738

.word 31163

.word 30466

.word 29648

.word 28714

.word 27666

.word 26509

.word 25247

.word 23886

.word 22431

.word 20886

.word 19260

.word 17557

.word 15786

.word 13952

.word 12062

.word 10126

.word 8149

.word 6140

.word 4107

.word 2057

.word 0

.word –2057

.word –4107

.word –6140

.word –8149

.word –10126

A-15

.word –12062

.word –13952

.word –15786

.word –17557

.word –19260

.word –20886

.word –22431

.word –23886

.word –25247

.word –26509

.word –27666

.word –28714

.word –29648

.word –30466

.word –31163

.word –31738

.word –32187

.word –32509

.word –32702

.word –32767

.word –32702

.word –32509

.word –32187

.word –31738

.word –31163

.word –30466

.word –29648

.word –28714

.word –27666

.word –26509

.word –25247

.word –23886

.word –22431

.word –20886

.word –19260

.word –17557

.word –15786

.word –13952

A-16

.word –12062

.word –10126

.word –8149

.word –6140

.word –4107

.word –2057

**********************************************************************************




* *



* *

*Status: *

* *

*Processor: C2xx *

* *



* Output: *




* *




* *


*________________________________________________________________________________*


*––––––––––––––|–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––*

* | *

* | *

**********************************************************************************


A-17

COS_SIN

MAR *+


;*stack: angle/X

LAC #size_tab

SACL *

;*stack: angle/TEMP



SACH *+ ;remainder


SACL * ;


LAC *,15

ANDK #0ffffh,15

SACH *–


BCND equal_sin,EQ




TBLR *+


ADD #1h




ADRK 1


ADD #18h

TBLR *+


ADD #1h


LAC *– ;calculate cos interpolate


A-18




LT *–


SBRK 1


MPY *


ADRK 2




LAC *+




SACL *–



SBRK 1


LAC *–




SACL *+


LT *–


MPY *




LAC *+




A-19


ADRK 3


LAC *

SBRK 2


SACL *

;*stack: sin/COS

RET

equal_sin





TBLR *+


ADDK 19h

TBLR *

;*stack: sin/COS

end_interp_sin

RET

**********************************************************************************

* Table

**********************************************************************************


Table_sin_cos_end

.word 0

**********************************************************************************


**********************************************************************************

.word 0

.word 2057

.word 4107

.word 6140

.word 8149

A-20

.word 10126

.word 12062

.word 13952

.word 15786

.word 17557

.word 19260

.word 20886

.word 22431

.word 23886

.word 25247

.word 26509

.word 27666

.word 28714

.word 29648

.word 30466

.word 31163

.word 31738

.word 32187

.word 32509

.word 32702

.word 32767

.word 32702

.word 32509

.word 32187

.word 31738

.word 31163

.word 30466

.word 29648

.word 28714

.word 27666

.word 26509

.word 25247

.word 23886

.word 22431

.word 20886

.word 19260

.word 17557

.word 15786

A-21

.word 13952

.word 12062

.word 10126

.word 8149

.word 6140

.word 4107

.word 2057

.word 0

.word –2057

.word –4107

.word –6140

.word –8149

.word –10126

.word –12062

.word –13952

.word –15786

.word –17557

.word –19260

.word –20886

.word –22431

.word –23886

.word –25247

.word –26509

.word –27666

.word –28714

.word –29648

.word –30466

.word –31163

.word –31738

.word –32187

.word –32509

.word –32702

.word –32767

.word –32702

.word –32509

.word –32187

.word –31738

.word –31163

A-22

.word –30466

.word –29648

.word –28714

.word –27666

.word –26509

.word –25247

.word –23886

.word –22431

.word –20886

.word –19260

.word –17557

.word –15786

.word –13952

.word –12062

.word –10126

.word –8149

.word –6140

.word –4107

.word –2057

.word 0

.word 2057

.word 4107

.word 6140

.word 8149

.word 10126

.word 12062

.word 13952

.word 15786

.word 17557

.word 19260

.word 20886

.word 22431

.word 23886

.word 25247

.word 26509

.word 27666

.word 28714

.word 29648

A-23

.word 30466

.word 31163

.word 31738

.word 32187

.word 32509

.word 32702

**********************************************************************************




* *



* *

*Status: *

* *

*Processor: C2xx *

* *





* *




* *

* *


*________________________________________________________________________________*


*––––––––––––––|–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––*

* | *

* | *

**********************************************************************************

sin_ser

SETC SXM

A-24

MAR *–

LAC *

BCND angle_neg,LT

angle_pos


;*stack : angle/X


PAC


;*stack : angle/RAD

LT *+


MPYK 985h ;0.0372

;



APAC ;ACCU : –0.2338 + angle * 0.0372


;angle in TREG


;temporary value


LAC #6f69h,10 ;0.0544


SACH *,2 ;temp


;angle in TREG


MPY * ;temp

LAC #7dc5h,13 ;0.9826



;temp

MPY * ;rad * temp

;temp * angle

LAC #05532,4 ;0.0013

APAC

A-25

SACH * ,3 ;result

LAC *–

;*stack : angle/SIN

RET

angle_neg


;*stack : angle/X


PAC


;*stack : angle/RAD

LT *+


MPYK 985h ;0.0372

;



APAC ;ACCU : –0.2338 + angle * 0.0372


;angle in TREG


;temporary value


LAC #6f69h,10 ;0.0544


SACH *,2 ;temp


;angle in TREG


MPY * ;temp

LAC #7dc5h,13 ;0.9826



MPY * ;rad * temp

;temp * angle

LAC #05532,4 ;0.0013

A-26

APAC

SACH *,3 ;result

LAC *–

;*stack : angle/SIN

RET

**********************************************************************************




* *




* *

*Status: *

* *

*Processor: C2xx *

* *





* *




* *


* *

*________________________________________________________________________________*


*––––––––––––––|–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––*

* | *

* | *

**********************************************************************************

_sin_ser


A-27

POPD *+

SAR AR1,*

LAR AR2,*,AR2


SPM 0

SETC SXM

LAC *

BCND angle_neg,LT

angle_pos


;*stack : angle/X


;in

PAC


;*stack : angle/RAD

LT *+


MPYK 985h ;0.0372

;



APAC ;ACCU : –0.2338 + angle * 0.0372


;angle in TREG


;temporary value


LAC #6f69h,10 ;0.0544


SACH *,2 ;temp


;angle in TREG


MPY * ;temp

LAC #7dc5h,13 ;0.9826

A-28



;temp

MPY * ;rad * temp

;temp * angle

LAC #05532,4 ;0.0013

APAC

SACH * ,3 ;result

LAC *–,0,AR1

;*stack : angle/SIN


PSHD *–

SBRK 1

RET

angle_neg


;*stack : angle/X


PAC


;*stack : angle/RAD

LT *+


MPYK 985h ;0.0372

;



APAC ;ACCU : –0.2338 + angle * 0.0372


;angle in TREG


;temporary value


LAC #6f69h,10 ;0.0544


SACH *,2 ;temp

A-29


;angle in TREG


MPY * ;temp

LAC #7dc5h,13 ;0.9826



MPY * ;rad * temp

;temp * angle

LAC #05532,4 ;0.0013

APAC

SACH *,3 ;result

LAC *–,0,AR1

;*stack : angle/SIN


PSHD *–

SBRK 1

RET

**********************************************************************************




* *



* *

*Status: *

* *

*Processor: C2xx *

* *

* *





A-30

* *




* *

* *


*________________________________________________________________________________*


*––––––––––––––|–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––*

* | *

* | *

**********************************************************************************

cos_ser

SETC SXM

MAR *–

LAC *

BCND angle_neg,LT

angle_pos


;*stack : angle/X


PAC


;*stack : angle/RAD

LT *+


MPYK 1070h ;0.0076 neg

;



APAC ;ACCU : +0.0595 + angle * 0.0076


;angle in TREG


;temporary value

A-31


LAC #0f532h,15 ;0.0211


SACH * ;temp


;angle in TREG


MPY * ;temp

LAC #0e0c6h,15 ;0.4879



MPY * ;rad * temp

;temp * angle

LAC #0a440h,5 ;0.0028

APAC

SACH *,2 ;result

MPY * ;

LAC #1000h,15 ;1

APAC

SETC OVM

SACH *,3

LAC *,16

ADD *,16

SACH *

LAC *–

;*stack : angle/SIN

RET

angle_neg


;*stack : angle/X


PAC


;*stack : angle/RAD

LT *+


A-32


;



APAC ;ACCU : +0.0595 + angle * 0.0076


;angle in TREG


;temporary value


LAC #00aceh,15 ;0.0211


SACH * ;temp


;angle in TREG


MPY * ;temp

LAC #0e0c6h,15 ;0.4879



;temp

MPY * ;rad * temp

;temp * angle

LAC #05bc0h,5 ;0.0028

APAC

SACH *,2 ;result

MPY * ;

LAC #1000h,15 ;1

APAC

SETC OVM

SACH *,3

LAC *,16

ADD *,16

SACH *

LAC *–

;*stack : angle/SIN

RET

A-33

**********************************************************************************




* *




* *

*Status: *

* *

*Processor: C2xx *

* *





* *




* *


* *

*________________________________________________________________________________*


*––––––––––––––|–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––*

* | *

* | *

**********************************************************************************

_cos_ser


POPD *+

SAR AR1,*

LAR AR2,*,AR2


A-34

SPM 0

SETC SXM

LAC *

BCND angle_neg,LT

angle_pos


;*stack : angle/X


PAC


;*stack : angle/RAD

LT *+


MPYK 1070h ;0.0076 neg

;



APAC ;ACCU : +0.0595 + angle * 0.0076


;angle in TREG


;temporary value


LAC #0f532h,15 ;0.0211


SACH * ;temp


;angle in TREG


MPY * ;temp

LAC #0e0c6h,15 ;0.4879



;temp

MPY * ;rad * temp

A-35

;temp * angle

LAC #0a440h,5 ;0.0028

APAC

SACH *,2 ;result

MPY * ;

LAC #1000h,15 ;1

APAC

SETC OVM

SACH *,3

LAC *,16

ADD *,16

SACH *

LAC *–,0,AR1

;*stack : angle/SIN


PSHD *–

SBRK 1

RET

angle_neg


;*stack : angle/X


PAC


;*stack : angle/RAD

LT *+



;



APAC ;ACCU : +0.0595 + angle * 0.0076


;angle in TREG


;temporary value

A-36


LAC #00aceh,15 ;0.0211


SACH * ;temp


;angle in TREG


MPY * ;temp

LAC #0e0c6h,15 ;0.4879



MPY * ;rad * temp


LAC #05bc0h,5 ;0.0028

SACH *,2 ;result

MPY * ;

LAC #1000h,15 ;1

APAC

SETC OVM

SACH *,3

LAC *,16

ADD *,16

SACH *

LAC *–,0,AR1

;*stack : angle/SIN


PSHD *–

SBRK 1

RET

A-37

Documents

Digital Sine-Wave Generation Using the TMS320C2xx … · Digital Sine-Wave Generation Using the TMS320C2xx iii ... 2.1 C- and Assembly-Compatible Functions 2 ... Digital Sine-Wave