Application
Report
1998
Digital Signal Processing Solutions
Printed in U.S.A., July 1998
SPRA179
1998
Application
Report
Digital Sine-Wave Generation
Using the TMS320C2xx
SPRA179
July 1998
Printed on Recycled Paper
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Contents
1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
2 Direct Look-Up and Linear Interpolation Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.1 C- and Assembly-Compatible Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.1.1 C-Compatible Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.1.2 Assembly-Compatible Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2 Interpolation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.3 Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.4 System Utilization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.5 Sine-Generation Precision . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.5.1 One-Sine-Period Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.5.2 Quarter-Sine-Period Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3 Sine/Cosine With Mathematical Series . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.1 C- and Assembly-Compatible Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.1.1 C-Compatible Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.1.2 Assembly-Compatible Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2 Sine/Cosine Mathematical Series . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.3 Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.4 System Utilization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.5 Sine-Generation Precision . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.5.1 One-Sine-Period Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.5.2 Quarter-Sine-Period Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2
2
2
2
3
3
3
4
4
7
10
10
10
10
11
11
11
12
13
14
Appendix A Examples of a C Program and an Assembly Program Calling Sine and
Cosine 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
Digital Sine-Wave Generation Using the TMS320C2xx
iii
Figures
List of Figures
1
The Formula and the Resulting Graph for Calculating the Table Interpolation
Value 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
iv
SPRA179
Tables
List of Tables
1
2
3
4
Processor Utilization (Maximum) When Using Direct Look-up and Interpolation . . . . . . . . . 4
Memory Utilization When Using Direct Look-up and Interpolation . . . . . . . . . . . . . . . . . . . . . . 4
Processor Utilization (Maximum) When Using Mathematical Series . . . . . . . . . . . . . . . . . . . 11
Memory Utilization When Using Mathematical Series . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
Digital Sine-Wave Generation Using the TMS320C2xx
v
vi
SPRA179
Digital Sine-Wave Generation Using the TMS320C2xx
ABSTRACT
This application report describes two methods for implementing a digital sine-wave
generator using the TMS320C2xx: the use of a direct look-up table with linear
interpolation, and the use of mathematical series. Both methods are explained in
terms of C-compatible and assembly-compatible functions. Formulas used for
calculating and graphing the results are included for each method to demonstrate
the differences.
1 Introduction
Sine-wave generators are fundamental building blocks of signal processing
systems for use in control applications. The following two methods
described in this application report are for implementing a digital sine-wave
generator using the TMS320C2xx:
• Direct look-up with linear interpolation to provide sine waves with a
minimum of harmonic distortion
• Realization of the sine/cosine functions with a mathematical series
The two methods respond to different constraints. The direct look-up
method is fast with minimal errors and is significant in ROM programming
requirements. The mathematical series method is fast and requires
minimum (ROM) programming but results in less precision.
Digital Sine-Wave Generation Using the TMS320C2xx
1
Direct Look-Up and Linear Interpolation Method
2 Direct Look-Up and Linear Interpolation Method
This section describes the Direct Look-Up and Linear Interpolation method
of 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 extended
table 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 and
cosine functions) are in the appendix.
2.1.1
C-Compatible Functions
Fully C-compatible functions employ C conventions to use the stack for
parameters passed to the functions. Parameters returned by the functions
are passed by a pointer. Responsibilities of called functions are managed
in a postfix expression called the function designator. Stack pointer AR1 is
well-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 are
not 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 AR1
register points to the stack just after the last argument. After the return from
the function, the results are placed in the stack. Registers AR0, AR6, and
AR7 are not modified.
2
SPRA179
Direct Look-Up and Linear Interpolation Method
2.2
Interpolation
Figure 1 shows the formula and the resulting graph for calculating the table
interpolation value COS(X) of an angle X.
y
y
Y=?
X –x
Y
=
y
i
+
i
x
i+ 1
r =
-
i+1
( y
i+ 1
x
y )
i
y
i
i
ratio
x
i
X
x
x
i+1
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 Table
Interpolation 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.
2. Interpolation: solving the above mentioned calculation to obtain Y.
2.3
Functions
Functions SINE, COSINE, and SINE + COSINE are illustrated by example
in the appendix. Conventions to interface with this function are:
•
•
2.4
Input: ANGLE parameters are in the stack pointed by AR1. The value
of this angle is unsigned.
0°
<->
0000h
90°
<->
4000h
180°
<->
8000h
240°
<->
C000h
Output: COS(angle) or SIN(angle) are in ACCUMULATOR in Q15
format (–1 to 1–215).
System Utilization
Table 1 shows processor utilization when using the direct look-up and linear
interpolation methods.
Digital Sine-Wave Generation Using the TMS320C2xx
3
Direct Look-Up and Linear Interpolation Method
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 linear
interpolation method.
Table 2. Memory Utilization When Using Direct Look-Up and Interpolation
FUNCTION
ROM
(WORDS)
STACKLEVELS
REGISTERS
USED
RAM
(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 assembly call
44 + 100
5
1
In stack
COS + SIN in one function†
assembly call
55 + 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 direct
look-up and linear interpolation sine functions. The precision measurement
is made by comparing the direct look-up and the floating-point C library
results.
2.5.1
One-Sine-Period Analysis
The sine period provides a general image of error calculation. In Figure 2
and Figure 3, results of the sine calculation are in Q15 format.
4
SPRA179
Direct Look-Up and Linear Interpolation Method
Figure 2. Direct Look-Up With Interpolation of Sine Calculation From 0 to 2*π
With a 0.015-Radian Step
Digital Sine-Wave Generation Using the TMS320C2xx
5
Direct Look-Up and Linear Interpolation Method
Figure 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
SPRA179
Direct Look-Up and Linear Interpolation Method
2.5.2
Quarter-Sine-Period Analysis
Figure 4, Figure 5, and Figure 6 graph another precise analysis using 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, interpolation
error 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
Digital Sine-Wave Generation Using the TMS320C2xx
7
Direct Look-Up and Linear Interpolation Method
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
8
SPRA179
Direct Look-Up and Linear Interpolation Method
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 %
Digital Sine-Wave Generation Using the TMS320C2xx
9
Sine/Cosine With Mathematical Series
3 Sine/Cosine With Mathematical Series
This section explains the second of two methods of implementing a digital
sine-wave generator using the TMS320C2xx.
3.1
C- and Assembly-Compatible Functions
The sine/cosine method calculates the sine/cosine functions with a
mathematical series for the sine period and a mathematical series for
cosine. Calculations are made with fixed-point instructions to optimize the
time calculation. The dynamics used in the calculation fit with maximum
precision without overflow.
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 and
cosine functions) are in the appendix.
3.1.1
C-Compatible Functions
Fully C-compatible functions employ C conventions to use the stack for
parameters passed to the functions. Parameters returned by functions are
passed by a pointer. Responsibilities of called functions are managed in a
postfix expression called the function designator. Stack pointer AR1 is
well-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 are
not used.
3.1.2
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 AR1
register points to the stack just after the last argument. After the return from
the function, the results are placed in the stack. Registers AR0, AR6, and
AR7 are not modified.
10
SPRA179
Sine/Cosine With Mathematical Series
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+0.0013
else
SIN(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.
X in radian,
If (X>=0.0)
COS(X)=(((((-0.0076*X)+0.0595)*X-0.0211)*X-0.4879)*X-0.0028)*X+1.0
else
COS(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 value
of this angle is unsigned.
0°
<->
0000h
90°
<->
4000h
180° <->
8000h
240° or -90° <-> C000h
• Output: COS(angle) or SIN(angle) are in ACCUMULATOR in Q15
format (–1 to 1–215).
3.4
System Utilization
Table 3 shows processor utilization when using the mathematical series
method.
Table 3. Processor Utilization (Maximum) When Using Mathematical Series
FUNCTION
CYCLES
EXECUTION TIME
SIN assembly main
27
1.35 µs
COS assembly main
37
1.85 µs
SIN fully C-compatible
34
1.70 µs
COS fully C-compatible
44
2.20 µs
SIN + COS of an angle – assembly main
64
3.20 µs
Digital Sine-Wave Generation Using the TMS320C2xx
11
Sine/Cosine With Mathematical Series
Table 4 shows memory utilization when using the mathematical series
method.
Table 4. Memory Utilization When Using Mathematical Series
3.5
FUNCTION
ROM
(WORDS)
STACK
LEVELS
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
Sine-Generation Precision
The following graphs present the precision of the mathematical series of
sine functions. The precision measurement is calculated by comparing the
mathematical series and floating-point C library results.
12
SPRA179
Sine/Cosine With Mathematical Series
3.5.1
One-Sine-Period Analysis
The sine period provides a general image of error calculation. In Figure 9
and 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
Digital Sine-Wave Generation Using the TMS320C2xx
13
Sine/Cosine With Mathematical Series
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 a
quarter of a half-sine period. In this case, the step is 0.0039 radian.
14
SPRA179
Sine/Cosine With Mathematical Series
Figure 11. Results of Mathematical Series Sine From 0 to π/2
With a 0.0039-Radian Step
Digital Sine-Wave Generation Using the TMS320C2xx
15
Sine/Cosine With Mathematical Series
Figure 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
SPRA179
Sine/Cosine With Mathematical Series
Figure 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 %
Digital Sine-Wave Generation Using the TMS320C2xx
17
18
SPRA179
Examples of a C Program and an Assembly Program Calling Sine and Cosine Functions
Appendix A
A.1
Examples of a C Program and an Assembly Program
Calling Sine and Cosine Functions
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);
.
}
Digital Sine-Wave Generation Using the TMS320C2xx
A-1
Examples of a C Program and an Assembly Program Calling Sine and Cosine Functions
A.2
Main Assembly Program to Call Sine or Cosine Functions
**********************************************************************************
*File Name:
Main_trig.asm
*
*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
*
*––––––––––––––|–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––*
*
|
*
**********************************************************************************
.mmregs
.def
_ser_sin
.sect
“vectors”
b
_c_int0
b
$
**********************************************************************************
* Main routine
**********************************************************************************
.text
_c_int0:
.
.
LAR
AR1,#60h
MAR
*,AR1
A-2
SPRA179
;stack preparation
Examples of a C Program and an Assembly Program Calling Sine and Cosine Functions
LACC
#4000h
;π/2
SACL
*+
;parameters in stack
CALL
_ser_sin
.
;result in ACCU
.
.end
Digital Sine-Wave Generation Using the TMS320C2xx
A-3
Examples of a C Program and an Assembly Program Calling Sine and Cosine Functions
A.3
COS Function With Direct Look-Up and Linear Interpolation for
Assembly Program
**********************************************************************************
*Routine Name:
COS
*
*Project:
DMC Mathematical Library
*
*Originator:
Pascal DORSTER (Texas Instruments)
*
*
*
*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
*
*
*
*Last Update:
16 Oct 96
*
*________________________________________________________________________________*
*Date of Mod
|
DESCRIPTION
*
*––––––––––––––|–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––*
*
*
**********************************************************************************
COS
MAR
*–
LACC
#4000h
ADDS
*
SACL
*
LT
*+
;add 0.5 for COS
;variable in size_sin
;*******stack : angle/X
LACC
A-4
#64h
SPRA179
Examples of a C Program and an Assembly Program Calling Sine and Cosine Functions
SACL
*
;*******stack : angle/TEMP
MPYU
*
PAC
SACH
;integer position in the table
;in High part of Acc
*+
;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
ADD
*–
;address of beginning of the table
;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
;*******stack : y1/Y2/remainder
SACL
*+
;*******stack : y1/temp/REMAINDER
LT
*–
MPY
*
;*******stack : y1/TEMP/remainder
;*******stack : y1/TEMP/remainder
SPH
*–
;interpolation between Y1 and Y2
;*******stack : Y1/temp/remainder
LACC
*+
ADD
*,1
;*******stack : y1/TEMP/remainder
;Y(Xdata) in ACCU
RET
Digital Sine-Wave Generation Using the TMS320C2xx
A-5
Examples of a C Program and an Assembly Program Calling Sine and Cosine Functions
equal_sin
LACC
#Table_sin
ADD
*–
;address of beginning of the table
;address of the pointed indice
;*******stack : RESULT/
TBLR
*
LACC
*+
end_interp_sin
RET
**********************************************************************************
* Table
**********************************************************************************
Table_sin
.include
Table_sin_end
.word
0
.end
A-6
SPRA179
sine.tab
Examples of a C Program and an Assembly Program Calling Sine and Cosine Functions
A.4
COS Function With Direct Look-Up and Linear Interpolation for
C Program
**********************************************************************************
*Routine Name:
_COS
*
*Project:
DMC Mathematical Library
*
*Originator:
Pascal DORSTER (Texas Instruments)
*
*
*
*Description:
COS function with Direct Look–up and
*
*
Interpolation C calling function, variables in C stack.
*
*
Fully C compatible
*
*
*
*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
*
*
*
*Last Update:
16 Oct 96
*
*
*
*________________________________________________________________________________*
*Date of Mod
|
DESCRIPTION
*
*––––––––––––––|–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––*
*
|
*
*
|
*
**********************************************************************************
_COS
ADRK
#2
POPD
*+
SAR
AR1,*
LAR
AR2,*,AR2
;C compatibility
Digital Sine-Wave Generation Using the TMS320C2xx
A-7
Examples of a C Program and an Assembly Program Calling Sine and Cosine Functions
SBRK
#3
SPM
0
LACC
#4000h
ADDS
*
SACL
*
LT
*+
;C compatibility
;add 0.5 for COS
;variable in size_sin
;*******stack : angle/X
LACC
#64h
SACL
*
MPYU
*
;*******stack : angle/TEMP
PAC
SACH
;integer position in the table
;in High part of Acc
*+
;remainder
;*******stack : angle/indice/X
SACL
*
LACC
*,15
AND
#0ffffh,15
SACH
*–
;
;*******stack : angle/indice/REMAINDER
;*******stack : angle/INDICE/remainder
BCND
equal_sin,EQ
LACC
#Table_sin
ADD
*–
;address of beginning of the table
;address of the nearest first indice
;*******stack : ANGLE/indice/remainder
TBLR
*+
ADD
#1h
TBLR
*
;*******stack : y1/INDICE/remainder
;Load Y2 with the ordinate of the
;*******stack : y1/Y2/remainder
;nearest second indice
LACC
*–
SUB
*+
;*******stack : Y1/y2/remainder
;difference between the two Y value
;*******stack : y1/Y2/remainder
SACL
*+
;*******stack : y1/temp/REMAINDER
LT
A-8
*–
SPRA179
Examples of a C Program and an Assembly Program Calling Sine and Cosine Functions
;*******stack : y1/TEMP/remainder
MPY
*
;*******stack : y1/TEMP/remainder
SPH
*–
LACC
*+
;interpolation between Y1 and Y2
;*******stack : Y1/temp/remainder
;*******stack : y1/TEMP/remainder
ADD
*,1,AR1
;Y(Xdata) in ACCU
MAR
*–
;C compatibility
PSHD
*–
SBRK
#1
RET
equal_sin
LACC
#Table_sin
ADD
*–
TBLR
*
LACC
*+,0,AR1
;address of beginning of the table
;address of the pointed indice
;*******stack : RESULT/
MAR
*–
PSHD
*–
SBRK
#1
;C compatibility
RET
**********************************************************************************
* Table
**********************************************************************************
Table_sin
.include
sine.tab
Table_sin_end
.word
0
.end
Digital Sine-Wave Generation Using the TMS320C2xx
A-9
Examples of a C Program and an Assembly Program Calling Sine and Cosine Functions
A.5
SIN Function With Direct Look-Up and Linear Interpolation for
Assembly Program
**********************************************************************************
*Routine Name:
SIN
*
*Project:
DMC Mathematical Library
*
*Originator:
Pascal DORSTER (Texas Instruments)
*
*
*
*Description:
SIN 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 : SIN(angle)*32767, Q15, in ACCU
*
*
Pointed register AR1
*
*
*
*Stack commentary:
*
*
Position of current register in Caps
*
*
Stack at beginning : angle/X
*
*
*
*
*
*Last Update:
16 Oct 96
*
*________________________________________________________________________________*
*Date of Mod
|
DESCRIPTION
*
*––––––––––––––|–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––*
*
|
*
*
|
*
**********************************************************************************
SIN
MAR
*+
LT
*+
LACC
#64h
SACL
*
;variable in size_sin
;*******stack : angle/X
A-10
SPRA179
Examples of a C Program and an Assembly Program Calling Sine and Cosine Functions
;*******stack : angle/TEMP
MPYU
*
PAC
SACH
;integer position in the table
;in High part of Acc
*+
;remainder
;*******stack : angle/indice/X
SACL
*
LACC
*,15
AND
#0ffffh,15
SACH
*–
BCND
equal_sin,EQ
LACC
#Table_sin
ADD
*–
;
;*******stack : angle/indice/REMAINDER
;*******stack : angle/INDICE/remainder
;address of beginning of the table
;address of the nearest first indice
;*******stack : ANGLE/indice/remainder
TBLR
*+
ADD
#1h
TBLR
*
;*******stack : y1/INDICE/remainder
;Load Y2 with the ordinate of the
;*******stack : y1/Y2/remainder
;nearest second indice
LACC
*–
SUB
*+
;*******stack : Y1/y2/remainder
;difference between the two Y value
;*******stack : y1/Y2/remainder
SACL
*+
LT
*–
;*******stack : y1/temp/REMAINDER
;*******stack : y1/TEMP/remainder
MPY
*
;*******stack : y1/TEMP/remainder
SPH
*–
LACC
*+
;interpolation between Y1 and Y2
;*******stack : Y1/temp/remainder
;*******stack : y1/TEMP/remainder
ADD
*,1
;Y(Xdata) in ACCU
RET
equal_sin
Digital Sine-Wave Generation Using the TMS320C2xx
A-11
Examples of a C Program and an Assembly Program Calling Sine and Cosine Functions
LACC
#Table_sin
ADD
*–
;address of beginning of the table
;address of the pointed indice
;*******stack : RESULT/
TBLR
*
LACC
*+
;*******stack : result/X
end_interp_sin
RET
*********************************************************************************
* Table
*********************************************************************************
Table_sin
.include
Table_sin_end
.word 0
A-12
SPRA179
sine.tab
Examples of a C Program and an Assembly Program Calling Sine and Cosine Functions
A.6
SIN Function With Direct Look-Up and Linear Interpolation for
C Program
**********************************************************************************
*Routine Name:
_SIN
*
*Project:
DMC Mathematical Library
*
*Originator:
Pascal DORSTER (Texas Instruments)
*
*
*
*Description:
*
SIN function with Direct Look–up + Interpolation
*
C calling function, variables in C stack.
*
*
Fully C compatible
*
*
*
*Status:
*
*
*
*Processor:
C2x
*
*
*
*Calling convention:
*
*
Input : Angle in stack value 0–360 degrees <=>0h–FFFFh
*
*
Output : SIN(angle)*32767, Q15, in ACCU
*
*
Pointed register AR1
*
*
*
*Stack commentary:
*
*
Position of current register in Caps
*
*
Stack at beginning : angle/X
*
*
*
*
*
*Last Update:
16 Oct 96
*
*
*
*________________________________________________________________________________*
*Date of Mod
|
DESCRIPTION
*
*––––––––––––––|–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––*
*
|
*
*
|
*
**********************************************************************************
_SIN
ADRK
#2
POPD
*+
;C compatibility
Digital Sine-Wave Generation Using the TMS320C2xx
A-13
Examples of a C Program and an Assembly Program Calling Sine and Cosine Functions
SAR
AR1,*
LAR
AR2,*,AR2
SBRK
#3
SPM
0
LT
*+
LACC
#64h
SACL
*
;C compatibility
;variable in size_sin
;*******stack : angle/X
;*******stack : angle/TEMP
MPYU
*
PAC
;integer position in the table
;in High part of Acc
SACH
*+
;remainder
SACL
*
;
;*******stack : angle/indice/X
;*******stack : angle/indice/REMAINDER
LACC
*,15
AND
#0ffffh,15
SACH
*–
BCND
equal_sin,EQ
LACC
#Table_sin
ADD
*–
;*******stack : angle/INDICE/remainder
;address of beginning of the table
;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
;*******stack : y1/Y2/remainder
SACL
*+
LT
*–
;*******stack : y1/temp/REMAINDER
;*******stack : y1/TEMP/remainder
A-14
SPRA179
Examples of a C Program and an Assembly Program Calling Sine and Cosine Functions
MPY
*
;*******stack : y1/TEMP/remainder
SPH
*–
;interpolation between Y1 and Y2
;*******stack : Y1/temp/remainder
LACC
*+
;*******stack : y1/TEMP/remainder
ADD
*,1,AR1
;Y(Xdata) in ACCU
MAR
*–
;C compatibility
PSHD
*–
SBRK
#1
RET
equal_sin
LACC
#Table_sin
ADD
*–
;address of beginning of the table
;address of the pointed indice
;*******stack : RESULT/...
TBLR
*
LACC
*+,0,AR1
;*******stack : result/X
MAR
*–
PSHD
*–
SBRK
#1
;C compatibility
RET
**********************************************************************************
* Table
**********************************************************************************
Table_sin
.include
sine.tab
Table_sin_end
.word
0
Digital Sine-Wave Generation Using the TMS320C2xx
A-15
Examples of a C Program and an Assembly Program Calling Sine and Cosine Functions
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
A-16
SPRA179
Examples of a C Program and an Assembly Program Calling Sine and Cosine Functions
.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
Digital Sine-Wave Generation Using the TMS320C2xx
A-17
Examples of a C Program and an Assembly Program Calling Sine and Cosine Functions
.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-18
SPRA179
Examples of a C Program and an Assembly Program Calling Sine and Cosine Functions
A.8
COS_SIN Function With Direct Look-Up and Linear Interpolation for
Assembly Program
**********************************************************************************
*Routine Name:
COS_SIN
*
*Project:
DMC Mathematical Library
*
*Originator:
Pascal DORSTER (Texas Instruments)
*
*
*
*Description:
COS+SIN 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:
*
*
SIN(angle)*32767, Q15, in stack pointed by AR1–1
*
*
COS(angle)*32767,Q15, in stack pointed by AR1
*
*
Pointed register AR1
*
*
*
*Stack commentary:
*
*
Position of current register in Caps
*
*
Stack at beginning : angle/X
*
*
*
*Last Update:
16 Oct 96
*
*________________________________________________________________________________*
*Date of Mod
|
DESCRIPTION
*
*––––––––––––––|–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––*
*
|
*
*
|
*
**********************************************************************************
size_tab .set
64h
;this is not an error
COS_SIN
MAR
*+
LT
*+
;variable in size_sin
Digital Sine-Wave Generation Using the TMS320C2xx
A-19
Examples of a C Program and an Assembly Program Calling Sine and Cosine Functions
;*stack: angle/X
LACC
#size_tab
SACL
*
MPYU
*
;*stack: angle/TEMP
PAC
SACH
;integer position in the table
;in High part of Acc
*+
;remainder
;*stack: angle/indice/X
SACL
*
;
;*stack: angle/indice/REMAINDER
LACC
*,15
AND
#0ffffh,15
SACH
*–
BCND
equal_sin,EQ
LACC
#Table_sin_cos
ADD
*–
;*stack: angle/INDICE/remainder
;address of beginning of the table
;address of the nearest first indice
;*stack: ANGLE/indice/remainder
TBLR
*+
ADD
#1h
TBLR
*+
;*stack: y1/INDICE/remainder
;Load Y2 with the ordinate of the
;nearest second indice
;*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
SUB
*+
;difference between the two Y value
SACL
*
;*stack: y1/y2/remainder/yy1/TEMP
LT
*–
;*stack: y1/y2/remainder/yy1/YY2
A-20
SPRA179
Examples of a C Program and an Assembly Program Calling Sine and Cosine Functions
;*stack: y1/y2/remainder/YY1
SBRK
#1
;*stack: y1/y2/REMAINDER/yy1
MPY
*
;*stack: y1/y2/REMAINDER/yy1
ADRK #2
;*stack: y1/y2/remainder/yy1/TEMP
SPH
*–
;interpolation between Y1 and Y2
;*stack: Y1/y2/remainder/YY1/temp
LACC
*+
ADD
*–,1
;*stack: y1/y2/remainder/yy1/TEMP
;Y(Xdata) in ACCU
;*stack: y1/y2/remainder/YY1
SACL
*–
;*stack: y1/y2/REMAINDER/cos
;calculate sin interpolate
SBRK
#1
;*stack: y1/Y2/remainder/cos
LACC
*–
SUB
*+
;*stack: Y1/y2/remainder
;difference between the two Y value
;*stack: y1/Y2/remainder/cos
SACL
*+
;*stack: y1/temp/REMAINDER/cos
LT
*–
;*stack: y1/TEMP/remainder/cos
MPY
*
;*stack: y1/TEMP/remainder/cos
SPH
*–
LACC
*+
;interpolation between Y1 and Y2
;*stack: Y1/temp/remainder/cos
;*stack: y1/TEMP/remainder/cos
ADD
*–,1
;Y(Xdata) in ACCU
;*stack: y1/temp/remainder/cos
SACL
*
ADRK
#3
;*stack: SIN/temp/remainder/cos
;*stack: sin/temp/remainder/COS
LACC
*
Digital Sine-Wave Generation Using the TMS320C2xx
A-21
Examples of a C Program and an Assembly Program Calling Sine and Cosine Functions
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/remainder
ADD
*–
;address of the pointed indice
;*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
A-22
0
SPRA179
Examples of a C Program and an Assembly Program Calling Sine and Cosine Functions
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
Digital Sine-Wave Generation Using the TMS320C2xx
A-23
Examples of a C Program and an Assembly Program Calling Sine and Cosine Functions
.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
A-24
SPRA179
Examples of a C Program and an Assembly Program Calling Sine and Cosine Functions
.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
Digital Sine-Wave Generation Using the TMS320C2xx
A-25
Examples of a C Program and an Assembly Program Calling Sine and Cosine Functions
.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-26
SPRA179
Examples of a C Program and an Assembly Program Calling Sine and Cosine Functions
A.10
SIN With Mathematical Series for Assembly Program
**********************************************************************************
*Routine Name:
sin_ser
*
*Project:
DMC Mathematical Library
*
*Originator:
Pascal DORSTER (Texas Instruments)
*
*
*
*Description:
SIN function with Mathematical Series
*
*
Assembly calling function, variables in s/w stack.
*
*
*
*Status:
*
*
*
*Processor:
C2xx
*
*
*
*Calling convention:
*
*
Input : Angle in stack value 0–360 degrees <=>0h–FFFFh
*
*
Output : SIN(angle)*32767, Q15, in ACCU
*
*
Pointed register AR1
*
*
*
*Stack commentary:
*
*
Position of current register in Caps
*
*
Stack at beginning : angle/X
*
*
*
*
*
*Last Update:
18 Oct 96
*
*________________________________________________________________________________*
*Date of Mod
|
DESCRIPTION
*
*––––––––––––––|–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––*
*
|
*
*
|
*
**********************************************************************************
sin_ser
SETC
SXM
MAR
*–
LAC
*
BCND
angle_neg,LT
angle_pos
Digital Sine-Wave Generation Using the TMS320C2xx
A-27
Examples of a C Program and an Assembly Program Calling Sine and Cosine Functions
LT
*+
;variable in size_sin
;*stack : angle/X
MPY
#0c90h
;abscissa scale modify degree –> rad
*,4
;angle in rad
PAC
SACH
;*stack : angle/RAD
LT
*+
;*stack : angle/rad/X
MPY
#985h
;0.0372
;
;PREG : angle * 0.0372
LACC
#0C426h,13
APAC
SACH
; in high ACCU
;ACCU : –0.2338 + angle * 0.0372
* ,3
;temporary value
;angle in TREG
MPY
*
;multiply by temporary value
;temporary value
;*stack : angle/rad/TEMP
LACC
#6f69h,10
APAC
SACH
;0.0544
;ACCU: temp + 0.0544
*,2
;temp
;*stack : angle/RAD/temp
;angle in TREG
;*stack : angle/rad/TEMP
MPY
*
;temp
LACC
#7dc5h,13
;0.9826
*,3
;treg = rad
APAC
SACH
;ACCU=0.9826+temp
;temp
MPY
*
;rad * temp
;temp * angle
LACC
#05532,4
;0.0013
SACH
* ,3
;result
LACC
*–
APAC
;*stack : angle/SIN
RET
A-28
SPRA179
Examples of a C Program and an Assembly Program Calling Sine and Cosine Functions
angle_neg
LT
*+
;variable in size_sin
MPY
#0c90h
;abscisse scale modif degre –> rad
*,4
;angle in rad
;*stack : angle/X
PAC
SACH
;*stack : angle/RAD
LT
*+
;*stack : angle/rad/X
MPY
#985h
;0.0372
;
;PREG : angle * 0.0372
LACC
#03bdah,13
APAC
; in high ACCU
;ACCU : –0.2338 + angle * 0.0372
SACH
* ,3
;temporary value
MPY
*
;multiply by temporary value
;angle in TREG
;temporary value
;*stack : angle/rad/TEMP
LACC
#6f69h,10
APAC
SACH
;0.0544
;ACCU: temp + 0.0544
*,2
;temp
;*stack : angle/RAD/temp
;angle in TREG
;*stack : angle/rad/TEMP
MPY
*
;temp
LACC
#7dc5h,13
;0.9826
SPAC
;ACCU=0.9826+temp
SACH
*,3
;treg = rad
MPY
*
;rad * temp
;temp * angle
LACC
#05532,4
;0.0013
SACH
*,3
;result
LACC
*–
APAC
;*stack : angle/SIN
RET
Digital Sine-Wave Generation Using the TMS320C2xx
A-29
Examples of a C Program and an Assembly Program Calling Sine and Cosine Functions
A.11
SIN With Mathematical Series for C Program
**********************************************************************************
*Routine Name:
_sin_ser
*
*Project:
DMC Mathematical Library
*
*Originator:
Pascal DORSTER (Texas Instruments)
*
*
*
*Description:
SIN function with Mathematical Series
*
*
C calling function, variables in C stack.
*
*
Fully C compatible
*
*
*
*Status:
*
*
*
*Processor:
C2xx
*
*
*
*Calling convention:
*
*
Input : Angle in stack value 0–360 degrees <=>0h–FFFFh
*
*
Output : SIN(angle)*32767, Q15, in ACCU
*
*
Pointed register AR1
*
*
*
*Stack commentary:
*
*
Position of current register in Caps
*
*
Stack at beginning : angle/X
*
*
*
*Last Update:
18 Oct 96
*
*
*
*________________________________________________________________________________*
*Date of Mod
|
DESCRIPTION
*
*––––––––––––––|–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––*
*
|
*
*
|
*
**********************************************************************************
_sin_ser
ADRK
#2
POPD
*+
SAR
AR1,*
LAR
AR2,*,AR2
SBRK
#3
A-30
SPRA179
;C compatibility
;C compatibility
Examples of a C Program and an Assembly Program Calling Sine and Cosine Functions
SPM
0
SETC
SXM
LACC
*
BCND
angle_neg,LT
angle_pos
LT
*+
;variable in size_sin
;*stack : angle/X
MPY
#0c90h
;abscissa scale modify degree –> rad
;in
PAC
SACH
*,4
LT
*+
;angle in rad
;*stack : angle/RAD
;*stack : angle/rad/X
MPY
#985h
;0.0372
;
;PREG : angle * 0.0372
LACC
#0C426h,13
APAC
; in high ACCU
;ACCU : –0.2338 + angle * 0.0372
SACH
* ,3
;temporary value
MPY
*
;multiply by temporary value
;angle in TREG
;temporary value
;*stack : angle/rad/TEMP
LACC
#6f69h,10
APAC
SACH
;0.0544
;ACCU: temp + 0.0544
*,2
;temp
;*stack : angle/RAD/temp
;angle in TREG
;*stack : angle/rad/TEMP
MPY
*
;temp
LACC
#7dc5h,13
;0.9826
APAC
SACH
;ACCU=0.9826+temp
*,3
;treg = rad
;temp
MPY
*
;rad * temp
Digital Sine-Wave Generation Using the TMS320C2xx
A-31
Examples of a C Program and an Assembly Program Calling Sine and Cosine Functions
;temp * angle
LACC
#05532,4
;0.0013
SACH
* ,3
;result
LACC
*–,0,AR1
APAC
;*stack : angle/SIN
MAR
*–
PSHD
*–
SBRK
#1
;C compatibility
RET
angle_neg
LT
*+
;variable in size_sin
;*stack : angle/X
MPY
#0c90h
;abscisse scale modif degre –> rad
*,4
;angle in rad
PAC
SACH
;*stack : angle/RAD
LT
*+
;*stack : angle/rad/X
MPY
#985h
;0.0372
;
;PREG : angle * 0.0372
LACC
#03bdah,13
APAC
SACH
; in high ACCU
;ACCU : –0.2338 + angle * 0.0372
* ,3
;temporary value
;angle in TREG
MPY
*
;multiply by temporary value
;temporary value
;*stack : angle/rad/TEMP
LACC
#6f69h,10
APAC
SACH
;0.0544
;ACCU: temp + 0.0544
*,2
;temp
;*stack : angle/RAD/temp
;angle in TREG
;*stack : angle/rad/TEMP
MPY
A-32
*
SPRA179
;temp
Examples of a C Program and an Assembly Program Calling Sine and Cosine Functions
LACC
#7dc5h,13
SPAC
;0.9826
;ACCU=0.9826+temp
SACH
*,3
;treg = rad
MPY
*
;rad * temp
;temp * angle
LACC
#05532,4
;0.0013
SACH
*,3
;result
LACC
*–,0,AR1
APAC
;*stack : angle/SIN
MAR
*–
PSHD
*–
SBRK
#1
;C compatibility
RET
Digital Sine-Wave Generation Using the TMS320C2xx
A-33
Examples of a C Program and an Assembly Program Calling Sine and Cosine Functions
A.12
COS With Mathematical Series for Assembly Program
**********************************************************************************
*Routine Name:
cos_ser
*
*Project:
DMC Mathematical Library
*
*Originator:
Pascal DORSTER (Texas Instruments)
*
*
*
*Description:
COS function with Mathematical Series
*
*
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
*
*
*
*
*
*Last Update:
18 Oct 96
*
*________________________________________________________________________________*
*Date of Mod
|
DESCRIPTION
*
*––––––––––––––|–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––*
*
|
*
*
|
*
**********************************************************************************
cos_ser
SETC
SXM
MAR
*–
LACC
*
BCND
angle_neg,LT
A-34
SPRA179
Examples of a C Program and an Assembly Program Calling Sine and Cosine Functions
angle_pos
LT
*+
;variable in size_sin
;*stack : angle/X
MPY
#0c90h
;abscisse scale modif degre –> rad
SACH
*,4
;angle in rad
LT
*+
PAC
;*stack : angle/RAD
;*stack : angle/rad/X
MPY
#1070h
;0.0076 neg
;
;PREG : angle * 0.0076
LACC
#01e76h,15
; in high ACCU
* ,3
;temporary value
APAC
SACH
;ACCU : +0.0595 + angle * 0.0076
;angle in TREG
MPY
*
;multiply by temporary value
;temporary value
;*stack : angle/rad/TEMP
LACC
#0f532h,15
APAC
SACH
;0.0211
;ACCU: temp + 0.0211
*
;temp
;*stack : angle/RAD/temp
;angle in TREG
;*stack : angle/rad/TEMP
MPY
*
;temp
LACC
#0e0c6h,15
;0.4879
APAC
;ACCU=0.9826+temp
SACH
*,2
;treg = rad
MPY
*
;rad * temp
;temp * angle
LACC
#0a440h,5
;0.0028
SACH
*,2
;result
MPY
*
;
LACC
#1000h,15
;1
APAC
APAC
Digital Sine-Wave Generation Using the TMS320C2xx
A-35
Examples of a C Program and an Assembly Program Calling Sine and Cosine Functions
SETC
OVM
SACH
*,3
LACC
*,16
ADD
*,16
SACH
*
LACC
*–
;*stack : angle/SIN
RET
angle_neg
LT
*+
;variable in size_sin
;*stack : angle/X
MPY
#0c90h
;abscisse scale modif degre –> rad
*,4
;angle in rad
PAC
SACH
;*stack : angle/RAD
LT
*+
;*stack : angle/rad/X
MPY
#0f90h
;0.0076 neg
;
;PREG : angle * 0.0076
LACC
#01e76h,15
; in high ACCU
* ,3
;temporary value
APAC
SACH
;ACCU : +0.0595 + angle * 0.0076
;angle in TREG
MPY
*
;multiply by temporary value
;temporary value
;*stack : angle/rad/TEMP
LACC
#00aceh,15
APAC
SACH
;0.0211
;ACCU: temp + 0.0211
*
;temp
;*stack : angle/RAD/temp
;angle in TREG
;*stack : angle/rad/TEMP
MPY
*
;temp
LACC
#0e0c6h,15
;0.4879
APAC
A-36
;ACCU=0.9826+temp
SPRA179
Examples of a C Program and an Assembly Program Calling Sine and Cosine Functions
SACH
*,2
;treg = rad
;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
Digital Sine-Wave Generation Using the TMS320C2xx
A-37
Examples of a C Program and an Assembly Program Calling Sine and Cosine Functions
A.13
COS With Mathematical Series for C Program
**********************************************************************************
*Routine Name:
_cos_ser
*
*Project:
DMC Mathematical Library
*
*Originator:
Pascal DORSTER (Texas Instruments)
*
*
*
*Description:
COS function with Mathematical Series
*
*
C calling function,
*
*
variables in C stack. Fully C compatible
*
*
*
*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
*
*
*
*Last Update:
18 Oct 96
*
*
*
*________________________________________________________________________________*
*Date of Mod
|
DESCRIPTION
*
*––––––––––––––|–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––*
*
|
*
*
|
*
**********************************************************************************
_cos_ser
ADRK
#2
POPD
*+
SAR
AR1,*
LAR
AR2,*,AR2
SBRK
#3
A-38
SPRA179
;C compatibility
;C compatibility
Examples of a C Program and an Assembly Program Calling Sine and Cosine Functions
SPM
0
SETC
SXM
LAC
*
BCND
angle_neg,LT
angle_pos
LT
*+
;variable in size_sin
;*stack : angle/X
MPY
#0c90h
;abscisse scale modif degre –> rad
SACH
*,4
;angle in rad
LT
*+
PAC
;*stack : angle/RAD
;*stack : angle/rad/X
MPY
#1070h
;0.0076 neg
;
;PREG : angle * 0.0076
LACC
#01e76h,15
APAC
; in high ACCU
;ACCU : +0.0595 + angle * 0.0076
SACH
* ,3
;temporary value
MPY
*
;multiply by temporary value
;angle in TREG
;temporary value
;*stack : angle/rad/TEMP
LACC
#0f532h,15
APAC
SACH
;0.0211
;ACCU: temp + 0.0211
*
;temp
;*stack : angle/RAD/temp
;angle in TREG
;*stack : angle/rad/TEMP
MPY
*
;temp
LACC
#0e0c6h,15
;0.4879
APAC
SACH
;ACCU=0.9826+temp
*,2
;treg = rad
;temp
Digital Sine-Wave Generation Using the TMS320C2xx
A-39
Examples of a C Program and an Assembly Program Calling Sine and Cosine Functions
MPY
*
;rad * temp
;temp * angle
LACC
#0a440h,5
;0.0028
SACH
*,2
;result
MPY
*
;
LACC
#1000h,15
;1
APAC
APAC
SETC
OVM
SACH
*,3
LACC
*,16
ADD
*,16
SACH
*
LACC
*–,0,AR1
;*stack : angle/SIN
MAR
*–
PSHD
*–
SBRK
#1
;C compatibility
RET
angle_neg
LT
*+
;variable in size_sin
;*stack : angle/X
MPY
#0c90h
;abscisse scale modif degre –> rad
*,4
;angle in rad
PAC
SACH
;*stack : angle/RAD
LT
*+
MPY
#0f90h
;*stack : angle/rad/X
;0.0076 neg
;
;PREG : angle * 0.0076
LACC
#01e76h,15
APAC
SACH
; in high ACCU
;ACCU : +0.0595 + angle * 0.0076
* ,3
;temporary value
;angle in TREG
MPY
A-40
*
SPRA179
;multiply by temporary value
Examples of a C Program and an Assembly Program Calling Sine and Cosine Functions
;temporary value
;*stack : angle/rad/TEMP
LACC
#00aceh,15
APAC
SACH
;0.0211
;ACCU: temp + 0.0211
*
;temp
;*stack : angle/RAD/temp
;angle in TREG
;*stack : angle/rad/TEMP
MPY
*
;temp
LACC
#0e0c6h,15
;0.4879
APAC
;ACCU=0.9826+temp
SACH
*,2
;treg = rad
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
MAR
*–
PSHD
*–
SBRK
#1
;C compatibility
RET
Digital Sine-Wave Generation Using the TMS320C2xx
A-41
A-42
SPRA179
Digital Sine-Wave Generation Using the TMS320C2xx
ABSTRACT
This application report describes two methods for implementing a digital sine-wave
generator using the TMS320C2xx: the use of a direct look-up table with linear
interpolation, and the use of mathematical series. Both methods are explained in
terms of C-compatible and assembly-compatible functions. Formulas used for
calculating and graphing the results are included for each method to demonstrate
the differences.
B Introduction
Sine-wave generators are fundamental building blocks of signal processing
systems for use in control applications. The following two methods are
described in this application report for implementing a digital sine-wave
generator using the TMS320C2xx:
• Direct look-up with linear interpolation to provide sine waves with a
minimum of harmonic distortion
• Realization of the sine/cosine functions with a mathematical series
The two methods respond to different constraints. The direct look-up
method is fast with minimum errors and is significant in ROM programming
requirements. The mathematical series method is fast and requires
minimum (ROM) programming but results in less precision.
Digital Sine-Wave Generation Using the TMS320C2xx
A-1
Direct Look-Up and Linear Interpolation Method
C Direct Look-Up and Linear Interpolation Method
This section describes the Direct Look- Up and Linear Interpolation method
of 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 extended
table 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 and
cosine functions) are in the appendix.
C.1.1
C-Compatible Functions
Fully C-compatible functions employ C conventions to use the stack for
parameters passed to the functions. Parameters returned by the functions
are passed by a pointer. Responsibilities of called functions are managed
in a postfix expression called the function designator. Stack pointer AR1 is
well-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 are
not used.
C.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 AR1
register points to the stack just after the last argument. After the return from
the function, the results are placed in the stack. Registers AR0, AR6, and
AR7 are not modified.
A-2
STDZ001A
Direct Look-Up and Linear Interpolation Method
C.2
Interpolation
Figure B–1 shows the formula and the resulting graph for calculating the
table interpolation value COS(X) of an angle X.
y
y
X –x
Y
=
y
+
i
x
i+ 1
r =
-
i+1
Y=?
i
( y
i+ 1
x
y )
i
y
i
i
ratio
x
i
X
x
x
i+1
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 Table
Interpolation 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.
•
C.3
Interpolation: solving the above mentioned calculation to obtain Y.
Functions
Functions SINE, COSINE, and SINE + COSINE are illustrated by example
in the appendix. Conventions to interface with this function are:
• Input: ANGLE parameters are in the stack pointed by AR1. The value
of this angle is unsigned.
0°
<->
0000h
90°
<->
4000h
180° <->
8000h
240° <->
C000h
• Output: COS(angle) or SIN(angle) are in ACCUMULATOR in Q15
format (–1 to 1–215).
C.4
System Utilization
Table E–1 shows processor utilization when using the direct look-up and
linear interpolation methods.
Digital Sine-Wave Generation Using the TMS320C2xx
A-3
Direct Look-Up and Linear Interpolation Method
Table E–1. Processor Utilization (Maximum) When Using
Table 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 E–2 shows memory utilization when using the direct look-up and
linear interpolation method.
Table E–2. Memory Utilization When Using Direct Look-Up and Interpolation
FUNCTION
ROM
(WORDS)
STACKLEVELS
REGISTERS
USED
RAM
(WORDS)
SIN ssembly call
32 + 100
3
1
In stack
COS assembly call
34 + 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 assembly call
44 + 100
5
1
In stack
COS + SIN in one function†
assembly call
55 + 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 the
direct look-up and linear interpolation sine functions. The precision
measurement is made by comparing the direct look-up and the floating-point
C library results.
C.5.1
One-Sine-Period Analysis
The sine period provides a general image of error calculation. In Figure B–2
and Figure B–3, results of the sine calculation are in Q15 format.
A-4
STDZ001A
Direct Look-Up and Linear Interpolation Method
Figure B–2. Direct Look-Up With Interpolation of Sine Calculation From 0 to 2*π
With a 0.015-Radian Step
Digital Sine-Wave Generation Using the TMS320C2xx
A-5
Direct Look-Up and Linear Interpolation Method
Figure B–3. Error Between the C Floating-Point Result and Direct Look-Up
Calculation From 0 to 2*π With a 0.015-Radian Step
A-6
STDZ001A
Direct Look-Up and Linear Interpolation Method
C.5.2
Quarter-Sine-Period Analysis
Figure B–4, Figure B–5, and Figure B–6 graph another precise analysis
using 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, interpolation
error 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-Radian
Step
Digital Sine-Wave Generation Using the TMS320C2xx
A-7
Direct Look-Up and Linear Interpolation Method
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
A-8
STDZ001A
Direct Look-Up and Linear Interpolation Method
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 %
Digital Sine-Wave Generation Using the TMS320C2xx
A-9
Sine/Cosine With Mathematical Series
D Sine/Cosine With Mathematical Series
This section explains the second of two methods of implementing a digital
sine-wave generator using the TMS320C2xx.
D.1
C- and Assembly-Compatible Functions
The sine/cosine method calculates the sine/cosine functions with a
mathematical series for the sine period and a mathematical series for
cosine. Calculations are made with fixed-point instructions to optimize the
time calculation. The dynamics used in the calculation fit with maximum
precision without overflow.
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 and
cosine functions) are in the appendix.
D.1.1
C-Compatible Functions
Fully C-compatible functions employ C conventions to use the stack for
parameters passed to the functions. Parameters returned by functions are
passed by a pointer. Responsibilities of called functions are managed in a
postfix expression called the function designator. Stack pointer AR1 is
well-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 are
not used.
D.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 AR1
register points to the stack just after the last argument. After the return from
the function, the results are placed in the stack. Registers AR0, AR6, and
AR7 are not modified.
A-10
STDZ001A
Sine/Cosine With Mathematical Series
D.2
Sine/Cosine Mathematical Series
Figure B–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+0.0013
else
SIN(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 angle
X.
X in radian,
If (X>=0.0)
COS(X)=(((((-0.0076*X)+0.0595)*X-0.0211)*X-0.4879)*X-0.0028)*X+1.0
else
COS(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
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 toby AR1. The value
of this angle is unsigned.
0º
<->
0000h
90 º
<->
4000h
180 º <->
8000h
240 º or -90º <-> C000h
• Output: COS(angle) or SIN(angle) are in ACCUMULATOR in Q15
format (–1 to 1–215).
D.4
System Utilization
Table E–3 shows processor utilization when using the mathematical series
method.
Table E–3. Processor Utilization (Maximum) When Using Mathematical Series
FUNCTION
CYCLES
EXECUTION TIME
SIN assembly main
27
1.35 µs
COS assembly main
37
1.85 µs
SIN fully C-compatible
34
1.70 µs
COS fully C-compatible
44
2.20 µs
SIN + COS of an angle – assembly main
64
3.20 µs
Digital Sine-Wave Generation Using the TMS320C2xx
A-11
Sine/Cosine With Mathematical Series
Table E–4 shows memory utilization when using the mathematical series
method.
Table E–4. Memory Utilization When Using Mathematical Series
D.5
FUNCTION
ROM
(WORDS)
STACK
LEVELS
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
Sine-Generation Precision
The following graphs present the precision of the mathematical series of
sine functions. The precision measurement is calculated by comparing the
mathematical series and floating-point C library results.
A-12
STDZ001A
Sine/Cosine With Mathematical Series
D.5.1
One-Sine-Period Analysis
The sine period provides a general image of error calculation. In Figure B–9
and 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
Digital Sine-Wave Generation Using the TMS320C2xx
A-13
Sine/Cosine With Mathematical Series
Figure B–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
D.5.2
Quarter-Sine-Period Analysis
Figure B–11, Figure B–12, and Figure B–13 graph another precise analysis
using a quarter of a half-sine period. In this case, the step is 0.0039 radian.
A-14
STDZ001A
Sine/Cosine With Mathematical Series
Figure B–11.
Results of Mathematical Series Sine From 0 to π/2
With a 0.0039-Radian Step
Digital Sine-Wave Generation Using the TMS320C2xx
A-15
Sine/Cosine With Mathematical Series
Figure B–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
A-16
STDZ001A
Sine/Cosine With Mathematical Series
Figure B–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 %
Digital Sine-Wave Generation Using the TMS320C2xx
A-17
********************************************************************************
*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);
.
}
**********************************************************************************
*File Name:
Main_trig.asm
*
*Project:
DMC Mathematical Library
*
*Originator:
Pascal DORSTER (Texas Instruments)
*
A-1
*
*
*Description:
Very simple main which calls COS or SIN function
*
*
*
*Processor:
C2xx
*
*Status:
*
*Last Update:
19 Oct 96
*
*________________________________________________________________________________*
*Date of Mod
|
DESCRIPTION
*
*––––––––––––––|–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––*
*
|
*
**********************************************************************************
.mmregs
.def
_ser_sin
.sect
“vectors”
b
_c_int0
b
$
**********************************************************************************
* Main routine
**********************************************************************************
.text
_c_int0:
.
.
LAR
AR1,#60h
MAR
*,AR1
A-2
;stack preparation
LAC
#4000h
;π/2
SACL
*+
;parameters in stack
CALL
_ser_sin
.
;result in ACCU
.
.end
**********************************************************************************
*Routine Name:
COS
*
*Project:
DMC Mathematical Library
*
*Originator:
Pascal DORSTER (Texas Instruments)
*
*
*
*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
*
*
*
*Last Update:
16 Oct 96
*
*________________________________________________________________________________*
*Date of Mod
|
DESCRIPTION
*
*––––––––––––––|–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––*
*
*
**********************************************************************************
COS
MAR
*–
LAC
#4000h
ADDS
*
;add 0.5 for COS
A-3
SACL
*
LT
*+
;variable in size_sin
;*******stack : angle/X
LAC
#64h
SACL
*
;*******stack : angle/TEMP
MPYU
*
PAC
SACH
;integer position in the table
;in High part of Acc
*+
;remainder
;*******stack : angle/indice/X
SACL
*
;
;*******stack : angle/indice/REMAINDER
LAC
*,15
ANDK
#0ffffh,15
SACH
*–
;*******stack : angle/INDICE/remainder
BCND
equal_sin,EQ
LALK
Table_sin
;address of beginning of the table
ADD
*–
;address of the nearest first indice
TBLR
*+
;*******stack : ANGLE/indice/remainder
;*******stack : y1/INDICE/remainder
ADD
#1h
TBLR
*
;Load Y2 with the ordinate of the
;*******stack : y1/Y2/remainder
;nearest second indice
LAC
*–
;*******stack : Y1/y2/remainder
SUB
*+
SACL
*+
;difference between the two Y value
;*******stack : y1/Y2/remainder
;*******stack : y1/temp/REMAINDER
LT
*–
;*******stack : y1/TEMP/remainder
MPY
*
SPH
*–
;*******stack : y1/TEMP/remainder
;interpolation between Y1 and Y2
;*******stack : Y1/temp/remainder
A-4
LAC
*+
;*******stack : y1/TEMP/remainder
ADD
*,1
;Y(Xdata) in ACCU
LALK
Table_sin
;address of beginning of the table
ADD
*–
;address of the pointed indice
RET
equal_sin
;*******stack : RESULT/
TBLR
*
LAC
*+
end_interp_sin
RET
**********************************************************************************
* Table
**********************************************************************************
Table_sin
.include
sine.tab
Table_sin_end
.word
0
.end
**********************************************************************************
*Routine Name:
_COS
*
*Project:
DMC Mathematical Library
*
*Originator:
Pascal DORSTER (Texas Instruments)
*
*
*
*Description:
COS function with Direct Look–up and
*
*
Interpolation C calling function, variables in C stack.
*
*
Fully C compatible
*
*
*
*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
*
A-5
*
*
*Stack commentary:
*
*
Position of current register in Caps
*
*
Stack at beginning : angle/X
*
*
*
*Last Update:
16 Oct 96
*
*
*
*________________________________________________________________________________*
*Date of Mod
|
DESCRIPTION
*
*––––––––––––––|–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––*
*
|
*
*
|
*
**********************************************************************************
_COS
ADRK
2
POPD
*+
SAR
AR1,*
LAR
AR2,*,AR2
SBRK
3
SPM
0
LAC
#4000h
ADDS
*
SACL
*
LT
*+
LAC
#64h
SACL
*
MPYU
*
;C compatibility
;C compatibility
;add 0.5 for COS
;variable in size_sin
;*******stack : angle/X
;*******stack : angle/TEMP
PAC
SACH
;integer position in the table
;in High part of Acc
*+
;remainder
;*******stack : angle/indice/X
SACL
*
LAC
*,15
ANDK
#0ffffh,15
;
;*******stack : angle/indice/REMAINDER
A-6
SACH
*–
;*******stack : angle/INDICE/remainder
BCND
equal_sin,EQ
LALK
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
LAC
*–
SUB
*+
;*******stack : Y1/y2/remainder
;difference between the two Y value
;*******stack : y1/Y2/remainder
SACL
*+
;*******stack : y1/temp/REMAINDER
LT
*–
MPY
*
;*******stack : y1/TEMP/remainder
;*******stack : y1/TEMP/remainder
SPH
*–
;interpolation between Y1 and Y2
;*******stack : Y1/temp/remainder
LAC
*+
;*******stack : y1/TEMP/remainder
ADD
*,1,AR1
;Y(Xdata) in ACCU
MAR
*–
;C compatibility
PSHD
*–
SBRK
1
RET
equal_sin
LALK
Table_sin
;address of beginning of the table
ADD
*–
;address of the pointed indice
TBLR
*
LAC
*+,0,AR1
;*******stack : RESULT/
A-7
MAR
*–
PSHD
*–
SBRK
1
;C compatibility
RET
**********************************************************************************
* Table
**********************************************************************************
Table_sin
.include
sine.tab
Table_sin_end
.word
0
.end
**********************************************************************************
*Routine Name:
SIN
*
*Project:
DMC Mathematical Library
*
*Originator:
Pascal DORSTER (Texas Instruments)
*
*
*
*Description:
SIN 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 : SIN(angle)*32767, Q15, in ACCU
*
*
Pointed register AR1
*
*
*
*Stack commentary:
*
*
Position of current register in Caps
*
*
Stack at beginning : angle/X
*
*
*
*
*Last Update:
*
16 Oct 96
*
*________________________________________________________________________________*
A-8
*Date of Mod
|
DESCRIPTION
*
*––––––––––––––|–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––*
*
|
*
*
|
*
**********************************************************************************
SIN
MAR
*+
LT
*+
;variable in size_sin
;*******stack : angle/X
LAC
#64h
SACL
*
;*******stack : angle/TEMP
MPYU
*
PAC
;integer position in the table
;in High part of Acc
SACH
*+
;remainder
SACL
*
;
;*******stack : angle/indice/X
;*******stack : angle/indice/REMAINDER
LAC
*,15
ANDK
#0ffffh,15
SACH
*–
BCND
equal_sin,EQ
LALK
Table_sin
;address of beginning of the table
ADD
*–
;address of the nearest first indice
TBLR
*+
;*******stack : angle/INDICE/remainder
;*******stack : ANGLE/indice/remainder
;*******stack : y1/INDICE/remainder
ADD
#1h
TBLR
*
;Load Y2 with the ordinate of the
;*******stack : y1/Y2/remainder
;nearest second indice
LAC
*–
;*******stack : Y1/y2/remainder
SUB
*+
;difference between the two Y value
;*******stack : y1/Y2/remainder
SACL
*+
A-9
;*******stack : y1/temp/REMAINDER
LT
*–
;*******stack : y1/TEMP/remainder
MPY
*
SPH
*–
;*******stack : y1/TEMP/remainder
;interpolation between Y1 and Y2
;*******stack : Y1/temp/remainder
LAC
*+
;*******stack : y1/TEMP/remainder
ADD
*,1
;Y(Xdata) in ACCU
LALK
Table_sin
;address of beginning of the table
ADD
*–
;address of the pointed indice
RET
equal_sin
;*******stack : RESULT/
TBLR
*
LAC
*+
;*******stack : result/X
end_interp_sin
RET
*********************************************************************************
* Table
*********************************************************************************
Table_sin
.include
sine.tab
Table_sin_end
.word 0
**********************************************************************************
*Routine Name:
_SIN
*
*Project:
DMC Mathematical Library
*
*Originator:
Pascal DORSTER (Texas Instruments)
*
*
*
*Description:
*
SIN function with Direct Look–up + Interpolation
*
C calling function, variables in C stack.
*
*
Fully C compatible
*
A-10
*
*
*Status:
*
*
*
*Processor:
C2x
*
*
*
*Calling convention:
*
*
Input : Angle in stack value 0–360 degrees <=>0h–FFFFh
*
*
Output : SIN(angle)*32767, Q15, in ACCU
*
*
Pointed register AR1
*
*
*
*Stack commentary:
*
*
Position of current register in Caps
*
*
Stack at beginning : angle/X
*
*
*
*
*
*Last Update:
16 Oct 96
*
*
*
*________________________________________________________________________________*
*Date of Mod
|
DESCRIPTION
*
*––––––––––––––|–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––*
*
|
*
*
|
*
**********************************************************************************
_SIN
ADRK
2
POPD
*+
SAR
AR1,*
LAR
AR2,*,AR2
SBRK
3
SPM
0
LT
*+
;C compatibility
;C compatibility
;variable in size_sin
;*******stack : angle/X
LAC
#64h
SACL
*
;*******stack : angle/TEMP
MPYU
*
;integer position in the table
A-11
PAC
SACH
;in High part of Acc
*+
;remainder
;*******stack : angle/indice/X
SACL
*
;
;*******stack : angle/indice/REMAINDER
LAC
*,15
ANDK
#0ffffh,15
SACH
*–
;*******stack : angle/INDICE/remainder
BCND
equal_sin,EQ
LALK
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
LAC
*–
;*******stack : Y1/y2/remainder
SUB
*+
SACL
*+
;difference between the two Y value
;*******stack : y1/Y2/remainder
;*******stack : y1/temp/REMAINDER
LT
*–
MPY
*
;*******stack : y1/TEMP/remainder
;*******stack : y1/TEMP/remainder
SPH
*–
;interpolation between Y1 and Y2
;*******stack : Y1/temp/remainder
LAC
*+
ADD
*,1,AR1
;Y(Xdata) in ACCU
MAR
*–
;C compatibility
PSHD
*–
SBRK
1
;*******stack : y1/TEMP/remainder
RET
A-12
equal_sin
LALK
Table_sin
;address of beginning of the table
ADD
*–
;address of the pointed indice
TBLR
*
LAC
*+,0,AR1
MAR
*–
PSHD
*–
SBRK
1
;*******stack : RESULT/...
;*******stack : result/X
;C compatibility
RET
**********************************************************************************
* Table
**********************************************************************************
Table_sin
.include
sine.tab
Table_sin_end
.word
0
**********************************************************************************
* 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
A-13
.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-14
.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-15
.word
–12062
.word
–10126
.word
–8149
.word
–6140
.word
–4107
.word
–2057
**********************************************************************************
*Routine Name:
COS_SIN
*
*Project:
DMC Mathematical Library
*
*Originator:
Pascal DORSTER (Texas Instruments)
*
*
*
*Description:
COS+SIN 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:
*
*
SIN(angle)*32767, Q15, in stack pointed by AR1–1
*
*
COS(angle)*32767,Q15, in stack pointed by AR1
*
*
Pointed register AR1
*
*
*
*Stack commentary:
*
*
Position of current register in Caps
*
*
Stack at beginning : angle/X
*
*
*
*Last Update:
16 Oct 96
*
*________________________________________________________________________________*
*Date of Mod
|
DESCRIPTION
*
*––––––––––––––|–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––*
*
|
*
*
|
*
**********************************************************************************
size_tab .set
A-16
64h
;this is not an error
COS_SIN
MAR
*+
LT
*+
;variable in size_sin
;*stack: angle/X
LAC
#size_tab
SACL
*
;*stack: angle/TEMP
MPYU
*
PAC
SACH
;integer position in the table
;in High part of Acc
*+
;remainder
;*stack: angle/indice/X
SACL
*
LAC
*,15
ANDK
#0ffffh,15
SACH
*–
;
;*stack: angle/indice/REMAINDER
;*stack: angle/INDICE/remainder
BCND
equal_sin,EQ
LALK
Table_sin_cos ;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
;nearest second indice
;*stack: y1/y2/REMAINDER
ADRK
1
ADD
#18h
TBLR
*+
ADD
#1h
TBLR
*
;*stack: y1/y2/remainder/yy1/YY2
LAC
*–
;calculate cos interpolate
;*stack: y1/y2/remainder/X
;*stack: y1/y2/remainder/yy1/X
;*stack: y1/y2/remainder/YY1/yy2
A-17
SUB
*+
;difference between the two Y value
;*stack: y1/y2/remainder/yy1/YY2
SACL
*
LT
*–
;*stack: y1/y2/remainder/yy1/TEMP
;*stack: y1/y2/remainder/YY1
SBRK
1
MPY
*
;*stack: y1/y2/REMAINDER/yy1
;*stack: y1/y2/REMAINDER/yy1
ADRK 2
;*stack: y1/y2/remainder/yy1/TEMP
SPH
*–
;interpolation between Y1 and Y2
;*stack: Y1/y2/remainder/YY1/temp
LAC
*+
;*stack: y1/y2/remainder/yy1/TEMP
ADD
*–,1
SACL
*–
;Y(Xdata) in ACCU
;*stack: y1/y2/remainder/YY1
;*stack: y1/y2/REMAINDER/cos
;calculate sin interpolate
SBRK
1
;*stack: y1/Y2/remainder/cos
LAC
*–
;*stack: Y1/y2/remainder
SUB
*+
;difference between the two Y value
;*stack: y1/Y2/remainder/cos
SACL
*+
;*stack: y1/temp/REMAINDER/cos
LT
*–
MPY
*
;*stack: y1/TEMP/remainder/cos
;*stack: y1/TEMP/remainder/cos
SPH
*–
;interpolation between Y1 and Y2
;*stack: Y1/temp/remainder/cos
LAC
*+
ADD
*–,1
;*stack: y1/TEMP/remainder/cos
;Y(Xdata) in ACCU
;*stack: y1/temp/remainder/cos
A-18
SACL
*
ADRK
3
;*stack: SIN/temp/remainder/cos
;*stack: sin/temp/remainder/COS
LAC
*
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/remainder
ADD
*–
TBLR
*+
;address of the pointed indice
;*stack: ANGLE/indice
;*stack: sin/INDICE/remainder
ADDK
19h
TBLR
*
;*stack: sin/COS
end_interp_sin
RET
**********************************************************************************
* Table
**********************************************************************************
Table_sin_cos
.include sin_cos.tab
Table_sin_cos_end
.word
0
**********************************************************************************
* TABLE Sine + Cosine for functions COS_SIN
*
**********************************************************************************
.word
0
.word
2057
.word
4107
.word
6140
.word
8149
A-19
.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-20
.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-21
.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-22
.word
30466
.word
31163
.word
31738
.word
32187
.word
32509
.word
32702
**********************************************************************************
*Routine Name:
sin_ser
*
*Project:
DMC Mathematical Library
*
*Originator:
Pascal DORSTER (Texas Instruments)
*
*
*
*Description:
SIN function with Mathematical Series
*
*
Assembly calling function, variables in s/w stack.
*
*
*
*Status:
*
*
*
*Processor:
C2xx
*
*
*
*Calling convention:
*
*
Input : Angle in stack value 0–360 degrees <=>0h–FFFFh
*
*
Output : SIN(angle)*32767, Q15, in ACCU
*
*
Pointed register AR1
*
*
*
*Stack commentary:
*
*
Position of current register in Caps
*
*
Stack at beginning : angle/X
*
*
*
*
*
*Last Update:
18 Oct 96
*
*________________________________________________________________________________*
*Date of Mod
|
DESCRIPTION
*
*––––––––––––––|–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––*
*
|
*
*
|
*
**********************************************************************************
sin_ser
SETC
SXM
A-23
MAR
*–
LAC
*
BCND
angle_neg,LT
angle_pos
LT
*+
;variable in size_sin
MPYK
0c90h
;abscissa scale modify degree –> rad
SACH
*,4
;angle in rad
LT
*+
;*stack : angle/X
PAC
;*stack : angle/RAD
;*stack : angle/rad/X
MPYK
985h
;0.0372
;
;PREG : angle * 0.0372
LAC
#0C426h,13
APAC
; in high ACCU
;ACCU : –0.2338 + angle * 0.0372
SACH
* ,3
;temporary value
MPY
*
;multiply by temporary value
;angle in TREG
;temporary value
;*stack : angle/rad/TEMP
LAC
#6f69h,10
APAC
SACH
;0.0544
;ACCU: temp + 0.0544
*,2
;temp
;*stack : angle/RAD/temp
;angle in TREG
;*stack : angle/rad/TEMP
MPY
*
;temp
LAC
#7dc5h,13
;0.9826
APAC
SACH
;ACCU=0.9826+temp
*,3
;treg = rad
;temp
MPY
*
;rad * temp
LAC
#05532,4
;0.0013
;temp * angle
APAC
A-24
SACH
* ,3
LAC
*–
;result
;*stack : angle/SIN
RET
angle_neg
LT
*+
;variable in size_sin
;*stack : angle/X
MPYK
0c90h
;abscisse scale modif degre –> rad
*,4
;angle in rad
PAC
SACH
;*stack : angle/RAD
LT
*+
;*stack : angle/rad/X
MPYK
985h
;0.0372
;
;PREG : angle * 0.0372
LAC
#03bdah,13
; in high ACCU
* ,3
;temporary value
APAC
SACH
;ACCU : –0.2338 + angle * 0.0372
;angle in TREG
MPY
*
;multiply by temporary value
;temporary value
;*stack : angle/rad/TEMP
LAC
#6f69h,10
APAC
SACH
;0.0544
;ACCU: temp + 0.0544
*,2
;temp
;*stack : angle/RAD/temp
;angle in TREG
;*stack : angle/rad/TEMP
MPY
*
;temp
LAC
#7dc5h,13
;0.9826
SPAC
;ACCU=0.9826+temp
SACH
*,3
;treg = rad
MPY
*
;rad * temp
;temp * angle
LAC
#05532,4
;0.0013
A-25
APAC
SACH
*,3
LAC
*–
;result
;*stack : angle/SIN
RET
**********************************************************************************
*Routine Name:
_sin_ser
*
*Project:
DMC Mathematical Library
*
*Originator:
Pascal DORSTER (Texas Instruments)
*
*
*
*Description:
SIN function with Mathematical Series
*
*
C calling function, variables in C stack.
*
*
Fully C compatible
*
*
*
*Status:
*
*
*
*Processor:
C2xx
*
*
*
*Calling convention:
*
*
Input : Angle in stack value 0–360 degrees <=>0h–FFFFh
*
*
Output : SIN(angle)*32767, Q15, in ACCU
*
*
Pointed register AR1
*
*
*
*Stack commentary:
*
*
Position of current register in Caps
*
*
Stack at beginning : angle/X
*
*
*
*Last Update:
18 Oct 96
*
*
*
*________________________________________________________________________________*
*Date of Mod
|
DESCRIPTION
*
*––––––––––––––|–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––*
*
|
*
*
|
*
**********************************************************************************
_sin_ser
ADRK
A-26
2
;C compatibility
POPD
*+
SAR
AR1,*
LAR
AR2,*,AR2
SBRK
3
SPM
0
SETC
SXM
LAC
*
BCND
angle_neg,LT
;C compatibility
angle_pos
LT
*+
;variable in size_sin
;*stack : angle/X
MPYK
0c90h
;abscissa scale modify degree –> rad
;in
PAC
SACH
*,4
;angle in rad
;*stack : angle/RAD
LT
*+
MPYK
985h
;*stack : angle/rad/X
;0.0372
;
;PREG : angle * 0.0372
LAC
#0C426h,13
APAC
; in high ACCU
;ACCU : –0.2338 + angle * 0.0372
SACH
* ,3
;temporary value
MPY
*
;multiply by temporary value
;angle in TREG
;temporary value
;*stack : angle/rad/TEMP
LAC
#6f69h,10
APAC
SACH
;0.0544
;ACCU: temp + 0.0544
*,2
;temp
;*stack : angle/RAD/temp
;angle in TREG
;*stack : angle/rad/TEMP
MPY
*
;temp
LAC
#7dc5h,13
;0.9826
A-27
APAC
SACH
;ACCU=0.9826+temp
*,3
;treg = rad
;temp
MPY
*
;rad * temp
;temp * angle
LAC
#05532,4
;0.0013
SACH
* ,3
;result
LAC
*–,0,AR1
APAC
;*stack : angle/SIN
MAR
*–
PSHD
*–
SBRK
1
;C compatibility
RET
angle_neg
LT
*+
;variable in size_sin
;*stack : angle/X
MPYK
0c90h
;abscisse scale modif degre –> rad
SACH
*,4
;angle in rad
LT
*+
PAC
;*stack : angle/RAD
;*stack : angle/rad/X
MPYK
985h
;0.0372
;
;PREG : angle * 0.0372
LAC
#03bdah,13
; in high ACCU
* ,3
;temporary value
APAC
SACH
;ACCU : –0.2338 + angle * 0.0372
;angle in TREG
MPY
*
;multiply by temporary value
;temporary value
;*stack : angle/rad/TEMP
LAC
#6f69h,10
APAC
SACH
A-28
;0.0544
;ACCU: temp + 0.0544
*,2
;temp
;*stack : angle/RAD/temp
;angle in TREG
;*stack : angle/rad/TEMP
MPY
*
;temp
LAC
#7dc5h,13
;0.9826
SPAC
;ACCU=0.9826+temp
SACH
*,3
;treg = rad
MPY
*
;rad * temp
;temp * angle
LAC
#05532,4
;0.0013
SACH
*,3
;result
LAC
*–,0,AR1
APAC
;*stack : angle/SIN
MAR
*–
PSHD
*–
SBRK
1
;C compatibility
RET
**********************************************************************************
*Routine Name:
cos_ser
*
*Project:
DMC Mathematical Library
*
*Originator:
Pascal DORSTER (Texas Instruments)
*
*
*
*Description:
COS function with Mathematical Series
*
*
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
*
A-29
*
*
*Stack commentary:
*
*
Position of current register in Caps
*
*
Stack at beginning : angle/X
*
*
*
*
*
*Last Update:
18 Oct 96
*
*________________________________________________________________________________*
*Date of Mod
|
DESCRIPTION
*
*––––––––––––––|–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––*
*
|
*
*
|
*
**********************************************************************************
cos_ser
SETC
SXM
MAR
*–
LAC
*
BCND
angle_neg,LT
angle_pos
LT
*+
;variable in size_sin
MPYK
0c90h
;abscisse scale modif degre –> rad
SACH
*,4
;angle in rad
LT
*+
;*stack : angle/X
PAC
;*stack : angle/RAD
;*stack : angle/rad/X
MPYK
1070h
;0.0076 neg
;
;PREG : angle * 0.0076
LAC
#01e76h,15
APAC
; in high ACCU
;ACCU : +0.0595 + angle * 0.0076
SACH
* ,3
;temporary value
MPY
*
;multiply by temporary value
;angle in TREG
;temporary value
A-30
;*stack : angle/rad/TEMP
LAC
#0f532h,15
APAC
SACH
;0.0211
;ACCU: temp + 0.0211
*
;temp
;*stack : angle/RAD/temp
;angle in TREG
;*stack : angle/rad/TEMP
MPY
*
;temp
LAC
#0e0c6h,15
;0.4879
APAC
;ACCU=0.9826+temp
SACH
*,2
;treg = rad
MPY
*
;rad * temp
LAC
#0a440h,5
;0.0028
;temp * angle
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
LT
*+
;variable in size_sin
;*stack : angle/X
MPYK
0c90h
;abscisse scale modif degre –> rad
SACH
*,4
;angle in rad
LT
*+
PAC
;*stack : angle/RAD
;*stack : angle/rad/X
A-31
MPYK
0f90h
;0.0076 neg
;
;PREG : angle * 0.0076
LAC
#01e76h,15
APAC
; in high ACCU
;ACCU : +0.0595 + angle * 0.0076
SACH
* ,3
;temporary value
MPY
*
;multiply by temporary value
;angle in TREG
;temporary value
;*stack : angle/rad/TEMP
LAC
#00aceh,15
APAC
SACH
;0.0211
;ACCU: temp + 0.0211
*
;temp
;*stack : angle/RAD/temp
;angle in TREG
;*stack : angle/rad/TEMP
MPY
*
;temp
LAC
#0e0c6h,15
;0.4879
APAC
SACH
;ACCU=0.9826+temp
*,2
;treg = rad
;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-32
**********************************************************************************
*Routine Name:
_cos_ser
*
*Project:
DMC Mathematical Library
*
*Originator:
Pascal DORSTER (Texas Instruments)
*
*
*
*Description:
COS function with Mathematical Series
*
*
C calling function,
*
*
variables in C stack. Fully C compatible
*
*
*
*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
*
*
*
*Last Update:
18 Oct 96
*
*
*
*________________________________________________________________________________*
*Date of Mod
|
DESCRIPTION
*
*––––––––––––––|–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––*
*
|
*
*
|
*
**********************************************************************************
_cos_ser
ADRK
2
POPD
*+
SAR
AR1,*
LAR
AR2,*,AR2
SBRK
3
;C compatibility
;C compatibility
A-33
SPM
0
SETC
SXM
LAC
*
BCND
angle_neg,LT
angle_pos
LT
*+
;variable in size_sin
;*stack : angle/X
MPYK
0c90h
;abscisse scale modif degre –> rad
*,4
;angle in rad
PAC
SACH
;*stack : angle/RAD
LT
*+
;*stack : angle/rad/X
MPYK
1070h
;0.0076 neg
;
;PREG : angle * 0.0076
LAC
#01e76h,15
; in high ACCU
* ,3
;temporary value
APAC
SACH
;ACCU : +0.0595 + angle * 0.0076
;angle in TREG
MPY
*
;multiply by temporary value
;temporary value
;*stack : angle/rad/TEMP
LAC
#0f532h,15
APAC
SACH
;0.0211
;ACCU: temp + 0.0211
*
;temp
;*stack : angle/RAD/temp
;angle in TREG
;*stack : angle/rad/TEMP
MPY
*
;temp
LAC
#0e0c6h,15
;0.4879
APAC
SACH
;ACCU=0.9826+temp
*,2
;treg = rad
;temp
MPY
A-34
*
;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
*–,0,AR1
MAR
*–
PSHD
*–
SBRK
1
;*stack : angle/SIN
;C compatibility
RET
angle_neg
LT
*+
;variable in size_sin
MPYK
0c90h
;abscisse scale modif degre –> rad
SACH
*,4
;angle in rad
LT
*+
;*stack : angle/X
PAC
;*stack : angle/RAD
;*stack : angle/rad/X
MPYK
0f90h
;0.0076 neg
;
;PREG : angle * 0.0076
LAC
#01e76h,15
APAC
; in high ACCU
;ACCU : +0.0595 + angle * 0.0076
SACH
* ,3
;temporary value
MPY
*
;multiply by temporary value
;angle in TREG
;temporary value
A-35
;*stack : angle/rad/TEMP
LAC
#00aceh,15
APAC
SACH
;0.0211
;ACCU: temp + 0.0211
*
;temp
;*stack : angle/RAD/temp
;angle in TREG
;*stack : angle/rad/TEMP
MPY
*
;temp
LAC
#0e0c6h,15
;0.4879
APAC
;ACCU=0.9826+temp
SACH
*,2
;treg = rad
MPY
*
;rad * temp
;temp * angle in Q28
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
MAR
*–
PSHD
*–
SBRK
1
RET
A-36
;C compatibility
A-37
********************************************************************************
*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);
.
}
**********************************************************************************
*File Name:
Main_trig.asm
*
*Project:
DMC Mathematical Library
*
*Originator:
Pascal DORSTER (Texas Instruments)
*
A-1
*
*
*Description:
Very simple main which calls COS or SIN function
*
*
*
*Processor:
C2xx
*
*Status:
*
*Last Update:
19 Oct 96
*
*________________________________________________________________________________*
*Date of Mod
|
DESCRIPTION
*
*––––––––––––––|–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––*
*
|
*
**********************************************************************************
.mmregs
.def
_ser_sin
.sect
“vectors”
b
_c_int0
b
$
**********************************************************************************
* Main routine
**********************************************************************************
.text
_c_int0:
.
.
LAR
AR1,#60h
MAR
*,AR1
A-2
;stack preparation
LAC
#4000h
;π/2
SACL
*+
;parameters in stack
CALL
_ser_sin
.
;result in ACCU
.
.end
**********************************************************************************
*Routine Name:
COS
*
*Project:
DMC Mathematical Library
*
*Originator:
Pascal DORSTER (Texas Instruments)
*
*
*
*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
*
*
*
*Last Update:
16 Oct 96
*
*________________________________________________________________________________*
*Date of Mod
|
DESCRIPTION
*
*––––––––––––––|–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––*
*
*
**********************************************************************************
COS
MAR
*–
LAC
#4000h
ADDS
*
;add 0.5 for COS
A-3
SACL
*
LT
*+
;variable in size_sin
;*******stack : angle/X
LAC
#64h
SACL
*
;*******stack : angle/TEMP
MPYU
*
PAC
SACH
;integer position in the table
;in High part of Acc
*+
;remainder
;*******stack : angle/indice/X
SACL
*
;
;*******stack : angle/indice/REMAINDER
LAC
*,15
ANDK
#0ffffh,15
SACH
*–
;*******stack : angle/INDICE/remainder
BCND
equal_sin,EQ
LALK
Table_sin
;address of beginning of the table
ADD
*–
;address of the nearest first indice
TBLR
*+
;*******stack : ANGLE/indice/remainder
;*******stack : y1/INDICE/remainder
ADD
#1h
TBLR
*
;Load Y2 with the ordinate of the
;*******stack : y1/Y2/remainder
;nearest second indice
LAC
*–
;*******stack : Y1/y2/remainder
SUB
*+
SACL
*+
;difference between the two Y value
;*******stack : y1/Y2/remainder
;*******stack : y1/temp/REMAINDER
LT
*–
;*******stack : y1/TEMP/remainder
MPY
*
SPH
*–
;*******stack : y1/TEMP/remainder
;interpolation between Y1 and Y2
;*******stack : Y1/temp/remainder
A-4
LAC
*+
;*******stack : y1/TEMP/remainder
ADD
*,1
;Y(Xdata) in ACCU
LALK
Table_sin
;address of beginning of the table
ADD
*–
;address of the pointed indice
RET
equal_sin
;*******stack : RESULT/
TBLR
*
LAC
*+
end_interp_sin
RET
**********************************************************************************
* Table
**********************************************************************************
Table_sin
.include
sine.tab
Table_sin_end
.word
0
.end
**********************************************************************************
*Routine Name:
_COS
*
*Project:
DMC Mathematical Library
*
*Originator:
Pascal DORSTER (Texas Instruments)
*
*
*
*Description:
COS function with Direct Look–up and
*
*
Interpolation C calling function, variables in C stack.
*
*
Fully C compatible
*
*
*
*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
*
A-5
*
*
*Stack commentary:
*
*
Position of current register in Caps
*
*
Stack at beginning : angle/X
*
*
*
*Last Update:
16 Oct 96
*
*
*
*________________________________________________________________________________*
*Date of Mod
|
DESCRIPTION
*
*––––––––––––––|–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––*
*
|
*
*
|
*
**********************************************************************************
_COS
ADRK
2
POPD
*+
SAR
AR1,*
LAR
AR2,*,AR2
SBRK
3
SPM
0
LAC
#4000h
ADDS
*
SACL
*
LT
*+
LAC
#64h
SACL
*
MPYU
*
;C compatibility
;C compatibility
;add 0.5 for COS
;variable in size_sin
;*******stack : angle/X
;*******stack : angle/TEMP
PAC
SACH
;integer position in the table
;in High part of Acc
*+
;remainder
;*******stack : angle/indice/X
SACL
*
LAC
*,15
ANDK
#0ffffh,15
;
;*******stack : angle/indice/REMAINDER
A-6
SACH
*–
;*******stack : angle/INDICE/remainder
BCND
equal_sin,EQ
LALK
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
LAC
*–
SUB
*+
;*******stack : Y1/y2/remainder
;difference between the two Y value
;*******stack : y1/Y2/remainder
SACL
*+
;*******stack : y1/temp/REMAINDER
LT
*–
MPY
*
;*******stack : y1/TEMP/remainder
;*******stack : y1/TEMP/remainder
SPH
*–
;interpolation between Y1 and Y2
;*******stack : Y1/temp/remainder
LAC
*+
;*******stack : y1/TEMP/remainder
ADD
*,1,AR1
;Y(Xdata) in ACCU
MAR
*–
;C compatibility
PSHD
*–
SBRK
1
RET
equal_sin
LALK
Table_sin
;address of beginning of the table
ADD
*–
;address of the pointed indice
TBLR
*
LAC
*+,0,AR1
;*******stack : RESULT/
A-7
MAR
*–
PSHD
*–
SBRK
1
;C compatibility
RET
**********************************************************************************
* Table
**********************************************************************************
Table_sin
.include
sine.tab
Table_sin_end
.word
0
.end
**********************************************************************************
*Routine Name:
SIN
*
*Project:
DMC Mathematical Library
*
*Originator:
Pascal DORSTER (Texas Instruments)
*
*
*
*Description:
SIN 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 : SIN(angle)*32767, Q15, in ACCU
*
*
Pointed register AR1
*
*
*
*Stack commentary:
*
*
Position of current register in Caps
*
*
Stack at beginning : angle/X
*
*
*
*
*Last Update:
*
16 Oct 96
*
*________________________________________________________________________________*
A-8
*Date of Mod
|
DESCRIPTION
*
*––––––––––––––|–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––*
*
|
*
*
|
*
**********************************************************************************
SIN
MAR
*+
LT
*+
;variable in size_sin
;*******stack : angle/X
LAC
#64h
SACL
*
;*******stack : angle/TEMP
MPYU
*
PAC
;integer position in the table
;in High part of Acc
SACH
*+
;remainder
SACL
*
;
;*******stack : angle/indice/X
;*******stack : angle/indice/REMAINDER
LAC
*,15
ANDK
#0ffffh,15
SACH
*–
BCND
equal_sin,EQ
LALK
Table_sin
;address of beginning of the table
ADD
*–
;address of the nearest first indice
TBLR
*+
;*******stack : angle/INDICE/remainder
;*******stack : ANGLE/indice/remainder
;*******stack : y1/INDICE/remainder
ADD
#1h
TBLR
*
;Load Y2 with the ordinate of the
;*******stack : y1/Y2/remainder
;nearest second indice
LAC
*–
;*******stack : Y1/y2/remainder
SUB
*+
;difference between the two Y value
;*******stack : y1/Y2/remainder
SACL
*+
A-9
;*******stack : y1/temp/REMAINDER
LT
*–
;*******stack : y1/TEMP/remainder
MPY
*
SPH
*–
;*******stack : y1/TEMP/remainder
;interpolation between Y1 and Y2
;*******stack : Y1/temp/remainder
LAC
*+
;*******stack : y1/TEMP/remainder
ADD
*,1
;Y(Xdata) in ACCU
LALK
Table_sin
;address of beginning of the table
ADD
*–
;address of the pointed indice
RET
equal_sin
;*******stack : RESULT/
TBLR
*
LAC
*+
;*******stack : result/X
end_interp_sin
RET
*********************************************************************************
* Table
*********************************************************************************
Table_sin
.include
sine.tab
Table_sin_end
.word 0
**********************************************************************************
*Routine Name:
_SIN
*
*Project:
DMC Mathematical Library
*
*Originator:
Pascal DORSTER (Texas Instruments)
*
*
*
*Description:
*
SIN function with Direct Look–up + Interpolation
*
C calling function, variables in C stack.
*
*
Fully C compatible
*
A-10
*
*
*Status:
*
*
*
*Processor:
C2x
*
*
*
*Calling convention:
*
*
Input : Angle in stack value 0–360 degrees <=>0h–FFFFh
*
*
Output : SIN(angle)*32767, Q15, in ACCU
*
*
Pointed register AR1
*
*
*
*Stack commentary:
*
*
Position of current register in Caps
*
*
Stack at beginning : angle/X
*
*
*
*
*
*Last Update:
16 Oct 96
*
*
*
*________________________________________________________________________________*
*Date of Mod
|
DESCRIPTION
*
*––––––––––––––|–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––*
*
|
*
*
|
*
**********************************************************************************
_SIN
ADRK
2
POPD
*+
SAR
AR1,*
LAR
AR2,*,AR2
SBRK
3
SPM
0
LT
*+
;C compatibility
;C compatibility
;variable in size_sin
;*******stack : angle/X
LAC
#64h
SACL
*
;*******stack : angle/TEMP
MPYU
*
;integer position in the table
A-11
PAC
SACH
;in High part of Acc
*+
;remainder
;*******stack : angle/indice/X
SACL
*
;
;*******stack : angle/indice/REMAINDER
LAC
*,15
ANDK
#0ffffh,15
SACH
*–
;*******stack : angle/INDICE/remainder
BCND
equal_sin,EQ
LALK
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
LAC
*–
;*******stack : Y1/y2/remainder
SUB
*+
SACL
*+
;difference between the two Y value
;*******stack : y1/Y2/remainder
;*******stack : y1/temp/REMAINDER
LT
*–
MPY
*
;*******stack : y1/TEMP/remainder
;*******stack : y1/TEMP/remainder
SPH
*–
;interpolation between Y1 and Y2
;*******stack : Y1/temp/remainder
LAC
*+
ADD
*,1,AR1
;Y(Xdata) in ACCU
MAR
*–
;C compatibility
PSHD
*–
SBRK
1
;*******stack : y1/TEMP/remainder
RET
A-12
equal_sin
LALK
Table_sin
;address of beginning of the table
ADD
*–
;address of the pointed indice
TBLR
*
LAC
*+,0,AR1
MAR
*–
PSHD
*–
SBRK
1
;*******stack : RESULT/...
;*******stack : result/X
;C compatibility
RET
**********************************************************************************
* Table
**********************************************************************************
Table_sin
.include
sine.tab
Table_sin_end
.word
0
**********************************************************************************
* 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
A-13
.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-14
.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-15
.word
–12062
.word
–10126
.word
–8149
.word
–6140
.word
–4107
.word
–2057
**********************************************************************************
*Routine Name:
COS_SIN
*
*Project:
DMC Mathematical Library
*
*Originator:
Pascal DORSTER (Texas Instruments)
*
*
*
*Description:
COS+SIN 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:
*
*
SIN(angle)*32767, Q15, in stack pointed by AR1–1
*
*
COS(angle)*32767,Q15, in stack pointed by AR1
*
*
Pointed register AR1
*
*
*
*Stack commentary:
*
*
Position of current register in Caps
*
*
Stack at beginning : angle/X
*
*
*
*Last Update:
16 Oct 96
*
*________________________________________________________________________________*
*Date of Mod
|
DESCRIPTION
*
*––––––––––––––|–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––*
*
|
*
*
|
*
**********************************************************************************
size_tab .set
A-16
64h
;this is not an error
COS_SIN
MAR
*+
LT
*+
;variable in size_sin
;*stack: angle/X
LAC
#size_tab
SACL
*
;*stack: angle/TEMP
MPYU
*
PAC
SACH
;integer position in the table
;in High part of Acc
*+
;remainder
;*stack: angle/indice/X
SACL
*
LAC
*,15
ANDK
#0ffffh,15
SACH
*–
;
;*stack: angle/indice/REMAINDER
;*stack: angle/INDICE/remainder
BCND
equal_sin,EQ
LALK
Table_sin_cos ;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
;nearest second indice
;*stack: y1/y2/REMAINDER
ADRK
1
ADD
#18h
TBLR
*+
ADD
#1h
TBLR
*
;*stack: y1/y2/remainder/yy1/YY2
LAC
*–
;calculate cos interpolate
;*stack: y1/y2/remainder/X
;*stack: y1/y2/remainder/yy1/X
;*stack: y1/y2/remainder/YY1/yy2
A-17
SUB
*+
;difference between the two Y value
;*stack: y1/y2/remainder/yy1/YY2
SACL
*
LT
*–
;*stack: y1/y2/remainder/yy1/TEMP
;*stack: y1/y2/remainder/YY1
SBRK
1
MPY
*
;*stack: y1/y2/REMAINDER/yy1
;*stack: y1/y2/REMAINDER/yy1
ADRK 2
;*stack: y1/y2/remainder/yy1/TEMP
SPH
*–
;interpolation between Y1 and Y2
;*stack: Y1/y2/remainder/YY1/temp
LAC
*+
;*stack: y1/y2/remainder/yy1/TEMP
ADD
*–,1
SACL
*–
;Y(Xdata) in ACCU
;*stack: y1/y2/remainder/YY1
;*stack: y1/y2/REMAINDER/cos
;calculate sin interpolate
SBRK
1
;*stack: y1/Y2/remainder/cos
LAC
*–
;*stack: Y1/y2/remainder
SUB
*+
;difference between the two Y value
;*stack: y1/Y2/remainder/cos
SACL
*+
;*stack: y1/temp/REMAINDER/cos
LT
*–
MPY
*
;*stack: y1/TEMP/remainder/cos
;*stack: y1/TEMP/remainder/cos
SPH
*–
;interpolation between Y1 and Y2
;*stack: Y1/temp/remainder/cos
LAC
*+
ADD
*–,1
;*stack: y1/TEMP/remainder/cos
;Y(Xdata) in ACCU
;*stack: y1/temp/remainder/cos
A-18
SACL
*
ADRK
3
;*stack: SIN/temp/remainder/cos
;*stack: sin/temp/remainder/COS
LAC
*
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/remainder
ADD
*–
TBLR
*+
;address of the pointed indice
;*stack: ANGLE/indice
;*stack: sin/INDICE/remainder
ADDK
19h
TBLR
*
;*stack: sin/COS
end_interp_sin
RET
**********************************************************************************
* Table
**********************************************************************************
Table_sin_cos
.include sin_cos.tab
Table_sin_cos_end
.word
0
**********************************************************************************
* TABLE Sine + Cosine for functions COS_SIN
*
**********************************************************************************
.word
0
.word
2057
.word
4107
.word
6140
.word
8149
A-19
.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-20
.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-21
.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-22
.word
30466
.word
31163
.word
31738
.word
32187
.word
32509
.word
32702
**********************************************************************************
*Routine Name:
sin_ser
*
*Project:
DMC Mathematical Library
*
*Originator:
Pascal DORSTER (Texas Instruments)
*
*
*
*Description:
SIN function with Mathematical Series
*
*
Assembly calling function, variables in s/w stack.
*
*
*
*Status:
*
*
*
*Processor:
C2xx
*
*
*
*Calling convention:
*
*
Input : Angle in stack value 0–360 degrees <=>0h–FFFFh
*
*
Output : SIN(angle)*32767, Q15, in ACCU
*
*
Pointed register AR1
*
*
*
*Stack commentary:
*
*
Position of current register in Caps
*
*
Stack at beginning : angle/X
*
*
*
*
*
*Last Update:
18 Oct 96
*
*________________________________________________________________________________*
*Date of Mod
|
DESCRIPTION
*
*––––––––––––––|–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––*
*
|
*
*
|
*
**********************************************************************************
sin_ser
SETC
SXM
A-23
MAR
*–
LAC
*
BCND
angle_neg,LT
angle_pos
LT
*+
;variable in size_sin
MPYK
0c90h
;abscissa scale modify degree –> rad
SACH
*,4
;angle in rad
LT
*+
;*stack : angle/X
PAC
;*stack : angle/RAD
;*stack : angle/rad/X
MPYK
985h
;0.0372
;
;PREG : angle * 0.0372
LAC
#0C426h,13
APAC
; in high ACCU
;ACCU : –0.2338 + angle * 0.0372
SACH
* ,3
;temporary value
MPY
*
;multiply by temporary value
;angle in TREG
;temporary value
;*stack : angle/rad/TEMP
LAC
#6f69h,10
APAC
SACH
;0.0544
;ACCU: temp + 0.0544
*,2
;temp
;*stack : angle/RAD/temp
;angle in TREG
;*stack : angle/rad/TEMP
MPY
*
;temp
LAC
#7dc5h,13
;0.9826
APAC
SACH
;ACCU=0.9826+temp
*,3
;treg = rad
;temp
MPY
*
;rad * temp
LAC
#05532,4
;0.0013
;temp * angle
APAC
A-24
SACH
* ,3
LAC
*–
;result
;*stack : angle/SIN
RET
angle_neg
LT
*+
;variable in size_sin
;*stack : angle/X
MPYK
0c90h
;abscisse scale modif degre –> rad
*,4
;angle in rad
PAC
SACH
;*stack : angle/RAD
LT
*+
;*stack : angle/rad/X
MPYK
985h
;0.0372
;
;PREG : angle * 0.0372
LAC
#03bdah,13
; in high ACCU
* ,3
;temporary value
APAC
SACH
;ACCU : –0.2338 + angle * 0.0372
;angle in TREG
MPY
*
;multiply by temporary value
;temporary value
;*stack : angle/rad/TEMP
LAC
#6f69h,10
APAC
SACH
;0.0544
;ACCU: temp + 0.0544
*,2
;temp
;*stack : angle/RAD/temp
;angle in TREG
;*stack : angle/rad/TEMP
MPY
*
;temp
LAC
#7dc5h,13
;0.9826
SPAC
;ACCU=0.9826+temp
SACH
*,3
;treg = rad
MPY
*
;rad * temp
;temp * angle
LAC
#05532,4
;0.0013
A-25
APAC
SACH
*,3
LAC
*–
;result
;*stack : angle/SIN
RET
**********************************************************************************
*Routine Name:
_sin_ser
*
*Project:
DMC Mathematical Library
*
*Originator:
Pascal DORSTER (Texas Instruments)
*
*
*
*Description:
SIN function with Mathematical Series
*
*
C calling function, variables in C stack.
*
*
Fully C compatible
*
*
*
*Status:
*
*
*
*Processor:
C2xx
*
*
*
*Calling convention:
*
*
Input : Angle in stack value 0–360 degrees <=>0h–FFFFh
*
*
Output : SIN(angle)*32767, Q15, in ACCU
*
*
Pointed register AR1
*
*
*
*Stack commentary:
*
*
Position of current register in Caps
*
*
Stack at beginning : angle/X
*
*
*
*Last Update:
18 Oct 96
*
*
*
*________________________________________________________________________________*
*Date of Mod
|
DESCRIPTION
*
*––––––––––––––|–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––*
*
|
*
*
|
*
**********************************************************************************
_sin_ser
ADRK
A-26
2
;C compatibility
POPD
*+
SAR
AR1,*
LAR
AR2,*,AR2
SBRK
3
SPM
0
SETC
SXM
LAC
*
BCND
angle_neg,LT
;C compatibility
angle_pos
LT
*+
;variable in size_sin
;*stack : angle/X
MPYK
0c90h
;abscissa scale modify degree –> rad
;in
PAC
SACH
*,4
;angle in rad
;*stack : angle/RAD
LT
*+
MPYK
985h
;*stack : angle/rad/X
;0.0372
;
;PREG : angle * 0.0372
LAC
#0C426h,13
APAC
; in high ACCU
;ACCU : –0.2338 + angle * 0.0372
SACH
* ,3
;temporary value
MPY
*
;multiply by temporary value
;angle in TREG
;temporary value
;*stack : angle/rad/TEMP
LAC
#6f69h,10
APAC
SACH
;0.0544
;ACCU: temp + 0.0544
*,2
;temp
;*stack : angle/RAD/temp
;angle in TREG
;*stack : angle/rad/TEMP
MPY
*
;temp
LAC
#7dc5h,13
;0.9826
A-27
APAC
SACH
;ACCU=0.9826+temp
*,3
;treg = rad
;temp
MPY
*
;rad * temp
;temp * angle
LAC
#05532,4
;0.0013
SACH
* ,3
;result
LAC
*–,0,AR1
APAC
;*stack : angle/SIN
MAR
*–
PSHD
*–
SBRK
1
;C compatibility
RET
angle_neg
LT
*+
;variable in size_sin
;*stack : angle/X
MPYK
0c90h
;abscisse scale modif degre –> rad
SACH
*,4
;angle in rad
LT
*+
PAC
;*stack : angle/RAD
;*stack : angle/rad/X
MPYK
985h
;0.0372
;
;PREG : angle * 0.0372
LAC
#03bdah,13
; in high ACCU
* ,3
;temporary value
APAC
SACH
;ACCU : –0.2338 + angle * 0.0372
;angle in TREG
MPY
*
;multiply by temporary value
;temporary value
;*stack : angle/rad/TEMP
LAC
#6f69h,10
APAC
SACH
A-28
;0.0544
;ACCU: temp + 0.0544
*,2
;temp
;*stack : angle/RAD/temp
;angle in TREG
;*stack : angle/rad/TEMP
MPY
*
;temp
LAC
#7dc5h,13
;0.9826
SPAC
;ACCU=0.9826+temp
SACH
*,3
;treg = rad
MPY
*
;rad * temp
;temp * angle
LAC
#05532,4
;0.0013
SACH
*,3
;result
LAC
*–,0,AR1
APAC
;*stack : angle/SIN
MAR
*–
PSHD
*–
SBRK
1
;C compatibility
RET
**********************************************************************************
*Routine Name:
cos_ser
*
*Project:
DMC Mathematical Library
*
*Originator:
Pascal DORSTER (Texas Instruments)
*
*
*
*Description:
COS function with Mathematical Series
*
*
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
*
A-29
*
*
*Stack commentary:
*
*
Position of current register in Caps
*
*
Stack at beginning : angle/X
*
*
*
*
*
*Last Update:
18 Oct 96
*
*________________________________________________________________________________*
*Date of Mod
|
DESCRIPTION
*
*––––––––––––––|–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––*
*
|
*
*
|
*
**********************************************************************************
cos_ser
SETC
SXM
MAR
*–
LAC
*
BCND
angle_neg,LT
angle_pos
LT
*+
;variable in size_sin
MPYK
0c90h
;abscisse scale modif degre –> rad
SACH
*,4
;angle in rad
LT
*+
;*stack : angle/X
PAC
;*stack : angle/RAD
;*stack : angle/rad/X
MPYK
1070h
;0.0076 neg
;
;PREG : angle * 0.0076
LAC
#01e76h,15
APAC
; in high ACCU
;ACCU : +0.0595 + angle * 0.0076
SACH
* ,3
;temporary value
MPY
*
;multiply by temporary value
;angle in TREG
;temporary value
A-30
;*stack : angle/rad/TEMP
LAC
#0f532h,15
APAC
SACH
;0.0211
;ACCU: temp + 0.0211
*
;temp
;*stack : angle/RAD/temp
;angle in TREG
;*stack : angle/rad/TEMP
MPY
*
;temp
LAC
#0e0c6h,15
;0.4879
APAC
;ACCU=0.9826+temp
SACH
*,2
;treg = rad
MPY
*
;rad * temp
LAC
#0a440h,5
;0.0028
;temp * angle
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
LT
*+
;variable in size_sin
;*stack : angle/X
MPYK
0c90h
;abscisse scale modif degre –> rad
SACH
*,4
;angle in rad
LT
*+
PAC
;*stack : angle/RAD
;*stack : angle/rad/X
A-31
MPYK
0f90h
;0.0076 neg
;
;PREG : angle * 0.0076
LAC
#01e76h,15
APAC
; in high ACCU
;ACCU : +0.0595 + angle * 0.0076
SACH
* ,3
;temporary value
MPY
*
;multiply by temporary value
;angle in TREG
;temporary value
;*stack : angle/rad/TEMP
LAC
#00aceh,15
APAC
SACH
;0.0211
;ACCU: temp + 0.0211
*
;temp
;*stack : angle/RAD/temp
;angle in TREG
;*stack : angle/rad/TEMP
MPY
*
;temp
LAC
#0e0c6h,15
;0.4879
APAC
SACH
;ACCU=0.9826+temp
*,2
;treg = rad
;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-32
**********************************************************************************
*Routine Name:
_cos_ser
*
*Project:
DMC Mathematical Library
*
*Originator:
Pascal DORSTER (Texas Instruments)
*
*
*
*Description:
COS function with Mathematical Series
*
*
C calling function,
*
*
variables in C stack. Fully C compatible
*
*
*
*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
*
*
*
*Last Update:
18 Oct 96
*
*
*
*________________________________________________________________________________*
*Date of Mod
|
DESCRIPTION
*
*––––––––––––––|–––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––*
*
|
*
*
|
*
**********************************************************************************
_cos_ser
ADRK
2
POPD
*+
SAR
AR1,*
LAR
AR2,*,AR2
SBRK
3
;C compatibility
;C compatibility
A-33
SPM
0
SETC
SXM
LAC
*
BCND
angle_neg,LT
angle_pos
LT
*+
;variable in size_sin
;*stack : angle/X
MPYK
0c90h
;abscisse scale modif degre –> rad
*,4
;angle in rad
PAC
SACH
;*stack : angle/RAD
LT
*+
;*stack : angle/rad/X
MPYK
1070h
;0.0076 neg
;
;PREG : angle * 0.0076
LAC
#01e76h,15
; in high ACCU
* ,3
;temporary value
APAC
SACH
;ACCU : +0.0595 + angle * 0.0076
;angle in TREG
MPY
*
;multiply by temporary value
;temporary value
;*stack : angle/rad/TEMP
LAC
#0f532h,15
APAC
SACH
;0.0211
;ACCU: temp + 0.0211
*
;temp
;*stack : angle/RAD/temp
;angle in TREG
;*stack : angle/rad/TEMP
MPY
*
;temp
LAC
#0e0c6h,15
;0.4879
APAC
SACH
;ACCU=0.9826+temp
*,2
;treg = rad
;temp
MPY
A-34
*
;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
*–,0,AR1
MAR
*–
PSHD
*–
SBRK
1
;*stack : angle/SIN
;C compatibility
RET
angle_neg
LT
*+
;variable in size_sin
MPYK
0c90h
;abscisse scale modif degre –> rad
SACH
*,4
;angle in rad
LT
*+
;*stack : angle/X
PAC
;*stack : angle/RAD
;*stack : angle/rad/X
MPYK
0f90h
;0.0076 neg
;
;PREG : angle * 0.0076
LAC
#01e76h,15
APAC
; in high ACCU
;ACCU : +0.0595 + angle * 0.0076
SACH
* ,3
;temporary value
MPY
*
;multiply by temporary value
;angle in TREG
;temporary value
A-35
;*stack : angle/rad/TEMP
LAC
#00aceh,15
APAC
SACH
;0.0211
;ACCU: temp + 0.0211
*
;temp
;*stack : angle/RAD/temp
;angle in TREG
;*stack : angle/rad/TEMP
MPY
*
;temp
LAC
#0e0c6h,15
;0.4879
APAC
;ACCU=0.9826+temp
SACH
*,2
;treg = rad
MPY
*
;rad * temp
;temp * angle in Q28
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
MAR
*–
PSHD
*–
SBRK
1
RET
A-36
;C compatibility
A-37