/*------------------------------------------------------------------------
* filename - coord.cas Version 1.0 /DEE 2-92
*
* function(s)
* rpc - Converts Rectangular to Polar Coordinates
* prc - Converts Polar to Rectangular Coordinates
* matan2 - Modified Arctangent routine
* David Edwards, 2-25-2006
*-----------------------------------------------------------------------*/
#pragma inline
#include <asmrules.h>
#include <math.h>
#include <_math.h>
/*--------------------------------------------------------------------------*
Name matan2 - trigonometric function
Usage void matan2(double y, double x); ST(0) = y, ST(1) = x
Prototype in None
Description
matan2 returns ST(0), the arc tangent of y/x and will
produce correct results even when resulting is near pi/2
or -pi/2 (x near 0).
Return value atan2 returns a value in the range -pi to pi on ST(0).
If a ratio of 0/0 is supplied then zero is returned
*---------------------------------------------------------------------------*/
static unsigned short piBy2 [] = {0xC235, 0x2168, 0xDAA2, 0xC90F, 0x3FFF};
#pragma warn -rvl
#pragma warn -use
void matan2 (double y, double x)
{
register SI, DI; /* prevent the compiler making its own usage */
asm mov ax, x [6] /* select MSW of x .. */
asm and al, 0F0h /* ignore fraction */
asm mov bx, y [6] /* .. and of y */
asm and bl, 0F0h
asm shl bx, 1 /* discard sign */
asm jz at2_yIsZero
asm shl ax, 1 /* discard sign */
asm jz at2_xIsZero
asm FDIVRP ST(1), ST(0)
asm _FAST_ (_FATAN_)
/* convert the simple answer to a four quadrant answer. */
at2_setQuad:
asm test BY0 (x [7]), 80h /* the sign bit */
asm jz at2_end
asm FLDPI
asm test BY0 (y [7]), 80h
asm jz at2_2ndQuad
at2_3rdQuad:
asm FSUBP ST(1), ST
asm jmp short at2_end
at2_2ndQuad:
asm FADDP ST(1), ST
at2_end:
return;
/* Special cases.
*/
at2_yIsZero:
asm shl ax, 1
asm jc at2_retPi /* x<0, return PI */
asm FSTP ST(1) /* else y is result */
asm jmp short at2_end
at2_retPi: /* y = 0, x < 0 */
asm FCOMPP /* discard x and y */
asm FLDPI /* and return PI */
asm jmp short at2_end
at2_xIsZero: /* and y is not zero */
/* or */
at2_yIsInf: /* and x is finite */
asm FCOMPP /* discard x and y */
asm FLD tbyte ptr (piBy2)
asm test BY0 (y [7]), 80h /* check sign of Y */
asm jz at2_HPi /* positive - return PI/2 */
asm FCHS /* negative - return -PI/2 */
at2_HPi:
asm jmp short at2_setQuad
at2_xIsInf:
asm FCOMPP /* discard x and y */
asm FLDZ
asm jmp short at2_setQuad
}
#pragma warn .rvl
#pragma warn .use
/*--------------------------------------------------------------------------*
Name rpc - Convert from Rectangular to Polar Coordinates
Usage void rpc(double x, double y, double *r, double *theta);
Prototype in math.h
Description The magnitude is the same result as "hypot" except the input
is not checked for the INF value.
r = (x^2 + y^2)^.5
The angle is in the range of -180 < theta <= 180.
Return value The function fills the variables pointed by "r" and "theta".
"theta" is in radians.
The function provides no error or overflow checking.
*---------------------------------------------------------------------------*/
void rpc (double x, double y, double *r, double *theta)
{
#if LDATA
asm push ES
#endif
asm FLD DOUBLE (x) /* x */
asm FLD st(0) /* st(1) = x */
asm FMUL st,st(0) /* x^2 */
asm FLD DOUBLE (y) /* y */
asm FLD st(0) /* 0=y,1=y,2=x^2,3=x */
asm FMUL st,st(0) /* y^2 */
asm FADDP st(2),st /* x^2 + y^2 */
asm FXCH /* Switch ST and ST(1) */
asm FSQRT /* sqrt ( ) */
asm LES_ bx,r
asm FSTP DOUBLE (ES_ [bx]) /* *r = (x^2 + y^2)^.5 */
matan2(y,x);
asm LES_ bx,theta
asm FSTP DOUBLE (ES_ [bx]) /* *theta = matan2(y/x) */
asm FWAIT /* Will bomb out w/o this */
#if LDATA
asm pop ES
#endif
}
/*--------------------------------------------------------------------------*
Name prc - Convert from Polar to Rectangular Coordinates
Usage void rpc(double r, double theta, double *x, double *y);
Prototype in math.h
Description Given the magnitude r, and the angle from the positive x-axis,
convert to x and y coordinates.
x=r*cos(theta)
y=r*sin(theta)
The angle is in the range of -180 < theta <= 180.
Return value The function fills the variables pointed by "r" and "theta".
The function provides no error or overflow checking.
*---------------------------------------------------------------------------*/
void prc (double r, double theta, double *x, double *y)
{
#if LDATA
asm push ES
#endif
asm FLD DOUBLE (r)
asm FLD DOUBLE (theta)
asm FLD st(0)
asm _FAST_ (_FCOS_) /* cos(theta) */
asm FMUL st,st(2) /* cos(theta)*r */
asm LES_ bx,x
asm FSTP DOUBLE (ES_ [bx]) /* x */
asm _FAST_ (_FSIN_)
asm FMULP /* y = r*sin(theta) */
asm LES_ bx,y
asm FSTP DOUBLE (ES_ [bx]) /* y */
asm FWAIT
/* Needs quadrant check for y=sqrt(r^2-x^2) */
asm FLD DOUBLE (r)
asm FLD st(0) /* r for later */
asm FMUL st,st(0) /* r^2 */
asm FLD DOUBLE (theta)
asm _FAST_ (_FCOS_) /* cos(theta) */
asm FMULP st(2),st /* x=r*cos(theta) */
asm FXCH
asm FMUL st,st(0) /* x^2 */
asm FSUBP /* r^2 - x^2 */
asm FSQRT /* y */
asm LES_ bx,y
asm FSTP DOUBLE (ES_ [bx]) /* y */
asm FWAIT /* Must have */
#if LDATA
asm pop ES
#endif
}