132 lines
3.9 KiB
C
132 lines
3.9 KiB
C
|
|
/* @(#)e_atan2.c 5.1 93/09/24 */
|
|
/*
|
|
* ====================================================
|
|
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
|
*
|
|
* Developed at SunPro, a Sun Microsystems, Inc. business.
|
|
* Permission to use, copy, modify, and distribute this
|
|
* software is freely granted, provided that this notice
|
|
* is preserved.
|
|
* ====================================================
|
|
*
|
|
*/
|
|
|
|
/* __ieee754_atan2(y,x)
|
|
* Method :
|
|
* 1. Reduce y to positive by atan2(y,x)=-atan2(-y,x).
|
|
* 2. Reduce x to positive by (if x and y are unexceptional):
|
|
* ARG (x+iy) = arctan(y/x) ... if x > 0,
|
|
* ARG (x+iy) = pi - arctan[y/(-x)] ... if x < 0,
|
|
*
|
|
* Special cases:
|
|
*
|
|
* ATAN2((anything), NaN ) is NaN;
|
|
* ATAN2(NAN , (anything) ) is NaN;
|
|
* ATAN2(+-0, +(anything but NaN)) is +-0 ;
|
|
* ATAN2(+-0, -(anything but NaN)) is +-pi ;
|
|
* ATAN2(+-(anything but 0 and NaN), 0) is +-pi/2;
|
|
* ATAN2(+-(anything but INF and NaN), +INF) is +-0 ;
|
|
* ATAN2(+-(anything but INF and NaN), -INF) is +-pi;
|
|
* ATAN2(+-INF,+INF ) is +-pi/4 ;
|
|
* ATAN2(+-INF,-INF ) is +-3pi/4;
|
|
* ATAN2(+-INF, (anything but,0,NaN, and INF)) is +-pi/2;
|
|
*
|
|
* Constants:
|
|
* The hexadecimal values are the intended ones for the following
|
|
* constants. The decimal values may be used, provided that the
|
|
* compiler will convert from decimal to binary accurately enough
|
|
* to produce the hexadecimal values shown.
|
|
*/
|
|
|
|
#include "fdlibm.h"
|
|
|
|
#ifndef _DOUBLE_IS_32BITS
|
|
|
|
#ifdef __STDC__
|
|
static const double
|
|
#else
|
|
static double
|
|
#endif
|
|
tiny = 1.0e-300,
|
|
zero = 0.0,
|
|
pi_o_4 = 7.8539816339744827900E-01, /* 0x3FE921FB, 0x54442D18 */
|
|
pi_o_2 = 1.5707963267948965580E+00, /* 0x3FF921FB, 0x54442D18 */
|
|
pi = 3.1415926535897931160E+00, /* 0x400921FB, 0x54442D18 */
|
|
pi_lo = 1.2246467991473531772E-16; /* 0x3CA1A626, 0x33145C07 */
|
|
|
|
#ifdef __STDC__
|
|
double __ieee754_atan2(double y, double x)
|
|
#else
|
|
double __ieee754_atan2(y,x)
|
|
double y,x;
|
|
#endif
|
|
{
|
|
double z;
|
|
__int32_t k,m,hx,hy,ix,iy;
|
|
__uint32_t lx,ly;
|
|
|
|
EXTRACT_WORDS(hx,lx,x);
|
|
ix = hx&0x7fffffff;
|
|
EXTRACT_WORDS(hy,ly,y);
|
|
iy = hy&0x7fffffff;
|
|
if(((ix|((lx|-lx)>>31))>0x7ff00000)||
|
|
((iy|((ly|-ly)>>31))>0x7ff00000)) /* x or y is NaN */
|
|
return x+y;
|
|
if((hx-0x3ff00000|lx)==0) return atan(y); /* x=1.0 */
|
|
m = ((hy>>31)&1)|((hx>>30)&2); /* 2*sign(x)+sign(y) */
|
|
|
|
/* when y = 0 */
|
|
if((iy|ly)==0) {
|
|
switch(m) {
|
|
case 0:
|
|
case 1: return y; /* atan(+-0,+anything)=+-0 */
|
|
case 2: return pi+tiny;/* atan(+0,-anything) = pi */
|
|
case 3: return -pi-tiny;/* atan(-0,-anything) =-pi */
|
|
}
|
|
}
|
|
/* when x = 0 */
|
|
if((ix|lx)==0) return (hy<0)? -pi_o_2-tiny: pi_o_2+tiny;
|
|
|
|
/* when x is INF */
|
|
if(ix==0x7ff00000) {
|
|
if(iy==0x7ff00000) {
|
|
switch(m) {
|
|
case 0: return pi_o_4+tiny;/* atan(+INF,+INF) */
|
|
case 1: return -pi_o_4-tiny;/* atan(-INF,+INF) */
|
|
case 2: return 3.0*pi_o_4+tiny;/*atan(+INF,-INF)*/
|
|
case 3: return -3.0*pi_o_4-tiny;/*atan(-INF,-INF)*/
|
|
}
|
|
} else {
|
|
switch(m) {
|
|
case 0: return zero ; /* atan(+...,+INF) */
|
|
case 1: return -zero ; /* atan(-...,+INF) */
|
|
case 2: return pi+tiny ; /* atan(+...,-INF) */
|
|
case 3: return -pi-tiny ; /* atan(-...,-INF) */
|
|
}
|
|
}
|
|
}
|
|
/* when y is INF */
|
|
if(iy==0x7ff00000) return (hy<0)? -pi_o_2-tiny: pi_o_2+tiny;
|
|
|
|
/* compute y/x */
|
|
k = (iy-ix)>>20;
|
|
if(k > 60) z=pi_o_2+0.5*pi_lo; /* |y/x| > 2**60 */
|
|
else if(hx<0&&k<-60) z=0.0; /* |y|/x < -2**60 */
|
|
else z=atan(fabs(y/x)); /* safe to do y/x */
|
|
switch (m) {
|
|
case 0: return z ; /* atan(+,+) */
|
|
case 1: {
|
|
__uint32_t zh;
|
|
GET_HIGH_WORD(zh,z);
|
|
SET_HIGH_WORD(z,zh ^ 0x80000000);
|
|
}
|
|
return z ; /* atan(-,+) */
|
|
case 2: return pi-(z-pi_lo);/* atan(+,-) */
|
|
default: /* case 3 */
|
|
return (z-pi_lo)-pi;/* atan(-,-) */
|
|
}
|
|
}
|
|
|
|
#endif /* defined(_DOUBLE_IS_32BITS) */
|