121 lines
3.4 KiB
C
121 lines
3.4 KiB
C
|
|
/* @(#)e_atan2.c 1.3 95/01/18 */
|
|
/* FreeBSD: head/lib/msun/src/e_atan2.c 176451 2008-02-22 02:30:36Z das */
|
|
/*
|
|
* ====================================================
|
|
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
|
*
|
|
* Developed at SunSoft, a Sun Microsystems, Inc. business.
|
|
* Permission to use, copy, modify, and distribute this
|
|
* software is freely granted, provided that this notice
|
|
* is preserved.
|
|
* ====================================================
|
|
*
|
|
*/
|
|
|
|
#include <sys/cdefs.h>
|
|
__FBSDID("$FreeBSD$");
|
|
|
|
/*
|
|
* See comments in e_atan2.c.
|
|
* Converted to long double by David Schultz <das@FreeBSD.ORG>.
|
|
*/
|
|
|
|
#include <float.h>
|
|
|
|
#include "invtrig.h"
|
|
#include "math.h"
|
|
#include "math_private.h"
|
|
|
|
static volatile long double
|
|
tiny = 1.0e-300;
|
|
static const long double
|
|
zero = 0.0;
|
|
|
|
#ifdef __i386__
|
|
/* XXX Work around the fact that gcc truncates long double constants on i386 */
|
|
static volatile double
|
|
pi1 = 3.14159265358979311600e+00, /* 0x1.921fb54442d18p+1 */
|
|
pi2 = 1.22514845490862001043e-16; /* 0x1.1a80000000000p-53 */
|
|
#define pi ((long double)pi1 + pi2)
|
|
#else
|
|
static const long double
|
|
pi = 3.14159265358979323846264338327950280e+00L;
|
|
#endif
|
|
|
|
long double
|
|
atan2l(long double y, long double x)
|
|
{
|
|
union IEEEl2bits ux, uy;
|
|
long double z;
|
|
int32_t k,m;
|
|
int16_t exptx, expsignx, expty, expsigny;
|
|
|
|
uy.e = y;
|
|
expsigny = uy.xbits.expsign;
|
|
expty = expsigny & 0x7fff;
|
|
ux.e = x;
|
|
expsignx = ux.xbits.expsign;
|
|
exptx = expsignx & 0x7fff;
|
|
|
|
if ((exptx==BIAS+LDBL_MAX_EXP &&
|
|
((ux.bits.manh&~LDBL_NBIT)|ux.bits.manl)!=0) || /* x is NaN */
|
|
(expty==BIAS+LDBL_MAX_EXP &&
|
|
((uy.bits.manh&~LDBL_NBIT)|uy.bits.manl)!=0)) /* y is NaN */
|
|
return nan_mix(x, y);
|
|
if (expsignx==BIAS && ((ux.bits.manh&~LDBL_NBIT)|ux.bits.manl)==0)
|
|
return atanl(y); /* x=1.0 */
|
|
m = ((expsigny>>15)&1)|((expsignx>>14)&2); /* 2*sign(x)+sign(y) */
|
|
|
|
/* when y = 0 */
|
|
if(expty==0 && ((uy.bits.manh&~LDBL_NBIT)|uy.bits.manl)==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(exptx==0 && ((ux.bits.manh&~LDBL_NBIT)|ux.bits.manl)==0)
|
|
return (expsigny<0)? -pio2_hi-tiny: pio2_hi+tiny;
|
|
|
|
/* when x is INF */
|
|
if(exptx==BIAS+LDBL_MAX_EXP) {
|
|
if(expty==BIAS+LDBL_MAX_EXP) {
|
|
switch(m) {
|
|
case 0: return pio2_hi*0.5+tiny;/* atan(+INF,+INF) */
|
|
case 1: return -pio2_hi*0.5-tiny;/* atan(-INF,+INF) */
|
|
case 2: return 1.5*pio2_hi+tiny;/*atan(+INF,-INF)*/
|
|
case 3: return -1.5*pio2_hi-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(expty==BIAS+LDBL_MAX_EXP)
|
|
return (expsigny<0)? -pio2_hi-tiny: pio2_hi+tiny;
|
|
|
|
/* compute y/x */
|
|
k = expty-exptx;
|
|
if(k > LDBL_MANT_DIG+2) { /* |y/x| huge */
|
|
z=pio2_hi+pio2_lo;
|
|
m&=1;
|
|
}
|
|
else if(expsignx<0&&k<-LDBL_MANT_DIG-2) z=0.0; /* |y/x| tiny, x<0 */
|
|
else z=atanl(fabsl(y/x)); /* safe to do y/x */
|
|
switch (m) {
|
|
case 0: return z ; /* atan(+,+) */
|
|
case 1: return -z ; /* atan(-,+) */
|
|
case 2: return pi-(z-pi_lo);/* atan(+,-) */
|
|
default: /* case 3 */
|
|
return (z-pi_lo)-pi;/* atan(-,-) */
|
|
}
|
|
}
|