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/* $OpenBSD: e_atan2l.c,v 1.2 2016/09/12 19:47:02 guenther Exp $ */
/* @(#)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.
* ====================================================
*
*/
/*
* See comments in e_atan2.c.
* Converted to long double by David Schultz <das@FreeBSD.ORG>.
* Adapted for OpenBSD by Martynas Venckus <martynas@openbsd.org>.
*/
#include <float.h>
#include <math.h>
#include "invtrig.h"
#include "math.h"
#include "math_private.h"
#ifdef EXT_IMPLICIT_NBIT
#define LDBL_NBIT 0
#else /* EXT_IMPLICIT_NBIT */
#define LDBL_NBIT 0x80000000
#endif /* EXT_IMPLICIT_NBIT */
static volatile long double
tiny = 1.0e-300;
static const long double
zero = 0.0;
#if defined(__amd64__) || defined(__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 {
long double e;
struct ieee_ext bits;
} ux, uy;
long double z;
int32_t k,m;
int16_t exptx, expsignx, expty, expsigny;
uy.e = y;
expsigny = (uy.bits.ext_sign << 15) | uy.bits.ext_exp;
expty = expsigny & 0x7fff;
ux.e = x;
expsignx = (ux.bits.ext_sign << 15) | ux.bits.ext_exp;
exptx = expsignx & 0x7fff;
if ((exptx==BIAS+LDBL_MAX_EXP &&
((ux.bits.ext_frach&~LDBL_NBIT)
#ifdef EXT_FRACHMBITS
| ux.bits.ext_frachm
#endif /* EXT_FRACHMBITS */
#ifdef EXT_FRACLMBITS
| ux.bits.ext_fraclm
#endif /* EXT_FRACLMBITS */
| ux.bits.ext_fracl)!=0) || /* x is NaN */
(expty==BIAS+LDBL_MAX_EXP &&
((uy.bits.ext_frach&~LDBL_NBIT)
#ifdef EXT_FRACHMBITS
| uy.bits.ext_frachm
#endif /* EXT_FRACHMBITS */
#ifdef EXT_FRACLMBITS
| uy.bits.ext_fraclm
#endif /* EXT_FRACLMBITS */
| uy.bits.ext_fracl)!=0)) /* y is NaN */
return x+y;
if (expsignx==BIAS && ((ux.bits.ext_frach&~LDBL_NBIT)
#ifdef EXT_FRACHMBITS
| ux.bits.ext_frachm
#endif /* EXT_FRACHMBITS */
#ifdef EXT_FRACLMBITS
| ux.bits.ext_fraclm
#endif /* EXT_FRACLMBITS */
| ux.bits.ext_fracl)==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.ext_frach&~LDBL_NBIT)
#ifdef EXT_FRACHMBITS
| uy.bits.ext_frachm
#endif /* EXT_FRACHMBITS */
#ifdef EXT_FRACLMBITS
| uy.bits.ext_fraclm
#endif /* EXT_FRACLMBITS */
| uy.bits.ext_fracl)==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.ext_frach&~LDBL_NBIT)
#ifdef EXT_FRACHMBITS
| ux.bits.ext_frachm
#endif /* EXT_FRACHMBITS */
#ifdef EXT_FRACLMBITS
| ux.bits.ext_fraclm
#endif /* EXT_FRACLMBITS */
| ux.bits.ext_fracl)==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(-,-) */
}
}
DEF_STD(atan2l);
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