/* origin: FreeBSD /usr/src/lib/msun/src/e_atan2l.c */
/*
* ====================================================
* 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 atan2.c.
* Converted to long double by David Schultz <das@FreeBSD.ORG>.
*/
#include "libm.h"
#if LDBL_MANT_DIG == 53 && LDBL_MAX_EXP == 1024
long double atan2l(long double y, long double x)
{
return atan2(y, x);
}
#elif (LDBL_MANT_DIG == 64 || LDBL_MANT_DIG == 113) && LDBL_MAX_EXP == 16384
#include "__invtrigl.h"
static const volatile long double
tiny = 1.0e-300;
static const long double
zero = 0.0;
/* XXX Work around the fact that gcc truncates long double constants on i386 */
static const volatile double
pi1 = 3.14159265358979311600e+00, /* 0x1.921fb54442d18p+1 */
pi2 = 1.22514845490862001043e-16; /* 0x1.1a80000000000p-53 */
#define pi ((long double)pi1 + pi2)
#if 0
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 x+y;
if (expsignx==BIAS && ((ux.bits.manh&~LDBL_NBIT)|ux.bits.manl)==0) /* x=1.0 */
return atanl(y);
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) /* |y/x| tiny, x<0 */
z = 0.0;
else /* safe to do y/x */
z = atanl(fabsl(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(-,-) */
}
}
#endif
