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/* e_atan2l.c -- long double version of e_atan2.c.
* Conversion to long double by Ulrich Drepper,
* Cygnus Support, drepper@cygnus.com.
*/
/*
* ====================================================
* 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.
* ====================================================
*/
#if defined(LIBM_SCCS) && !defined(lint)
static char rcsid[] = "$NetBSD: $";
#endif
/* __ieee754_atan2l(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 "math.h"
#include "math_private.h"
#ifdef __STDC__
static const long double
#else
static long double
#endif
tiny = 1.0e-4900L,
zero = 0.0,
pi_o_4 = 7.85398163397448309628202E-01L, /* 0x3FFE, 0xC90FDAA2, 0x2168C235 */
pi_o_2 = 1.5707963267948966192564E+00L, /* 0x3FFF, 0xC90FDAA2, 0x2168C235 */
pi = 3.14159265358979323851281E+00L, /* 0x4000, 0xC90FDAA2, 0x2168C235 */
pi_lo = -5.01655761266833202345176e-20L;/* 0xBFBE, 0xECE675D1, 0xFC8F8CBB */
#ifdef __STDC__
long double __ieee754_atan2l(long double y, long double x)
#else
long double __ieee754_atan2l(y,x)
long double y,x;
#endif
{
long double z;
int32_t k,m,hx,hy,ix,iy;
u_int32_t sx,sy,lx,ly;
EXTRACT_LDOUBLE_WORDS(sx,hx,lx,x);
ix = sx&0x7fff;
lx |= hx & 0x7fffffff;
EXTRACT_LDOUBLE_WORDS(sy,hy,ly,y);
iy = sy&0x7fff;
ly |= hy & 0x7fffffff;
if(((2*ix|((lx|-lx)>>31))>0xfffe)||
((2*iy|((ly|-ly)>>31))>0xfffe)) /* x or y is NaN */
return x+y;
if((sx-0x3fff|lx)==0) return __atanl(y); /* x=1.0 */
m = ((sy>>15)&1)|((sx>>14)&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 (sy>=0x8000)? -pi_o_2-tiny: pi_o_2+tiny;
/* when x is INF */
if(ix==0x7fff) {
if(iy==0x7fff) {
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==0x7fff) return (sy>=0x8000)? -pi_o_2-tiny: pi_o_2+tiny;
/* compute y/x */
k = sy-sx;
if(k > 70) z=pi_o_2+0.5*pi_lo; /* |y/x| > 2**70 */
else if(sx>=0x8000&&k<-70) z=0.0; /* |y|/x < -2**70 */
else z=__atanl(fabsl(y/x)); /* safe to do y/x */
switch (m) {
case 0: return z ; /* atan(+,+) */
case 1: {
u_int32_t sz;
GET_LDOUBLE_EXP(sz,z);
SET_LDOUBLE_EXP(z,sz ^ 0x8000);
}
return z ; /* atan(-,+) */
case 2: return pi-(z-pi_lo);/* atan(+,-) */
default: /* case 3 */
return (z-pi_lo)-pi;/* atan(-,-) */
}
}
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