/* origin: FreeBSD /usr/src/lib/msun/src/e_atan2.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.
* ====================================================
*
*/
/* 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 "libm.h"
static const volatile double
tiny = 1.0e-300;
static const double
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 */
static const volatile double
pi_lo = 1.2246467991473531772E-16; /* 0x3CA1A626, 0x33145C07 */
double atan2(double y, double x)
{
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) /* x = 1.0 */
return atan(y);
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) { /* |y/x| > 2**60 */
z = pi_o_2+0.5*pi_lo;
m &= 1;
} else if (hx < 0 && k < -60) /* 0 > |y|/x > -2**-60 */
z = 0.0;
else /* safe to do y/x */
z = atan(fabs(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(-,-) */
}
}
