# shithub: 9ferno

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```/* derived from /netlib/fdlibm */

/* @(#)e_atan2.c 1.3 95/01/18 */
/*
* ====================================================
*
* 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.
* ====================================================
*
*/

/* __ieee754_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 "fdlibm.h"

static const double
tiny  = 1.0e-300,
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 */
pi_lo   = 1.2246467991473531772E-16; /* 0x3CA1A626, 0x33145C07 */

double __ieee754_atan2(double y, double x)
{
double z;
int k,m,hx,hy,ix,iy;
unsigned lx,ly;

hx = __HI(x); ix = hx&0x7fffffff;
lx = __LO(x);
hy = __HI(y); iy = hy&0x7fffffff;
ly = __LO(y);
if(((ix|((lx|-lx)>>31))>0x7ff00000)||
((iy|((ly|-ly)>>31))>0x7ff00000))	/* x or y is NaN */
return x+y;
if((hx-0x3ff00000|lx)==0) return atan(y);   /* x=1.0 */
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) z=pi_o_2+0.5*pi_lo; 	/* |y/x| >  2**60 */
else if(hx<0&&k<-60) z=0.0; 	/* |y|/x < -2**60 */
else z=atan(fabs(y/x));		/* safe to do y/x */
switch (m) {
case 0: return       z  ;	/* atan(+,+) */
case 1: __HI(z) ^= 0x80000000;
return       z  ;	/* atan(-,+) */
case 2: return  pi-(z-pi_lo);/* atan(+,-) */
default: /* case 3 */
return  (z-pi_lo)-pi;/* atan(-,-) */
}
}
```