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

/*

 * ====================================================

 * 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.

 * ====================================================

 *

 */

/* __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"

#ifdef __STDC__

static const double 

#else

static double 

#endif

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 */

#ifdef __STDC__

	double __ieee754_atan2(double y, double x)

#else

	double __ieee754_atan2(y,x)

	double  y,x;

#endif

{  

	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(-,-) */

	}

}