e_atan2.c

/* @(#)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 ieee_atan2(y,x)=-ieee_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 ieee_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; 	/* ieee_atan(+-0,+anything)=+-0 */
		case 2: return  pi+tiny;/* ieee_atan(+0,-anything) = pi */
		case 3: return -pi-tiny;/* ieee_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;/* ieee_atan(+INF,+INF) */
		    case 1: return -pi_o_4-tiny;/* ieee_atan(-INF,+INF) */
		    case 2: return  3.0*pi_o_4+tiny;/*ieee_atan(+INF,-INF)*/
		    case 3: return -3.0*pi_o_4-tiny;/*ieee_atan(-INF,-INF)*/
		}
	    } else {
		switch(m) {
		    case 0: return  zero  ;	/* ieee_atan(+...,+INF) */
		    case 1: return -zero  ;	/* ieee_atan(-...,+INF) */
		    case 2: return  pi+tiny  ;	/* ieee_atan(+...,-INF) */
		    case 3: return -pi-tiny  ;	/* ieee_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=ieee_atan(ieee_fabs(y/x));		/* safe to do y/x */
	switch (m) {
	    case 0: return       z  ;	/* ieee_atan(+,+) */
	    case 1: __HI(z) ^= 0x80000000;
		    return       z  ;	/* ieee_atan(-,+) */
	    case 2: return  pi-(z-pi_lo);/* ieee_atan(+,-) */
	    default: /* case 3 */
	    	    return  (z-pi_lo)-pi;/* ieee_atan(-,-) */
	}
}