musl/src/math/atan2.c

/* 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
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  0.0;     /* atan(+...,+INF) */
			case 1: return -0.0;     /* 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(-,-) */
	}
}