musl/src/math/atan2f.c

/* origin: FreeBSD /usr/src/lib/msun/src/e_atan2f.c */
/*
 * Conversion to float by Ian Lance Taylor, Cygnus Support, [email protected].
 */
/*
 * ====================================================
 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
 *
 * Developed at SunPro, a Sun Microsystems, Inc. business.
 * Permission to use, copy, modify, and distribute this
 * software is freely granted, provided that this notice
 * is preserved.
 * ====================================================
 */

#include "libm.h"

static const volatile float
tiny = 1.0e-30;
static const float
zero = 0.0,
pi_o_4 = 7.8539818525e-01, /* 0x3f490fdb */
pi_o_2 = 1.5707963705e+00, /* 0x3fc90fdb */
pi     = 3.1415927410e+00; /* 0x40490fdb */
static const volatile float
pi_lo  = -8.7422776573e-08; /* 0xb3bbbd2e */

float atan2f(float y, float x)
{
	float z;
	int32_t k,m,hx,hy,ix,iy;

	GET_FLOAT_WORD(hx, x);
	ix = hx & 0x7fffffff;
	GET_FLOAT_WORD(hy, y);
	iy = hy & 0x7fffffff;
	if (ix > 0x7f800000 || iy > 0x7f800000)  /* x or y is NaN */
		return x+y;
	if (hx == 0x3f800000)  /* x=1.0 */
		return atanf(y);
	m = ((hy>>31)&1) | ((hx>>30)&2);  /* 2*sign(x)+sign(y) */

	/* when y = 0 */
	if (iy == 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 == 0)
		return hy < 0 ? -pi_o_2-tiny : pi_o_2+tiny;
	/* when x is INF */
	if (ix == 0x7f800000) {
		if (iy == 0x7f800000) {
			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 3.0f*pi_o_4+tiny;  /*atan(+INF,-INF)*/
			case 3: return -3.0f*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 == 0x7f800000)
		return hy < 0 ? -pi_o_2-tiny : pi_o_2+tiny;

	/* compute y/x */
	k = (iy-ix)>>23;
	if (k > 26) {                  /* |y/x| >  2**26 */
		z = pi_o_2 + 0.5f*pi_lo;
		m &= 1;
	} else if (k < -26 && hx < 0)  /* 0 > |y|/x > -2**-26 */
		z = 0.0;
	else                           /* safe to do y/x */
		z = atanf(fabsf(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(-,-) */
	}
}