musl/src/math/atan2l.c

/* origin: FreeBSD /usr/src/lib/msun/src/e_atan2l.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.
 * ====================================================
 *
 */
/*
 * See comments in atan2.c.
 * Converted to long double by David Schultz <[email protected]>.
 */

#include "libm.h"

#if LDBL_MANT_DIG == 53 && LDBL_MAX_EXP == 1024
long double atan2l(long double y, long double x)
{
	return atan2(y, x);
}
#elif (LDBL_MANT_DIG == 64 || LDBL_MANT_DIG == 113) && LDBL_MAX_EXP == 16384
#include "__invtrigl.h"
static const volatile long double
tiny = 1.0e-300;
static const long double
pi = 3.14159265358979323846264338327950280e+00L;

long double atan2l(long double y, long double x)
{
	union IEEEl2bits ux, uy;
	long double z;
	int32_t k,m;
	int16_t exptx, expsignx, expty, expsigny;

	uy.e = y;
	expsigny = uy.xbits.expsign;
	expty = expsigny & 0x7fff;
	ux.e = x;
	expsignx = ux.xbits.expsign;
	exptx = expsignx & 0x7fff;
	if ((exptx==BIAS+LDBL_MAX_EXP &&
	     ((ux.bits.manh&~LDBL_NBIT)|ux.bits.manl)!=0) || /* x is NaN */
	    (expty==BIAS+LDBL_MAX_EXP &&
	     ((uy.bits.manh&~LDBL_NBIT)|uy.bits.manl)!=0))   /* y is NaN */
		return x+y;
	if (expsignx==BIAS && ((ux.bits.manh&~LDBL_NBIT)|ux.bits.manl)==0) /* x=1.0 */
		return atanl(y);
	m = ((expsigny>>15)&1) | ((expsignx>>14)&2);  /* 2*sign(x)+sign(y) */

	/* when y = 0 */
	if (expty==0 && ((uy.bits.manh&~LDBL_NBIT)|uy.bits.manl)==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 (exptx==0 && ((ux.bits.manh&~LDBL_NBIT)|ux.bits.manl)==0)
		return expsigny < 0 ? -pio2_hi-tiny : pio2_hi+tiny;
	/* when x is INF */
	if (exptx == BIAS+LDBL_MAX_EXP) {
		if (expty == BIAS+LDBL_MAX_EXP) {
			switch(m) {
			case 0: return  pio2_hi*0.5+tiny; /* atan(+INF,+INF) */
			case 1: return -pio2_hi*0.5-tiny; /* atan(-INF,+INF) */
			case 2: return  1.5*pio2_hi+tiny; /*atan(+INF,-INF)*/
			case 3: return -1.5*pio2_hi-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 (expty == BIAS+LDBL_MAX_EXP)
		return expsigny < 0 ? -pio2_hi-tiny : pio2_hi+tiny;

	/* compute y/x */
	k = expty-exptx;
	if(k > LDBL_MANT_DIG+2) { /* |y/x| huge */
		z = pio2_hi+pio2_lo;
		m &= 1;
	} else if (expsignx < 0 && k < -LDBL_MANT_DIG-2) /* |y/x| tiny, x<0 */
		z = 0.0;
	else                     /* safe to do y/x */
		z = atanl(fabsl(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(-,-) */
	}
}
#endif