/* e_atan2l.c -- long double version of e_atan2.c.

 * Conversion to long double by Jakub Jelinek, jj@ultra.linux.cz.

 */

/*

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

 * 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.

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

 */

/* __ieee754_atan2l(y,x)

 * Method :

 *	1. Reduce y to positive by atan2l(y,x)=-atan2l(-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 <math.h>

#include <math_private.h>

static const _Float128

tiny  = L(1.0e-4900),

zero  = 0.0,

pi_o_4  = L(7.85398163397448309615660845819875699e-01), /* 3ffe921fb54442d18469898cc51701b8 */

pi_o_2  = L(1.57079632679489661923132169163975140e+00), /* 3fff921fb54442d18469898cc51701b8 */

pi      = L(3.14159265358979323846264338327950280e+00), /* 4000921fb54442d18469898cc51701b8 */

pi_lo   = L(8.67181013012378102479704402604335225e-35); /* 3f8dcd129024e088a67cc74020bbea64 */

_Float128

__ieee754_atan2l(_Float128 y, _Float128 x)

{

	_Float128 z;

	int64_t k,m,hx,hy,ix,iy;

	uint64_t lx,ly;

	GET_LDOUBLE_WORDS64(hx,lx,x);

	ix = hx&0x7fffffffffffffffLL;

	GET_LDOUBLE_WORDS64(hy,ly,y);

	iy = hy&0x7fffffffffffffffLL;

	if(((ix|((lx|-lx)>>63))>0x7fff000000000000LL)||

	   ((iy|((ly|-ly)>>63))>0x7fff000000000000LL))	/* x or y is NaN */

	   return x+y;

	if(((hx-0x3fff000000000000LL)|lx)==0) return __atanl(y);   /* x=1.0L */

	m = ((hy>>63)&1)|((hx>>62)&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==0x7fff000000000000LL) {

	    if(iy==0x7fff000000000000LL) {

		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*pi_o_4+tiny;/*atan(+INF,-INF)*/

		    case 3: return -3*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==0x7fff000000000000LL) return (hy<0)? -pi_o_2-tiny: pi_o_2+tiny;

    /* compute y/x */

	k = (iy-ix)>>48;

	if(k > 120) z=pi_o_2+L(0.5)*pi_lo;	/* |y/x| >  2**120 */

	else if(hx<0&&k<-120) z=0;		/* |y|/x < -2**120 */

	else z=__atanl(fabsl(y/x));		/* safe to do y/x */

	switch (m) {

	    case 0: return       z  ;	/* atan(+,+) */

	    case 1: {

		      uint64_t zh;

		      GET_LDOUBLE_MSW64(zh,z);

		      SET_LDOUBLE_MSW64(z,zh ^ 0x8000000000000000ULL);

		    }

		    return       z  ;	/* atan(-,+) */

	    case 2: return  pi-(z-pi_lo);/* atan(+,-) */

	    default: /* case 3 */

		    return  (z-pi_lo)-pi;/* atan(-,-) */

	}

}

strong_alias (__ieee754_atan2l, __atan2l_finite)