/* @(#)e_atan2.c 1.3 95/01/18 */

/*
 * Copyright (c) 2015-2017 Carsten Sonne Larsen  <cs@innolan.dk>
 * All rights reserved.
 *
 * Redistribution and use in source and binary forms, with or without
 * modification, are permitted provided that the following conditions
 * are met:
 * 1. Redistributions of source code must retain the above copyright
 *    notice, this list of conditions and the following disclaimer.
 * 2. Redistributions in binary form must reproduce the above copyright
 *    notice, this list of conditions and the following disclaimer in the
 *    documentation and/or other materials provided with the distribution.
 *
 * THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS OR
 * IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES
 * OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED.
 * IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY DIRECT, INDIRECT,
 * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
 * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
 * DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
 * THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
 * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF
 * THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
 *
 * The origin source code can be obtained from:
 * http://www.netlib.org/fdlibm/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.
 * ====================================================
 *
 */

#include "prim.h"
#include "math.h"

#ifdef _WIN32
#pragma warning( disable : 4146 )
#endif

/* 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.
 */

static const double
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 */

double atan2(double y, double x)
{
    double z;
    sword k,m,hx,hy,ix,iy;
    uword 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) return 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; 	/* 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  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==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=atan(fabs(y/x));		/* safe to do y/x */
    switch (m) {
    case 0:
        return       z  ;	/* atan(+,+) */
    case 1: {
        uword zh;
        GET_HIGH_WORD(zh,z);
        SET_HIGH_WORD(z, zh ^ 0x80000000);
    }
    return       z  ;	/* atan(-,+) */
    case 2:
        return  pi-(z-pi_lo);/* atan(+,-) */
    default: /* case 3 */
        return  (z-pi_lo)-pi;/* atan(-,-) */
    }
}
