source: asp3_tinet_ecnl_arm/trunk/musl-1.1.18/src/math/atan2.c@ 352

/* 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 double
pi     = 3.1415926535897931160E+00, /* 0x400921FB, 0x54442D18 */
pi_lo  = 1.2246467991473531772E-16; /* 0x3CA1A626, 0x33145C07 */

double atan2(double y, double x)
{
        double z;
        uint32_t m,lx,ly,ix,iy;

        if (isnan(x) || isnan(y))
                return x+y;
        EXTRACT_WORDS(ix, lx, x);
        EXTRACT_WORDS(iy, ly, y);
        if ((ix-0x3ff00000 | lx) == 0)  /* x = 1.0 */
                return atan(y);
        m = ((iy>>31)&1) | ((ix>>30)&2);  /* 2*sign(x)+sign(y) */
        ix = ix & 0x7fffffff;
        iy = iy & 0x7fffffff;

        /* when y = 0 */
        if ((iy|ly) == 0) {
                switch(m) {
                case 0:
                case 1: return y;   /* atan(+-0,+anything)=+-0 */
                case 2: return  pi; /* atan(+0,-anything) = pi */
                case 3: return -pi; /* atan(-0,-anything) =-pi */
                }
        }
        /* when x = 0 */
        if ((ix|lx) == 0)
                return m&1 ? -pi/2 : pi/2;
        /* when x is INF */
        if (ix == 0x7ff00000) {
                if (iy == 0x7ff00000) {
                        switch(m) {
                        case 0: return  pi/4;   /* atan(+INF,+INF) */
                        case 1: return -pi/4;   /* atan(-INF,+INF) */
                        case 2: return  3*pi/4; /* atan(+INF,-INF) */
                        case 3: return -3*pi/4; /* atan(-INF,-INF) */
                        }
                } else {
                        switch(m) {
                        case 0: return  0.0; /* atan(+...,+INF) */
                        case 1: return -0.0; /* atan(-...,+INF) */
                        case 2: return  pi;  /* atan(+...,-INF) */
                        case 3: return -pi;  /* atan(-...,-INF) */
                        }
                }
        }
        /* |y/x| > 0x1p64 */
        if (ix+(64<<20) < iy || iy == 0x7ff00000)
                return m&1 ? -pi/2 : pi/2;

        /* z = atan(|y/x|) without spurious underflow */
        if ((m&2) && iy+(64<<20) < ix)  /* |y/x| < 0x1p-64, x<0 */
                z = 0;
        else
                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(-,-) */
        }
}