e_atan2.c

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/* @(#)e_atan2.c 5.1 93/09/24 */
/*
 * ====================================================
 * 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.
 * ====================================================
 */

/* 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 <sys/cdefs.h>
#include <float.h>
#include <math.h>

#include "math_private.h"

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;
    int32_t k,m,hx,hy,ix,iy;
    u_int32_t 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: {
                  u_int32_t 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(-,-) */
    }
}

#if LDBL_MANT_DIG == 53
#ifdef __weak_alias
__weak_alias(atan2l, atan2);
#endif /* __weak_alias */
#endif /* LDBL_MANT_DIG == 53 */