e_atan2.c

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/*
 * ====================================================
 * 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_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 "math_libm.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 attribute_hidden __ieee754_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|-(int32_t)lx)>>31))>0x7ff00000)||
     ((iy|((ly|-(int32_t)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(-,-) */
  }
}