prime/src/Runtime/e_atan2.c

/* @(#)e_atan2.c 1.2 95/01/04 */
/*
 * ====================================================
 * 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 "fdlibm.h"

#ifdef __STDC__
static const double
#else
static double
#endif
    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 */

#ifdef __STDC__
double __ieee754_atan2(double y, double x)
#else
double __ieee754_atan2(y, x)
double y, x;
#endif
{
  double z;
  _INT32 k, m, hx, hy, ix, iy; /*- cc 020130 -*/
  _UINT32 lx, ly;              /*- cc 020130 -*/

  hx = __HI(x);
  ix = hx & 0x7fffffff;
  lx = __LO(x);
  hy = __HI(y);
  iy = hy & 0x7fffffff;
  ly = __LO(y);
  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:
    __HI(z) ^= 0x80000000;
    return z; /* atan(-,+) */
  case 2:
    return pi - (z - pi_lo); /* atan(+,-) */
  default:                   /* case 3 */
    return (z - pi_lo) - pi; /* atan(-,-) */
  }
}