Quelle e_atan2.cpp Sprache: C

/* @(#)e_atan2.c 1.3 95/01/18 */
/*
* ====================================================
* 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 <sys/cdefs.h>
//__FBSDID("$FreeBSD$");

/* __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 <float.h>

#include "math_private.h"

static volatile double
tiny  = 1.0e-300;
static const double
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 */
static volatile double
pi_lo   = 1.2246467991473531772E-16; /* 0x3CA1A626, 0x33145C07 */

double
__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|-lx)>>31))>0x7ff00000)||
    ((iy|((ly|-ly)>>31))>0x7ff00000)) /* x or y is NaN */
     return nan_mix(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) {    /* |y/x| >  2**60 */
     z=pi_o_2+0.5*pi_lo;
     m&=1;
}
else if(hx<0&&k<-60) z=0.0;  /* 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: return      -z  ; /* atan(-,+) */
     case 2: return  pi-(z-pi_lo);/* atan(+,-) */
     default: /* case 3 */
          return  (z-pi_lo)-pi;/* atan(-,-) */
}
}

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