sysdeps/libm-ieee754/e_atan2.c

   1 /* @(#)e_atan2.c 5.1 93/09/24 */
   2 /*
   3  * ====================================================
   4  * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
   5  *
   6  * Developed at SunPro, a Sun Microsystems, Inc. business.
   7  * Permission to use, copy, modify, and distribute this
   8  * software is freely granted, provided that this notice
   9  * is preserved.
  10  * ====================================================
  11  */
  12
  13 #if defined(LIBM_SCCS) && !defined(lint)
  14 static char rcsid[] = "$NetBSD: e_atan2.c,v 1.8 1995/05/10 20:44:51 jtc Exp $";
  15 #endif
  16
  17 /* __ieee754_atan2(y,x)
  18  * Method :
  19  *      1. Reduce y to positive by atan2(y,x)=-atan2(-y,x).
  20  *      2. Reduce x to positive by (if x and y are unexceptional):
  21  *              ARG (x+iy) = arctan(y/x)           ... if x > 0,
  22  *              ARG (x+iy) = pi - arctan[y/(-x)]   ... if x < 0,
  23  *
  24  * Special cases:
  25  *
  26  *      ATAN2((anything), NaN ) is NaN;
  27  *      ATAN2(NAN , (anything) ) is NaN;
  28  *      ATAN2(+-0, +(anything but NaN)) is +-0  ;
  29  *      ATAN2(+-0, -(anything but NaN)) is +-pi ;
  30  *      ATAN2(+-(anything but 0 and NaN), 0) is +-pi/2;
  31  *      ATAN2(+-(anything but INF and NaN), +INF) is +-0 ;
  32  *      ATAN2(+-(anything but INF and NaN), -INF) is +-pi;
  33  *      ATAN2(+-INF,+INF ) is +-pi/4 ;
  34  *      ATAN2(+-INF,-INF ) is +-3pi/4;
  35  *      ATAN2(+-INF, (anything but,0,NaN, and INF)) is +-pi/2;
  36  *
  37  * Constants:
  38  * The hexadecimal values are the intended ones for the following
  39  * constants. The decimal values may be used, provided that the
  40  * compiler will convert from decimal to binary accurately enough
  41  * to produce the hexadecimal values shown.
  42  */
  43
  44 #include "math.h"
  45 #include "math_private.h"
  46
  47 #ifdef __STDC__
  48 static const double
  49 #else
  50 static double
  51 #endif
  52 tiny  = 1.0e-300,
  53 zero  = 0.0,
  54 pi_o_4  = 7.8539816339744827900E-01, /* 0x3FE921FB, 0x54442D18 */
  55 pi_o_2  = 1.5707963267948965580E+00, /* 0x3FF921FB, 0x54442D18 */
  56 pi      = 3.1415926535897931160E+00, /* 0x400921FB, 0x54442D18 */
  57 pi_lo   = 1.2246467991473531772E-16; /* 0x3CA1A626, 0x33145C07 */
  58
  59 #ifdef __STDC__
  60         double __ieee754_atan2(double y, double x)
  61 #else
  62         double __ieee754_atan2(y,x)
  63         double  y,x;
  64 #endif
  65 {
  66         double z;
  67         int32_t k,m,hx,hy,ix,iy;
  68         u_int32_t lx,ly;
  69
  70         EXTRACT_WORDS(hx,lx,x);
  71         ix = hx&0x7fffffff;
  72         EXTRACT_WORDS(hy,ly,y);
  73         iy = hy&0x7fffffff;
  74         if(((ix|((lx|-lx)>>31))>0x7ff00000)||
  75            ((iy|((ly|-ly)>>31))>0x7ff00000))    /* x or y is NaN */
  76            return x+y;
  77         if((hx-0x3ff00000|lx)==0) return __atan(y);   /* x=1.0 */
  78         m = ((hy>>31)&1)|((hx>>30)&2);  /* 2*sign(x)+sign(y) */
  79
  80     /* when y = 0 */
  81         if((iy|ly)==0) {
  82             switch(m) {
  83                 case 0:
  84                 case 1: return y;       /* atan(+-0,+anything)=+-0 */
  85                 case 2: return  pi+tiny;/* atan(+0,-anything) = pi */
  86                 case 3: return -pi-tiny;/* atan(-0,-anything) =-pi */
  87             }
  88         }
  89     /* when x = 0 */
  90         if((ix|lx)==0) return (hy<0)?  -pi_o_2-tiny: pi_o_2+tiny;
  91
  92     /* when x is INF */
  93         if(ix==0x7ff00000) {
  94             if(iy==0x7ff00000) {
  95                 switch(m) {
  96                     case 0: return  pi_o_4+tiny;/* atan(+INF,+INF) */
  97                     case 1: return -pi_o_4-tiny;/* atan(-INF,+INF) */
  98                     case 2: return  3.0*pi_o_4+tiny;/*atan(+INF,-INF)*/
  99                     case 3: return -3.0*pi_o_4-tiny;/*atan(-INF,-INF)*/
 100                 }
 101             } else {
 102                 switch(m) {
 103                     case 0: return  zero  ;     /* atan(+...,+INF) */
 104                     case 1: return -zero  ;     /* atan(-...,+INF) */
 105                     case 2: return  pi+tiny  ;  /* atan(+...,-INF) */
 106                     case 3: return -pi-tiny  ;  /* atan(-...,-INF) */
 107                 }
 108             }
 109         }
 110     /* when y is INF */
 111         if(iy==0x7ff00000) return (hy<0)? -pi_o_2-tiny: pi_o_2+tiny;
 112
 113     /* compute y/x */
 114         k = (iy-ix)>>20;
 115         if(k > 60) z=pi_o_2+0.5*pi_lo;  /* |y/x| >  2**60 */
 116         else if(hx<0&&k<-60) z=0.0;     /* |y|/x < -2**60 */
 117         else z=__atan(fabs(y/x));       /* safe to do y/x */
 118         switch (m) {
 119             case 0: return       z  ;   /* atan(+,+) */
 120             case 1: {
 121                       u_int32_t zh;
 122                       GET_HIGH_WORD(zh,z);
 123                       SET_HIGH_WORD(z,zh ^ 0x80000000);
 124                     }
 125                     return       z  ;   /* atan(-,+) */
 126             case 2: return  pi-(z-pi_lo);/* atan(+,-) */
 127             default: /* case 3 */
 128                     return  (z-pi_lo)-pi;/* atan(-,-) */
 129         }
 130 }