lib/libm/src/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  * $NetBSD: e_atan2.c,v 1.12 2002/05/26 22:01:48 wiz Exp $
  13  * $DragonFly: src/lib/libm/src/e_atan2.c,v 1.1 2005/07/26 21:15:20 joerg Exp $
  14  */
  15
  16 /* atan2(y,x)
  17  * Method :
  18  *      1. Reduce y to positive by atan2(y,x)=-atan2(-y,x).
  19  *      2. Reduce x to positive by (if x and y are unexceptional):
  20  *              ARG (x+iy) = arctan(y/x)           ... if x > 0,
  21  *              ARG (x+iy) = pi - arctan[y/(-x)]   ... if x < 0,
  22  *
  23  * Special cases:
  24  *
  25  *      ATAN2((anything), NaN ) is NaN;
  26  *      ATAN2(NAN , (anything) ) is NaN;
  27  *      ATAN2(+-0, +(anything but NaN)) is +-0  ;
  28  *      ATAN2(+-0, -(anything but NaN)) is +-pi ;
  29  *      ATAN2(+-(anything but 0 and NaN), 0) is +-pi/2;
  30  *      ATAN2(+-(anything but INF and NaN), +INF) is +-0 ;
  31  *      ATAN2(+-(anything but INF and NaN), -INF) is +-pi;
  32  *      ATAN2(+-INF,+INF ) is +-pi/4 ;
  33  *      ATAN2(+-INF,-INF ) is +-3pi/4;
  34  *      ATAN2(+-INF, (anything but,0,NaN, and INF)) is +-pi/2;
  35  *
  36  * Constants:
  37  * The hexadecimal values are the intended ones for the following
  38  * constants. The decimal values may be used, provided that the
  39  * compiler will convert from decimal to binary accurately enough
  40  * to produce the hexadecimal values shown.
  41  */
  42
  43 #include <math.h>
  44 #include "math_private.h"
  45
  46 static const double
  47 tiny  = 1.0e-300,
  48 zero  = 0.0,
  49 pi_o_4  = 7.8539816339744827900E-01, /* 0x3FE921FB, 0x54442D18 */
  50 pi_o_2  = 1.5707963267948965580E+00, /* 0x3FF921FB, 0x54442D18 */
  51 pi      = 3.1415926535897931160E+00, /* 0x400921FB, 0x54442D18 */
  52 pi_lo   = 1.2246467991473531772E-16; /* 0x3CA1A626, 0x33145C07 */
  53
  54 double
  55 atan2(double y, double x)
  56 {
  57         double z;
  58         int32_t k,m,hx,hy,ix,iy;
  59         u_int32_t lx,ly;
  60
  61         EXTRACT_WORDS(hx,lx,x);
  62         ix = hx&0x7fffffff;
  63         EXTRACT_WORDS(hy,ly,y);
  64         iy = hy&0x7fffffff;
  65         if(((ix|((lx|-lx)>>31))>0x7ff00000)||
  66            ((iy|((ly|-ly)>>31))>0x7ff00000))    /* x or y is NaN */
  67            return x+y;
  68         if(((hx-0x3ff00000)|lx)==0) return atan(y);   /* x=1.0 */
  69         m = ((hy>>31)&1)|((hx>>30)&2);  /* 2*sign(x)+sign(y) */
  70
  71     /* when y = 0 */
  72         if((iy|ly)==0) {
  73             switch(m) {
  74                 case 0:
  75                 case 1: return y;       /* atan(+-0,+anything)=+-0 */
  76                 case 2: return  pi+tiny;/* atan(+0,-anything) = pi */
  77                 case 3: return -pi-tiny;/* atan(-0,-anything) =-pi */
  78             }
  79         }
  80     /* when x = 0 */
  81         if((ix|lx)==0) return (hy<0)?  -pi_o_2-tiny: pi_o_2+tiny;
  82
  83     /* when x is INF */
  84         if(ix==0x7ff00000) {
  85             if(iy==0x7ff00000) {
  86                 switch(m) {
  87                     case 0: return  pi_o_4+tiny;/* atan(+INF,+INF) */
  88                     case 1: return -pi_o_4-tiny;/* atan(-INF,+INF) */
  89                     case 2: return  3.0*pi_o_4+tiny;/*atan(+INF,-INF)*/
  90                     case 3: return -3.0*pi_o_4-tiny;/*atan(-INF,-INF)*/
  91                 }
  92             } else {
  93                 switch(m) {
  94                     case 0: return  zero  ;     /* atan(+...,+INF) */
  95                     case 1: return -zero  ;     /* atan(-...,+INF) */
  96                     case 2: return  pi+tiny  ;  /* atan(+...,-INF) */
  97                     case 3: return -pi-tiny  ;  /* atan(-...,-INF) */
  98                 }
  99             }
 100         }
 101     /* when y is INF */
 102         if(iy==0x7ff00000) return (hy<0)? -pi_o_2-tiny: pi_o_2+tiny;
 103
 104     /* compute y/x */
 105         k = (iy-ix)>>20;
 106         if(k > 60) z=pi_o_2+0.5*pi_lo;  /* |y/x| >  2**60 */
 107         else if(hx<0&&k<-60) z=0.0;     /* |y|/x < -2**60 */
 108         else z=atan(fabs(y/x));         /* safe to do y/x */
 109         switch (m) {
 110             case 0: return       z  ;   /* atan(+,+) */
 111             case 1: {
 112                       u_int32_t zh;
 113                       GET_HIGH_WORD(zh,z);
 114                       SET_HIGH_WORD(z,zh ^ 0x80000000);
 115                     }
 116                     return       z  ;   /* atan(-,+) */
 117             case 2: return  pi-(z-pi_lo);/* atan(+,-) */
 118             default: /* case 3 */
 119                     return  (z-pi_lo)-pi;/* atan(-,-) */
 120         }
 121 }