js/src/fdlibm/e_atan2.c

   1 /* -*- Mode: C; tab-width: 8; indent-tabs-mode: nil; c-basic-offset: 4 -*-
   2  *
   3  * ***** BEGIN LICENSE BLOCK *****
   4  * Version: MPL 1.1/GPL 2.0/LGPL 2.1
   5  *
   6  * The contents of this file are subject to the Mozilla Public License Version
   7  * 1.1 (the "License"); you may not use this file except in compliance with
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   9  * http://www.mozilla.org/MPL/
  10  *
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  12  * WITHOUT WARRANTY OF ANY KIND, either express or implied. See the License
  13  * for the specific language governing rights and limitations under the
  14  * License.
  15  *
  16  * The Original Code is Mozilla Communicator client code, released
  17  * March 31, 1998.
  18  *
  19  * The Initial Developer of the Original Code is
  20  * Sun Microsystems, Inc.
  21  * Portions created by the Initial Developer are Copyright (C) 1998
  22  * the Initial Developer. All Rights Reserved.
  23  *
  24  * Contributor(s):
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  26  * Alternatively, the contents of this file may be used under the terms of
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  38  * ***** END LICENSE BLOCK ***** */
  39
  40 /* @(#)e_atan2.c 1.3 95/01/18 */
  41 /*
  42  * ====================================================
  43  * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
  44  *
  45  * Developed at SunSoft, a Sun Microsystems, Inc. business.
  46  * Permission to use, copy, modify, and distribute this
  47  * software is freely granted, provided that this notice
  48  * is preserved.
  49  * ====================================================
  50  *
  51  */
  52
  53 /* __ieee754_atan2(y,x)
  54  * Method :
  55  *      1. Reduce y to positive by atan2(y,x)=-atan2(-y,x).
  56  *      2. Reduce x to positive by (if x and y are unexceptional):
  57  *              ARG (x+iy) = arctan(y/x)           ... if x > 0,
  58  *              ARG (x+iy) = pi - arctan[y/(-x)]   ... if x < 0,
  59  *
  60  * Special cases:
  61  *
  62  *      ATAN2((anything), NaN ) is NaN;
  63  *      ATAN2(NAN , (anything) ) is NaN;
  64  *      ATAN2(+-0, +(anything but NaN)) is +-0  ;
  65  *      ATAN2(+-0, -(anything but NaN)) is +-pi ;
  66  *      ATAN2(+-(anything but 0 and NaN), 0) is +-pi/2;
  67  *      ATAN2(+-(anything but INF and NaN), +INF) is +-0 ;
  68  *      ATAN2(+-(anything but INF and NaN), -INF) is +-pi;
  69  *      ATAN2(+-INF,+INF ) is +-pi/4 ;
  70  *      ATAN2(+-INF,-INF ) is +-3pi/4;
  71  *      ATAN2(+-INF, (anything but,0,NaN, and INF)) is +-pi/2;
  72  *
  73  * Constants:
  74  * The hexadecimal values are the intended ones for the following
  75  * constants. The decimal values may be used, provided that the
  76  * compiler will convert from decimal to binary accurately enough
  77  * to produce the hexadecimal values shown.
  78  */
  79
  80 #include "fdlibm.h"
  81
  82 #ifdef __STDC__
  83 static const double
  84 #else
  85 static double
  86 #endif
  87 tiny  = 1.0e-300,
  88 zero  = 0.0,
  89 pi_o_4  = 7.8539816339744827900E-01, /* 0x3FE921FB, 0x54442D18 */
  90 pi_o_2  = 1.5707963267948965580E+00, /* 0x3FF921FB, 0x54442D18 */
  91 pi      = 3.1415926535897931160E+00, /* 0x400921FB, 0x54442D18 */
  92 pi_lo   = 1.2246467991473531772E-16; /* 0x3CA1A626, 0x33145C07 */
  93
  94 #ifdef __STDC__
  95         double __ieee754_atan2(double y, double x)
  96 #else
  97         double __ieee754_atan2(y,x)
  98         double  y,x;
  99 #endif
 100 {
 101         fd_twoints ux, uy, uz;
 102         double z;
 103         int k,m,hx,hy,ix,iy;
 104         unsigned lx,ly;
 105
 106         ux.d = x; uy.d = y;
 107         hx = __HI(ux); ix = hx&0x7fffffff;
 108         lx = __LO(ux);
 109         hy = __HI(uy); iy = hy&0x7fffffff;
 110         ly = __LO(uy);
 111         if(((ix|((lx|-(int)lx)>>31))>0x7ff00000)||
 112            ((iy|((ly|-(int)ly)>>31))>0x7ff00000))       /* x or y is NaN */
 113            return x+y;
 114         if(((hx-0x3ff00000)|lx)==0) return fd_atan(y);   /* x=1.0 */
 115         m = ((hy>>31)&1)|((hx>>30)&2);  /* 2*sign(x)+sign(y) */
 116
 117     /* when y = 0 */
 118         if((iy|ly)==0) {
 119             switch(m) {
 120                 case 0:
 121                 case 1: return y;       /* atan(+-0,+anything)=+-0 */
 122                 case 2: return  pi+tiny;/* atan(+0,-anything) = pi */
 123                 case 3: return -pi-tiny;/* atan(-0,-anything) =-pi */
 124             }
 125         }
 126     /* when x = 0 */
 127         if((ix|lx)==0) return (hy<0)?  -pi_o_2-tiny: pi_o_2+tiny;
 128
 129     /* when x is INF */
 130         if(ix==0x7ff00000) {
 131             if(iy==0x7ff00000) {
 132                 switch(m) {
 133                     case 0: return  pi_o_4+tiny;/* atan(+INF,+INF) */
 134                     case 1: return -pi_o_4-tiny;/* atan(-INF,+INF) */
 135                     case 2: return  3.0*pi_o_4+tiny;/*atan(+INF,-INF)*/
 136                     case 3: return -3.0*pi_o_4-tiny;/*atan(-INF,-INF)*/
 137                 }
 138             } else {
 139                 switch(m) {
 140                     case 0: return  zero  ;     /* atan(+...,+INF) */
 141                     case 1: return -zero  ;     /* atan(-...,+INF) */
 142                     case 2: return  pi+tiny  ;  /* atan(+...,-INF) */
 143                     case 3: return -pi-tiny  ;  /* atan(-...,-INF) */
 144                 }
 145             }
 146         }
 147     /* when y is INF */
 148         if(iy==0x7ff00000) return (hy<0)? -pi_o_2-tiny: pi_o_2+tiny;
 149
 150     /* compute y/x */
 151         k = (iy-ix)>>20;
 152         if(k > 60) z=pi_o_2+0.5*pi_lo;  /* |y/x| >  2**60 */
 153         else if(hx<0&&k<-60) z=0.0;     /* |y|/x < -2**60 */
 154         else z=fd_atan(fd_fabs(y/x));           /* safe to do y/x */
 155         switch (m) {
 156             case 0: return       z  ;   /* atan(+,+) */
 157             case 1: uz.d = z;
 158                     __HI(uz) ^= 0x80000000;
 159                     z = uz.d;
 160                     return       z  ;   /* atan(-,+) */
 161             case 2: return  pi-(z-pi_lo);/* atan(+,-) */
 162             default: /* case 3 */
 163                     return  (z-pi_lo)-pi;/* atan(-,-) */
 164         }
 165 }