StdLib/LibC/Math/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 #include  <LibConfig.h>
  13 #include  <sys/EfiCdefs.h>
  14 #if defined(LIBM_SCCS) && !defined(lint)
  15 __RCSID("$NetBSD: e_atan2.c,v 1.12 2002/05/26 22:01:48 wiz Exp $");
  16 #endif
  17
  18 #if defined(_MSC_VER)           /* Handle Microsoft VC++ compiler specifics. */
  19   // unary minus operator applied to unsigned type, result still unsigned
  20   #pragma warning ( disable : 4146 )
  21 #endif
  22
  23 /* __ieee754_atan2(y,x)
  24  * Method :
  25  *  1. Reduce y to positive by atan2(y,x)=-atan2(-y,x).
  26  *  2. Reduce x to positive by (if x and y are unexceptional):
  27  *    ARG (x+iy) = arctan(y/x)       ... if x > 0,
  28  *    ARG (x+iy) = pi - arctan[y/(-x)]   ... if x < 0,
  29  *
  30  * Special cases:
  31  *
  32  *  ATAN2((anything), NaN ) is NaN;
  33  *  ATAN2(NAN , (anything) ) is NaN;
  34  *  ATAN2(+-0, +(anything but NaN)) is +-0  ;
  35  *  ATAN2(+-0, -(anything but NaN)) is +-pi ;
  36  *  ATAN2(+-(anything but 0 and NaN), 0) is +-pi/2;
  37  *  ATAN2(+-(anything but INF and NaN), +INF) is +-0 ;
  38  *  ATAN2(+-(anything but INF and NaN), -INF) is +-pi;
  39  *  ATAN2(+-INF,+INF ) is +-pi/4 ;
  40  *  ATAN2(+-INF,-INF ) is +-3pi/4;
  41  *  ATAN2(+-INF, (anything but,0,NaN, and INF)) is +-pi/2;
  42  *
  43  * Constants:
  44  * The hexadecimal values are the intended ones for the following
  45  * constants. The decimal values may be used, provided that the
  46  * compiler will convert from decimal to binary accurately enough
  47  * to produce the hexadecimal values shown.
  48  */
  49
  50 #include "math.h"
  51 #include "math_private.h"
  52
  53 static const double
  54 tiny  = 1.0e-300,
  55 zero  = 0.0,
  56 pi_o_4  = 7.8539816339744827900E-01, /* 0x3FE921FB, 0x54442D18 */
  57 pi_o_2  = 1.5707963267948965580E+00, /* 0x3FF921FB, 0x54442D18 */
  58 pi      = 3.1415926535897931160E+00, /* 0x400921FB, 0x54442D18 */
  59 pi_lo   = 1.2246467991473531772E-16; /* 0x3CA1A626, 0x33145C07 */
  60
  61 double
  62 __ieee754_atan2(double y, double x)
  63 {
  64   double z;
  65   int32_t k,m,hx,hy,ix,iy;
  66   u_int32_t lx,ly;
  67
  68   EXTRACT_WORDS(hx,lx,x);
  69   ix = hx&0x7fffffff;
  70   EXTRACT_WORDS(hy,ly,y);
  71   iy = hy&0x7fffffff;
  72   if(((ix|((lx|-lx)>>31))>0x7ff00000)||
  73      ((iy|((ly|-ly)>>31))>0x7ff00000))  /* x or y is NaN */
  74      return x+y;
  75   if(((hx-0x3ff00000)|lx)==0) return atan(y);   /* x=1.0 */
  76   m = ((hy>>31)&1)|((hx>>30)&2);  /* 2*sign(x)+sign(y) */
  77
  78     /* when y = 0 */
  79   if((iy|ly)==0) {
  80       switch(m) {
  81     case 0:
  82     case 1: return y;   /* atan(+-0,+anything)=+-0 */
  83     case 2: return  pi+tiny;/* atan(+0,-anything) = pi */
  84     case 3: return -pi-tiny;/* atan(-0,-anything) =-pi */
  85       }
  86   }
  87     /* when x = 0 */
  88   if((ix|lx)==0) return (hy<0)?  -pi_o_2-tiny: pi_o_2+tiny;
  89
  90     /* when x is INF */
  91   if(ix==0x7ff00000) {
  92       if(iy==0x7ff00000) {
  93     switch(m) {
  94         case 0: return  pi_o_4+tiny;/* atan(+INF,+INF) */
  95         case 1: return -pi_o_4-tiny;/* atan(-INF,+INF) */
  96         case 2: return  3.0*pi_o_4+tiny;/*atan(+INF,-INF)*/
  97         case 3: return -3.0*pi_o_4-tiny;/*atan(-INF,-INF)*/
  98     }
  99       } else {
 100     switch(m) {
 101         case 0: return  zero  ; /* atan(+...,+INF) */
 102         case 1: return -zero  ; /* atan(-...,+INF) */
 103         case 2: return  pi+tiny  ;  /* atan(+...,-INF) */
 104         case 3: return -pi-tiny  ;  /* atan(-...,-INF) */
 105     }
 106       }
 107   }
 108     /* when y is INF */
 109   if(iy==0x7ff00000) return (hy<0)? -pi_o_2-tiny: pi_o_2+tiny;
 110
 111     /* compute y/x */
 112   k = (iy-ix)>>20;
 113   if(k > 60) z=pi_o_2+0.5*pi_lo;  /* |y/x| >  2**60 */
 114   else if(hx<0&&k<-60) z=0.0;   /* |y|/x < -2**60 */
 115   else z=atan(fabs(y/x));   /* safe to do y/x */
 116   switch (m) {
 117       case 0: return       z  ; /* atan(+,+) */
 118       case 1: {
 119               u_int32_t zh;
 120           GET_HIGH_WORD(zh,z);
 121           SET_HIGH_WORD(z,zh ^ 0x80000000);
 122         }
 123         return       z  ; /* atan(-,+) */
 124       case 2: return  pi-(z-pi_lo);/* atan(+,-) */
 125       default: /* case 3 */
 126             return  (z-pi_lo)-pi;/* atan(-,-) */
 127   }
 128 }