toolchain/gcc/newlib/libm/math/e_atan2.c

   1
   2 /* @(#)e_atan2.c 5.1 93/09/24 */
   3 /*
   4  * ====================================================
   5  * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
   6  *
   7  * Developed at SunPro, a Sun Microsystems, Inc. business.
   8  * Permission to use, copy, modify, and distribute this
   9  * software is freely granted, provided that this notice
  10  * is preserved.
  11  * ====================================================
  12  *
  13  */
  14
  15 /* __ieee754_atan2(y,x)
  16  * Method :
  17  *      1. Reduce y to positive by atan2(y,x)=-atan2(-y,x).
  18  *      2. Reduce x to positive by (if x and y are unexceptional):
  19  *              ARG (x+iy) = arctan(y/x)           ... if x > 0,
  20  *              ARG (x+iy) = pi - arctan[y/(-x)]   ... if x < 0,
  21  *
  22  * Special cases:
  23  *
  24  *      ATAN2((anything), NaN ) is NaN;
  25  *      ATAN2(NAN , (anything) ) is NaN;
  26  *      ATAN2(+-0, +(anything but NaN)) is +-0  ;
  27  *      ATAN2(+-0, -(anything but NaN)) is +-pi ;
  28  *      ATAN2(+-(anything but 0 and NaN), 0) is +-pi/2;
  29  *      ATAN2(+-(anything but INF and NaN), +INF) is +-0 ;
  30  *      ATAN2(+-(anything but INF and NaN), -INF) is +-pi;
  31  *      ATAN2(+-INF,+INF ) is +-pi/4 ;
  32  *      ATAN2(+-INF,-INF ) is +-3pi/4;
  33  *      ATAN2(+-INF, (anything but,0,NaN, and INF)) is +-pi/2;
  34  *
  35  * Constants:
  36  * The hexadecimal values are the intended ones for the following
  37  * constants. The decimal values may be used, provided that the
  38  * compiler will convert from decimal to binary accurately enough
  39  * to produce the hexadecimal values shown.
  40  */
  41
  42 #include "fdlibm.h"
  43
  44 #ifndef _DOUBLE_IS_32BITS
  45
  46 #ifdef __STDC__
  47 static const double
  48 #else
  49 static double
  50 #endif
  51 tiny  = 1.0e-300,
  52 zero  = 0.0,
  53 pi_o_4  = 7.8539816339744827900E-01, /* 0x3FE921FB, 0x54442D18 */
  54 pi_o_2  = 1.5707963267948965580E+00, /* 0x3FF921FB, 0x54442D18 */
  55 pi      = 3.1415926535897931160E+00, /* 0x400921FB, 0x54442D18 */
  56 pi_lo   = 1.2246467991473531772E-16; /* 0x3CA1A626, 0x33145C07 */
  57
  58 #ifdef __STDC__
  59         double __ieee754_atan2(double y, double x)
  60 #else
  61         double __ieee754_atan2(y,x)
  62         double  y,x;
  63 #endif
  64 {
  65         double z;
  66         __int32_t k,m,hx,hy,ix,iy;
  67         __uint32_t lx,ly;
  68
  69         EXTRACT_WORDS(hx,lx,x);
  70         ix = hx&0x7fffffff;
  71         EXTRACT_WORDS(hy,ly,y);
  72         iy = hy&0x7fffffff;
  73         if(((ix|((lx|-lx)>>31))>0x7ff00000)||
  74            ((iy|((ly|-ly)>>31))>0x7ff00000))    /* x or y is NaN */
  75            return x+y;
  76         if((hx-0x3ff00000|lx)==0) return atan(y);   /* x=1.0 */
  77         m = ((hy>>31)&1)|((hx>>30)&2);  /* 2*sign(x)+sign(y) */
  78
  79     /* when y = 0 */
  80         if((iy|ly)==0) {
  81             switch(m) {
  82                 case 0:
  83                 case 1: return y;       /* atan(+-0,+anything)=+-0 */
  84                 case 2: return  pi+tiny;/* atan(+0,-anything) = pi */
  85                 case 3: return -pi-tiny;/* atan(-0,-anything) =-pi */
  86             }
  87         }
  88     /* when x = 0 */
  89         if((ix|lx)==0) return (hy<0)?  -pi_o_2-tiny: pi_o_2+tiny;
  90
  91     /* when x is INF */
  92         if(ix==0x7ff00000) {
  93             if(iy==0x7ff00000) {
  94                 switch(m) {
  95                     case 0: return  pi_o_4+tiny;/* atan(+INF,+INF) */
  96                     case 1: return -pi_o_4-tiny;/* atan(-INF,+INF) */
  97                     case 2: return  3.0*pi_o_4+tiny;/*atan(+INF,-INF)*/
  98                     case 3: return -3.0*pi_o_4-tiny;/*atan(-INF,-INF)*/
  99                 }
 100             } else {
 101                 switch(m) {
 102                     case 0: return  zero  ;     /* atan(+...,+INF) */
 103                     case 1: return -zero  ;     /* atan(-...,+INF) */
 104                     case 2: return  pi+tiny  ;  /* atan(+...,-INF) */
 105                     case 3: return -pi-tiny  ;  /* atan(-...,-INF) */
 106                 }
 107             }
 108         }
 109     /* when y is INF */
 110         if(iy==0x7ff00000) return (hy<0)? -pi_o_2-tiny: pi_o_2+tiny;
 111
 112     /* compute y/x */
 113         k = (iy-ix)>>20;
 114         if(k > 60) z=pi_o_2+0.5*pi_lo;  /* |y/x| >  2**60 */
 115         else if(hx<0&&k<-60) z=0.0;     /* |y|/x < -2**60 */
 116         else z=atan(fabs(y/x));         /* safe to do y/x */
 117         switch (m) {
 118             case 0: return       z  ;   /* atan(+,+) */
 119             case 1: {
 120                       __uint32_t zh;
 121                       GET_HIGH_WORD(zh,z);
 122                       SET_HIGH_WORD(z,zh ^ 0x80000000);
 123                     }
 124                     return       z  ;   /* atan(-,+) */
 125             case 2: return  pi-(z-pi_lo);/* atan(+,-) */
 126             default: /* case 3 */
 127                     return  (z-pi_lo)-pi;/* atan(-,-) */
 128         }
 129 }
 130
 131 #endif /* defined(_DOUBLE_IS_32BITS) */