libm/e_atan2.c

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