gonzui

    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: 
   13: /* atan2(y,x)
   14:  * Method :
   15:  *      1. Reduce y to positive by atan2(y,x)=-atan2(-y,x).
   16:  *      2. Reduce x to positive by (if x and y are unexceptional): 
   17:  *              ARG (x+iy) = arctan(y/x)       ... if x > 0,
   18:  *              ARG (x+iy) = pi - arctan[y/(-x)]   ... if x < 0,
   19:  *
   20:  * Special cases:
   21:  *
   22:  *      ATAN2((anything), NaN ) is NaN;
   23:  *      ATAN2(NAN , (anything) ) is NaN;
   24:  *      ATAN2(+-0, +(anything but NaN)) is +-0  ;
   25:  *      ATAN2(+-0, -(anything but NaN)) is +-pi ;
   26:  *      ATAN2(+-(anything but 0 and NaN), 0) is +-pi/2;
   27:  *      ATAN2(+-(anything but INF and NaN), +INF) is +-0 ;
   28:  *      ATAN2(+-(anything but INF and NaN), -INF) is +-pi;
   29:  *      ATAN2(+-INF,+INF ) is +-pi/4 ;
   30:  *      ATAN2(+-INF,-INF ) is +-3pi/4;
   31:  *      ATAN2(+-INF, (anything but,0,NaN, and INF)) is +-pi/2;
   32:  *
   33:  * Constants:
   34:  * The hexadecimal values are the intended ones for the following 
   35:  * constants. The decimal values may be used, provided that the 
   36:  * compiler will convert from decimal to binary accurately enough 
   37:  * to produce the hexadecimal values shown.
   38:  */
   39: 
   40: /* LINTLIBRARY */
   41: 
   42: #include <sys/cdefs.h>
   43: #include <float.h>
   44: #include <math.h>
   45: 
   46: #include "math_private.h"
   47: 
   48: static const double 
   49: tiny  = 1.0e-300,
   50: zero  = 0.0,
   51: pi_o_4  = 7.8539816339744827900E-01, /* 0x3FE921FB, 0x54442D18 */
   52: pi_o_2  = 1.5707963267948965580E+00, /* 0x3FF921FB, 0x54442D18 */
   53: pi      = 3.1415926535897931160E+00, /* 0x400921FB, 0x54442D18 */
   54: pi_lo   = 1.2246467991473531772E-16; /* 0x3CA1A626, 0x33145C07 */
   55: 
   56: double
   57: atan2(double y, double x)
   58: {  
   59:         double z;
   60:         int32_t k,m,hx,hy,ix,iy;
   61:         u_int32_t lx,ly;
   62: 
   63:         EXTRACT_WORDS(hx,lx,x);
   64:         ix = hx&0x7fffffff;
   65:         EXTRACT_WORDS(hy,ly,y);
   66:         iy = hy&0x7fffffff;
   67:         if(((ix|((lx|-lx)>>31))>0x7ff00000)||
   68:            ((iy|((ly|-ly)>>31))>0x7ff00000))   /* x or y is NaN */
   69:            return x+y;
   70:         if(((hx-0x3ff00000)|lx)==0) return atan(y);   /* x=1.0 */
   71:         m = ((hy>>31)&1)|((hx>>30)&2); /* 2*sign(x)+sign(y) */
   72: 
   73:     /* when y = 0 */
   74:         if((iy|ly)==0) {
   75:             switch(m) {
   76:                 case 0: 
   77:                 case 1: return y;     /* atan(+-0,+anything)=+-0 */
   78:                 case 2: return  pi+tiny;/* atan(+0,-anything) = pi */
   79:                 case 3: return -pi-tiny;/* atan(-0,-anything) =-pi */
   80:             }
   81:         }
   82:     /* when x = 0 */
   83:         if((ix|lx)==0) return (hy<0)?  -pi_o_2-tiny: pi_o_2+tiny;
   84:             
   85:     /* when x is INF */
   86:         if(ix==0x7ff00000) {
   87:             if(iy==0x7ff00000) {
   88:                 switch(m) {
   89:                     case 0: return  pi_o_4+tiny;/* atan(+INF,+INF) */
   90:                     case 1: return -pi_o_4-tiny;/* atan(-INF,+INF) */
   91:                     case 2: return  3.0*pi_o_4+tiny;/*atan(+INF,-INF)*/
   92:                     case 3: return -3.0*pi_o_4-tiny;/*atan(-INF,-INF)*/
   93:                 }
   94:             } else {
   95:                 switch(m) {
   96:                     case 0: return  zero  ;   /* atan(+...,+INF) */
   97:                     case 1: return -zero  ;   /* atan(-...,+INF) */
   98:                     case 2: return  pi+tiny  ;        /* atan(+...,-INF) */
   99:                     case 3: return -pi-tiny  ;        /* atan(-...,-INF) */
  100:                 }
  101:             }
  102:         }
  103:     /* when y is INF */
  104:         if(iy==0x7ff00000) return (hy<0)? -pi_o_2-tiny: pi_o_2+tiny;
  105: 
  106:     /* compute y/x */
  107:         k = (iy-ix)>>20;
  108:         if(k > 60) z=pi_o_2+0.5*pi_lo;         /* |y/x| >  2**60 */
  109:         else if(hx<0&&k<-60) z=0.0;    /* |y|/x < -2**60 */
  110:         else z=atan(fabs(y/x));                /* safe to do y/x */
  111:         switch (m) {
  112:             case 0: return       z  ;  /* atan(+,+) */
  113:             case 1: {
  114:                      u_int32_t zh;
  115:                       GET_HIGH_WORD(zh,z);
  116:                       SET_HIGH_WORD(z,zh ^ 0x80000000);
  117:                     }
  118:                     return       z  ; /* atan(-,+) */
  119:             case 2: return  pi-(z-pi_lo);/* atan(+,-) */
  120:             default: /* case 3 */
  121:                    return  (z-pi_lo)-pi;/* atan(-,-) */
  122:         }
  123: }
  124: 
  125: #if     LDBL_MANT_DIG == 53
  126: #ifdef  lint
  127: /* PROTOLIB1 */
  128: long double atan2l(long double, long double);
  129: #else   /* lint */
  130: __weak_alias(atan2l, atan2);
  131: #endif  /* lint */
  132: #endif  /* LDBL_MANT_DIG == 53 */