gonzui

    1: /* @(#)s_atan.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: /* atan(x)
   14:  * Method
   15:  *   1. Reduce x to positive by atan(x) = -atan(-x).
   16:  *   2. According to the integer k=4t+0.25 chopped, t=x, the argument
   17:  *      is further reduced to one of the following intervals and the
   18:  *      arctangent of t is evaluated by the corresponding formula:
   19:  *
   20:  *      [0,7/16]      atan(x) = t-t^3*(a1+t^2*(a2+...(a10+t^2*a11)...)
   21:  *      [7/16,11/16]  atan(x) = atan(1/2) + atan( (t-0.5)/(1+t/2) )
   22:  *      [11/16.19/16] atan(x) = atan( 1 ) + atan( (t-1)/(1+t) )
   23:  *      [19/16,39/16] atan(x) = atan(3/2) + atan( (t-1.5)/(1+1.5t) )
   24:  *      [39/16,INF]   atan(x) = atan(INF) + atan( -1/t )
   25:  *
   26:  * Constants:
   27:  * The hexadecimal values are the intended ones for the following 
   28:  * constants. The decimal values may be used, provided that the 
   29:  * compiler will convert from decimal to binary accurately enough 
   30:  * to produce the hexadecimal values shown.
   31:  */
   32: 
   33: /* LINTLIBRARY */
   34: 
   35: #include <sys/cdefs.h>
   36: #include <float.h>
   37: #include <math.h>
   38: 
   39: #include "math_private.h"
   40: 
   41: static const double atanhi[] = {
   42:   4.63647609000806093515e-01, /* atan(0.5)hi 0x3FDDAC67, 0x0561BB4F */
   43:   7.85398163397448278999e-01, /* atan(1.0)hi 0x3FE921FB, 0x54442D18 */
   44:   9.82793723247329054082e-01, /* atan(1.5)hi 0x3FEF730B, 0xD281F69B */
   45:   1.57079632679489655800e+00, /* atan(inf)hi 0x3FF921FB, 0x54442D18 */
   46: };
   47: 
   48: static const double atanlo[] = {
   49:   2.26987774529616870924e-17, /* atan(0.5)lo 0x3C7A2B7F, 0x222F65E2 */
   50:   3.06161699786838301793e-17, /* atan(1.0)lo 0x3C81A626, 0x33145C07 */
   51:   1.39033110312309984516e-17, /* atan(1.5)lo 0x3C700788, 0x7AF0CBBD */
   52:   6.12323399573676603587e-17, /* atan(inf)lo 0x3C91A626, 0x33145C07 */
   53: };
   54: 
   55: static const double aT[] = {
   56:   3.33333333333329318027e-01, /* 0x3FD55555, 0x5555550D */
   57:  -1.99999999998764832476e-01, /* 0xBFC99999, 0x9998EBC4 */
   58:   1.42857142725034663711e-01, /* 0x3FC24924, 0x920083FF */
   59:  -1.11111104054623557880e-01, /* 0xBFBC71C6, 0xFE231671 */
   60:   9.09088713343650656196e-02, /* 0x3FB745CD, 0xC54C206E */
   61:  -7.69187620504482999495e-02, /* 0xBFB3B0F2, 0xAF749A6D */
   62:   6.66107313738753120669e-02, /* 0x3FB10D66, 0xA0D03D51 */
   63:  -5.83357013379057348645e-02, /* 0xBFADDE2D, 0x52DEFD9A */
   64:   4.97687799461593236017e-02, /* 0x3FA97B4B, 0x24760DEB */
   65:  -3.65315727442169155270e-02, /* 0xBFA2B444, 0x2C6A6C2F */
   66:   1.62858201153657823623e-02, /* 0x3F90AD3A, 0xE322DA11 */
   67: };
   68: 
   69: static const double 
   70: one   = 1.0,
   71: huge   = 1.0e300;
   72: 
   73: double
   74: atan(double x)
   75: {
   76:         double w,s1,s2,z;
   77:         int32_t ix,hx,id;
   78: 
   79:         GET_HIGH_WORD(hx,x);
   80:         ix = hx&0x7fffffff;
   81:         if(ix>=0x44100000) {   /* if |x| >= 2^66 */
   82:             u_int32_t low;
   83:             GET_LOW_WORD(low,x);
   84:             if(ix>0x7ff00000||
   85:                 (ix==0x7ff00000&&(low!=0)))
   86:                 return x+x;           /* NaN */
   87:             if(hx>0) return  atanhi[3]+atanlo[3];
   88:             else     return -atanhi[3]-atanlo[3];
   89:         } if (ix < 0x3fdc0000) {       /* |x| < 0.4375 */
   90:             if (ix < 0x3e200000) {     /* |x| < 2^-29 */
   91:                 if(huge+x>one) return x;      /* raise inexact */
   92:             }
   93:             id = -1;
   94:         } else {
   95:         x = fabs(x);
   96:         if (ix < 0x3ff30000) {         /* |x| < 1.1875 */
   97:             if (ix < 0x3fe60000) {     /* 7/16 <=|x|<11/16 */
   98:                 id = 0; x = (2.0*x-one)/(2.0+x); 
   99:             } else {                   /* 11/16<=|x|< 19/16 */
  100:                 id = 1; x  = (x-one)/(x+one); 
  101:             }
  102:         } else {
  103:             if (ix < 0x40038000) {     /* |x| < 2.4375 */
  104:                 id = 2; x  = (x-1.5)/(one+1.5*x);
  105:             } else {                   /* 2.4375 <= |x| < 2^66 */
  106:                 id = 3; x  = -1.0/x;
  107:             }
  108:         }}
  109:     /* end of argument reduction */
  110:         z = x*x;
  111:         w = z*z;
  112:     /* break sum from i=0 to 10 aT[i]z**(i+1) into odd and even poly */
  113:         s1 = z*(aT[0]+w*(aT[2]+w*(aT[4]+w*(aT[6]+w*(aT[8]+w*aT[10])))));
  114:         s2 = w*(aT[1]+w*(aT[3]+w*(aT[5]+w*(aT[7]+w*aT[9]))));
  115:         if (id<0) return x - x*(s1+s2);
  116:         else {
  117:             z = atanhi[id] - ((x*(s1+s2) - atanlo[id]) - x);
  118:             return (hx<0)? -z:z;
  119:         }
  120: }
  121: 
  122: #if     LDBL_MANT_DIG == 53
  123: #ifdef  lint
  124: /* PROTOLIB1 */
  125: long double atanl(long double);
  126: #else   /* lint */
  127: __weak_alias(atanl, atan);
  128: #endif  /* lint */
  129: #endif  /* LDBL_MANT_DIG == 53 */