lib/libm/src/s_atan.c

   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 #include <sys/cdefs.h>
  14 #if defined(LIBM_SCCS) && !defined(lint)
  15 __RCSID("$NetBSD: s_atan.c,v 1.11 2002/05/26 22:01:54 wiz Exp $");
  16 #endif
  17
  18 /* atan(x)
  19  * Method
  20  *   1. Reduce x to positive by atan(x) = -atan(-x).
  21  *   2. According to the integer k=4t+0.25 chopped, t=x, the argument
  22  *      is further reduced to one of the following intervals and the
  23  *      arctangent of t is evaluated by the corresponding formula:
  24  *
  25  *      [0,7/16]      atan(x) = t-t^3*(a1+t^2*(a2+...(a10+t^2*a11)...)
  26  *      [7/16,11/16]  atan(x) = atan(1/2) + atan( (t-0.5)/(1+t/2) )
  27  *      [11/16.19/16] atan(x) = atan( 1 ) + atan( (t-1)/(1+t) )
  28  *      [19/16,39/16] atan(x) = atan(3/2) + atan( (t-1.5)/(1+1.5t) )
  29  *      [39/16,INF]   atan(x) = atan(INF) + atan( -1/t )
  30  *
  31  * Constants:
  32  * The hexadecimal values are the intended ones for the following
  33  * constants. The decimal values may be used, provided that the
  34  * compiler will convert from decimal to binary accurately enough
  35  * to produce the hexadecimal values shown.
  36  */
  37
  38 #include "math.h"
  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 }