sysdeps/libm-ieee754/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 /* Modified by Naohiko Shimizu/Tokai University, Japan 1997/08/25,
  13    for performance improvement on pipelined processors.
  14 */
  15
  16 #if defined(LIBM_SCCS) && !defined(lint)
  17 static char rcsid[] = "$NetBSD: s_atan.c,v 1.8 1995/05/10 20:46:45 jtc Exp $";
  18 #endif
  19
  20 /* atan(x)
  21  * Method
  22  *   1. Reduce x to positive by atan(x) = -atan(-x).
  23  *   2. According to the integer k=4t+0.25 chopped, t=x, the argument
  24  *      is further reduced to one of the following intervals and the
  25  *      arctangent of t is evaluated by the corresponding formula:
  26  *
  27  *      [0,7/16]      atan(x) = t-t^3*(a1+t^2*(a2+...(a10+t^2*a11)...)
  28  *      [7/16,11/16]  atan(x) = atan(1/2) + atan( (t-0.5)/(1+t/2) )
  29  *      [11/16.19/16] atan(x) = atan( 1 ) + atan( (t-1)/(1+t) )
  30  *      [19/16,39/16] atan(x) = atan(3/2) + atan( (t-1.5)/(1+1.5t) )
  31  *      [39/16,INF]   atan(x) = atan(INF) + atan( -1/t )
  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 #include "math.h"
  41 #include "math_private.h"
  42
  43 #ifdef __STDC__
  44 static const double atanhi[] = {
  45 #else
  46 static double atanhi[] = {
  47 #endif
  48   4.63647609000806093515e-01, /* atan(0.5)hi 0x3FDDAC67, 0x0561BB4F */
  49   7.85398163397448278999e-01, /* atan(1.0)hi 0x3FE921FB, 0x54442D18 */
  50   9.82793723247329054082e-01, /* atan(1.5)hi 0x3FEF730B, 0xD281F69B */
  51   1.57079632679489655800e+00, /* atan(inf)hi 0x3FF921FB, 0x54442D18 */
  52 };
  53
  54 #ifdef __STDC__
  55 static const double atanlo[] = {
  56 #else
  57 static double atanlo[] = {
  58 #endif
  59   2.26987774529616870924e-17, /* atan(0.5)lo 0x3C7A2B7F, 0x222F65E2 */
  60   3.06161699786838301793e-17, /* atan(1.0)lo 0x3C81A626, 0x33145C07 */
  61   1.39033110312309984516e-17, /* atan(1.5)lo 0x3C700788, 0x7AF0CBBD */
  62   6.12323399573676603587e-17, /* atan(inf)lo 0x3C91A626, 0x33145C07 */
  63 };
  64
  65 #ifdef __STDC__
  66 static const double aT[] = {
  67 #else
  68 static double aT[] = {
  69 #endif
  70   3.33333333333329318027e-01, /* 0x3FD55555, 0x5555550D */
  71  -1.99999999998764832476e-01, /* 0xBFC99999, 0x9998EBC4 */
  72   1.42857142725034663711e-01, /* 0x3FC24924, 0x920083FF */
  73  -1.11111104054623557880e-01, /* 0xBFBC71C6, 0xFE231671 */
  74   9.09088713343650656196e-02, /* 0x3FB745CD, 0xC54C206E */
  75  -7.69187620504482999495e-02, /* 0xBFB3B0F2, 0xAF749A6D */
  76   6.66107313738753120669e-02, /* 0x3FB10D66, 0xA0D03D51 */
  77  -5.83357013379057348645e-02, /* 0xBFADDE2D, 0x52DEFD9A */
  78   4.97687799461593236017e-02, /* 0x3FA97B4B, 0x24760DEB */
  79  -3.65315727442169155270e-02, /* 0xBFA2B444, 0x2C6A6C2F */
  80   1.62858201153657823623e-02, /* 0x3F90AD3A, 0xE322DA11 */
  81 };
  82
  83 #ifdef __STDC__
  84         static const double
  85 #else
  86         static double
  87 #endif
  88 one   = 1.0,
  89 huge   = 1.0e300;
  90
  91 #ifdef __STDC__
  92         double __atan(double x)
  93 #else
  94         double __atan(x)
  95         double x;
  96 #endif
  97 {
  98         double w,s1,z,s,w2,w4,s11,s12,s13,s21,s22,s23;
  99         int32_t ix,hx,id;
 100
 101         GET_HIGH_WORD(hx,x);
 102         ix = hx&0x7fffffff;
 103         if(ix>=0x44100000) {    /* if |x| >= 2^66 */
 104             u_int32_t low;
 105             GET_LOW_WORD(low,x);
 106             if(ix>0x7ff00000||
 107                 (ix==0x7ff00000&&(low!=0)))
 108                 return x+x;             /* NaN */
 109             if(hx>0) return  atanhi[3]+atanlo[3];
 110             else     return -atanhi[3]-atanlo[3];
 111         } if (ix < 0x3fdc0000) {        /* |x| < 0.4375 */
 112             if (ix < 0x3e200000) {      /* |x| < 2^-29 */
 113                 if(huge+x>one) return x;        /* raise inexact */
 114             }
 115             id = -1;
 116         } else {
 117         x = fabs(x);
 118         if (ix < 0x3ff30000) {          /* |x| < 1.1875 */
 119             if (ix < 0x3fe60000) {      /* 7/16 <=|x|<11/16 */
 120                 id = 0; x = (2.0*x-one)/(2.0+x);
 121             } else {                    /* 11/16<=|x|< 19/16 */
 122                 id = 1; x  = (x-one)/(x+one);
 123             }
 124         } else {
 125             if (ix < 0x40038000) {      /* |x| < 2.4375 */
 126                 id = 2; x  = (x-1.5)/(one+1.5*x);
 127             } else {                    /* 2.4375 <= |x| < 2^66 */
 128                 id = 3; x  = -1.0/x;
 129             }
 130         }}
 131     /* end of argument reduction */
 132         z = x*x;
 133         w = z*z;
 134     /* break sum from i=0 to 10 aT[i]z**(i+1) into odd and even poly */
 135 #ifdef DO_NOT_USE_THIS
 136         s1 = z*(aT[0]+w*(aT[2]+w*(aT[4]+w*(aT[6]+w*(aT[8]+w*aT[10])))));
 137         s2 = w*(aT[1]+w*(aT[3]+w*(aT[5]+w*(aT[7]+w*aT[9]))));
 138         if (id<0) return x - x*(s1+s2);
 139         else {
 140             z = atanhi[id] - ((x*(s1+s2) - atanlo[id]) - x);
 141             return (hx<0)? -z:z;
 142         }
 143 #else
 144         s11 = aT[8]+w*aT[10]; w2=w*w;
 145         s12 = aT[4]+w*aT[6]; w4=w2*w2;
 146         s13 = aT[0]+w*aT[2];
 147         s21 = aT[7]+w*aT[9];
 148         s22 = aT[3]+w*aT[5];
 149         s23 = w*aT[1];
 150         s1 = s13 + w2*s12 + w4*s11;
 151         s = s23 + w2*s22 + w4*s21 + z*s1;
 152         if (id<0) return x - x*(s);
 153         else {
 154             z = atanhi[id] - ((x*(s) - atanlo[id]) - x);
 155             return (hx<0)? -z:z;
 156         }
 157 #endif
 158 }
 159 weak_alias (__atan, atan)
 160 #ifdef NO_LONG_DOUBLE
 161 strong_alias (__atan, __atanl)
 162 weak_alias (__atan, atanl)
 163 #endif