toolchain/gcc/newlib/libm/math/s_atan.c

   1
   2 /* @(#)s_atan.c 5.1 93/09/24 */
   3 /*
   4  * ====================================================
   5  * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
   6  *
   7  * Developed at SunPro, a Sun Microsystems, Inc. business.
   8  * Permission to use, copy, modify, and distribute this
   9  * software is freely granted, provided that this notice
  10  * is preserved.
  11  * ====================================================
  12  *
  13  */
  14
  15 /*
  16 FUNCTION
  17         <<atan>>, <<atanf>>---arc tangent
  18
  19 INDEX
  20    atan
  21 INDEX
  22    atanf
  23
  24 ANSI_SYNOPSIS
  25         #include <math.h>
  26         double atan(double <[x]>);
  27         float atanf(float <[x]>);
  28
  29 TRAD_SYNOPSIS
  30         #include <math.h>
  31         double atan(<[x]>);
  32         double <[x]>;
  33
  34         float atanf(<[x]>);
  35         float <[x]>;
  36
  37 DESCRIPTION
  38
  39 <<atan>> computes the inverse tangent (arc tangent) of the input value.
  40
  41 <<atanf>> is identical to <<atan>>, save that it operates on <<floats>>.
  42
  43 RETURNS
  44 @ifnottex
  45 <<atan>> returns a value in radians, in the range of -pi/2 to pi/2.
  46 @end ifnottex
  47 @tex
  48 <<atan>> returns a value in radians, in the range of $-\pi/2$ to $\pi/2$.
  49 @end tex
  50
  51 PORTABILITY
  52 <<atan>> is ANSI C.  <<atanf>> is an extension.
  53
  54 */
  55
  56 /* atan(x)
  57  * Method
  58  *   1. Reduce x to positive by atan(x) = -atan(-x).
  59  *   2. According to the integer k=4t+0.25 chopped, t=x, the argument
  60  *      is further reduced to one of the following intervals and the
  61  *      arctangent of t is evaluated by the corresponding formula:
  62  *
  63  *      [0,7/16]      atan(x) = t-t^3*(a1+t^2*(a2+...(a10+t^2*a11)...)
  64  *      [7/16,11/16]  atan(x) = atan(1/2) + atan( (t-0.5)/(1+t/2) )
  65  *      [11/16.19/16] atan(x) = atan( 1 ) + atan( (t-1)/(1+t) )
  66  *      [19/16,39/16] atan(x) = atan(3/2) + atan( (t-1.5)/(1+1.5t) )
  67  *      [39/16,INF]   atan(x) = atan(INF) + atan( -1/t )
  68  *
  69  * Constants:
  70  * The hexadecimal values are the intended ones for the following
  71  * constants. The decimal values may be used, provided that the
  72  * compiler will convert from decimal to binary accurately enough
  73  * to produce the hexadecimal values shown.
  74  */
  75
  76 #include "fdlibm.h"
  77
  78 #ifndef _DOUBLE_IS_32BITS
  79
  80 #ifdef __STDC__
  81 static const double atanhi[] = {
  82 #else
  83 static double atanhi[] = {
  84 #endif
  85   4.63647609000806093515e-01, /* atan(0.5)hi 0x3FDDAC67, 0x0561BB4F */
  86   7.85398163397448278999e-01, /* atan(1.0)hi 0x3FE921FB, 0x54442D18 */
  87   9.82793723247329054082e-01, /* atan(1.5)hi 0x3FEF730B, 0xD281F69B */
  88   1.57079632679489655800e+00, /* atan(inf)hi 0x3FF921FB, 0x54442D18 */
  89 };
  90
  91 #ifdef __STDC__
  92 static const double atanlo[] = {
  93 #else
  94 static double atanlo[] = {
  95 #endif
  96   2.26987774529616870924e-17, /* atan(0.5)lo 0x3C7A2B7F, 0x222F65E2 */
  97   3.06161699786838301793e-17, /* atan(1.0)lo 0x3C81A626, 0x33145C07 */
  98   1.39033110312309984516e-17, /* atan(1.5)lo 0x3C700788, 0x7AF0CBBD */
  99   6.12323399573676603587e-17, /* atan(inf)lo 0x3C91A626, 0x33145C07 */
 100 };
 101
 102 #ifdef __STDC__
 103 static const double aT[] = {
 104 #else
 105 static double aT[] = {
 106 #endif
 107   3.33333333333329318027e-01, /* 0x3FD55555, 0x5555550D */
 108  -1.99999999998764832476e-01, /* 0xBFC99999, 0x9998EBC4 */
 109   1.42857142725034663711e-01, /* 0x3FC24924, 0x920083FF */
 110  -1.11111104054623557880e-01, /* 0xBFBC71C6, 0xFE231671 */
 111   9.09088713343650656196e-02, /* 0x3FB745CD, 0xC54C206E */
 112  -7.69187620504482999495e-02, /* 0xBFB3B0F2, 0xAF749A6D */
 113   6.66107313738753120669e-02, /* 0x3FB10D66, 0xA0D03D51 */
 114  -5.83357013379057348645e-02, /* 0xBFADDE2D, 0x52DEFD9A */
 115   4.97687799461593236017e-02, /* 0x3FA97B4B, 0x24760DEB */
 116  -3.65315727442169155270e-02, /* 0xBFA2B444, 0x2C6A6C2F */
 117   1.62858201153657823623e-02, /* 0x3F90AD3A, 0xE322DA11 */
 118 };
 119
 120 #ifdef __STDC__
 121         static const double
 122 #else
 123         static double
 124 #endif
 125 one   = 1.0,
 126 huge   = 1.0e300;
 127
 128 #ifdef __STDC__
 129         double atan(double x)
 130 #else
 131         double atan(x)
 132         double x;
 133 #endif
 134 {
 135         double w,s1,s2,z;
 136         __int32_t ix,hx,id;
 137
 138         GET_HIGH_WORD(hx,x);
 139         ix = hx&0x7fffffff;
 140         if(ix>=0x44100000) {    /* if |x| >= 2^66 */
 141             __uint32_t low;
 142             GET_LOW_WORD(low,x);
 143             if(ix>0x7ff00000||
 144                 (ix==0x7ff00000&&(low!=0)))
 145                 return x+x;             /* NaN */
 146             if(hx>0) return  atanhi[3]+atanlo[3];
 147             else     return -atanhi[3]-atanlo[3];
 148         } if (ix < 0x3fdc0000) {        /* |x| < 0.4375 */
 149             if (ix < 0x3e200000) {      /* |x| < 2^-29 */
 150                 if(huge+x>one) return x;        /* raise inexact */
 151             }
 152             id = -1;
 153         } else {
 154         x = fabs(x);
 155         if (ix < 0x3ff30000) {          /* |x| < 1.1875 */
 156             if (ix < 0x3fe60000) {      /* 7/16 <=|x|<11/16 */
 157                 id = 0; x = (2.0*x-one)/(2.0+x);
 158             } else {                    /* 11/16<=|x|< 19/16 */
 159                 id = 1; x  = (x-one)/(x+one);
 160             }
 161         } else {
 162             if (ix < 0x40038000) {      /* |x| < 2.4375 */
 163                 id = 2; x  = (x-1.5)/(one+1.5*x);
 164             } else {                    /* 2.4375 <= |x| < 2^66 */
 165                 id = 3; x  = -1.0/x;
 166             }
 167         }}
 168     /* end of argument reduction */
 169         z = x*x;
 170         w = z*z;
 171     /* break sum from i=0 to 10 aT[i]z**(i+1) into odd and even poly */
 172         s1 = z*(aT[0]+w*(aT[2]+w*(aT[4]+w*(aT[6]+w*(aT[8]+w*aT[10])))));
 173         s2 = w*(aT[1]+w*(aT[3]+w*(aT[5]+w*(aT[7]+w*aT[9]))));
 174         if (id<0) return x - x*(s1+s2);
 175         else {
 176             z = atanhi[id] - ((x*(s1+s2) - atanlo[id]) - x);
 177             return (hx<0)? -z:z;
 178         }
 179 }
 180
 181 #endif /* _DOUBLE_IS_32BITS */