sysdeps/libm-ieee754/e_expf.c

   1 /* Single-precision floating point e^x.
   2    Copyright (C) 1997, 1998 Free Software Foundation, Inc.
   3    This file is part of the GNU C Library.
   4    Contributed by Geoffrey Keating <geoffk@ozemail.com.au>
   5
   6    The GNU C Library is free software; you can redistribute it and/or
   7    modify it under the terms of the GNU Library General Public License as
   8    published by the Free Software Foundation; either version 2 of the
   9    License, or (at your option) any later version.
  10
  11    The GNU C Library is distributed in the hope that it will be useful,
  12    but WITHOUT ANY WARRANTY; without even the implied warranty of
  13    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
  14    Library General Public License for more details.
  15
  16    You should have received a copy of the GNU Library General Public
  17    License along with the GNU C Library; see the file COPYING.LIB.  If not,
  18    write to the Free Software Foundation, Inc., 59 Temple Place - Suite 330,
  19    Boston, MA 02111-1307, USA.  */
  20
  21 /* How this works:
  22
  23    The input value, x, is written as
  24
  25    x = n * ln(2) + t/512 + delta[t] + x;
  26
  27    where:
  28    - n is an integer, 127 >= n >= -150;
  29    - t is an integer, 177 >= t >= -177
  30    - delta is based on a table entry, delta[t] < 2^-28
  31    - x is whatever is left, |x| < 2^-10
  32
  33    Then e^x is approximated as
  34
  35    e^x = 2^n ( e^(t/512 + delta[t])
  36                + ( e^(t/512 + delta[t])
  37                    * ( p(x + delta[t] + n * ln(2)) - delta ) ) )
  38
  39    where
  40    - p(x) is a polynomial approximating e(x)-1;
  41    - e^(t/512 + delta[t]) is obtained from a table.
  42
  43    The table used is the same one as for the double precision version;
  44    since we have the table, we might as well use it.
  45
  46    It turns out to be faster to do calculations in double precision than
  47    to perform an 'accurate table method' expf, because of the range reduction
  48    overhead (compare exp2f).
  49    */
  50 #ifndef _GNU_SOURCE
  51 #define _GNU_SOURCE
  52 #endif
  53 #include <float.h>
  54 #include <ieee754.h>
  55 #include <math.h>
  56 #include <fenv.h>
  57 #include <inttypes.h>
  58 #include <math_private.h>
  59
  60 extern const float __exp_deltatable[178];
  61 extern const double __exp_atable[355] /* __attribute__((mode(DF))) */;
  62
  63 static const volatile float TWOM100 = 7.88860905e-31;
  64 static const volatile float TWO127 = 1.7014118346e+38;
  65
  66 float
  67 __ieee754_expf (float x)
  68 {
  69   static const float himark = 88.72283935546875;
  70   static const float lomark = -103.972084045410;
  71   /* Check for usual case.  */
  72   if (isless (x, himark) && isgreater (x, lomark))
  73     {
  74       static const float THREEp42 = 13194139533312.0;
  75       static const float THREEp22 = 12582912.0;
  76       /* 1/ln(2).  */
  77 #undef M_1_LN2
  78       static const float M_1_LN2 = 1.44269502163f;
  79       /* ln(2) */
  80 #undef M_LN2
  81       static const double M_LN2 = .6931471805599452862;
  82
  83       int tval;
  84       double x22, t, result, dx;
  85       float n, delta;
  86       union ieee754_double ex2_u;
  87       fenv_t oldenv;
  88
  89       feholdexcept (&oldenv);
  90 #ifdef FE_TONEAREST
  91       fesetround (FE_TONEAREST);
  92 #endif
  93
  94       /* Calculate n.  */
  95       n = x * M_1_LN2 + THREEp22;
  96       n -= THREEp22;
  97       dx = x - n*M_LN2;
  98
  99       /* Calculate t/512.  */
 100       t = dx + THREEp42;
 101       t -= THREEp42;
 102       dx -= t;
 103
 104       /* Compute tval = t.  */
 105       tval = (int) (t * 512.0);
 106
 107       if (t >= 0)
 108         delta = - __exp_deltatable[tval];
 109       else
 110         delta = __exp_deltatable[-tval];
 111
 112       /* Compute ex2 = 2^n e^(t/512+delta[t]).  */
 113       ex2_u.d = __exp_atable[tval+177];
 114       ex2_u.ieee.exponent += (int) n;
 115
 116       /* Approximate e^(dx+delta) - 1, using a second-degree polynomial,
 117          with maximum error in [-2^-10-2^-28,2^-10+2^-28]
 118          less than 5e-11.  */
 119       x22 = (0.5000000496709180453 * dx + 1.0000001192102037084) * dx + delta;
 120
 121       /* Return result.  */
 122       fesetenv (&oldenv);
 123
 124       result = x22 * ex2_u.d + ex2_u.d;
 125       return (float) result;
 126     }
 127   /* Exceptional cases:  */
 128   else if (isless (x, himark))
 129     {
 130       if (__isinff (x))
 131         /* e^-inf == 0, with no error.  */
 132         return 0;
 133       else
 134         /* Underflow */
 135         return TWOM100 * TWOM100;
 136     }
 137   else
 138     /* Return x, if x is a NaN or Inf; or overflow, otherwise.  */
 139     return TWO127*x;
 140 }