tests/test-exp.h

   1 /* Test of exp*() function family.
   2    Copyright (C) 2012-2021 Free Software Foundation, Inc.
   3
   4    This program is free software: you can redistribute it and/or modify
   5    it under the terms of the GNU General Public License as published by
   6    the Free Software Foundation; either version 3 of the License, or
   7    (at your option) any later version.
   8
   9    This program is distributed in the hope that it will be useful,
  10    but WITHOUT ANY WARRANTY; without even the implied warranty of
  11    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
  12    GNU General Public License for more details.
  13
  14    You should have received a copy of the GNU General Public License
  15    along with this program.  If not, see <https://www.gnu.org/licenses/>.  */
  16
  17 static void
  18 test_function (void)
  19 {
  20   int i;
  21   int j;
  22   const DOUBLE TWO_MANT_DIG =
  23     /* Assume MANT_DIG <= 5 * 31.
  24        Use the identity
  25          n = floor(n/5) + floor((n+1)/5) + ... + floor((n+4)/5).  */
  26     (DOUBLE) (1U << ((MANT_DIG - 1) / 5))
  27     * (DOUBLE) (1U << ((MANT_DIG - 1 + 1) / 5))
  28     * (DOUBLE) (1U << ((MANT_DIG - 1 + 2) / 5))
  29     * (DOUBLE) (1U << ((MANT_DIG - 1 + 3) / 5))
  30     * (DOUBLE) (1U << ((MANT_DIG - 1 + 4) / 5));
  31
  32   /* Randomized tests.  */
  33   {
  34     /* Error bound, in ulps.  */
  35     const DOUBLE err_bound =
  36       (sizeof (DOUBLE) > sizeof (double) ?
  37 #if defined __i386__ && defined __FreeBSD__
  38        /* On FreeBSD/x86 6.4, the 'long double' type really has only 53 bits of
  39           precision in the compiler but 64 bits of precision at runtime.  See
  40           <https://lists.gnu.org/r/bug-gnulib/2008-07/msg00063.html>.
  41           The compiler has truncated all 'long double' literals in expl.c to
  42           53 bits of precision.  */
  43        L_(1350.0)
  44 #else
  45        L_(4.0)
  46 #endif
  47        : L_(2.0));
  48
  49     for (i = 0; i < SIZEOF (RANDOM); i++)
  50       {
  51         DOUBLE x = L_(16.0) * RANDOM[i]; /* 0.0 <= x <= 16.0 */
  52         DOUBLE y = EXP (x);
  53         DOUBLE z = EXP (- x);
  54         DOUBLE err = y * z - L_(1.0);
  55         ASSERT (y > L_(0.0));
  56         ASSERT (z > L_(0.0));
  57         ASSERT (err > - err_bound / TWO_MANT_DIG
  58                 && err < err_bound / TWO_MANT_DIG);
  59       }
  60   }
  61
  62   {
  63     /* Error bound, in ulps.  */
  64     const DOUBLE err_bound =
  65       (sizeof (DOUBLE) > sizeof (double) ?
  66 #if defined __i386__ && defined __FreeBSD__
  67        L_(2400.0)
  68 #else
  69        L_(24.0)
  70 #endif
  71        : L_(24.0));
  72
  73     for (i = 0; i < SIZEOF (RANDOM) / 5; i++)
  74       for (j = 0; j < SIZEOF (RANDOM) / 5; j++)
  75         {
  76           DOUBLE x = L_(32.0) * RANDOM[i] - L_(16.0); /* -16.0 <= x <= 16.0 */
  77           DOUBLE y = L_(32.0) * RANDOM[j] - L_(16.0); /* -16.0 <= y <= 16.0 */
  78           DOUBLE z = - x - y;
  79           /* Approximately  x + y + z = 0.  */
  80           DOUBLE err = EXP (x) * EXP (y) * EXP (z) - L_(1.0);
  81           ASSERT (err > - err_bound / TWO_MANT_DIG
  82                   && err < err_bound / TWO_MANT_DIG);
  83         }
  84   }
  85 }
  86
  87 volatile DOUBLE x;
  88 DOUBLE y;