tests/test-expm1.h

   1 /* Test of expm1*() function family.
   2    Copyright (C) 2012-2020 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   /* Arguments near zero.  */
  33   {
  34     DOUBLE x;
  35
  36     for (i = -1, x = L_(0.5); i >= MIN_EXP; i--, x *= L_(0.5))
  37       {
  38         DOUBLE y;
  39
  40         y = EXPM1 (x);
  41 #ifdef __MINGW32__ /* mingw returns a value that is slightly too small.  */
  42         ASSERT (y >= x * (L_(1.0) - L_(1.0) / TWO_MANT_DIG));
  43 #else
  44         ASSERT (y >= x);
  45 #endif
  46         ASSERT (y < L_(1.5) * x);
  47
  48         y = EXPM1 (- x);
  49         ASSERT (y >= - x);
  50         ASSERT (y < - L_(0.5) * x);
  51       }
  52   }
  53
  54   /* Randomized tests.  */
  55   {
  56     /* Error bound, in ulps.  */
  57     const DOUBLE err_bound =
  58       (sizeof (DOUBLE) > sizeof (double) ?
  59 #if defined __i386__ && defined __FreeBSD__
  60        /* On FreeBSD/x86 6.4, the 'long double' type really has only 53 bits of
  61           precision in the compiler but 64 bits of precision at runtime.  See
  62           <https://lists.gnu.org/r/bug-gnulib/2008-07/msg00063.html>.
  63           The compiler has truncated all 'long double' literals in expl.c to
  64           53 bits of precision.  */
  65        L_(1024.0)
  66 #else
  67        L_(5.0)
  68 #endif
  69        : L_(5.0));
  70
  71     for (i = 0; i < SIZEOF (RANDOM); i++)
  72       {
  73         DOUBLE x = L_(2.0) * RANDOM[i]; /* 0.0 <= x <= 2.0 */
  74         DOUBLE y = EXPM1 (x);
  75         DOUBLE z = EXPM1 (- x);
  76         DOUBLE err = y + (1 + y) * z;
  77         ASSERT (y >= L_(0.0));
  78         ASSERT (z <= L_(0.0));
  79         ASSERT (err > - err_bound / TWO_MANT_DIG
  80                 && err < err_bound / TWO_MANT_DIG);
  81       }
  82   }
  83
  84   {
  85     /* Error bound, in ulps.  */
  86     const DOUBLE err_bound =
  87       (sizeof (DOUBLE) > sizeof (double) ?
  88 #if defined __i386__ && defined __FreeBSD__
  89        L_(1536.0)
  90 #else
  91        L_(11.0)
  92 #endif
  93        : L_(9.0));
  94
  95     for (i = 0; i < SIZEOF (RANDOM) / 5; i++)
  96       for (j = 0; j < SIZEOF (RANDOM) / 5; j++)
  97         {
  98           DOUBLE x = L_(2.0) * RANDOM[i] - L_(1.0); /* -1.0 <= x <= 1.0 */
  99           DOUBLE y = L_(2.0) * RANDOM[j] - L_(1.0); /* -1.0 <= y <= 1.0 */
 100           DOUBLE z = - x - y;
 101           /* Approximately  x + y + z = 0.  */
 102           {
 103             DOUBLE a = EXPM1 (x);
 104             DOUBLE b = EXPM1 (y);
 105             DOUBLE c = EXPM1 (z);
 106             DOUBLE err = a + (1 + a) * (b + (1 + b) * c);
 107             ASSERT (err > - err_bound / TWO_MANT_DIG
 108                     && err < err_bound / TWO_MANT_DIG);
 109           }
 110         }
 111   }
 112 }
 113
 114 volatile DOUBLE x;
 115 DOUBLE y;