tests/test-log2.h

   1 /* Test of log2*() function family.
   2    Copyright (C) 2012-2024 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   /* Pole.  */
  33   ASSERT (LOG2 (L_(0.0)) == - HUGEVAL);
  34   ASSERT (LOG2 (MINUS_ZERO) == - HUGEVAL);
  35
  36   /* Integral values.  */
  37   {
  38     DOUBLE x = L_(1.0);
  39     DOUBLE y = LOG2 (x);
  40     ASSERT (y == L_(0.0));
  41   }
  42   {
  43     int e;
  44     DOUBLE x;
  45     DOUBLE y;
  46     for (e = 0, x = L_(0.0), y = L_(1.0);
  47          e <= MAX_EXP - 1;
  48          e++, x = x + L_(1.0), y = y * L_(2.0))
  49       {
  50         /* Invariant: x = e, y = 2^e.  */
  51         DOUBLE z = LOG2 (y);
  52         ASSERT (z == x);
  53       }
  54   }
  55   {
  56     int e;
  57     DOUBLE x;
  58     DOUBLE y;
  59     for (e = 0, x = L_(0.0), y = L_(1.0);
  60          e >= MIN_EXP - 1;
  61          e--, x = x - L_(1.0), y = y * L_(0.5))
  62       {
  63         /* Invariant: x = e, y = 2^e.  */
  64         DOUBLE z = LOG2 (y);
  65         ASSERT (z == x);
  66       }
  67   }
  68
  69   /* Randomized tests.  */
  70   {
  71     /* Error bound, in ulps.  */
  72     const DOUBLE err_bound =
  73       (sizeof (DOUBLE) > sizeof (double) ?
  74 #if defined __i386__ && defined __FreeBSD__
  75        /* On FreeBSD/x86 6.4, the 'long double' type really has only 53 bits of
  76           precision in the compiler but 64 bits of precision at runtime.  See
  77           <https://lists.gnu.org/r/bug-gnulib/2008-07/msg00063.html>.
  78           The compiler has truncated all 'long double' literals in log2l.c to
  79           53 bits of precision.  */
  80        L_(8193.0)
  81 #else
  82        L_(5.0)
  83 #endif
  84        : L_(5.0));
  85
  86     for (i = 0; i < SIZEOF (RANDOM); i++)
  87       {
  88         DOUBLE x = L_(16.0) * RANDOM[i] + L_(1.0); /* 1.0 <= x <= 17.0 */
  89         DOUBLE y = LOG2 (x);
  90         DOUBLE z = LOG2 (L_(1.0) / x);
  91         DOUBLE err = y + z;
  92         ASSERT (y >= L_(0.0));
  93         ASSERT (z <= L_(0.0));
  94         ASSERT (err > - err_bound / TWO_MANT_DIG
  95                 && err < err_bound / TWO_MANT_DIG);
  96       }
  97   }
  98
  99   {
 100     /* Error bound, in ulps.  */
 101     const DOUBLE err_bound =
 102       (sizeof (DOUBLE) > sizeof (double) ?
 103 #if defined __i386__ && defined __FreeBSD__
 104        /* On FreeBSD/x86 6.4, the 'long double' type really has only 53 bits of
 105           precision in the compiler but 64 bits of precision at runtime.  See
 106           <https://lists.gnu.org/r/bug-gnulib/2008-07/msg00063.html>.
 107           The compiler has truncated all 'long double' literals in log2l.c to
 108           53 bits of precision.  */
 109        L_(8193.0)
 110 #else
 111        L_(9.0)
 112 #endif
 113        : L_(9.0));
 114
 115     for (i = 0; i < SIZEOF (RANDOM) / 5; i++)
 116       for (j = 0; j < SIZEOF (RANDOM) / 5; j++)
 117         {
 118           DOUBLE x = L_(17.0) / (L_(16.0) - L_(15.0) * RANDOM[i]) - L_(1.0);
 119           DOUBLE y = L_(17.0) / (L_(16.0) - L_(15.0) * RANDOM[j]) - L_(1.0);
 120           /* 1/16 <= x,y <= 16 */
 121           DOUBLE z = L_(1.0) / (x * y);
 122           /* Approximately  x * y * z = 1.  */
 123           DOUBLE err = LOG2 (x) + LOG2 (y) + LOG2 (z);
 124           ASSERT (err > - err_bound / TWO_MANT_DIG
 125                   && err < err_bound / TWO_MANT_DIG);
 126         }
 127   }
 128 }
 129
 130 volatile DOUBLE x;
 131 DOUBLE y;