tests/test-fmod.h

   1 /* Test of fmod*() 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 DOUBLE
  18 my_ldexp (DOUBLE x, int d)
  19 {
  20   for (; d > 0; d--)
  21     x *= L_(2.0);
  22   for (; d < 0; d++)
  23     x *= L_(0.5);
  24   return x;
  25 }
  26
  27 static void
  28 test_function (void)
  29 {
  30   int i;
  31   int j;
  32   const DOUBLE TWO_MANT_DIG =
  33     /* Assume MANT_DIG <= 5 * 31.
  34        Use the identity
  35          n = floor(n/5) + floor((n+1)/5) + ... + floor((n+4)/5).  */
  36     (DOUBLE) (1U << ((MANT_DIG - 1) / 5))
  37     * (DOUBLE) (1U << ((MANT_DIG - 1 + 1) / 5))
  38     * (DOUBLE) (1U << ((MANT_DIG - 1 + 2) / 5))
  39     * (DOUBLE) (1U << ((MANT_DIG - 1 + 3) / 5))
  40     * (DOUBLE) (1U << ((MANT_DIG - 1 + 4) / 5));
  41
  42   /* Randomized tests.  */
  43   for (i = 0; i < SIZEOF (RANDOM) / 5; i++)
  44     for (j = 0; j < SIZEOF (RANDOM) / 5; j++)
  45       {
  46         DOUBLE x = L_(16.0) * RANDOM[i]; /* 0.0 <= x <= 16.0 */
  47         DOUBLE y = RANDOM[j]; /* 0.0 <= y < 1.0 */
  48         if (y > L_(0.0))
  49           {
  50             DOUBLE z = FMOD (x, y);
  51             ASSERT (z >= L_(0.0));
  52             ASSERT (z < y);
  53             z -= x - (int) (x / y) * y;
  54             ASSERT (/* The common case.  */
  55                     (z > - L_(16.0) / TWO_MANT_DIG
  56                      && z < L_(16.0) / TWO_MANT_DIG)
  57                     || /* rounding error: x / y computed too large */
  58                        (z > y - L_(16.0) / TWO_MANT_DIG
  59                         && z < y + L_(16.0) / TWO_MANT_DIG)
  60                     || /* rounding error: x / y computed too small */
  61                        (z > - y - L_(16.0) / TWO_MANT_DIG
  62                         && z < - y + L_(16.0) / TWO_MANT_DIG));
  63           }
  64       }
  65
  66   for (i = 0; i < SIZEOF (RANDOM) / 5; i++)
  67     for (j = 0; j < SIZEOF (RANDOM) / 5; j++)
  68       {
  69         DOUBLE x = L_(1.0e9) * RANDOM[i]; /* 0.0 <= x <= 10^9 */
  70         DOUBLE y = RANDOM[j]; /* 0.0 <= y < 1.0 */
  71         if (y > L_(0.0))
  72           {
  73             DOUBLE z = FMOD (x, y);
  74             DOUBLE r;
  75             ASSERT (z >= L_(0.0));
  76             ASSERT (z < y);
  77             {
  78               /* Determine the quotient x / y in two steps, because it
  79                  may be > 2^31.  */
  80               int q1 = (int) (x / y / L_(65536.0));
  81               int q2 = (int) ((x - q1 * L_(65536.0) * y) / y);
  82               DOUBLE q = (DOUBLE) q1 * L_(65536.0) + (DOUBLE) q2;
  83               r = x - q * y;
  84             }
  85             /* The absolute error of z can be up to 1e9/2^MANT_DIG.
  86                The absolute error of r can also be up to 1e9/2^MANT_DIG.
  87                Therefore the error of z - r can be twice as large.  */
  88             z -= r;
  89             ASSERT (/* The common case.  */
  90                     (z > - L_(2.0) * L_(1.0e9) / TWO_MANT_DIG
  91                      && z < L_(2.0) * L_(1.0e9) / TWO_MANT_DIG)
  92                     || /* rounding error: x / y computed too large */
  93                        (z > y - L_(2.0) * L_(1.0e9) / TWO_MANT_DIG
  94                         && z < y + L_(2.0) * L_(1.0e9) / TWO_MANT_DIG)
  95                     || /* rounding error: x / y computed too small */
  96                        (z > - y - L_(2.0) * L_(1.0e9) / TWO_MANT_DIG
  97                         && z < - y + L_(2.0) * L_(1.0e9) / TWO_MANT_DIG));
  98           }
  99       }
 100
 101   {
 102     int large_exp = (MAX_EXP - 1 < 1000 ? MAX_EXP - 1 : 1000);
 103     DOUBLE large = my_ldexp (L_(1.0), large_exp); /* = 2^large_exp */
 104     for (i = 0; i < SIZEOF (RANDOM) / 10; i++)
 105       for (j = 0; j < SIZEOF (RANDOM) / 10; j++)
 106         {
 107           DOUBLE x = large * RANDOM[i]; /* 0.0 <= x <= 2^large_exp */
 108           DOUBLE y = RANDOM[j]; /* 0.0 <= y < 1.0 */
 109           if (y > L_(0.0))
 110             {
 111               DOUBLE z = FMOD (x, y);
 112               /* Regardless how large the rounding errors are, the result
 113                  must be >= 0, < y.  */
 114               ASSERT (z >= L_(0.0));
 115               ASSERT (z < y);
 116             }
 117         }
 118   }
 119 }
 120
 121 volatile DOUBLE x;
 122 volatile DOUBLE y;
 123 DOUBLE z;