remainder* tests: More tests.

[gnulib.git] / tests / test-remainder.h

diff --git a/tests/test-remainder.h b/tests/test-remainder.h
new file mode 100644 (file)
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--- /dev/null
+++ b/tests/test-remainder.h
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+/* Test of remainder*() function family.
+   Copyright (C) 2012 Free Software Foundation, Inc.
+
+   This program is free software: you can redistribute it and/or modify
+   it under the terms of the GNU General Public License as published by
+   the Free Software Foundation; either version 3 of the License, or
+   (at your option) any later version.
+
+   This program is distributed in the hope that it will be useful,
+   but WITHOUT ANY WARRANTY; without even the implied warranty of
+   MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+   GNU General Public License for more details.
+
+   You should have received a copy of the GNU General Public License
+   along with this program.  If not, see <http://www.gnu.org/licenses/>.  */
+
+static DOUBLE
+my_ldexp (DOUBLE x, int d)
+{
+  for (; d > 0; d--)
+    x *= L_(2.0);
+  for (; d < 0; d++)
+    x *= L_(0.5);
+  return x;
+}
+
+static void
+test_function (void)
+{
+  int i;
+  int j;
+  const DOUBLE TWO_MANT_DIG =
+    /* Assume MANT_DIG <= 5 * 31.
+       Use the identity
+         n = floor(n/5) + floor((n+1)/5) + ... + floor((n+4)/5).  */
+    (DOUBLE) (1U << ((MANT_DIG - 1) / 5))
+    * (DOUBLE) (1U << ((MANT_DIG - 1 + 1) / 5))
+    * (DOUBLE) (1U << ((MANT_DIG - 1 + 2) / 5))
+    * (DOUBLE) (1U << ((MANT_DIG - 1 + 3) / 5))
+    * (DOUBLE) (1U << ((MANT_DIG - 1 + 4) / 5));
+
+  /* Randomized tests.  */
+  for (i = 0; i < SIZEOF (RANDOM) / 5; i++)
+    for (j = 0; j < SIZEOF (RANDOM) / 5; j++)
+      {
+        DOUBLE x = L_(16.0) * RANDOM[i]; /* 0.0 <= x <= 16.0 */
+        DOUBLE y = RANDOM[j]; /* 0.0 <= y < 1.0 */
+        if (y > L_(0.0))
+          {
+            DOUBLE z = REMAINDER (x, y);
+            ASSERT (z >= - L_(0.5) * y);
+            ASSERT (z <= L_(0.5) * y);
+            z -= x - (int) ((L_(2.0) * x + y) / (L_(2.0) * y)) * y;
+            ASSERT (/* The common case.  */
+                    (z > - L_(2.0) * L_(16.0) / TWO_MANT_DIG
+                     && z < L_(2.0) * L_(16.0) / TWO_MANT_DIG)
+                    || /* rounding error: 2x+y / 2y computed too large */
+                       (z > y - L_(2.0) * L_(16.0) / TWO_MANT_DIG
+                        && z < y + L_(2.0) * L_(16.0) / TWO_MANT_DIG)
+                    || /* rounding error: 2x+y / 2y computed too small */
+                       (z > - y - L_(2.0) * L_(16.0) / TWO_MANT_DIG
+                        && z < - y + L_(2.0) * L_(16.0) / TWO_MANT_DIG));
+          }
+      }
+
+  for (i = 0; i < SIZEOF (RANDOM) / 5; i++)
+    for (j = 0; j < SIZEOF (RANDOM) / 5; j++)
+      {
+        DOUBLE x = L_(1.0e9) * RANDOM[i]; /* 0.0 <= x <= 10^9 */
+        DOUBLE y = RANDOM[j]; /* 0.0 <= y < 1.0 */
+        if (y > L_(0.0))
+          {
+            DOUBLE z = REMAINDER (x, y);
+            DOUBLE r;
+            ASSERT (z >= - L_(0.5) * y);
+            ASSERT (z <= L_(0.5) * y);
+            {
+              /* Determine the quotient 2x+y / 2y in two steps, because it
+                 may be > 2^31.  */
+              int q1 = (int) (x / y / L_(65536.0));
+              int q2 = (int) ((L_(2.0) * (x - q1 * L_(65536.0) * y) + y)
+                              / (L_(2.0) * y));
+              DOUBLE q = (DOUBLE) q1 * L_(65536.0) + (DOUBLE) q2;
+              r = x - q * y;
+            }
+            /* The absolute error of z can be up to 1e9/2^MANT_DIG.
+               The absolute error of r can also be up to 1e9/2^MANT_DIG.
+               Therefore the error of z - r can be twice as large.  */
+            z -= r;
+            ASSERT (/* The common case.  */
+                    (z > - L_(2.0) * L_(1.0e9) / TWO_MANT_DIG
+                     && z < L_(2.0) * L_(1.0e9) / TWO_MANT_DIG)
+                    || /* rounding error: 2x+y / 2y computed too large */
+                       (z > y - L_(2.0) * L_(1.0e9) / TWO_MANT_DIG
+                        && z < y + L_(2.0) * L_(1.0e9) / TWO_MANT_DIG)
+                    || /* rounding error: 2x+y / 2y computed too small */
+                       (z > - y - L_(2.0) * L_(1.0e9) / TWO_MANT_DIG
+                        && z < - y + L_(2.0) * L_(1.0e9) / TWO_MANT_DIG));
+          }
+      }
+
+  {
+    int large_exp = (MAX_EXP - 1 < 1000 ? MAX_EXP - 1 : 1000);
+    DOUBLE large = my_ldexp (L_(1.0), large_exp); /* = 2^large_exp */
+    for (i = 0; i < SIZEOF (RANDOM) / 10; i++)
+      for (j = 0; j < SIZEOF (RANDOM) / 10; j++)
+        {
+          DOUBLE x = large * RANDOM[i]; /* 0.0 <= x <= 2^large_exp */
+          DOUBLE y = RANDOM[j]; /* 0.0 <= y < 1.0 */
+          if (y > L_(0.0))
+            {
+              DOUBLE z = REMAINDER (x, y);
+              /* Regardless how large the rounding errors are, the result
+                 must be >= -y/2, <= y/2.  */
+              ASSERT (z >= - L_(0.5) * y);
+              ASSERT (z <= L_(0.5) * y);
+            }
+        }
+  }
+}
+
+volatile DOUBLE x;
+volatile DOUBLE y;
+DOUBLE z;