--- /dev/null
+/* Test of log2() function.
+ Copyright (C) 2010-2012 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/>. */
+
+/* Written by Bruno Haible <bruno@clisp.org>, 2012. */
+
+#include <config.h>
+
+#include <math.h>
+
+#include "signature.h"
+SIGNATURE_CHECK (log2, double, (double));
+
+#include <float.h>
+
+#include "minus-zero.h"
+#include "macros.h"
+
+#define DOUBLE double
+#define HUGEVAL HUGE_VAL
+#define L_(literal) literal
+#define MANT_DIG DBL_MANT_DIG
+#define MAX_EXP DBL_MAX_EXP
+#define MIN_EXP DBL_MIN_EXP
+#define MINUS_ZERO minus_zerod
+#define LOG2 log2
+#define RANDOM randomd
+#include "test-log2.h"
+
+int
+main ()
+{
+ /* A particular value. */
+ x = 0.6;
+ y = log2 (x);
+ ASSERT (y >= -0.7369655942 && y <= -0.7369655941);
+
+ test_function ();
+
+ return 0;
+}
--- /dev/null
+/* Test of log2*() 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 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));
+
+ /* Pole. */
+ ASSERT (LOG2 (L_(0.0)) == - HUGEVAL);
+ ASSERT (LOG2 (MINUS_ZERO) == - HUGEVAL);
+
+ /* Integral values. */
+ {
+ DOUBLE x = L_(1.0);
+ DOUBLE y = LOG2 (x);
+ ASSERT (y == L_(0.0));
+ }
+ {
+ int e;
+ DOUBLE x;
+ DOUBLE y;
+ for (e = 0, x = L_(0.0), y = L_(1.0);
+ e <= MAX_EXP - 1;
+ e++, x = x + L_(1.0), y = y * L_(2.0))
+ {
+ /* Invariant: x = e, y = 2^e. */
+ DOUBLE z = LOG2 (y);
+ ASSERT (z == x);
+ }
+ }
+ {
+ int e;
+ DOUBLE x;
+ DOUBLE y;
+ for (e = 0, x = L_(0.0), y = L_(1.0);
+ e >= MIN_EXP - 1;
+ e--, x = x - L_(1.0), y = y * L_(0.5))
+ {
+ /* Invariant: x = e, y = 2^e. */
+ DOUBLE z = LOG2 (y);
+ ASSERT (z == x);
+ }
+ }
+
+ /* Randomized tests. */
+ {
+ /* Error bound, in ulps. */
+ const DOUBLE err_bound =
+ (sizeof (DOUBLE) > sizeof (double) ?
+#if defined __i386__ && defined __FreeBSD__
+ /* On FreeBSD/x86 6.4, the 'long double' type really has only 53 bits of
+ precision in the compiler but 64 bits of precision at runtime. See
+ <http://lists.gnu.org/archive/html/bug-gnulib/2008-07/msg00063.html>.
+ The compiler has truncated all 'long double' literals in log2l.c to
+ 53 bits of precision. */
+ L_(8193.0)
+#else
+ L_(5.0)
+#endif
+ : L_(5.0));
+
+ for (i = 0; i < SIZEOF (RANDOM); i++)
+ {
+ DOUBLE x = L_(16.0) * RANDOM[i] + L_(1.0); /* 1.0 <= x <= 17.0 */
+ DOUBLE y = LOG2 (x);
+ DOUBLE z = LOG2 (L_(1.0) / x);
+ DOUBLE err = y + z;
+ ASSERT (y >= L_(0.0));
+ ASSERT (z <= L_(0.0));
+ ASSERT (err > - err_bound / TWO_MANT_DIG
+ && err < err_bound / TWO_MANT_DIG);
+ }
+ }
+
+ {
+ /* Error bound, in ulps. */
+ const DOUBLE err_bound =
+ (sizeof (DOUBLE) > sizeof (double) ?
+#if defined __i386__ && defined __FreeBSD__
+ /* On FreeBSD/x86 6.4, the 'long double' type really has only 53 bits of
+ precision in the compiler but 64 bits of precision at runtime. See
+ <http://lists.gnu.org/archive/html/bug-gnulib/2008-07/msg00063.html>.
+ The compiler has truncated all 'long double' literals in log2l.c to
+ 53 bits of precision. */
+ L_(8193.0)
+#else
+ L_(9.0)
+#endif
+ : L_(9.0));
+
+ for (i = 0; i < SIZEOF (RANDOM) / 5; i++)
+ for (j = 0; j < SIZEOF (RANDOM) / 5; j++)
+ {
+ DOUBLE x = L_(17.0) / (L_(16.0) - L_(15.0) * RANDOM[i]) - L_(1.0);
+ DOUBLE y = L_(17.0) / (L_(16.0) - L_(15.0) * RANDOM[j]) - L_(1.0);
+ /* 1/16 <= x,y <= 16 */
+ DOUBLE z = L_(1.0) / (x * y);
+ /* Approximately x * y * z = 1. */
+ DOUBLE err = LOG2 (x) + LOG2 (y) + LOG2 (z);
+ ASSERT (err > - err_bound / TWO_MANT_DIG
+ && err < err_bound / TWO_MANT_DIG);
+ }
+ }
+}
+
+volatile DOUBLE x;
+DOUBLE y;