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/* Test of log2*() function family.
Copyright (C) 2012-2014 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;
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