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/* Test of exp2*() function family.
Copyright (C) 2012-2020 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 <https://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));
/* Integral arguments. */
{
DOUBLE x = L_(0.0);
DOUBLE y = EXP2 (x);
ASSERT (y == L_(1.0));
}
/* <https://sourceware.org/bugzilla/show_bug.cgi?id=13824> */
#if !(defined __linux__ && (defined __sparc__ || defined __powerpc__))
{
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 = EXP2 (x);
ASSERT (z == y);
}
}
{
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 = EXP2 (x);
ASSERT (z == y);
}
}
#endif
/* 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
<https://lists.gnu.org/r/bug-gnulib/2008-07/msg00063.html>.
The compiler has truncated all 'long double' literals in exp2l.c to
53 bits of precision. */
L_(1350.0)
#else
L_(3.0)
#endif
: L_(3.0));
for (i = 0; i < SIZEOF (RANDOM); i++)
{
DOUBLE x = L_(16.0) * RANDOM[i]; /* 0.0 <= x <= 16.0 */
DOUBLE y = EXP2 (x);
DOUBLE z = EXP2 (- x);
DOUBLE err = y * z - L_(1.0);
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__
L_(2300.0)
#else
L_(29.0)
#endif
: L_(11.0));
for (i = 0; i < SIZEOF (RANDOM) / 5; i++)
for (j = 0; j < SIZEOF (RANDOM) / 5; j++)
{
DOUBLE x = L_(32.0) * RANDOM[i] - L_(16.0); /* -16.0 <= x <= 16.0 */
DOUBLE y = L_(32.0) * RANDOM[j] - L_(16.0); /* -16.0 <= y <= 16.0 */
DOUBLE z = - x - y;
/* Approximately x + y + z = 0. */
DOUBLE err = EXP2 (x) * EXP2 (y) * EXP2 (z) - L_(1.0);
ASSERT (err > - err_bound / TWO_MANT_DIG
&& err < err_bound / TWO_MANT_DIG);
}
}
}
volatile DOUBLE x;
DOUBLE y;
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