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/* Test of expm1*() 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));
/* Arguments near zero. */
{
DOUBLE x;
for (i = -1, x = L_(0.5); i >= MIN_EXP; i--, x *= L_(0.5))
{
DOUBLE y;
y = EXPM1 (x);
#ifdef __MINGW32__ /* mingw returns a value that is slightly too small. */
ASSERT (y >= x * (L_(1.0) - L_(1.0) / TWO_MANT_DIG));
#else
ASSERT (y >= x);
#endif
ASSERT (y < L_(1.5) * x);
y = EXPM1 (- x);
ASSERT (y >= - x);
ASSERT (y < - L_(0.5) * 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
<https://lists.gnu.org/r/bug-gnulib/2008-07/msg00063.html>.
The compiler has truncated all 'long double' literals in expl.c to
53 bits of precision. */
L_(1024.0)
#else
L_(5.0)
#endif
: L_(5.0));
for (i = 0; i < SIZEOF (RANDOM); i++)
{
DOUBLE x = L_(2.0) * RANDOM[i]; /* 0.0 <= x <= 2.0 */
DOUBLE y = EXPM1 (x);
DOUBLE z = EXPM1 (- x);
DOUBLE err = y + (1 + 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__
L_(1536.0)
#else
L_(11.0)
#endif
: L_(9.0));
for (i = 0; i < SIZEOF (RANDOM) / 5; i++)
for (j = 0; j < SIZEOF (RANDOM) / 5; j++)
{
DOUBLE x = L_(2.0) * RANDOM[i] - L_(1.0); /* -1.0 <= x <= 1.0 */
DOUBLE y = L_(2.0) * RANDOM[j] - L_(1.0); /* -1.0 <= y <= 1.0 */
DOUBLE z = - x - y;
/* Approximately x + y + z = 0. */
{
DOUBLE a = EXPM1 (x);
DOUBLE b = EXPM1 (y);
DOUBLE c = EXPM1 (z);
DOUBLE err = a + (1 + a) * (b + (1 + b) * c);
ASSERT (err > - err_bound / TWO_MANT_DIG
&& err < err_bound / TWO_MANT_DIG);
}
}
}
}
volatile DOUBLE x;
DOUBLE y;
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