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/* Test of remainder*() function family.
Copyright (C) 2012-2023 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 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;
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