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/* Compute a product of X, X+1, ..., with an error estimate.
Copyright (C) 2013-2024 Free Software Foundation, Inc.
This file is part of the GNU C Library.
The GNU C Library is free software; you can redistribute it and/or
modify it under the terms of the GNU Lesser General Public
License as published by the Free Software Foundation; either
version 2.1 of the License, or (at your option) any later version.
The GNU C Library 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
Lesser General Public License for more details.
You should have received a copy of the GNU Lesser General Public
License along with the GNU C Library; if not, see
<https://www.gnu.org/licenses/>. */
#include <math.h>
#include <math_private.h>
#include <fenv_private.h>
#include <mul_split.h>
/* Compute the product of X + X_EPS, X + X_EPS + 1, ..., X + X_EPS + N
- 1, in the form R * (1 + *EPS) where the return value R is an
approximation to the product and *EPS is set to indicate the
approximate error in the return value. X is such that all the
values X + 1, ..., X + N - 1 are exactly representable, and X_EPS /
X is small enough that factors quadratic in it can be
neglected. */
double
__gamma_product (double x, double x_eps, int n, double *eps)
{
SET_RESTORE_ROUND (FE_TONEAREST);
double ret = x;
*eps = x_eps / x;
for (int i = 1; i < n; i++)
{
*eps += x_eps / (x + i);
double lo;
mul_split (&ret, &lo, ret, x + i);
*eps += lo / ret;
}
return ret;
}
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