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/* Compute a product of 1 + (T/X), 1 + (T/(X+1)), ....
Copyright (C) 2015-2024 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 <mul_splitl.h>
/* Compute the product of 1 + (T / (X + X_EPS)), 1 + (T / (X + X_EPS +
1)), ..., 1 + (T / (X + X_EPS + N - 1)), minus 1. 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. */
_Float128
__lgamma_productl (_Float128 t, _Float128 x, _Float128 x_eps, int n)
{
_Float128 ret = 0, ret_eps = 0;
for (int i = 0; i < n; i++)
{
_Float128 xi = x + i;
_Float128 quot = t / xi;
_Float128 mhi, mlo;
mul_splitl (&mhi, &mlo, quot, xi);
_Float128 quot_lo = (t - mhi - mlo) / xi - t * x_eps / (xi * xi);
/* We want (1 + RET + RET_EPS) * (1 + QUOT + QUOT_LO) - 1. */
_Float128 rhi, rlo;
mul_splitl (&rhi, &rlo, ret, quot);
_Float128 rpq = ret + quot;
_Float128 rpq_eps = (ret - rpq) + quot;
_Float128 nret = rpq + rhi;
_Float128 nret_eps = (rpq - nret) + rhi;
ret_eps += (rpq_eps + nret_eps + rlo + ret_eps * quot
+ quot_lo + quot_lo * (ret + ret_eps));
ret = nret;
}
return ret + ret_eps;
}
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