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+/* Compute a product of 1 + (T/X), 1 + (T/(X+1)), ....
+ Copyright (C) 2015-2017 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
+ <http://www.gnu.org/licenses/>. */
+
+#include <math.h>
+#include <math_private.h>
+#include <mul_split.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. */
+
+double
+__lgamma_product (double t, double x, double x_eps, int n)
+{
+ double ret = 0, ret_eps = 0;
+ for (int i = 0; i < n; i++)
+ {
+ double xi = x + i;
+ double quot = t / xi;
+ double mhi, mlo;
+ mul_split (&mhi, &mlo, quot, xi);
+ double quot_lo = (t - mhi - mlo) / xi - t * x_eps / (xi * xi);
+ /* We want (1 + RET + RET_EPS) * (1 + QUOT + QUOT_LO) - 1. */
+ double rhi, rlo;
+ mul_split (&rhi, &rlo, ret, quot);
+ double rpq = ret + quot;
+ double rpq_eps = (ret - rpq) + quot;
+ double nret = rpq + rhi;
+ double 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;
+}