1/* Compute a product of 1 + (T/X), 1 + (T/(X+1)), ....
2 Copyright (C) 2015-2020 Free Software Foundation, Inc.
3 This file is part of the GNU C Library.
4
5 The GNU C Library is free software; you can redistribute it and/or
6 modify it under the terms of the GNU Lesser General Public
7 License as published by the Free Software Foundation; either
8 version 2.1 of the License, or (at your option) any later version.
9
10 The GNU C Library is distributed in the hope that it will be useful,
11 but WITHOUT ANY WARRANTY; without even the implied warranty of
12 MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
13 Lesser General Public License for more details.
14
15 You should have received a copy of the GNU Lesser General Public
16 License along with the GNU C Library; if not, see
17 <https://www.gnu.org/licenses/>. */
18
19#include <math.h>
20#include <math_private.h>
21#include <mul_splitl.h>
22
23/* Compute the product of 1 + (T / (X + X_EPS)), 1 + (T / (X + X_EPS +
24 1)), ..., 1 + (T / (X + X_EPS + N - 1)), minus 1. X is such that
25 all the values X + 1, ..., X + N - 1 are exactly representable, and
26 X_EPS / X is small enough that factors quadratic in it can be
27 neglected. */
28
29long double
30__lgamma_productl (long double t, long double x, long double x_eps, int n)
31{
32 long double ret = 0, ret_eps = 0;
33 for (int i = 0; i < n; i++)
34 {
35 long double xi = x + i;
36 long double quot = t / xi;
37 long double mhi, mlo;
38 mul_splitl (&mhi, &mlo, quot, xi);
39 long double quot_lo = (t - mhi - mlo) / xi - t * x_eps / (xi * xi);
40 /* We want (1 + RET + RET_EPS) * (1 + QUOT + QUOT_LO) - 1. */
41 long double rhi, rlo;
42 mul_splitl (&rhi, &rlo, ret, quot);
43 long double rpq = ret + quot;
44 long double rpq_eps = (ret - rpq) + quot;
45 long double nret = rpq + rhi;
46 long double nret_eps = (rpq - nret) + rhi;
47 ret_eps += (rpq_eps + nret_eps + rlo + ret_eps * quot
48 + quot_lo + quot_lo * (ret + ret_eps));
49 ret = nret;
50 }
51 return ret + ret_eps;
52}
53