1/* Compute a product of 1 + (T/X), 1 + (T/(X+1)), ....
2   Copyright (C) 2015-2018 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   <http://www.gnu.org/licenses/>.  */
18
19#include "quadmath-imp.h"
20
21/* Compute the product of 1 + (T / (X + X_EPS)), 1 + (T / (X + X_EPS +
22   1)), ..., 1 + (T / (X + X_EPS + N - 1)), minus 1.  X is such that
23   all the values X + 1, ..., X + N - 1 are exactly representable, and
24   X_EPS / X is small enough that factors quadratic in it can be
25   neglected.  */
26
27__float128
28__quadmath_lgamma_productq (__float128 t, __float128 x, __float128 x_eps, int n)
29{
30  __float128 ret = 0, ret_eps = 0;
31  for (int i = 0; i < n; i++)
32    {
33      __float128 xi = x + i;
34      __float128 quot = t / xi;
35      __float128 mhi, mlo;
36      mul_splitq (&mhi, &mlo, quot, xi);
37      __float128 quot_lo = (t - mhi - mlo) / xi - t * x_eps / (xi * xi);
38      /* We want (1 + RET + RET_EPS) * (1 + QUOT + QUOT_LO) - 1.  */
39      __float128 rhi, rlo;
40      mul_splitq (&rhi, &rlo, ret, quot);
41      __float128 rpq = ret + quot;
42      __float128 rpq_eps = (ret - rpq) + quot;
43      __float128 nret = rpq + rhi;
44      __float128 nret_eps = (rpq - nret) + rhi;
45      ret_eps += (rpq_eps + nret_eps + rlo + ret_eps * quot
46		  + quot_lo + quot_lo * (ret + ret_eps));
47      ret = nret;
48    }
49  return ret + ret_eps;
50}
51