| /* Compute a product of 1 + (T/X), 1 + (T/(X+1)), .... |
| Copyright (C) 2015-2018 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; |
| } |
