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4239f144 JM |
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 | } |