| 1 | /* Compute a product of 1 + (T/X), 1 + (T/(X+1)), .... |
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| 2 | Copyright (C) 2015-2022 Free Software Foundation, Inc. |
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| 3 | This file is part of the GNU C Library. |
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| 4 | |
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| 5 | The GNU C Library is free software; you can redistribute it and/or |
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| 6 | modify it under the terms of the GNU Lesser General Public |
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| 7 | License as published by the Free Software Foundation; either |
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| 8 | version 2.1 of the License, or (at your option) any later version. |
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| 9 | |
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| 10 | The GNU C Library is distributed in the hope that it will be useful, |
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| 11 | but WITHOUT ANY WARRANTY; without even the implied warranty of |
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| 12 | MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU |
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| 13 | Lesser General Public License for more details. |
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| 14 | |
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| 15 | You should have received a copy of the GNU Lesser General Public |
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| 16 | License along with the GNU C Library; if not, see |
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| 17 | <https://www.gnu.org/licenses/>. */ |
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| 18 | |
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| 19 | #include <math.h> |
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| 20 | #include <math_private.h> |
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| 21 | #include <mul_split.h> |
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| 22 | |
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| 23 | /* Compute the product of 1 + (T / (X + X_EPS)), 1 + (T / (X + X_EPS + |
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| 24 | 1)), ..., 1 + (T / (X + X_EPS + N - 1)), minus 1. X is such that |
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| 25 | all the values X + 1, ..., X + N - 1 are exactly representable, and |
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| 26 | X_EPS / X is small enough that factors quadratic in it can be |
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| 27 | neglected. */ |
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| 28 | |
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| 29 | double |
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| 30 | __lgamma_product (double t, double x, double x_eps, int n) |
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| 31 | { |
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| 32 | double ret = 0, ret_eps = 0; |
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| 33 | for (int i = 0; i < n; i++) |
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| 34 | { |
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| 35 | double xi = x + i; |
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| 36 | double quot = t / xi; |
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| 37 | double mhi, mlo; |
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| 38 | mul_split (hi: &mhi, lo: &mlo, x: quot, y: xi); |
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| 39 | double quot_lo = (t - mhi - mlo) / xi - t * x_eps / (xi * xi); |
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| 40 | /* We want (1 + RET + RET_EPS) * (1 + QUOT + QUOT_LO) - 1. */ |
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| 41 | double rhi, rlo; |
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| 42 | mul_split (hi: &rhi, lo: &rlo, x: ret, y: quot); |
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| 43 | double rpq = ret + quot; |
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| 44 | double rpq_eps = (ret - rpq) + quot; |
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| 45 | double nret = rpq + rhi; |
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| 46 | double nret_eps = (rpq - nret) + rhi; |
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| 47 | ret_eps += (rpq_eps + nret_eps + rlo + ret_eps * quot |
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| 48 | + quot_lo + quot_lo * (ret + ret_eps)); |
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| 49 | ret = nret; |
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| 50 | } |
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| 51 | return ret + ret_eps; |
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| 52 | } |
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| 53 | |
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