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