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53 lines
2.0 KiB
C
53 lines
2.0 KiB
C
/* Compute a product of 1 + (T/X), 1 + (T/(X+1)), ....
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Copyright (C) 2015-2024 Free Software Foundation, Inc.
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This file is part of the GNU C Library.
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The GNU C Library is free software; you can redistribute it and/or
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modify it under the terms of the GNU Lesser General Public
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License as published by the Free Software Foundation; either
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version 2.1 of the License, or (at your option) any later version.
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The GNU C Library is distributed in the hope that it will be useful,
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but WITHOUT ANY WARRANTY; without even the implied warranty of
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MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
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Lesser General Public License for more details.
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You should have received a copy of the GNU Lesser General Public
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License along with the GNU C Library; if not, see
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<https://www.gnu.org/licenses/>. */
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#include <math.h>
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#include <math_private.h>
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#include <mul_splitl.h>
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/* Compute the product of 1 + (T / (X + X_EPS)), 1 + (T / (X + X_EPS +
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1)), ..., 1 + (T / (X + X_EPS + N - 1)), minus 1. X is such that
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all the values X + 1, ..., X + N - 1 are exactly representable, and
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X_EPS / X is small enough that factors quadratic in it can be
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neglected. */
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long double
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__lgamma_productl (long double t, long double x, long double x_eps, int n)
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{
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long double ret = 0, ret_eps = 0;
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for (int i = 0; i < n; i++)
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{
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long double xi = x + i;
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long double quot = t / xi;
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long double mhi, mlo;
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mul_splitl (&mhi, &mlo, quot, xi);
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long double quot_lo = (t - mhi - mlo) / xi - t * x_eps / (xi * xi);
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/* We want (1 + RET + RET_EPS) * (1 + QUOT + QUOT_LO) - 1. */
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long double rhi, rlo;
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mul_splitl (&rhi, &rlo, ret, quot);
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long double rpq = ret + quot;
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long double rpq_eps = (ret - rpq) + quot;
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long double nret = rpq + rhi;
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long double nret_eps = (rpq - nret) + rhi;
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ret_eps += (rpq_eps + nret_eps + rlo + ret_eps * quot
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+ quot_lo + quot_lo * (ret + ret_eps));
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ret = nret;
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}
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return ret + ret_eps;
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}
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