83 lines
2.7 KiB
C
83 lines
2.7 KiB
C
/* Compute a product of 1 + (T/X), 1 + (T/(X+1)), ....
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Copyright (C) 2015 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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<http://www.gnu.org/licenses/>. */
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#include <math.h>
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#include <math_private.h>
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#include <float.h>
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/* Calculate X * Y exactly and store the result in *HI + *LO. It is
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given that the values are small enough that no overflow occurs and
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large enough (or zero) that no underflow occurs. */
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static void
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mul_split (double *hi, double *lo, double x, double y)
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{
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#ifdef __FP_FAST_FMA
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/* Fast built-in fused multiply-add. */
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*hi = x * y;
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*lo = __builtin_fma (x, y, -*hi);
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#elif defined FP_FAST_FMA
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/* Fast library fused multiply-add, compiler before GCC 4.6. */
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*hi = x * y;
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*lo = __fma (x, y, -*hi);
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#else
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/* Apply Dekker's algorithm. */
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*hi = x * y;
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# define C ((1 << (DBL_MANT_DIG + 1) / 2) + 1)
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double x1 = x * C;
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double y1 = y * C;
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# undef C
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x1 = (x - x1) + x1;
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y1 = (y - y1) + y1;
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double x2 = x - x1;
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double y2 = y - y1;
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*lo = (((x1 * y1 - *hi) + x1 * y2) + x2 * y1) + x2 * y2;
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#endif
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}
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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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double
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__lgamma_product (double t, double x, double x_eps, int n)
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{
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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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double xi = x + i;
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double quot = t / xi;
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double mhi, mlo;
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mul_split (&mhi, &mlo, quot, xi);
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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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double rhi, rlo;
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mul_split (&rhi, &rlo, ret, quot);
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double rpq = ret + quot;
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double rpq_eps = (ret - rpq) + quot;
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double nret = rpq + rhi;
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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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