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76 lines
2.5 KiB
C
76 lines
2.5 KiB
C
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/* Compute a product of X, X+1, ..., with an error estimate.
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Copyright (C) 2013 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 inline void
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mul_split (long double *hi, long double *lo, long double x, long double y)
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{
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#ifdef __FP_FAST_FMAL
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/* Fast built-in fused multiply-add. */
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*hi = x * y;
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*lo = __builtin_fmal (x, y, -*hi);
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#elif defined FP_FAST_FMAL
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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 = __fmal (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 ((1LL << (LDBL_MANT_DIG + 1) / 2) + 1)
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long double x1 = x * C;
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long 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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long double x2 = x - x1;
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long 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 X + X_EPS, X + X_EPS + 1, ..., X + X_EPS + N
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- 1, in the form R * (1 + *EPS) where the return value R is an
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approximation to the product and *EPS is set to indicate the
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approximate error in the return value. X is such that all the
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values X + 1, ..., X + N - 1 are exactly representable, and X_EPS /
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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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__gamma_productl (long double x, long double x_eps, int n, long double *eps)
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{
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SET_RESTORE_ROUNDL (FE_TONEAREST);
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long double ret = x;
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*eps = x_eps / x;
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for (int i = 1; i < n; i++)
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{
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*eps += x_eps / (x + i);
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long double lo;
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mul_split (&ret, &lo, ret, x + i);
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*eps += lo / ret;
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}
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return ret;
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}
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