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/* Compute a product of X, X+1, ..., with an error estimate.
Copyright (C) 2013 Free Software Foundation, Inc.
This file is part of the GNU C Library.
The GNU C Library is free software; you can redistribute it and/or
modify it under the terms of the GNU Lesser General Public
License as published by the Free Software Foundation; either
version 2.1 of the License, or (at your option) any later version.
The GNU C Library is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
Lesser General Public License for more details.
You should have received a copy of the GNU Lesser General Public
License along with the GNU C Library; if not, see
<http://www.gnu.org/licenses/>. */
#include <math.h>
#include <math_private.h>
#include <float.h>
/* Calculate X * Y exactly and store the result in *HI + *LO. It is
given that the values are small enough that no overflow occurs and
large enough (or zero) that no underflow occurs. */
static void
mul_split (double *hi, double *lo, double x, double y)
{
#ifdef __FP_FAST_FMA
/* Fast built-in fused multiply-add. */
*hi = x * y;
*lo = __builtin_fma (x, y, -*hi);
#elif defined FP_FAST_FMA
/* Fast library fused multiply-add, compiler before GCC 4.6. */
*hi = x * y;
*lo = __fma (x, y, -*hi);
#else
/* Apply Dekker's algorithm. */
*hi = x * y;
# define C ((1 << (DBL_MANT_DIG + 1) / 2) + 1)
double x1 = x * C;
double y1 = y * C;
# undef C
x1 = (x - x1) + x1;
y1 = (y - y1) + y1;
double x2 = x - x1;
double y2 = y - y1;
*lo = (((x1 * y1 - *hi) + x1 * y2) + x2 * y1) + x2 * y2;
#endif
}
/* Compute the product of X + X_EPS, X + X_EPS + 1, ..., X + X_EPS + N
- 1, in the form R * (1 + *EPS) where the return value R is an
approximation to the product and *EPS is set to indicate the
approximate error in the return value. X is such that all the
values X + 1, ..., X + N - 1 are exactly representable, and X_EPS /
X is small enough that factors quadratic in it can be
neglected. */
double
__gamma_product (double x, double x_eps, int n, double *eps)
{
SET_RESTORE_ROUND (FE_TONEAREST);
double ret = x;
*eps = x_eps / x;
for (int i = 1; i < n; i++)
{
*eps += x_eps / (x + i);
double lo;
mul_split (&ret, &lo, ret, x + i);
*eps += lo / ret;
}
return ret;
}
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