mirror of
git://sourceware.org/git/glibc.git
synced 2024-12-21 04:31:04 +08:00
76 lines
2.5 KiB
C
76 lines
2.5 KiB
C
/* 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 inline void
|
|
mul_split (long double *hi, long double *lo, long double x, long double y)
|
|
{
|
|
#ifdef __FP_FAST_FMAL
|
|
/* Fast built-in fused multiply-add. */
|
|
*hi = x * y;
|
|
*lo = __builtin_fmal (x, y, -*hi);
|
|
#elif defined FP_FAST_FMAL
|
|
/* Fast library fused multiply-add, compiler before GCC 4.6. */
|
|
*hi = x * y;
|
|
*lo = __fmal (x, y, -*hi);
|
|
#else
|
|
/* Apply Dekker's algorithm. */
|
|
*hi = x * y;
|
|
# define C ((1LL << (LDBL_MANT_DIG + 1) / 2) + 1)
|
|
long double x1 = x * C;
|
|
long double y1 = y * C;
|
|
# undef C
|
|
x1 = (x - x1) + x1;
|
|
y1 = (y - y1) + y1;
|
|
long double x2 = x - x1;
|
|
long 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. */
|
|
|
|
long double
|
|
__gamma_productl (long double x, long double x_eps, int n, long double *eps)
|
|
{
|
|
SET_RESTORE_ROUNDL (FE_TONEAREST);
|
|
long double ret = x;
|
|
*eps = x_eps / x;
|
|
for (int i = 1; i < n; i++)
|
|
{
|
|
*eps += x_eps / (x + i);
|
|
long double lo;
|
|
mul_split (&ret, &lo, ret, x + i);
|
|
*eps += lo / ret;
|
|
}
|
|
return ret;
|
|
}
|