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/* Compute a product of 1 + (T/X), 1 + (T/(X+1)), ....
Copyright (C) 2015 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 1 + (T / (X + X_EPS)), 1 + (T / (X + X_EPS +
1)), ..., 1 + (T / (X + X_EPS + N - 1)), minus 1. 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
__lgamma_product (double t, double x, double x_eps, int n)
{
double ret = 0, ret_eps = 0;
for (int i = 0; i < n; i++)
{
double xi = x + i;
double quot = t / xi;
double mhi, mlo;
mul_split (&mhi, &mlo, quot, xi);
double quot_lo = (t - mhi - mlo) / xi - t * x_eps / (xi * xi);
/* We want (1 + RET + RET_EPS) * (1 + QUOT + QUOT_LO) - 1. */
double rhi, rlo;
mul_split (&rhi, &rlo, ret, quot);
double rpq = ret + quot;
double rpq_eps = (ret - rpq) + quot;
double nret = rpq + rhi;
double nret_eps = (rpq - nret) + rhi;
ret_eps += (rpq_eps + nret_eps + rlo + ret_eps * quot
+ quot_lo + quot_lo * (ret + ret_eps));
ret = nret;
}
return ret + ret_eps;
}
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