1/* Compute a product of 1 + (T/X), 1 + (T/(X+1)), ....
2 Copyright (C) 2015-2016 Free Software Foundation, Inc.
3 This file is part of the GNU C Library.
4
5 The GNU C Library is free software; you can redistribute it and/or
6 modify it under the terms of the GNU Lesser General Public
7 License as published by the Free Software Foundation; either
8 version 2.1 of the License, or (at your option) any later version.
9
10 The GNU C Library is distributed in the hope that it will be useful,
11 but WITHOUT ANY WARRANTY; without even the implied warranty of
12 MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
13 Lesser General Public License for more details.
14
15 You should have received a copy of the GNU Lesser General Public
16 License along with the GNU C Library; if not, see
17 <http://www.gnu.org/licenses/>. */
18
19#include <math.h>
20#include <math_private.h>
21#include <float.h>
22
23/* Calculate X * Y exactly and store the result in *HI + *LO. It is
24 given that the values are small enough that no overflow occurs and
25 large enough (or zero) that no underflow occurs. */
26
27static void
28mul_split (long double *hi, long double *lo, long double x, long double y)
29{
30#ifdef __FP_FAST_FMAL
31 /* Fast built-in fused multiply-add. */
32 *hi = x * y;
33 *lo = __builtin_fmal (x, y, -*hi);
34#elif defined FP_FAST_FMAL
35 /* Fast library fused multiply-add, compiler before GCC 4.6. */
36 *hi = x * y;
37 *lo = __fmal (x, y, -*hi);
38#else
39 /* Apply Dekker's algorithm. */
40 *hi = x * y;
41# define C ((1LL << (LDBL_MANT_DIG + 1) / 2) + 1)
42 long double x1 = x * C;
43 long double y1 = y * C;
44# undef C
45 x1 = (x - x1) + x1;
46 y1 = (y - y1) + y1;
47 long double x2 = x - x1;
48 long double y2 = y - y1;
49 *lo = (((x1 * y1 - *hi) + x1 * y2) + x2 * y1) + x2 * y2;
50#endif
51}
52
53/* Compute the product of 1 + (T / (X + X_EPS)), 1 + (T / (X + X_EPS +
54 1)), ..., 1 + (T / (X + X_EPS + N - 1)), minus 1. X is such that
55 all the values X + 1, ..., X + N - 1 are exactly representable, and
56 X_EPS / X is small enough that factors quadratic in it can be
57 neglected. */
58
59long double
60__lgamma_productl (long double t, long double x, long double x_eps, int n)
61{
62 long double ret = 0, ret_eps = 0;
63 for (int i = 0; i < n; i++)
64 {
65 long double xi = x + i;
66 long double quot = t / xi;
67 long double mhi, mlo;
68 mul_split (&mhi, &mlo, quot, xi);
69 long double quot_lo = (t - mhi - mlo) / xi - t * x_eps / (xi * xi);
70 /* We want (1 + RET + RET_EPS) * (1 + QUOT + QUOT_LO) - 1. */
71 long double rhi, rlo;
72 mul_split (&rhi, &rlo, ret, quot);
73 long double rpq = ret + quot;
74 long double rpq_eps = (ret - rpq) + quot;
75 long double nret = rpq + rhi;
76 long double nret_eps = (rpq - nret) + rhi;
77 ret_eps += (rpq_eps + nret_eps + rlo + ret_eps * quot
78 + quot_lo + quot_lo * (ret + ret_eps));
79 ret = nret;
80 }
81 return ret + ret_eps;
82}
83