1/* Compute a product of X, X+1, ..., with an error estimate.
2 Copyright (C) 2013-2016 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 inline 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 X + X_EPS, X + X_EPS + 1, ..., X + X_EPS + N
54 - 1, in the form R * (1 + *EPS) where the return value R is an
55 approximation to the product and *EPS is set to indicate the
56 approximate error in the return value. X is such that all the
57 values X + 1, ..., X + N - 1 are exactly representable, and X_EPS /
58 X is small enough that factors quadratic in it can be
59 neglected. */
60
61long double
62__gamma_productl (long double x, long double x_eps, int n, long double *eps)
63{
64 SET_RESTORE_ROUNDL (FE_TONEAREST);
65 long double ret = x;
66 *eps = x_eps / x;
67 for (int i = 1; i < n; i++)
68 {
69 *eps += x_eps / (x + i);
70 long double lo;
71 mul_split (&ret, &lo, ret, x + i);
72 *eps += lo / ret;
73 }
74 return ret;
75}
76