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 | |
27 | static void |
28 | mul_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 | |
59 | long 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 | |