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d8cd06db | 1 | /* Compute a product of X, X+1, ..., with an error estimate. |
b168057a | 2 | Copyright (C) 2013-2015 Free Software Foundation, Inc. |
d8cd06db JM |
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 (double *hi, double *lo, double x, double y) | |
29 | { | |
30 | #ifdef __FP_FAST_FMA | |
31 | /* Fast built-in fused multiply-add. */ | |
32 | *hi = x * y; | |
33 | *lo = __builtin_fma (x, y, -*hi); | |
34 | #elif defined FP_FAST_FMA | |
35 | /* Fast library fused multiply-add, compiler before GCC 4.6. */ | |
36 | *hi = x * y; | |
37 | *lo = __fma (x, y, -*hi); | |
38 | #else | |
39 | /* Apply Dekker's algorithm. */ | |
40 | *hi = x * y; | |
41 | # define C ((1 << (DBL_MANT_DIG + 1) / 2) + 1) | |
42 | double x1 = x * C; | |
43 | double y1 = y * C; | |
44 | # undef C | |
45 | x1 = (x - x1) + x1; | |
46 | y1 = (y - y1) + y1; | |
47 | double x2 = x - x1; | |
48 | 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 | ||
61 | double | |
62 | __gamma_product (double x, double x_eps, int n, double *eps) | |
63 | { | |
64 | SET_RESTORE_ROUND (FE_TONEAREST); | |
65 | double ret = x; | |
66 | *eps = x_eps / x; | |
67 | for (int i = 1; i < n; i++) | |
68 | { | |
69 | *eps += x_eps / (x + i); | |
70 | double lo; | |
71 | mul_split (&ret, &lo, ret, x + i); | |
72 | *eps += lo / ret; | |
73 | } | |
74 | return ret; | |
75 | } |