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.
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.
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.
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/>. */
20 #include <math_private.h>
21 #include <mul_splitl.h>
23 /* Compute the product of 1 + (T / (X + X_EPS)), 1 + (T / (X + X_EPS +
24 1)), ..., 1 + (T / (X + X_EPS + N - 1)), minus 1. X is such that
25 all the values X + 1, ..., X + N - 1 are exactly representable, and
26 X_EPS / X is small enough that factors quadratic in it can be
30 __lgamma_productl (long double t
, long double x
, long double x_eps
, int n
)
32 long double ret
= 0, ret_eps
= 0;
33 for (int i
= 0; i
< n
; i
++)
35 long double xi
= x
+ i
;
36 long double quot
= t
/ xi
;
38 mul_splitl (&mhi
, &mlo
, quot
, xi
);
39 long double quot_lo
= (t
- mhi
- mlo
) / xi
- t
* x_eps
/ (xi
* xi
);
40 /* We want (1 + RET + RET_EPS) * (1 + QUOT + QUOT_LO) - 1. */
42 mul_splitl (&rhi
, &rlo
, ret
, quot
);
43 long double rpq
= ret
+ quot
;
44 long double rpq_eps
= (ret
- rpq
) + quot
;
45 long double nret
= rpq
+ rhi
;
46 long double nret_eps
= (rpq
- nret
) + rhi
;
47 ret_eps
+= (rpq_eps
+ nret_eps
+ rlo
+ ret_eps
* quot
48 + quot_lo
+ quot_lo
* (ret
+ ret_eps
));