1 /*
2 Copyright (C) 2013 Fredrik Johansson
3
4 This file is part of Arb.
5
6 Arb is free software: you can redistribute it and/or modify it under
7 the terms of the GNU Lesser General Public License (LGPL) as published
8 by the Free Software Foundation; either version 2.1 of the License, or
9 (at your option) any later version. See <http://www.gnu.org/licenses/>.
10 */
11
12 #include "acb.h"
13
14 void acb_hypgeom_gamma_stirling_choose_param(int * reflect, slong * r, slong * n,
15 const acb_t x, int use_reflect, int digamma, slong prec);
16
17 void acb_gamma_stirling_eval(acb_t s, const acb_t z, slong nterms, int digamma, slong prec);
18
19 void
acb_digamma(acb_t y,const acb_t x,slong prec)20 acb_digamma(acb_t y, const acb_t x, slong prec)
21 {
22 int reflect;
23 slong r, n, wp;
24 acb_t t, u, v;
25
26 if (acb_is_real(x))
27 {
28 arb_digamma(acb_realref(y), acb_realref(x), prec);
29 arb_zero(acb_imagref(y));
30 return;
31 }
32
33 wp = prec + FLINT_BIT_COUNT(prec);
34
35 acb_hypgeom_gamma_stirling_choose_param(&reflect, &r, &n, x, 1, 1, wp);
36
37 acb_init(t);
38 acb_init(u);
39 acb_init(v);
40
41 /* psi(x) = psi((1-x)+r) - h(1-x,r) - pi*cot(pi*x) */
42 if (reflect)
43 {
44 acb_sub_ui(t, x, 1, wp);
45 acb_neg(t, t);
46 acb_cot_pi(v, x, wp);
47 arb_const_pi(acb_realref(u), wp);
48 acb_mul_arb(v, v, acb_realref(u), wp);
49 acb_rising2_ui(y, u, t, r, wp);
50 acb_div(u, u, y, wp);
51 acb_add(v, v, u, wp);
52 acb_add_ui(t, t, r, wp);
53 acb_gamma_stirling_eval(u, t, n, 1, wp);
54 acb_sub(y, u, v, wp);
55 }
56 else
57 {
58 acb_add_ui(t, x, r, wp);
59 acb_gamma_stirling_eval(u, t, n, 1, wp);
60 acb_rising2_ui(y, t, x, r, wp);
61 acb_div(t, t, y, wp);
62 acb_sub(y, u, t, prec);
63 }
64
65 acb_clear(t);
66 acb_clear(u);
67 acb_clear(v);
68 }
69
70