1 /*
2 Copyright (C) 2015 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_cot_pi(acb_t r,const acb_t z,slong prec)15 acb_cot_pi(acb_t r, const acb_t z, slong prec)
16 {
17 if (arb_is_zero(acb_imagref(z)))
18 {
19 arb_cot_pi(acb_realref(r), acb_realref(z), prec);
20 arb_zero(acb_imagref(r));
21 }
22 else if (arb_is_zero(acb_realref(z)))
23 {
24 arb_t t;
25 arb_init(t);
26 arb_const_pi(t, prec + 4);
27 arb_mul(t, acb_imagref(z), t, prec + 4);
28 arb_coth(acb_imagref(r), t, prec);
29 arb_neg(acb_imagref(r), acb_imagref(r));
30 arb_zero(acb_realref(r));
31 arb_clear(t);
32 }
33 else
34 {
35 acb_t t;
36 acb_init(t);
37
38 if (arf_cmpabs_2exp_si(arb_midref(acb_imagref(z)), 0) < 0)
39 {
40 acb_sin_cos_pi(r, t, z, prec + 4);
41 acb_div(r, t, r, prec);
42 }
43 else
44 {
45 acb_mul_2exp_si(t, z, 1);
46
47 if (arf_sgn(arb_midref(acb_imagref(z))) > 0)
48 {
49 acb_exp_pi_i(t, t, prec + 4);
50 acb_sub_ui(r, t, 1, prec + 4);
51 acb_div(r, t, r, prec + 4);
52 acb_mul_2exp_si(r, r, 1);
53 acb_sub_ui(r, r, 1, prec);
54 acb_mul_onei(r, r);
55 }
56 else
57 {
58 acb_neg(t, t);
59 acb_exp_pi_i(t, t, prec + 4);
60 acb_sub_ui(r, t, 1, prec + 4);
61 acb_div(r, t, r, prec + 4);
62 acb_mul_2exp_si(r, r, 1);
63 acb_sub_ui(r, r, 1, prec);
64 acb_div_onei(r, r);
65 }
66 }
67
68 acb_clear(t);
69 }
70 }
71
72