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_csch(acb_t res,const acb_t z,slong prec)15 acb_csch(acb_t res, const acb_t z, slong prec)
16 {
17 if (acb_contains_zero(z) || !acb_is_finite(z))
18 {
19 acb_indeterminate(res);
20 }
21 else if (arb_is_zero(acb_imagref(z)))
22 {
23 arb_csch(acb_realref(res), acb_realref(z), prec);
24 arb_zero(acb_imagref(res));
25 }
26 else if (arb_is_zero(acb_realref(z)))
27 {
28 arb_csc(acb_imagref(res), acb_imagref(z), prec);
29 arb_neg(acb_imagref(res), acb_imagref(res));
30 arb_zero(acb_realref(res));
31 }
32 else
33 {
34 if (arf_cmpabs_2exp_si(arb_midref(acb_realref(z)), 0) > 0)
35 {
36 acb_t t;
37 acb_init(t);
38
39 if (arf_sgn(arb_midref(acb_realref(z))) > 0)
40 {
41 acb_neg(t, z);
42 acb_exp(t, t, prec + 4);
43 acb_mul(res, t, t, prec + 4);
44 acb_sub_ui(res, res, 1, prec + 4);
45 acb_div(res, t, res, prec);
46 acb_neg(res, res);
47 }
48 else
49 {
50 acb_exp(t, z, prec + 4);
51 acb_mul(res, t, t, prec + 4);
52 acb_sub_ui(res, res, 1, prec + 4);
53 acb_div(res, t, res, prec);
54 }
55
56 acb_mul_2exp_si(res, res, 1);
57 acb_clear(t);
58 }
59 else
60 {
61 acb_sinh(res, z, prec + 4);
62 acb_inv(res, res, prec);
63 }
64 }
65 }
66
67