1 /*
2     Copyright (C) 2017 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 "arb.h"
13 
14 void
arb_csch(arb_t res,const arb_t x,slong prec)15 arb_csch(arb_t res, const arb_t x, slong prec)
16 {
17     if (arb_contains_zero(x) || !arb_is_finite(x))
18     {
19         arb_indeterminate(res);
20     }
21     else if (arf_cmpabs_2exp_si(arb_midref(x), 0) > 0)
22     {
23         arb_t t;
24         arb_init(t);
25 
26         if (arf_sgn(arb_midref(x)) > 0)
27         {
28             arb_neg(t, x);
29             arb_exp(t, t, prec + 4);
30             arb_mul(res, t, t, prec + 4);
31             arb_sub_ui(res, res, 1, prec + 4);
32             arb_div(res, t, res, prec);
33             arb_neg(res, res);
34         }
35         else
36         {
37             arb_exp(t, x, prec + 4);
38             arb_mul(res, t, t, prec + 4);
39             arb_sub_ui(res, res, 1, prec + 4);
40             arb_div(res, t, res, prec);
41         }
42 
43         arb_mul_2exp_si(res, res, 1);
44         arb_clear(t);
45     }
46     else
47     {
48         arb_sinh(res, x, prec + 4);
49         arb_inv(res, res, prec);
50     }
51 }
52 
53