1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
/*
Copyright (C) 2017 Fredrik Johansson
This file is part of FLINT.
FLINT is free software: you can redistribute it and/or modify it under
the terms of the GNU Lesser General Public License (LGPL) as published
by the Free Software Foundation; either version 3 of the License, or
(at your option) any later version. See <https://www.gnu.org/licenses/>.
*/
#include "acb.h"
void
acb_sech(acb_t res, const acb_t z, slong prec)
{
if (arb_is_zero(acb_imagref(z)))
{
arb_sech(acb_realref(res), acb_realref(z), prec);
arb_zero(acb_imagref(res));
}
else if (arb_is_zero(acb_realref(z)))
{
arb_sec(acb_realref(res), acb_imagref(z), prec);
arb_zero(acb_imagref(res));
}
else
{
if (arf_cmpabs_2exp_si(arb_midref(acb_realref(z)), 0) > 0)
{
acb_t t;
acb_init(t);
if (arf_sgn(arb_midref(acb_realref(z))) > 0)
{
acb_neg(t, z);
acb_exp(t, t, prec + 4);
}
else
{
acb_exp(t, z, prec + 4);
}
acb_mul(res, t, t, prec + 4);
acb_add_ui(res, res, 1, prec + 4);
acb_div(res, t, res, prec);
acb_mul_2exp_si(res, res, 1);
acb_clear(t);
}
else
{
acb_cosh(res, z, prec + 4);
acb_inv(res, res, prec);
}
}
}