1 /*-
2 * Copyright (c) 2014-2018 Carsten Sonne Larsen <cs@innolan.net>
3 * All rights reserved.
4 *
5 * Redistribution and use in source and binary forms, with or without
6 * modification, are permitted provided that the following conditions
7 * are met:
8 * 1. Redistributions of source code must retain the above copyright
9 * notice, this list of conditions and the following disclaimer.
10 * 2. Redistributions in binary form must reproduce the above copyright
11 * notice, this list of conditions and the following disclaimer in the
12 * documentation and/or other materials provided with the distribution.
13 *
14 * THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS OR
15 * IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES
16 * OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED.
17 * IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY DIRECT, INDIRECT,
18 * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
19 * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
20 * DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
21 * THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
22 * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF
23 * THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
24 *
25 * Project homepage:
26 * https://amath.innolan.net
27 *
28 */
29
30 #include "prim.h"
31
32 /**
33 * @brief Inverse secant expressed using complex logarithms:
34 * @details
35 * Inverse secant expressed using complex logarithms:
36 * <pre>
37 * arcsec z = -i * log(i * sqr(1 - 1/(z*z)) + 1/z)
38 * </pre>
39 * More info is available at Wikipedia: <BR>
40 * https://wikipedia.org/wiki/Inverse_trigonometric_functions#Logarithmic_forms
41 */
casec(complex z)42 complex casec(complex z)
43 {
44 complex one = cpack(1.0, 0.0);
45 complex i = cpack(0.0, 1.0);
46 complex j = cpack(0.0, -1.0);
47 complex rz = creci(z);
48 complex z2 = cmul(z, z);
49 complex p = cdiv(one, z2);
50 complex q = csqrt(csub(one, p));
51 complex w = cmul(j, clog(cadd(cmul(i, q), rz)));
52 return w;
53 }
54