mirror of https://gitlab.com/rnger/amath
53 lines
2.0 KiB
C
53 lines
2.0 KiB
C
/*-
|
|
* Copyright (c) 2014-2018 Carsten Sonne Larsen <cs@innolan.net>
|
|
* All rights reserved.
|
|
*
|
|
* Redistribution and use in source and binary forms, with or without
|
|
* modification, are permitted provided that the following conditions
|
|
* are met:
|
|
* 1. Redistributions of source code must retain the above copyright
|
|
* notice, this list of conditions and the following disclaimer.
|
|
* 2. Redistributions in binary form must reproduce the above copyright
|
|
* notice, this list of conditions and the following disclaimer in the
|
|
* documentation and/or other materials provided with the distribution.
|
|
*
|
|
* THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS OR
|
|
* IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES
|
|
* OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED.
|
|
* IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY DIRECT, INDIRECT,
|
|
* INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
|
|
* NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
|
|
* DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
|
|
* THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
|
|
* (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF
|
|
* THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
|
|
*
|
|
* Project homepage:
|
|
* https://amath.innolan.net
|
|
*
|
|
*/
|
|
|
|
#include "prim.h"
|
|
|
|
/**
|
|
* @brief Inverse cotangent of complex number
|
|
* @details
|
|
* Inverse cotangent expressed using complex logarithms:
|
|
* <pre>
|
|
* arccot z = i/2 * (log(1 - i/z) - log(1 + i/z))
|
|
* </pre>
|
|
* More info is available at Wikipedia: <BR>
|
|
* https://wikipedia.org/wiki/Inverse_trigonometric_functions#Logarithmic_forms
|
|
*/
|
|
complex cacot(complex z)
|
|
{
|
|
complex one = cpack(1.0, 0.0);
|
|
complex two = cpack(2.0, 0.0);
|
|
complex i = cpack(0.0, 1.0);
|
|
complex iz = cdiv(i, z);
|
|
complex p = clog(csub(one, iz));
|
|
complex q = clog(cadd(one, iz));
|
|
complex w = cmul(cdiv(i, two), csub(p, q));
|
|
return w;
|
|
}
|