mirror of https://gitlab.com/rnger/amath
52 lines
2.0 KiB
C
52 lines
2.0 KiB
C
/*-
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* Copyright (c) 2014-2018 Carsten Sonne Larsen <cs@innolan.net>
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* All rights reserved.
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*
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* Redistribution and use in source and binary forms, with or without
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* modification, are permitted provided that the following conditions
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* are met:
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* 1. Redistributions of source code must retain the above copyright
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* notice, this list of conditions and the following disclaimer.
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* 2. Redistributions in binary form must reproduce the above copyright
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* notice, this list of conditions and the following disclaimer in the
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* documentation and/or other materials provided with the distribution.
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*
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* THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS OR
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* IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES
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* OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED.
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* IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY DIRECT, INDIRECT,
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* INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
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* NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
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* DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
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* THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
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* (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF
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* THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
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*
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* Project homepage:
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* https://amath.innolan.net
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*
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*/
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#include "prim.h"
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/**
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* @brief Inverse hyperbolic tangent of complex number
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* @details
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* Inverse hyperbolic tangent expressed using complex logarithms:
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* <pre>
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* atanh(z) = 1/2 * ((log(1 + z) - log(1 - z))
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* </pre>
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* More info is available at Wikipedia: <BR>
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* https://wikipedia.org/wiki/Inverse_hyperbolic_function#Logarithmic_representation
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*/
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complex catanh(complex z)
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{
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complex half = cpack(0.5, 0.0);
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complex one = cpack(1.0, 0.0);
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complex a = clog(cadd(one, z));
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complex b = clog(csub(one, z));
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complex c = csub(a, b);
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complex w = cmul(half, c);
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return w;
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}
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