csech.c

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/*-
 * 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
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 */

#include "prim.h"

/**
 * @brief  Hyperbolic secant of a complex number
 * @details
 * Calculated as in Open Office:<BR>
 * https://wiki.openoffice.org/wiki/Documentation/How_Tos/Calc:_IMSECH_function
 * <pre>
 * a+bi
 *             2.0 * cosh(a) * cos(b)
 * real  = ------------------------------
 *          cosh(2.0 * a) + cos(2.0 * b)
 *
 *         -2.0 * sinh(2.0 * a) * sin(b)
 * imag  = ------------------------------
 *          cosh(2.0 * a) + cos(2.0 * b)
 * </pre>
 */
complex csech(complex z)
{
    complex w;
    double a, b;
    double d;

    a = creal(z);
    b = cimag(z);
    d = cosh(2.0 * a) + cos(2.0 * b);
    w = cpack((2.0 * cosh(a) * cos(b) / d), (-2.0 * sinh(a) * sin(b) / d));

    return w;
}