catanh.c

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/*-
 * Copyright (c) 2014-2018 Carsten Sonne Larsen <cs@innolan.net>
 * All rights reserved.
 *
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#include "prim.h"

/**
 * @brief  Inverse hyperbolic tangent of complex number
 * @details
 * Inverse hyperbolic tangent expressed using complex logarithms:
 * <pre>
 * atanh(z) = 1/2 * ((log(1 + z) - log(1 - z))
 * </pre>
 * More info is available at Wikipedia: <BR>
 * https://wikipedia.org/wiki/Inverse_hyperbolic_function#Logarithmic_representation
 */
complex catanh(complex z)
{
    complex half = cpack(0.5, 0.0);
    complex one = cpack(1.0, 0.0);
    complex a = clog(cadd(one, z));
    complex b = clog(csub(one, z));
    complex c = csub(a, b);
    complex w = cmul(half, c);
    return w;
}