cacsch.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 cosecant of complex number
 * @details
 * Inverse hyperbolic cosecant expressed using complex logarithms:
 * <pre>
 * acsch(z) = log(sqrt(1 + 1 / (z * z)) + 1/z)
 * </pre>
 * More info is available at Wikipedia: <BR>
 * https://wikipedia.org/wiki/Inverse_hyperbolic_function#Logarithmic_representation
 */
complex cacsch(complex z)
{
    complex one = cpack(1.0, 0.0);
    complex a = creci(cmul(z, z));
    complex b = csqrt(cadd(one, a));
    complex c = cadd(b, creci(z));
    complex w = clog(c);
    return w;
}