casech.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
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 * 2. Redistributions in binary form must reproduce the above copyright
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 *
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#include "prim.h"

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