cacot.c

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/*-
 * Copyright (c) 2014-2018 Carsten Sonne Larsen <cs@innolan.net>
 * All rights reserved.
 *
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 * 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 cotangent of complex number
 * @details
 * Inverse cotangent expressed using complex logarithms:
 * <pre>
 * arccot z = i/2 * (log(1 - i/z) - log(1 + i/z))
 * </pre>
 * More info is available at Wikipedia: <BR>
 * https://wikipedia.org/wiki/Inverse_trigonometric_functions#Logarithmic_forms
 */
complex cacot(complex z)
{
    complex one = cpack(1.0, 0.0);
    complex two = cpack(2.0, 0.0);
    complex i = cpack(0.0, 1.0);
    complex iz = cdiv(i, z);
    complex p = clog(csub(one, iz));
    complex q = clog(cadd(one, iz));
    complex w = cmul(cdiv(i, two), csub(p, q));
    return w;
}