casinh.c

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

/**
 * @brief  Inverse hyperbolic sine of complex number
 * @details
 * Inverse hyperbolic sine expressed using complex logarithms:
 * <pre>
 * asinh(z) = log(z + sqrt(z*z + 1))
 *
 * With branch cuts: -i INF to -i and i to i INF
 *
 * Domain: -INF to INF
 * Range:  -INF to INF
 * </pre>
 * More info is available at Wikipedia: <BR>
 * https://wikipedia.org/wiki/Inverse_hyperbolic_function#Logarithmic_representation
 */
complex casinh(complex z)
{
    // TODO: Fix branch cuts
    complex one = cpack(1.0, 0.0);
    complex a = cadd(cmul(z, z), one);
    complex b = cadd(z, csqrt(a));
    complex w = clog(b);
    return w;
}