acoth.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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 *
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/**
 * @file  acoth.c
 * @brief Inverse hyperbolic cotangent function
 */

#include "prim.h"

/**
 * @brief   Inverse hyperbolic cotangent function
 * @details
 * <pre>
 * Method
 *                           x + 1
 *     acoth(x) = 0.5 * ln( ------- )
 *                           x - 1
 *     when x in [-1, 1]
 *     acoth(x) = NaN
 * </pre>
 */
double acoth(double x)
{
    double a, b, c, d;

    if (x <= 1 && x >= -1)
    {
        return NAN;
    }

    a = x + 1.0;
    b = x - 1.0;
    c = a / b;
    d = 0.5 * log(c);
    return d;
}