acsch.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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 *
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/**
 * @file  acsch.c
 * @brief Inverse hyperbolic cosecant function
 */

#include "prim.h"

/**
 * @brief   Inverse hyperbolic cosecant function
 * @details
 * <pre>
 * Method
 *                     1+sqrt(1+x*x)
 *     acsch(x) = ln( --------------- )
 *                           x
 *     when x is 0
 *     acsch(x) = NaN
 * </pre>
 */
double acsch(double x)
{
    double a, b, c, d, e, f;

    if (TRIG_INEXACT(x))
    {
        return NAN;
    }

    a = x * x;
    b = a + 1.0;
    c = sqrt(b);
    d = 1.0 + c;
    e = d / x;
    f = log(e);
    return f;
}