asech.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
 *    notice, this list of conditions and the following disclaimer in the
 *    documentation and/or other materials provided with the distribution.
 *
 * THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS OR
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 * IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY DIRECT, INDIRECT,
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/**
 * @file  asech.c
 * @brief Inverse hyperbolic secant function
 */

#include "prim.h"

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

    if (TRIG_INEXACT(x) || x < 0.0 || x > 1.0)
    {
        return NAN;
    }

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