aexs.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  aexs.c
 * @brief Inverse exsecant function
 */

#include "prim.h"

/**
 * @brief   Inverse exsecant function
 * @details
 * <pre>
 * Method
 *     aexsec(x) = arcsec(x+1)
 *               = arccos(1/(x+1))
 *               = arctan(sqrt(x^2+2*X))
 * </pre>
 */
double aexs(double x)
{
    double a, b, c;

    if (x > -2.0 && x < 0.0)
        return NAN;

    a = x * x + 2 * x;
    b = sqrt(a);
    c = atan(b);
    return c;
}