aver.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
 * are met:
 * 1. Redistributions of source code must retain the above copyright
 *    notice, this list of conditions and the following disclaimer.
 * 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
 * IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES
 * OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED.
 * IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY DIRECT, INDIRECT,
 * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
 * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
 * DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
 * THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
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 * Project homepage:
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 */

/**
 * @file  aver.c
 * @brief Inverse versed sine function
 */

#include "prim.h"

/**
 * @brief Inverse versed sine function
 */
double aver(double x)
{
    double a, b, c, d;

    if (x < 0.0 || x > 2.0)
    {
        return NAN;
    }

    a = 2.0 * x - x * x;
    b = sqrt(a);
    c = 1.0 - x;

    if (TRIG_INEXACT(c))
    {
        return INFP;
    }

    d = atan(b / c);
    return d;
}