Quartic.h

/***************************************************************************
 *   Copyright (C) 2016 by Саша Миленковић                                 *
 *   sasa.milenkovic.xyz@gmail.com                                         *
 *                                                                         *
 *   This program is free software; you can redistribute it and/or modify  *
 *   it under the terms of the GNU General Public License as published by  *
 *   the Free Software Foundation; either version 2 of the License, or     *
 *   (at your option) any later version.                                   *
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 *   but WITHOUT ANY WARRANTY; without even the implied warranty of        *
 *   MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the         *
 *   GNU General Public License for more details.                          *
 *   ( http://www.gnu.org/licenses/gpl-3.0.en.html )                       *
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 *   You should have received a copy of the GNU General Public License     *
 *   along with this program; if not, write to the                         *
 *   Free Software Foundation, Inc.,                                       *
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/*
 * Modified by Gaurav Jalan @HiPeRLab Berkeley
 * Changed function arguments
 * Added new Quartic namespace
 */
 
#ifndef QUARTIC_H_INCLUDED
#define QUARTIC_H_INCLUDED
 
#include <complex>
 
namespace Quartic
{
 
    const double PI = 3.141592653589793238463L;
    const double M_2PI = 2 * PI;
    const double eps = 1e-12;
 
    typedef std::complex<double> DComplex;
 
    //---------------------------------------------------------------------------
    // useful for testing
    inline DComplex polinom_2(DComplex x, double a, double b)
    {
        // Horner's scheme for x*x + a*x + b
        return x * (x + a) + b;
    }
 
    //---------------------------------------------------------------------------
    // useful for testing
    inline DComplex polinom_3(DComplex x, double a, double b, double c)
    {
        // Horner's scheme for x*x*x + a*x*x + b*x + c;
        return x * (x * (x + a) + b) + c;
    }
 
    //---------------------------------------------------------------------------
    // useful for testing
    inline DComplex polinom_4(DComplex x, double a, double b, double c, double d)
    {
        // Horner's scheme for x*x*x*x + a*x*x*x + b*x*x + c*x + d;
        return x * (x * (x * (x + a) + b) + c) + d;
    }
 
    //---------------------------------------------------------------------------
    // x - array of size 3
    // In case 3 real roots: => x[0], x[1], x[2], return 3
    //         2 real roots: x[0], x[1],          return 2
    //         1 real root : x[0], x[1] ± i*x[2], return 1
    unsigned int solveP3(double a, double b, double c, double *x);
 
    //---------------------------------------------------------------------------
    // solve quartic equation x^4 + a*x^3 + b*x^2 + c*x + d
    // Attention - this function returns dynamically allocated array. It has to be released afterwards.
    size_t solve_quartic(const double &a, const double &b, const double &c, const double &d, double root[]);
 
#endif  // QUARTIC_H_INCLUDED
}