Saf/Math/Algebra/Number.h

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/*
    This file is part of Simple Application Framework (Saf) library.
    Copyright (C) 2010 - 2012 Ondrej Danek <ondrej.danek@gmail.com>

    This library 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 3 of the License, or
    (at your option) any later version.

    Saf is distributed in the hope that it will be useful,
    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.

    You should have received a copy of the GNU General Public License
    along with Simple Application Framework library. If not, 
    see <http://www.gnu.org/licenses/>.
*/

#ifndef SAF_MATH_ALGEBRA_NUMBER_H
#define SAF_MATH_ALGEBRA_NUMBER_H

#include "../../Type.h"
#include "../Basic.h"
#include "../../Type/IteratorTraits.h"

namespace Saf
{
    namespace Math
    {
        namespace Algebra
        {
            template <class T>
            T Gcd(T a, T b)
            {
                a = Abs(a);
                b = Abs(b);

                while (b != 0)
                {
                    T t = b;
                    b = a % b;
                    a = t;
                }

                return a;
            }

            template <class T>
            T Gcd(T a, T b, T c)
            {
                return Gcd(a, Gcd(b,c));
            }

            template <class FwdIter>
            typename Type::IteratorTraits<FwdIter>::ValType Gcd(FwdIter begin, FwdIter end)
            {
                typename Type::IteratorTraits<FwdIter>::ValType t = 0;

                while (begin != end)
                {
                    t = Gcd(t, *begin);
                    ++begin;
                }

                return t;
            }

            template <class T>
            T Lcm(T a, T b)
            {
                return (a / Gcd(a,b)) * b;
            }

            template <class T>
            T Lcm(T a, T b, T c)
            {     
                return Lcm(a, Lcm(b,c));
            }

            template <class FwdIter>
            typename Type::IteratorTraits<FwdIter>::ValType Lcm(FwdIter begin, FwdIter end)
            {
                typename Type::IteratorTraits<FwdIter>::ValType t = 1;

                while (begin != end)
                {
                    t = Lcm(t, *begin);
                    ++begin;
                }

                return t;
            }
        }
    }
}

#endif