polynomial.hpp

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/*
 * Copyright (C) 2023  Christopher J. Howard
 *
 * This file is part of Antkeeper source code.
 *
 * Antkeeper source code 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.
 *
 * Antkeeper source code 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 Antkeeper source code.  If not, see <http://www.gnu.org/licenses/>.
 */
 
#ifndef ANTKEEPER_MATH_POLYNOMIAL_HPP
#define ANTKEEPER_MATH_POLYNOMIAL_HPP
 
#include <engine/math/numbers.hpp>
#include <engine/math/map.hpp>
 
namespace math {
 
namespace polynomial {
 
template <class InputIt, class T>
[[nodiscard]] constexpr T horner(InputIt first, InputIt last, T x)
{
    T y = *first;
    for (++first; first != last; ++first)
    {
        y = y * x + *first;
    }
    return y;
}
 
namespace chebyshev {
 
    template <class InputIt, class T>
    [[nodiscard]] T evaluate(InputIt first, InputIt last, T x)
    {
        T y = *(first++);
        y += *(first++) * x;
        
        T n2 = T{1};
        T n1 = x;
        T n0;
        
        x += x;
        
        for (; first != last; n2 = n1, n1 = n0)
        {
            n0 = x * n1 - n2;
            y += *(first++) * n0;
        }
        
        return y;
    }
    
    template <class InputIt, class T>
    [[nodiscard]] T evaluate(InputIt first, InputIt last, T min, T max, T x)
    {
        return evaluate<InputIt, T>(first, last, math::map<T>(x, min, max, T{-1}, T{1}));
    }
 
} // namespace chebyshev
 
} // namespace polynomial
} // namespace math
 
#endif // ANTKEEPER_MATH_POLYNOMIAL_HPP