source/src/math/polynomial.hpp

/*
 * 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 "math/numbers.hpp"
#include "math/map.hpp"

namespace math {

/// Polynomial functions.
namespace polynomial {

/**
 * Evaluates a polynomial using Horner's method.
 *
 * @param first,last Range of polynomial coefficients, in descending order of degree.
 * @param x Variable value.
 * @return Evaluation of P(x).
 *
 * @see https://en.wikipedia.org/wiki/Horner%27s_method
 */
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;
}

/** Chebychev polynomials.
 *
 * @see https://en.wikipedia.org/wiki/Chebyshev_polynomials
 */
namespace chebyshev {

	/**
	 * Evaluates a Chebyshev polynomial.
	 *
	 * @param[in] first,last Range of Chebychev polynomial coefficients.
	 * @param[in] x Value on the interval `[-1, 1]`.
	 *
	 * @return Evaluated value.
	 */
	template <class InputIt, class T>
	[[nodiscard]] T evaluate(InputIt first, InputIt last, T x)
	{
		T y = *(first++);
		y += *(first++) * x;
		
		T n2 = T(1), n1 = x, n0;
		x *= T(2);
		
		for (; first != last; n2 = n1, n1 = n0)
		{
			n0 = x * n1 - n2;
			y += *(first++) * n0;
		}
		
		return y;
	}

	/**
	 * Evaluates a Chebyshev polynomial.
	 *
	 * @param first,last Range of Chebychev polynomial coefficients.
	 * @param min,max Domain of the approximated function.
	 * @param x Value on the interval `[min, max]`.
	 *
	 * @return Evaluated value.
	 */
	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