💿🐜 Antkeeper source code
https://antkeeper.com
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101 lines
2.5 KiB
101 lines
2.5 KiB
/*
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* Copyright (C) 2021 Christopher J. Howard
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*
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* This file is part of Antkeeper source code.
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*
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* Antkeeper source code is free software: you can redistribute it and/or modify
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* it under the terms of the GNU General Public License as published by
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* the Free Software Foundation, either version 3 of the License, or
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* (at your option) any later version.
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*
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* Antkeeper source code is distributed in the hope that it will be useful,
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* but WITHOUT ANY WARRANTY; without even the implied warranty of
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* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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* GNU General Public License for more details.
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*
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* You should have received a copy of the GNU General Public License
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* along with Antkeeper source code. If not, see <http://www.gnu.org/licenses/>.
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*/
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#ifndef ANTKEEPER_MATH_POLYNOMIAL_HPP
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#define ANTKEEPER_MATH_POLYNOMIAL_HPP
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#include "math/constants.hpp"
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#include "math/map.hpp"
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namespace math {
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/// Polynomial functions.
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namespace polynomial {
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/**
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* Evaluates a polynomial using Horner's method.
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*
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* @param first,last Range of polynomial coefficients, in descending order of degree.
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* @param x Variable value.
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* @return Evaluation of P(x).
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*
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* @see https://en.wikipedia.org/wiki/Horner%27s_method
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*/
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template <class InputIt, class T>
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T horner(InputIt first, InputIt last, T x)
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{
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T y = *first;
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for (++first; first != last; ++first)
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y = y * x + *first;
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return y;
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}
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/** Chebychev polynomials.
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*
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* @see https://en.wikipedia.org/wiki/Chebyshev_polynomials
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*/
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namespace chebyshev {
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/**
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* Evaluates a Chebyshev polynomial.
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*
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* @param[in] first,last Range of Chebychev polynomial coefficients.
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* @param[in] x Value on the interval `[-1, 1]`.
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*
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* @return Evaluated value.
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*/
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template <class InputIt, class T>
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T evaluate(InputIt first, InputIt last, T x)
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{
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T y = *(first++);
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y += *(first++) * x;
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T n2 = T(1), n1 = x, n0;
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x *= T(2);
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for (; first != last; n2 = n1, n1 = n0)
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{
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n0 = x * n1 - n2;
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y += *(first++) * n0;
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}
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return y;
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}
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/**
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* Evaluates a Chebyshev polynomial.
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*
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* @param first,last Range of Chebychev polynomial coefficients.
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* @param min,max Domain of the approximated function.
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* @param x Value on the interval `[min, max]`.
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*
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* @return Evaluated value.
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*/
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template <class InputIt, class T>
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T evaluate(InputIt first, InputIt last, T min, T max, T x)
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{
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return evaluate<InputIt, T>(first, last, math::map<T>(x, min, max, T(-1), T(1)));
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}
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} // namespace chebyshev
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} // namespace polynomial
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} // namespace math
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#endif // ANTKEEPER_MATH_POLYNOMIAL_HPP
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