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/* * Copyright Thomas Dybdahl Ahle, Nick Thompson, Matt Borland, John Maddock, 2023 * Use, modification and distribution are subject to the * Boost Software License, Version 1.0. (See accompanying file * LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) */ #ifndef BOOST_MATH_TOOLS_ESTRIN_HPP #define BOOST_MATH_TOOLS_ESTRIN_HPP #include #include #include #include namespace boost { namespace math { namespace tools { template inline RealOrComplex evaluate_polynomial_estrin(RandomAccessContainer1 const &coeffs, RandomAccessContainer2 &scratch, RealOrComplex z) { // Does anyone care about the complex coefficients, real argument case? // I've never seen it used, and this static assert makes the error messages much better: static_assert(std::is_same::value, "The value type of the scratch space must be the same as the abscissa."); auto n = coeffs.size(); BOOST_MATH_ASSERT_MSG(scratch.size() >= (n + 1) / 2, "The scratch space must be at least N+1/2"); if (n == 0) { return static_cast(0); } for (decltype(n) i = 0; i < n / 2; i++) { scratch[i] = coeffs[2 * i] + coeffs[2 * i + 1] * z; } if (n & 1) { scratch[n / 2] = coeffs[n - 1]; } auto m = (n + 1) / 2; while (m != 1) { z = z * z; for (decltype(n) i = 0; i < m / 2; i++) { scratch[i] = scratch[2 * i] + scratch[2 * i + 1] * z; } if (m & 1) { scratch[m / 2] = scratch[m - 1]; } m = (m + 1) / 2; } return scratch[0]; } // The std::array template specialization doesn't need to allocate: template inline RealOrComplex2 evaluate_polynomial_estrin(const std::array &coeffs, RealOrComplex2 z) { std::array ds; return evaluate_polynomial_estrin(coeffs, ds, z); } template inline RealOrComplex evaluate_polynomial_estrin(const RandomAccessContainer &coeffs, RealOrComplex z) { auto n = coeffs.size(); // Normally, I'd make `ds` a RandomAccessContainer, but its value type needs to be RealOrComplex, // and the value_type of the passed RandomAccessContainer can just be Real. // Allocation of the std::vector is not ideal, but I have no other ideas at the moment: std::vector ds((n + 1) / 2); return evaluate_polynomial_estrin(coeffs, ds, z); } } // namespace tools } // namespace math } // namespace boost #endif