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/* Translated from Cython into C++ by SciPy developers in 2024. * * Original author: Josh Wilson, 2016. */ /* Evaluate polynomials. * * All of the coefficients are stored in reverse order, i.e. if the * polynomial is * * u_n x^n + u_{n - 1} x^{n - 1} + ... + u_0, * * then coeffs[0] = u_n, coeffs[1] = u_{n - 1}, ..., coeffs[n] = u_0. * * References * ---------- * [1] Knuth, "The Art of Computer Programming, Volume II" */ #pragma once #include "config.h" namespace xsf { XSF_HOST_DEVICE inline std::complex<double> cevalpoly(const double *coeffs, int degree, std::complex<double> z) { /* Evaluate a polynomial with real coefficients at a complex point. * * Uses equation (3) in section 4.6.4 of [1]. Note that it is more * efficient than Horner's method. */ double a = coeffs[0]; double b = coeffs[1]; double r = 2 * z.real(); double s = std::norm(z); double tmp; for (int j = 2; j < degree + 1; j++) { tmp = b; b = std::fma(-s, a, coeffs[j]); a = std::fma(r, a, tmp); } return z * a + b; } } // namespace xsf