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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
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