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#pragma once
#include "defs.h"
using Poly = array<int, N + 1>;
template <typename T>
T eval(const Poly &p, int nterms, T pt) {
T value = p[nterms - 1];
for (int i = nterms - 2; i >= 0; i--) {
value = pt * value + (double)p[i];
}
return value;
}
template <typename T>
T eval(const Poly &p, T pt) {
return eval(p, p.size(), pt);
}
inline Poly derivative(const Poly &p) {
Poly res;
for (int i = res.size() - 2; i >= 0; i--) {
res[i] = (i+1) * p[i+1];
}
return res;
}
inline double maxRootNorm(const Poly &poly) {
// Cauchy's bound: https://en.wikipedia.org/wiki/Geometrical_properties_of_polynomial_roots#Lagrange's_and_Cauchy's_bounds
double value = 0;
double last = (double)poly.back();
for (int i = 0; i < (int)poly.size() - 1; i++) {
value = max(value, abs(poly[i] / last));
}
return 1 + value;
}
ostream& operator<<(ostream &os, const Poly &p);
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