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#include <random>
#include <cmath>
#include "host_aberth.h"
using namespace std;
struct AberthState {
// boundPoly is 's' in the stop condition formulated at p.189-190 of
// https://link.springer.com/article/10.1007%2FBF02207694
const Poly &poly;
Poly deriv;
Poly boundPoly;
AApprox approx;
double radius;
AberthState(const Poly &poly);
void regenerate();
bool step();
void iterate();
};
static thread_local minstd_rand randgenerator = minstd_rand(random_device()());
AberthState::AberthState(const Poly &poly)
: poly(poly), deriv(derivative(poly)), radius(maxRootNorm(poly)) {
regenerate();
for (int i = 0; i <= N; i++) {
boundPoly[i] = abs(poly[i]) * (4 * i + 1);
}
}
void AberthState::regenerate() {
auto genCoord = [this]() {
return uniform_real_distribution<double>(-radius, radius)(randgenerator);
};
for (int i = 0; i < N; i++) {
approx[i] = Com(genCoord(), genCoord());
}
}
// Lagrange-style step where the new elements are computed in parallel from the previous values
bool AberthState::step() {
array<Com, N * N> pairs;
for (int i = 0; i < N - 1; i++) {
for (int j = i + 1; j < N; j++) {
pairs[N * i + j] = 1.0 / (approx[i] - approx[j]);
}
}
bool allConverged = true;
AApprox newapprox;
AApprox offsets;
for (int i = 0; i < N; i++) {
Com pval = eval(poly, approx[i]);
Com derivval = eval(deriv, poly.size() - 1, approx[i]);
Com quo = pval / derivval;
Com sum = 0;
for (int j = 0; j < i; j++) sum -= pairs[N * j + i];
for (int j = i + 1; j < N; j++) sum += pairs[N * i + j];
offsets[i] = quo / (1.0 - quo * sum);
newapprox[i] = approx[i] - offsets[i];
double sval = eval(boundPoly, abs(newapprox[i]));
if (abs(pval) > 1e-5 * sval) allConverged = false;
}
approx = newapprox;
return allConverged;
}
void AberthState::iterate() {
int tries = 1, stepIdx = 1;
while (!step()) {
stepIdx++;
if (stepIdx > tries * 100) {
regenerate();
stepIdx = 0;
tries++;
}
}
}
AApprox aberth(const Poly &poly) {
AberthState state(poly);
state.iterate();
return state.approx;
}
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