find-root.cpp

#include <cmath>
#include <iostream>

using namespace std;

const double eps = 0.000001;

int signof(double x) {
	return x == 0 ? 0 : (x > 0 ? 1 : -1);
}

double root(int k, int n) {

	double guess = k / n;
	double err = 0.;
	double step = 1;
	int lastSign = 1;
	
	do {
		err = pow(guess, n) - k;
		if (signof(err) != lastSign) {
			step *= 0.75;
			lastSign = -lastSign;
		}
		
		if (err > 0) {
			guess *= 1/(1 + step);
		} else {
			guess *= (1 + step);
		}

	} while (fabs(err) > eps);

	return guess;
}


bool eq(double a, double b) {
	return fabs(a - b) < eps;
}

int main() {
	for (int c = 100; c < 1000; c++) {
		for (int r = 2; r < 5; ++r) {

			double mroot = root(c, r);
			double rroot = pow(c, 1.0 / (double)r);

			cout << "root(" << c << "," << r << ") = " << mroot << " -> " << rroot << endl;
		}
	}

}