newton

newton.cpp

#include <iostream>
#include <random>
#include <cassert>
#include <cstdint>

template< typename T, typename F, typename DF >
T newton(T x, F f, DF df)
{
	using std::abs;
	T y = f(x);
	while (abs(y) > static_cast< T >(1.0e-12))
	{
		x = x - y / df(x);
		y = f(x);
	}
	return x;
}

int main() {
	double n = 69;
	std::cout << std::sqrt(n) << '\n';
	std::cout << newton(8., [=](double x) { return x*x - n; }, [](double x) { return 2.*x; }) << '\n';
}