#include <Rcpp.h>
using namespace Rcpp;

// Note: this function is not exported.
double distance_from_origin(double x, double y) {
    return sqrt(x * x + y * y);
}

// [[Rcpp::export]]
int escapeTime(double x0, double y0, int limit=256) {
    double x = x0, y = y0;
    int n_jumps;
    for (n_jumps = 0; n_jumps < limit; n_jumps++) {
	if (distance_from_origin(x, y) >= 2.0)
	    break;
	double old_x = x;
	double old_y = y; // (Not a necessary variable.)
	x = old_x * old_x - old_y * old_y + x0;
	y = 2.0 * old_x * old_y + y0;
    }
    return n_jumps;
}