Generate uniform random points in a unit disk using two methods

randpoints.cpp

#include <cmath>
#include <iostream>
#include <random>
#include <vector>
#include <chrono>

using namespace std;

template <typename T>
vector<pair<double, double>> tinybrain(const int n,
                                       uniform_real_distribution<double> &unif,
                                       T &engine) {
    vector<pair<double, double>> points(n);
    for (auto &p : points) {
        while (true) {
            double x = unif(engine);
            double y = unif(engine);
            if (x * x + y * y <= 1.0) {
                p = make_pair(x, y);
                break;
            }
        }
    }
    return points;
}

template <typename T>
vector<pair<double, double>> smallbrain(const int n,
                                        uniform_real_distribution<double> &unif_r,
                                        uniform_real_distribution<double> &unif_t,
                                        T &engine) {
    vector<pair<double, double>> points(n);
    for (auto &p : points) {
        double rho = unif_r(engine);
        double t = unif_t(engine);
        double r = sqrt(rho);

        double x = r * sin(t);
        double y = r * cos(t);
        p = make_pair(x, y);
    }
    return points;
}

int main() {
    random_device rd;
    mt19937 engine(rd());
    uniform_real_distribution<double> uniform_dist_1_1(-1.0, 1.0);
    uniform_real_distribution<double> uniform_dist_0_1(0.0, 1.0);
    uniform_real_distribution<double> uniform_dist_0_2pi(0.0, 2.0 * M_PI);

    const int n = 100000000;
    auto start = chrono::steady_clock::now();
    vector<pair<double, double>> tinybrain_out =
        tinybrain(n, uniform_dist_1_1, engine);
    auto end = chrono::steady_clock::now();
    chrono::duration<double> elapsed = end - start;
    cout << "tiny brain: " << elapsed.count() << " seconds" << endl;


    start = chrono::steady_clock::now();
    vector<pair<double, double>> smallbrain_out =
        smallbrain(n, uniform_dist_0_1, uniform_dist_0_2pi, engine);
    end = chrono::steady_clock::now();
    elapsed = end - start;
    cout << "small brain: " << elapsed.count() << " seconds" << endl;
}