Ytdyklly

#include <iostream>

#include <iomanip>





#ifdef USE_OLD_RAND



#include <stdlib.h>

inline double getRandDart() {return rand() * 1.0 / RAND_MAX;}



#else



#include <random>

std::default_random_engine              generator;

std::uniform_real_distribution<double>  distribution(0,1);

inline double getRandDart() {return distribution(generator);}



#endif





// Monte Carlo Simulator to estimate the value of PI.

//

// If we have a circle with a radius of 1.

// Then the smallest square that encloses the circle as sides of length 2.

//

//      Area of circle pi r^2   = pi

//      Area of square 2.r.2.r  = 4

//

//          Ratio of overlapping area:      pi/4

//

// If we throw darts randomly at a dart board (with an even distribution) and always hit the square.

// Then the ratio of darts falling into the circle should be pi/4 of the total number of darts thrown.

//

//      pi/4 * countInSquare  = countInCircle

//

//      pi = 4 . countInCircle / countInSquare

//

// To simplify the maths.

// We will set the center point as 0,0 and only use the top right quadrant of the circle.

// We have 1/4 the size of the square and circle but the same maths still apply.

//

// A dart thrown has a random x/y value in the range 0->1 (top right quadrant).

// A dart is outside the circle if x^2 + y^2 > 1  (note 1^2 is 1)

//



int main()

{



    long     countInSquare   = 0;

    long     countInCircle   = 0;



    for(long iteration = 0; iteration <= 10'000'000'000; ++iteration) {

        double x = getRandDart();

        double y = getRandDart();



        double d = (x * x) + (y * y);



        countInSquare   += 1;

        countInCircle   += (d >= 1.0) ? 0 : 1;



        if (iteration % 10'000'000 == 0) {

            std::cout << iteration << " " << (4.0 * countInCircle / countInSquare) << "n";

        }

    }

    std::cout << "nn" << std::setprecision(9) << (4.0 * countInCircle / countInSquare) << "n";



}

Output:

> ./a.out

9990000000 3.14158

10000000000 3.14158





3.14158355

One could consider at least the following points:

• Instead of including <stdlib.h>, I'd include <cstdlib>.




• In getRandDart(), it might in this case be more readable to do static_cast<double>(rand()) / RAND_MAX; instead of multiplying by 1.0.




• In the for loop, all of x, y and d can be const, so I'd make them const. This has the potential to protect the programmer from unintended mistakes, and can sometimes allow the compiler to optimize better.




• When you increment by one (in countInSquare += 1;), it makes more sense to use the ++ operator, i.e., to just write ++countInSquare. This is more idiomatic and protects us from unintended mistakes: ++ conveys the meaning of increment (by one), whereas with += we might accidentally write += 2; and that would be perfectly valid (but not what we wanted).




• Regardless of the above point, notice that during the for-loop, it holds that iteration == countInSquare. So strictly speaking, the variable countInSquare is unnecessary and could be replaced by just iteration when needed.




• You could consider making the number of iterations and the second operand of the % operand constants to allow for easier modification and perhaps to slightly improve readability.




• Instead of typing (4.0 * countInCircle / countInSquare) twice, we could make a function that takes the two variables as parameters. This would allow us to save some typing, and again to protect us from unintended mistakes.