Examples

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Estimating Pi, π, with Monte Carlo

• Check out page 3 of this document (PDF) for more info.
• Increase the number of iterations or samples to obtain a more precise value.

REPL.IT

Code only

let number_of_iterations = 25;
let number_of_samples = 500;
let radius = 200;
let radius_squared = power(radius, 2);
let sample_space = linspace(0, radius, 10000);
let pi = 0;

for(let i = 0; i < number_of_iterations; i = i + 1) {
    let x_array = random_choose(sample_space, number_of_samples);
    let y_array = random_choose(sample_space, number_of_samples);

    let count = 0;
    for(let k = 0; k < number_of_samples; k = k + 1) {
        let distance_squared = power(x_array[k], 2) + power(y_array[k], 2);
        if (distance_squared <= radius_squared) {
            // Inside circle
            count = count + 1;
        }
    }
    pi = pi + count / number_of_samples;
    println 4 * pi /number_of_iterations;
}

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Using FFT for polynomial multiplication

• The Fast Fourier Transform (FFT) can be used to compute the resulting polynomial coefficients of a polynomial multiplication.
• For more info, refer to this StackExchange answer.

Laziness strikes again

• Oops, seems like I forgot to add sine and cosine among the built-in functions, so I Can't Go For That until I am productive again.

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Fibonacci (Slow)

• This implementation of the Fibonacci sequence is slow because it uses a recursive function, which results in many stack frames as explained here.

REPL.IT

Code only

fn fibonacci_slow(n) {
    if (n <= 1) {
        return n;
    }
    return fib(n - 2) + fib(n - 1);
}

for (let i = 0; i < 20; i = i + 1) {
    println fibonacci_slow(i);
}

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Fibonacci (Fast)

• This implementation of the Fibonacci sequence is much faster than the previous example.

REPL.IT

Code only

let a = 0;
let temp = 0;

for (let b = 1; a < 10000; b = temp + b) {
    println a;
    temp = a;
    a = b;
}