Editing Box–Muller transform (section)

==Implementation==

=== C++ ===
The standard Box–Muller transform generates values from the standard normal distribution (''i.e.'' [[standard normal deviate]]s) with mean ''0'' and standard deviation ''1''. The implementation below in standard [[C++]] generates values from any normal distribution with mean <math>\mu</math> and variance <math>\sigma^2</math>.  If <math>Z</math> is a standard normal deviate, then <math>X = Z\sigma + \mu</math> will have a normal distribution with mean <math>\mu</math> and standard deviation <math>\sigma</math>.  The random number generator has been [[Random seed|seeded]] to ensure that new, pseudo-random values will be returned from sequential calls to the <code>generateGaussianNoise</code> function.

<syntaxhighlight lang="cpp">
#include <cmath>
#include <limits>
#include <random>
#include <utility>

//"mu" is the mean of the distribution, and "sigma" is the standard deviation.
std::pair<double, double> generateGaussianNoise(double mu, double sigma)
{
    constexpr double two_pi = 2.0 * M_PI;

    //initialize the random uniform number generator (runif) in a range 0 to 1
    static std::mt19937 rng(std::random_device{}()); // Standard mersenne_twister_engine seeded with rd()
    static std::uniform_real_distribution<> runif(0.0, 1.0);

    //create two random numbers, make sure u1 is greater than zero
    double u1, u2;
    do
    {
        u1 = runif(rng);
    }
    while (u1 == 0);
    u2 = runif(rng);

    //compute z0 and z1
    auto mag = sigma * sqrt(-2.0 * log(u1));
    auto z0  = mag * cos(two_pi * u2) + mu;
    auto z1  = mag * sin(two_pi * u2) + mu;

    return std::make_pair(z0, z1);
}
</syntaxhighlight>

=== JavaScript ===
<syntaxhighlight lang="javascript">
/* Syntax:
 *
 *   [ x, y ]  =   rand_normal();
 *     x       =   rand_normal()[0];
 *     y       =   rand_normal()[1];
 */
function rand_normal() {
    let theta  = 2 * Math.PI * Math.random();
    let R   = Math.sqrt(-2 * Math.log(Math.random()));
    let x   = R * Math.cos(theta);
    let y   = R * Math.sin(theta);

    return [ x, y ];
}
</syntaxhighlight>

=== Julia ===
<syntaxhighlight lang="julia">
"""
    boxmullersample(N)

Generate `2N` samples from the standard normal distribution using the Box-Muller method.
"""
function boxmullersample(N)
    z = Array{Float64}(undef,N,2);
    for i in axes(z,1)
        z[i,:] .= sincospi(2 * rand());
        z[i,:] .*= sqrt(-2 * log(rand()));
    end
    vec(z)
end

"""
    boxmullersample(n,μ,σ)

Generate `n` samples from the normal distribution with mean `μ` and standard deviation `σ` using the Box-Muller method.
"""
function boxmullersample(n,μ,σ)
    μ .+ σ*boxmullersample(cld(n,2))[1:n];
end
</syntaxhighlight>