How to Generate Normally Distributed Random Numbers in C/C using the Box-Muller Transform?

Generating Normally Distributed Random Numbers in C/C

Generating random numbers that adhere to a normal distribution in C or C is a frequent task in various computational and statistical applications. This can be achieved effectively using the Box-Muller transform, a widely employed technique that leverages two uniform random numbers to produce a pair of normally distributed ones.

The Box-Muller transform relies on a simple mathematical formula:

x = sqrt(-2 * ln(u1)) * cos(2 * pi * u2)
y = sqrt(-2 * ln(u1)) * sin(2 * pi * u2)

where u1 and u2 are two independent uniform random numbers generated in the range [0, 1]. These two equations define two independent random variables, x and y, which follow a normal distribution with zero mean and unit variance.

To implement this method in C/C , the following steps can be taken:

1. Include the standard library header for accessing the rand() function.
2. Define a function to generate a uniform random double following a range [0, 1). This can be done using:

double rand0to1() {
    return rand() / (RAND_MAX + 1.0);
}

3. Implement the Box-Muller transform function:

pair<double, double> box_muller() {
    double u1 = rand0to1();
    double u2 = rand0to1();
    double x = sqrt(-2.0 * log(u1)) * cos(2.0 * M_PI * u2);
    double y = sqrt(-2.0 * log(u1)) * sin(2.0 * M_PI * u2);
    return {x, y};
}

4. Call the box_muller function to generate normally distributed random numbers as needed.

This method effectively generates random numbers that follow a normal distribution without the need for external libraries.

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