Generating Random Numbers with a Normal Distribution in C/C

Question:

How do I easily generate random numbers following a normal distribution in C or C without using Boost libraries?

Answer:

Box-Muller Transform

The Box-Muller transform is a widely used method for generating normally distributed numbers from a uniform random number generator. It produces values that accurately adhere to a Gaussian distribution.

The mathematical formula for the Box-Muller transform is as follows:

x = sqrt(-2 * log(U1)) * cos(2 * π * U2)
y = sqrt(-2 * log(U1)) * sin(2 * π * U2)

where:

• U1 and U2 are uniformly distributed random numbers between 0 and 1
• x and y are normally distributed random numbers with mean 0 and standard deviation 1

Implementation:

To implement the Box-Muller transform in C/C , you can use the following code:

#include 
#include 

double box_muller() {
  std::random_device rd;  // Seed the random number generator with a system clock seed
  std::default_random_engine rng(rd());
  std::uniform_real_distribution dist(0.0, 1.0);

  double U1 = dist(rng);
  double U2 = dist(rng);

  double x = sqrt(-2 * log(U1)) * cos(2 * M_PI * U2);
  return x;
}

Usage:

To generate a normally distributed random number, simply call the box_muller() function:

double random_number = box_muller();

The value of random_number will be a Gaussian-distributed random variable with mean 0 and standard deviation 1.

Note:

• The Box-Muller transform also produces a second result, y, but this can be discarded or saved for later use.
• If you need to generate normally distributed numbers with a mean other than 0 or a standard deviation other than 1, you can multiply the result by a constant.