There are many methods to generate Gaussian-distributed numbers from a regular RNG.

The Box-Muller transform is commonly used. It correctly produces values with a normal distribution. The math is easy. You generate two (uniform) random numbers, and by applying an formula to them, you get two normally distributed random numbers. Return one, and save the other for the next request for a random number.

C++11

C++11 offers std::normal_distribution, which is the way I would go today.

C or older C++

Here are some solutions in order of ascending complexity:

1. Add 12 uniform random numbers from 0 to 1 and subtract 6. This will match mean and standard deviation of a normal variable. An obvious drawback is that the range is limited to ±6 – unlike a true normal distribution.

2. The Box-Muller transform. This is listed above, and is relatively simple to implement. If you need very precise samples, however, be aware that the Box-Muller transform combined with some uniform generators suffers from an anomaly called Neave Effect¹.

3. For best precision, I suggest drawing uniforms and applying the inverse cumulative normal distribution to arrive at normally distributed variates. Here is a very good algorithm for inverse cumulative normal distributions.

^{1. H. R. Neave, “On using the Box-Muller transformation with multiplicative congruential pseudorandom number generators,” Applied Statistics, 22, 92-97, 1973}

A quick and easy method is just to sum a number of evenly distributed random numbers and take their average. See the Central Limit Theorem for a full explanation of why this works.

Use std::tr1::normal_distribution.

The std::tr1 namespace is not a part of boost. It's the namespace that contains the library additions from the C++ Technical Report 1 and is available in up to date Microsoft compilers and gcc, independently of boost.

The comp.lang.c FAQ list shares three different ways to easily generate random numbers with a Gaussian distribution.

You may take a look of it: http://c-faq.com/lib/gaussian.html

1) Graphically intuitive way you can generate Gaussian random numbers is by using something similar to the Monte Carlo method. You would generate a random point in a box around the Gaussian curve using your pseudo-random number generator in C. You can calculate if that point is inside or underneath the Gaussian distribution using the equation of the distribution. If that point is inside the Gaussian distribution, then you have got your Gaussian random number as the x value of the point.

This method isn't perfect because technically the Gaussian curve goes on towards infinity, and you couldn't create a box that approaches infinity in the x dimension. But the Guassian curve approaches 0 in the y dimension pretty fast so I wouldn't worry about that. The constraint of the size of your variables in C may be more of a limiting factor to your accuracy.

2) Another way would be to use the Central Limit Theorem which states that when independent random variables are added, they form a normal distribution. Keeping this theorem in mind, you can approximate a Gaussian random number by adding a large amount of independent random variables.

These methods aren't the most practical, but that is to be expected when you don't want to use a preexisting library. Keep in mind this answer is coming from someone with little or no calculus or statistics experience.

Monte Carlo method The most intuitive way to do this would be to use a monte carlo method. Take a suitable range -X, +X. Larger values of X will result in a more accurate normal distribution, but takes longer to converge. a. Choose a random number z between -X to X. b. Keep with a probability of N(z, mean, variance) where N is the gaussian distribution. Drop otherwise and go back to step (a).