Simple Random Number Generation

• Download demo project - 5.64 KB
• Download source - 2.39 KB

Introduction

Random number generation is tricky business. Good random number generation algorithms are tricky to invent. Code implementing the algorithms is tricky to test. And code using random number generators is tricky to test. This article will describe SimpleRNG, a very simple random number generator. The generator uses a well-tested algorithm and is quite efficient. Because it is so simple, it is easy to drop into projects and easy to debug into.

SimpleRNG can be used to generate random unsigned integers and double values with several statistical distributions:

• Beta
• Cauchy
• Chi square
• Exponential
• Inverse gamma
• Laplace (double exponential)
• Normal
• Student t
• Uniform
• Weibull

Why Not Just Use the .NET Random Number Generator?

For many applications, it hardly matters what random number generator you use, and the one included in the .NET runtime would be the most convenient. However, sometimes it helps to have your own random number generator. Here are some examples.

1. When debugging, it's convenient to have full access to the random number generator. You may want to examine the internal state of the generator, and it helps if that state is small. Also, it may be helpful to change the generator temporarily, making the output predictable to help debug code that uses the generator.
2. Sometimes it is necessary to compare the output of programs written in different languages. For example, at my work we often take prototype code that was written in R and rewrite it in C++ to make it more efficient. If both programs use their own library's random number generator, the outputs are not directly comparable. But if both programs use the same algorithm, such as the one used here, the results might be directly comparable. (The results still might not match due to other differences.)
3. The statistical quality of the built-in generator might not be adequate for some tasks. Also, the attributes of the generator could change without notice when you apply a service pack.

Background

George Marsaglia is one of the leading experts in random number generation. He's come up with some simple algorithms that nevertheless produce high quality output. The generator presented here, SimpleRNG, uses Marsaglia's MWC (multiply with carry) algorithm. The algorithm is mysterious but very succinct. The algorithm passes Marsaglia's DIEHARD battery of tests, the acid test suite for random number generators.

The heart of SimpleRNG is three lines of code. Here is the method that generates uniformly distributed unsigned integers.

private static uint GetUint()
{
    m_z = 36969 * (m_z & 65535) + (m_z >> 16);
    m_w = 18000 * (m_w & 65535) + (m_w >> 16);
    return (m_z << 16) + m_w;
}

Here m_w and m_z are unsigned integers, the only member variables of the class. It's not at all obvious why this code should produce quality random numbers, but it does.

The unsigned integer is then turned into a double in the open interval (0, 1). ("Open" means that the end points are not included; the method will not return 0 or 1, only numbers in between.)

public static double GetUniform()
{
    // 0 <= u < 2^32
    uint u = GetUint();
    // The magic number below is 1/(2^32 + 2).
    // The result is strictly between 0 and 1.
    return (u + 1.0) * 2.328306435454494e-10;
}

Using the Code

The SimpleRNG class has two seeds. These have default values, or they can be specified by calling SetSeed() with one or two arguments. These arguments must be non-zero; if an argument is zero, it is replaced by the default value. Some may prefer to throw an exception in this case rather than silently fix the problem. There is also an option to set the seed values from the system clock using SetSeedFromSystemTime(). Once the class is initialized, there is only one public method to call, GetUniform().

Points of Interest

The code to test SimpleRNG is more complicated than SimpleRNG itself. The test code included as a demo uses a statistical test, the Kolmogorov-Smirnov test, to confirm that the output of the generator has the expected statistical properties. If this test were applied repeatedly with ideal random input, the test would fail on average once in every thousand applications. This is highly unusual in software testing: the test should fail occasionally! That's statistics for you. Don't be alarmed if the test fails. Try again with another seed and it will most likely pass. The test is good enough to catch most coding errors since a bug would likely result in the test failing far more often. The test code also uses RunningStat, a class for accurately computing sample mean and variance as values accumulate.

Further Reading

For more information on random number generation, particularly on subtle things that can go wrong, see the CodeProject article Pitfalls in Random Number Generation. If you are using C++, see Random number generation using C++ TR1.

History

• 11^th April, 2008: Initial post
• 13^th April, 2008: Revised article to explain why this generator might be preferable to the built-in generator
• 30^th September, 2008: Added further reading section
• 4^th October, 2008: Fixed two bugs based on reader feedback. Now seeds cannot be 0, and GetUniform cannot return 0.
• 22^nd October, 2008: Added methods for generating normal (Gaussian) and exponential random samples
• 19^th February, 2010: Fixed incompatibility with Marsaglia's MWC algorithm
• 30^th April, 2010: Added methods for new distributions, extended the test code
• 27^th July, 2010: Updated article
• 6^th January, 2011: Updated article and download files
• 16^th March, 2011: Updated article and download files per Craig McQueen‘s comment regarding the lower bits of the core generator