Normal-Distribution-Random-Number-Generator

Description

A fast, lightweight normal distribution random number generator(RNG) based on Box-Muller method, with SSE and AVX2 accelerated versions.

Quality&Performance

We implemented a simple LCG at the bottom to directly generate uniform distributed floats.

• The normal distribution RNG passed the Kolmogorov-Smirnov test with α=0.01. During the test, the value of max{abs(Fobs(xi)-Fexp(xi))} was almost the same as that of numpy.
• For performance, the bare Floats is a bit slower than numpy, i.e. about 1.45 times slower. But as we use FloatsSSE, the speed will boost to about 3 times higher than numpy. If we continue with FloatsAVX2, it can be 7x faster than numpy! Howerer, as numpy generates np.float64, our comparison is quite unfair. *** So this RNG should ONLY be used on occasions where you just want speed and don't need doubles. ***

List of exported functions

void CreateGenerator(float mu, float sigma_square);
float NextFloat();
float* Floats(unsigned int count);
float* FloatsSSE(unsigned int count);
float* FloatsAVX2(unsigned int count);

How to use

After loading the DLL library, call CreateGenerator(float mu, float sigma_square) to create a generator. Then, call the following functions based on your need:

• NextFloat(): Get next normal distributed float. Nan will be returned if you have never called CreateGenerator before.
• Floats(unsigned int count): Generate count normal distributed floats in an array, and return a pointer to the first element. nullptr will be returned if you have never called CreateGenerator before, which also applies to the following two functions.
• FloatsSSE(unsigned int count): SSE accelerated Floats (~4x faster). *** NOTE: SSE, SSE2, SSE4.1 intrinsics MUST be supported by your CPU, or your program will crash. ***
• FloatsAVX2(unsigned int count): AVX+AVX2 accelerated Floats (~8x faster). *** NOTE: AVX and AVX2 intrinsics MUST be supported by your CPU, or your program will crash. ***

Analysis figures

1. Fobs and Fexp figure in K-S test (μ=-3, σ²=9, count=100000):

2. Random number distribution histogram (v.s. numpy, μ=10, σ²=20, count=100000):

3. Performance benchmark (count=10000000, i7-8565U):

Happy Coding!