ZIGGURAT
Ziggurat Method for Exponential or Normal Random Numbers

ZIGGURAT is a MATLAB library which rapidly generates random variates from the uniform, normal or exponential distributions, by Marsaglia and Tsang.

The uniform numbers are generated directly. The ziggurate method is used to compute the normal and exponential values.

In the reference, the underlying generators are implemented "inline", invoking a function call only in exceptional cases. This results in very fast execution.

In this implementation, the advantages of inline code are not used. All the routines and inline functions are isolated in a separate file, so that a user invokes them through the familiar library interface.

This code is a translation of software written in C. The C code used unsigned integers for the underlying SHR3 algorithm. Getting the MATLAB code to reproduce the results of the C code has been somewhat tricky. The results seem to match the C code, but I have not tried to be efficient in my modifications.

Licensing:

The computer code and data files described and made available on this web page are distributed under the GNU LGPL license.

Languages:

ZIGGURAT is available in a C version and a C++ version and a FORTRAN77 version and a FORTRAN90 version and a MATLAB version.

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Author:

George Marsaglia, Wai Wan Tsang.

Reference:

1. George Marsaglia, Wai Wan Tsang,
   The Ziggurat Method for Generating Random Variables,
   Journal of Statistical Software,
   Volume 5, Number 8, October 2000, seven pages.

Source Code:

• r4_exp.m returns an exponentially distributed single precision real value.
• r4_exp_setup.m sets data needed by R4_EXP.
• r4_nor.m returns a normally distributed single precision real value.
• r4_nor_setup.m sets data needed by R4_NOR.
• r4_uni.m returns a uniformly distributed real value.
• shr3.m evaluates the SHR3 generator for integers.
• timestamp.m returns the YMDHMS date as a timestamp.

Examples and Tests:

• ziggurat_test.m calls all the tests.
• ziggurat_test_output.txt, the output file.
• ziggurat_test001.m checks the behavior of SHR3 based on the seed value.
• ziggurat_test02.m checks the behavior of R4_UNI based on the seed value.
• ziggurat_test03.m checks the behavior of R4_NOR based on the seed value.
• ziggurat_test04.m checks the behavior of R4_EXP based on the seed value.
• ziggurat_test05.m times SHR3.
• ziggurat_test06.m times R4_UNI.
• ziggurat_test07.m times R4_NOR.
• ziggurat_test08.m times R4_EXP.

You can go up one level to the MATLAB source codes.