ZIGGURAT
Ziggurat Method for Exponential or Normal Random Numbers

ZIGGURAT is a FORTRAN90 library which rapidly generates random variates from the uniform, normal or exponential distributions.

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. The FORTRAN90 code uses signed integers, and for this reason, the FORTRAN90 version of the exponential random number algorithm does not match the C version - that is, for the same initial seed value, different results emerge from the two codes. Whether this seriously affects the validity of the FORTRAN90 results remains to be checked.

Licensing:

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

Related Data and Programs:

CVT is a FORTRAN90 library which computes elements of a Centroidal Voronoi Tessellation.

FAURE is a FORTRAN90 library which computes elements of a Faure quasirandom sequence.

GRID is a FORTRAN90 library which computes elements of a grid dataset.

HALTON is a FORTRAN90 library which computes elements of a Halton quasirandom sequence.

HAMMERSLEY is a FORTRAN90 library which computes elements of a Hammersley quasirandom sequence.

HEX_GRID is a FORTRAN90 library which computes elements of a hexagonal grid dataset.

HEX_GRID_ANGLE is a FORTRAN90 library which computes elements of an angled hexagonal grid dataset.

IHS is a FORTRAN90 library which computes elements of an improved distributed Latin hypercube dataset.

LATIN_CENTER is a FORTRAN90 library which computes elements of a Latin Hypercube dataset, choosing center points.

LATIN_EDGE is a FORTRAN90 library which computes elements of a Latin Hypercube dataset, choosing edge points.

LATIN_RANDOM is a FORTRAN90 library which computes elements of a Latin Hypercube dataset, choosing points at random.

LCVT is a FORTRAN90 library which computes a latinized Centroidal Voronoi Tessellation.

NIEDERREITER2 is a FORTRAN90 library which computes elements of a Niederreiter quasirandom sequence with base 2.

NORMAL is a FORTRAN90 library which computes elements of a sequence of pseudorandom normally distributed values.

RBOX is a C program which generates a set of points in a region, selected at random according to a given distribution.

SOBOL is a FORTRAN90 library which computes elements of a Sobol quasirandom sequence.

UNIFORM is a FORTRAN90 library which computes elements of uniform pseudorandom sequence.

VAN_DER_CORPUT is a FORTRAN90 library which computes elements of a van der Corput quasirandom sequence.

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

ZIGGURAT_OPEN_MP, a FORTRAN90 program which demonstrates how the ZIGGURAT library can be used to generate random numbers in an OpenMP parallel program.

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:

• ziggurat.f90, the source code.
• ziggurat.csh, commands to compile the source code.

Examples and Tests:

• ziggurat_prb.f90 a sample calling program.
• ziggurat_prb.csh, commands to compile and run the sample program.
• ziggurat_prb_output.txt, the output file.

List of Routines:

• R4_EXP returns an exponentially distributed single precision real value.
• R4_EXP_SETUP sets data needed by R4_EXP.
• R4_NOR returns a normally distributed single precision real value.
• R4_NOR_SETUP sets data needed by R4_NOR.
• R4_UNI returns a uniformly distributed real value.
• SHR3 evaluates the SHR3 generator for integers.

You can go up one level to the FORTRAN90 source codes.