ZIGGURAT_OPENMP
Using the ZIGGURAT Library with OpenMP


ZIGGURAT_OPENMP is a FORTRAN90 library which explores how the ZIGGURAT library may be used, in conjunction with OpenMP, to compute random numbers efficiently and correctly.

The primary worry, when computing random numbers in OpenMP, occurs when the user calls a random number generator which may have some internal memory. In that case, the internal memory may become corrupted if multiple threads are invoking the code at the same time.

A safe way to compute random numbers is to ensure that the seed value, and any other data or tables needed by the computation, are stored externally, in the user program. That way, each thread can have a separate copy of the data, and multiple threads of random number calculations can be going along simultaneously without fear of overwriting or memory contention.

The program presented here is somewhat awkward, because it wishes to verify that OpenMP can compute exactly the same data as a sequential program. To do so, we need to create separate seeds for each threads, and ensure that the threads execute the loop iterations in some predictable sequence. When the sequential program goes through the same calculations, we again have to do some acrobatics to ensure that it is doing the same things that the parallel program did.

So some of the complications in this program are there to ensure that we can exhibit the same results sequentially and in parallel. Once you are convinced of that, and see how to go about this, your own program can be set up without some of the overhead and special instructions used in this demonstration.

On an Apple PowerPC G5 with two processors, the following results were observed:
ThreadsTest01Test02Test03Test04
10.592 s1.240 s1.579 s1.478 s
20.315 s0.638 s0.791 s0.796 s
40.303 s0.635 s0.826 s0.773 s

Usage:

In the BASH shell, the program could be run with 2 threads using the commands:

        export OMP_NUM_THREADS=2
        ./ziggurat_openmp
      

Licensing:

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

Languages:

ZIGGURAT_OPENMP is available in a C version and a C++ version and a FORTRAN77 version and a FORTRAN90 version.

Related Data and Programs:

DIJKSTRA_OPENMP, a FORTRAN90 program which uses OpenMP to parallelize a simple example of Dijkstra's minimum distance algorithm for graphs.

FFT_OPENMP, a FORTRAN90 program which demonstrates the computation of a Fast Fourier Transform in parallel, using OpenMP.

HEATED_PLATE_OPENMP, a FORTRAN90 program which solves the steady (time independent) heat equation in a 2D rectangular region, using OpenMP to run in parallel.

HELLO_OPENMP, a FORTRAN90 program which prints out "Hello, world!" using the OpenMP parallel programming environment.

MD_OPENMP, a FORTRAN90 program which carries out a molecular dynamics simulation using OpenMP.

MULTITASK_OPENMP, a FORTRAN90 program which demonstrates how to "multitask", that is, to execute several unrelated and distinct tasks simultaneously, using OpenMP for parallel execution.

MXM_OPENMP, a FORTRAN90 program which computes a dense matrix product C=A*B, using OpenMP for parallel execution.

OPENMP, FORTRAN90 programs which illustrate the use of the OpenMP application program interface for carrying out parallel computations in a shared memory environment.

OPENMP_RCC, FORTRAN90 programs which illustrate how a FORTRAN90 program, using OpenMP, can be compiled and run in batch mode on the FSU High Performance Computing (HPC) cluster operated by the Research Computing Center (RCC).

POISSON_OPENMP, a FORTRAN90 program which computes an approximate solution to the Poisson equation in a rectangle, using the Jacobi iteration to solve the linear system, and OpenMP to carry out the Jacobi iteration in parallel.

PRIME_OPENMP, a FORTRAN90 program which counts the number of primes between 1 and N, using OpenMP for parallel execution.

QUAD_OPENMP, a FORTRAN90 program which approximates an integral using a quadrature rule, and carries out the computation in parallel using OpenMP.

RANDOM_OPENMP, a FORTRAN90 program which illustrates how a parallel program using OpenMP can generate multiple distinct streams of random numbers.

SATISFY_OPENMP, a FORTRAN90 program which demonstrates, for a particular circuit, an exhaustive search for solutions of the circuit satisfiability problem, using OpenMP for parallel execution.

SCHEDULE_OPENMP, a FORTRAN90 program which demonstrates the default, static, and dynamic methods of "scheduling" loop iterations in OpenMP to avoid work imbalance.

SGEFA_OPENMP, a FORTRAN90 program which reimplements the SGEFA/SGESL linear algebra routines from LINPACK for use with OpenMP.

ZIGGURAT, a FORTRAN90 program which generates points from a uniform, normal or exponential distribution, using the ziggurat method.

Reference:

  1. Philip Leong, Guanglie Zhang, Dong-U Lee, Wayne Luk, John Villasenor,
    A comment on the implementation of the ziggurat method,
    Journal of Statistical Software,
    Volume 12, Number 7, February 2005.
  2. 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:

Examples and Tests:

ZIGGURAT_LOCAL_GFORTRAN compiles, links, loads and runs the program using 1, 2 and 4 threads, the local interactive environment, and the GNU Fortran compiler.

ZIGGURAT_LOCAL_IFORT compiles, links, loads and runs the program using 1, 2 and 4 threads, the local interactive environment, and the Intel Ifort Fortran compiler.

ZIGGURAT_ITHACA_GFORTRAN compiles, links, loads and runs the program using 1, 2 and 4 threads, using the PBS queueing system on Virginia Tech's Ithaca cluster, and the GNU Fortran compiler.

ZIGGURAT_ITHACA_IFORT compiles, links, loads and runs the program using 1, 2 and 4 threads, using the PBS queueing system on Virginia Tech's Ithaca cluster, and the Intel Ifort Fortran compiler.

List of Routines:

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


Last revised on 06 September 2009.