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<html>
<head>
<title>
ZIGGURAT_OPENMP - Using the ZIGGURAT Library with OpenMP
</title>
</head>
<body bgcolor="#EEEEEE" link="#CC0000" alink="#FF3300" vlink="#000055">
<h1 align = "center">
ZIGGURAT_OPENMP <br> Using the ZIGGURAT Library with OpenMP
</h1>
<hr>
<p>
<b>ZIGGURAT_OPENMP</b>
is a C++ library which
explores how the ZIGGURAT library may be used, in conjunction with
OpenMP, to compute random numbers efficiently and correctly.
</p>
<p>
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.
</p>
<p>
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.
</p>
<p>
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.
</p>
<p>
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.
</p>
<p>
On an Apple PowerPC G5 with two processors, the following results were
observed:
<table border="1" align="center">
<tr>
<th>Threads</th><th>Test01</th><th>Test02</th><th>Test03</th><th>Test04</th>
</tr>
<tr>
<td>1</td><td>0.521 s</td><td>2.342 s</td><td>1.175 s</td><td>1.223 s</td>
</tr>
<tr>
<td>2</td><td>0.226 s</td><td>1.202 s</td><td>0.595 s</td><td>0.615 s</td>
</tr>
<tr>
<td>4</td><td>0.225 s</td><td>1.187 s</td><td>0.592 s</td><td>0.614 s</td>
</tr>
</table>
</p>
<h3 align = "center">
Usage:
</h3>
<p>
In the BASH shell, the program could be run with 2 threads using the commands:
<pre>
export OMP_NUM_THREADS=2
./ziggurat_openmp
</pre>
</p>
<h3 align = "center">
Licensing:
</h3>
<p>
The computer code and data files described and made available on this web page
are distributed under
<a href = "../../txt/gnu_lgpl.txt">the GNU LGPL license.</a>
</p>
<h3 align = "center">
Languages:
</h3>
<p>
<b>ZIGGURAT_OPENMP</b> is available in
<a href = "../../c_src/ziggurat_openmp/ziggurat_openmp.html">a C version</a> and
<a href = "../../cpp_src/ziggurat_openmp/ziggurat_openmp.html">a C++ version</a> and
<a href = "../../f77_src/ziggurat_openmp/ziggurat_openmp.html">a FORTRAN77 version</a> and
<a href = "../../f_src/ziggurat_openmp/ziggurat_openmp.html">a FORTRAN90 version</a>.
</p>
<h3 align = "center">
Related Data and Programs:
</h3>
<p>
<a href = "../../cpp_src/dijkstra_openmp/dijkstra_openmp.html">
DIJKSTRA_OPENMP</a>,
a C++ program which
uses OpenMP to parallelize a simple example of Dijkstra's
minimum distance algorithm for graphs.
</p>
<p>
<a href = "../../cpp_src/fft_openmp/fft_openmp.html">
FFT_OPENMP</a>,
a C++ program which
demonstrates the computation of a Fast Fourier Transform
in parallel, using OpenMP.
</p>
<p>
<a href = "../../cpp_src/heated_plate_openmp/heated_plate_openmp.html">
HEATED_PLATE_OPENMP</a>,
a C++ program which
solves the steady (time independent) heat equation in a 2D
rectangular region, using OpenMP to run in parallel.
</p>
<p>
<a href = "../../cpp_src/hello_openmp/hello_openmp.html">
HELLO_OPENMP</a>,
a C++ program which
prints out "Hello, world!" using the OpenMP parallel programming environment.
</p>
<p>
<a href = "../../cpp_src/md_openmp/md_openmp.html">
MD_OPENMP</a>,
a C++ program which
carries out a molecular dynamics simulation using OpenMP.
<p>
<p>
<a href = "../../cpp_src/multitask_openmp/multitask_openmp.html">
MULTITASK_OPENMP</a>,
a C++ program which
demonstrates how to "multitask", that is, to execute several unrelated
and distinct tasks simultaneously, using OpenMP for parallel execution.
</p>
<p>
<a href = "../../cpp_src/mxv_openmp/mxv_openmp.html">
MXM_OPENMP</a>,
a C++ program which
computes a dense matrix product C=A*B,
using OpenMP for parallel execution.
<p>
<p>
<a href = "../../cpp_src/mxv_openmp/mxv_openmp.html">
MXV_OPENMP</a>,
a C++ program which
compares the performance of plain vanilla Fortran and the FORTRAN90
intrinsic routine MATMUL, for the matrix multiplication problem
y=A*x, with and without parallelization by OpenMP.
<p>
<p>
<a href = "../../cpp_src/openmp/openmp.html">
OPENMP</a>,
C++ programs which
illustrate the use of the OpenMP application program interface
for carrying out parallel computations in a shared memory environment.
</p>
<p>
<a href = "../../cpp_src/poisson_openmp/poisson_openmp.html">
POISSON_OPENMP</a>,
a C++ 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.
</p>
<p>
<a href = "../../cpp_src/prime_openmp/prime_openmp.html">
PRIME_OPENMP</a>,
a C++ program which
counts the number of primes between 1 and N, using OpenMP for parallel execution.
</p>
<p>
<a href = "../../cpp_src/quad_openmp/quad_openmp.html">
QUAD_OPENMP</a>,
a C++ program which
approximates an integral using a quadrature rule, and carries out the
computation in parallel using OpenMP.
</p>
<p>
<a href = "../../cpp_src/random_openmp/random_openmp.html">
RANDOM_OPENMP</a>,
a C++ program which
illustrates how a parallel program using OpenMP can generate multiple
distinct streams of random numbers.
</p>
<p>
<a href = "../../cpp_src/satisfy_openmp/satisfy_openmp.html">
SATISFY_OPENMP</a>,
a C++ program which
demonstrates, for a particular circuit, an exhaustive search
for solutions of the circuit satisfy problem,
using OpenMP for parallel execution.
<p>
<p>
<a href = "../../cpp_src/schedule_openmp/schedule_openmp.html">
SCHEDULE_OPENMP</a>,
a C++ program which
demonstrates the default, static, and dynamic methods of "scheduling"
loop iterations in OpenMP to avoid work imbalance.
<p>
<p>
<a href = "../../cpp_src/sgefa_openmp/sgefa_openmp.html">
SGEFA_OPENMP</a>,
a C++ program which
reimplements the SGEFA/SGESL linear algebra routines from
LINPACK for use with OpenMP.
</p>
<p>
<a href = "../../cpp_src/ziggurat/ziggurat.html">
ZIGGURAT</a>,
a C++ program which
generates points from a uniform, normal or exponential distribution, using
the ziggurat method.
</p>
<h3 align = "center">
Reference:
</h3>
<p>
<ol>
<li>
Philip Leong, Guanglie Zhang, Dong-U Lee, Wayne Luk, John Villasenor,<br>
A comment on the implementation of the ziggurat method,<br>
Journal of Statistical Software,<br>
Volume 12, Number 7, February 2005.
</li>
<li>
George Marsaglia, Wai Wan Tsang,<br>
The Ziggurat Method for Generating Random Variables,<br>
Journal of Statistical Software,<br>
Volume 5, Number 8, October 2000, seven pages.
</li>
</ol>
</p>
<h3 align = "center">
Source Code:
</h3>
<p>
<ul>
<li>
<a href = "ziggurat_openmp.cpp">ziggurat_openmp.cpp</a>, the source code.
</li>
</ul>
</p>
<h3 align = "center">
Examples and Tests:
</h3>
<p>
<b>ZIGGURAT_LOCAL</b> compiles, links, loads and runs the program
using 1, 2 and 4 threads, the local interactive environment,
and the GNU G++ compiler.
<ul>
<li>
<a href = "ziggurat_local.sh">ziggurat_local.sh</a>,
BASH commands.
</li>
<li>
<a href = "ziggurat_local_output.txt">ziggurat_local_output.txt</a>,
the output file;
</li>
</ul>
</p>
<h3 align = "center">
List of Routines:
</h3>
<p>
<ul>
<li>
<b>MAIN</b> is the main program for ZIGGURAT_OPENMP.
</li>
<li>
<b>TEST01</b> tests SHR3.
</li>
<li>
<b>TEST02</b> tests R4_UNI.
</li>
<li>
<b>TEST03</b> tests R4_NOR.
</li>
<li>
<b>TEST04</b> tests R4_EXP.
</li>
<li>
<b>R4_EXP</b> returns an exponentially distributed single precision real value.
</li>
<li>
<b>R4_EXP_SETUP</b> sets data needed by R4_EXP.
</li>
<li>
<b>R4_NOR</b> returns a normally distributed single precision real value.
</li>
<li>
<b>R4_NOR_SETUP</b> sets data needed by R4_NOR.
</li>
<li>
<b>R4_UNI</b> returns a uniformly distributed real value.
</li>
<li>
<b>SHR3</b> evaluates the SHR3 generator for integers.
</li>
<li>
<b>TIMESTAMP</b> prints the current YMDHMS date as a time stamp.
</li>
</ul>
</p>
<p>
You can go up one level to <a href = "../cpp_src.html">
the C++ source codes</a>.
</p>
<hr>
<i>
Last revised on 04 October 2013.
</i>
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