# PRIME_SPMD Counting Primes in Parallel using SPMD

PRIME_SPMD is a MATLAB program which counts the number of primes between 1 and N, executing in parallel using MATLAB's SPMD facility.

The algorithm is completely naive. For each integer I, it simply checks whether any smaller J evenly divides it. The total amount of work for a given N is thus roughly proportional to 1/2*N^2.

There is very little memory traffic and no communication, so this program is a good test for the pure computational speedup offered by MATLAB's Parallel Programming Toolbox.

The basic function has the form:

function total = prime_fun ( n )
where
• n, the largest integer to check.
• total, the number of primes between 1 and n.

Depending on the situation, the function could be executed in parallel:

• interactively, and locally, using the matlabpool command;
• indirectly, and locally, using the batch command;
• indirectly, and on the Ithaca cluster, using the batch command;
• indirectly, and on the FSU HPC cluster, using the fsuClusterMatlab command;

### Licensing:

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

### Languages:

PRIME_SPMD is available in a MATLAB version.

### Related Data and Programs:

CELL_DETECTION_TASKS, a MATLAB program which creates modified versions of a sequence of gray-scale TIF files containing images of cells; the process of each file is carried out independently, using the "task" feature of MATLAB's parallel computing toolbox.

CG_DISTRIBUTED, a MATLAB program which implements a version of the NAS CG conjugate gradient benchmark, using distributed memory.

COLLATZ_PARFOR, a MATLAB program which seeks the maximum Collatz sequence between 1 and N, running in parallel using MATLAB's "PARFOR" feature.

CONTRAST_SPMD, a MATLAB program which demonstrates the SPMD parallel programming feature for image operations; the client reads an image, the workers increase contrast over separate portions, and the client assembles and displays the results.

CONTRAST2_SPMD, a MATLAB program which demonstrates the SPMD parallel programming feature for image operations; this improves the contrast_spmd program by allowing the workers to share some data; this makes it possible to eliminate artificial "seams" in the processed image.

DIJKSTRA_SPMD, a MATLAB program which uses the SPMD feature to parallelize a simple example of Dijkstra's minimum distance algorithm for graphs.

FACE_SPMD, a MATLAB program which demonstrates the SPMD parallel programming feature; the client has a 3D box that has been dissected into tetrahedrons. Multiple workers cooperate to construct a list of the triangular faces that lie on the boundaries of the box.

FD2D_HEAT_EXPLICIT_SPMD, a MATLAB program which uses the finite difference method and explicit time stepping to solve the time dependent heat equation in 2D. A black and white image is used as the "initial condition". MATLAB's SPMD facility is used to carry out the computation in parallel.

FMINCON_PARALLEL, a MATLAB program which demonstrates the use of MATLAB's FMINCON constrained minimization function, taking advantage of MATLAB's Parallel Computing Toolbox for faster execution.

IMAGE_DENOISE_SPMD, a MATLAB program which demonstrates the SPMD parallel programming feature for image operations; the client reads an image, the workers process portions of it, and the client assembles and displays the results.

LINEAR_SOLVE_DISTRIBUTED a MATLAB program which solves a linear system A*x=b using MATLAB's spmd facility, so that the matrix A is "distributed" across multiple MATLAB workers.

MATLAB_PARALLEL, MATLAB programs which illustrate "local" parallel programming on a single computer with MATLAB's Parallel Computing Toolbox.

MATRIX_ASSEMBLE_SPMD, a MATLAB program which demonstrates the SPMD parallel programming feature by having each worker assemble part of the Hilbert matrix, which is then combined into one array by the client program.

MD_PARFOR, a MATLAB program which carries out a molecular dynamics simulation, running in parallel using MATLAB's "PARFOR" feature.

ODE_SWEEP_PARFOR, a MATLAB program which demonstrates how the PARFOR command can be used to parallelize the computation of a grid of solutions to a parameterized system of ODE's.

PLOT_SPMD, a MATLAB library which demonstrates the SPMD parallel programming feature, by having a number of labs compute parts of a sine plot, which is then displayed by the client process.

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

PRIME_PARFOR, a MATLAB program which counts the number of primes between 1 and N; running in parallel using MATLAB's "PARFOR" feature.

PRIME_PLOT a MATLAB program which displays a box plot of the prime and composite numbers.

PRIME_SERIAL, a MATLAB program which counts the number of primes between 1 and N, intended as a starting point for the creation of a parallel version.

QUAD_PARFOR, a MATLAB program which estimates an integral using quadrature; running in parallel using MATLAB's "PARFOR" feature.

QUAD_SPMD, a MATLAB program which estimates an integral using quadrature; running in parallel using MATLAB's "SPMD" feature.

QUAD_TASKS, a MATLAB program which estimates an integral using quadrature; running in parallel using MATLAB's "TASK" feature.

RANDOM_WALK_2D_AVOID_TASKS, a MATLAB program which computes many self avoiding random walks in 2D by creating a job which defines each walk as a task, and then computes these independently using MATLAB's Parallel Computing Toolbox task computing capability.

SATISFY_PARFOR, a MATLAB program which demonstrates, for a particular circuit, an exhaustive search for solutions of the circuit satisfiability problem, running in parallel using MATLAB's "PARFOR" feature.

SUBSET_SUM_TASKS, a MATLAB program which solves a subset sum problem by exhaustive search, subdividing the search range among separate tasks.

### Reference:

The User's Guide for the Parallel Computing Toolbox is available at http://www.mathworks.com/access/helpdesk/help/pdf_doc/distcomp/distcomp.pdf

1. Gaurav Sharma, Jos Martin,
MATLAB: A Language for Parallel Computing,
International Journal of Parallel Programming,
Volume 37, Number 1, pages 3-36, February 2009.

### Examples and Tests:

• prime_fun.m the function which performs the computations.
• prime_pool.m a script which uses the MATLABPOOL command to run the function locally and interactively.
• prime_script.m a script which calls the function, necessary for the BATCH command.
• prime_batch_local.m a script which uses the BATCH command to run the function indirectly and locally.
• prime_batch_ithaca.m a script which uses the BATCH command to run the function indirectly on the Ithaca cluster.
• prime_fsu.m a script which uses the fsuClusterMatlab command to run the function indirectly on the FSU HPC cluster.

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

Last revised on 01 June 2010.