prime_openmp, a FORTRAN90 code which counts the number of primes between 1 and N, using OpenMP to carry out the calculation in parallel.
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.
This program is mainly a starting point for investigations into parallelization.
Here are the counts of the number of primes for some selected values of N:
| N | Pi(N), Number of Primes |
|---|---|
| 1 | 0 |
| 2 | 1 |
| 4 | 2 |
| 8 | 4 |
| 16 | 6 |
| 32 | 11 |
| 64 | 18 |
| 128 | 31 |
| 256 | 54 |
| 512 | 97 |
| 1024 | 172 |
| 2048 | 309 |
| 4096 | 564 |
| 8192 | 1028 |
| 16384 | 1900 |
| 32768 | 3512 |
| 65536 | 6542 |
| 131072 | 12251 |
In the BASH shell, the program could be run with 2 threads using the commands:
export OMP_NUM_THREADS=2
./prime_openmp
The computer code and data files described and made available on this web page are distributed under the MIT license
prime_openmp is available in a C version and a C++ version and a FORTRAN90 version.
DIJKSTRA_OPENMP, a FORTRAN90 code which uses OpenMP to parallelize a simple example of Dijkstra's minimum distance algorithm for graphs.
FFT_OPENMP, a FORTRAN90 code which demonstrates the computation of a Fast Fourier Transform in parallel, using OpenMP.
HEATED_PLATE_OPENMP, a FORTRAN90 code which solves the steady (time independent) heat equation in a 2D rectangular region, using OpenMP to run in parallel.
HELLO_OPENMP, a FORTRAN90 code which prints out "Hello, world!" using the OpenMP parallel programming environment.
JACOBI_OPENMP, a FORTRAN90 code which illustrates the use of the OpenMP application program interface to parallelize a Jacobi iteration solving A*x=b.
MANDELBROT_OPENMP, a FORTRAN90 code which generates an ASCII Portable Pixel Map (PPM) image of the Mandelbrot fractal set, using OpenMP for parallel execution.
MD_OPENMP, a FORTRAN90 code which carries out a molecular dynamics simulation in parallel, using OpenMP.
MXM_OPENMP, a FORTRAN90 code which computes a dense matrix product C=A*B, using OpenMP for parallel execution.
openmp_test, FORTRAN90 codes which use the OpenMP application code interface for carrying out parallel computations in a shared memory environment.
POISSON_OPENMP, a FORTRAN90 code 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_MPI, a FORTRAN90 code which counts the number of primes between 1 and N, using MPI for parallel execution.
PRIME_PARFOR, a MATLAB program which counts the number of primes between 1 and N; it runs in parallel using MATLAB's "parfor" facility.
PRIME_SERIAL, a FORTRAN90 code which counts the number of primes between 1 and N, intended as a starting point for the creation of a parallel version.
QUAD_OPENMP, a FORTRAN90 code which approximates an integral using a quadrature rule, and carries out the computation in parallel using OpenMP.
RANDOM_OPENMP, a FORTRAN90 code which illustrates how a parallel program using OpenMP can generate multiple distinct streams of random numbers.
SATISFY_OPENMP, a FORTRAN90 code 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 code which demonstrates the default, static, and dynamic methods of "scheduling" loop iterations in OpenMP to avoid work imbalance.
SGEFA_OPENMP, a FORTRAN90 code which reimplements the SGEFA/SGESL linear algebra routines from LINPACK for use with OpenMP.
ZIGGURAT_OPENMP, a FORTRAN90 code which demonstrates how the ZIGGURAT library can be used to generate random numbers in an OpenMP parallel program.