FFT_OPENMP
Fast Fourier Transform Using OpenMP

FFT_OPENMP is a FORTRAN77 program which demonstrates the computation of a Fast Fourier Transform in parallel, using OpenMP.

On an Apple PowerPC G5 with two processors, the following results were observed:

Threads	N	Time	MegaFLOPS
1	131072	0.094	117.7
2	131072	0.054	203.0
4	131072	0.056	198.8

The relatively low size of N seems to be due to a limitation in the FORTRAN77 compiler.

Usage:

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

        export OMP_NUM_THREADS=2
        ./fft_openmp
      

Licensing:

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

Languages:

FFT_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 FORTRAN77 program which uses OpenMP to parallelize a simple example of Dijkstra's minimum distance algorithm for graphs.

FFT_SERIAL, a FORTRAN77 program which demonstrates the computation of a Fast Fourier Transform, and is intended as a starting point for implementing a parallel version using OpenMP.

FFTW3, FORTRAN77 programs which illustrate the use of the FFTW3 library for Fast Fourier Transforms, by Matteo Frigo and Steven Johnson.

HEATED_PLATE_OPENMP, a FORTRAN77 program which solves the steady (time independent) heat equation in a 2D rectangular region, using OpenMP to run in parallel.

HELLO_OPENMP, a FORTRAN77 program which prints out "Hello, world!" using the OpenMP parallel programming environment.

MANDELBROT_OPENMP, a FORTRAN77 program which generates an ASCII Portable Pixel Map (PPM) image of the Mandelbrot fractal set, using OpenMP for parallel execution.

MD_OPENMP, a FORTRAN77 program which carries out a molecular dynamics simulation using OpenMP.

MULTITASK_OPENMP, a FORTRAN77 program which demonstrates how to "multitask", that is, to execute several unrelated and distinct tasks simultaneously, using OpenMP for parallel execution.

MXM_OPENMP, a FORTRAN77 program which computes a dense matrix product C=A*B, using OpenMP for parallel execution.

MXV_OPENMP, a FORTRAN77 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.

OPENMP, FORTRAN77 programs which illustrate the use of the OpenMP application program interface for carrying out parallel computations in a shared memory environment.

POISSON_OPENMP, a FORTRAN77 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 FORTRAN77 program which counts the number of primes between 1 and N, using OpenMP for parallel execution.

QUAD_OPENMP, a FORTRAN77 program which approximates an integral using a quadrature rule, and carries out the computation in parallel using OpenMP.

RANDOM_OPENMP, a FORTRAN77 program which illustrates how a parallel program using OpenMP can generate multiple distinct streams of random numbers.

SATISFY_OPENMP, a FORTRAN77 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 FORTRAN77 program which demonstrates the default, static, and dynamic methods of "scheduling" loop iterations in OpenMP to avoid work imbalance.

SFTPACK, a FORTRAN77 library which implements the "slow" Fourier transform, intended as a teaching tool and comparison with the fast Fourier transform.

SGEFA_OPENMP, a FORTRAN77 program which solves a linear system by Gaussian elimination, using OpenMP.

ZIGGURAT_OPENMP, a FORTRAN77 program which demonstrates how the ZIGGURAT library can be used to generate random numbers in an OpenMP parallel program.

Reference:

1. Wesley Petersen, Peter Arbenz,
   Introduction to Parallel Computing - A practical guide with examples in C,
   Oxford University Press,
   ISBN: 0-19-851576-6,
   LC: QA76.58.P47.
2. Rohit Chandra, Leonardo Dagum, Dave Kohr, Dror Maydan, Jeff McDonald, Ramesh Menon,
   Parallel Programming in OpenMP,
   Morgan Kaufmann, 2001,
   ISBN: 1-55860-671-8,
   LC: QA76.642.P32.
3. Barbara Chapman, Gabriele Jost, Ruud vanderPas, David Kuck,
   Using OpenMP: Portable Shared Memory Parallel Processing,
   MIT Press, 2007,
   ISBN13: 978-0262533027,
   LC: QA76.642.C49.

Source Code:

• fft_openmp.f, the source code.

Examples and Tests:

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

• fft_local_gfortran.sh, BASH commands.
• fft_local_gfortran_output.txt, the output file;

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

• fft_local_ifort.sh, BASH commands.
• fft_local_ifort_output.txt, the output file;

FFT_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 GFORTRAN Fortran compiler.

• fft_ithaca_gfortran.sh, BASH commands.
• fft_ithaca_gfortran_output.txt, the output file;

FFT_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 IFORT Fortran compiler.

• fft_ithaca_ifort.sh, BASH commands.
• fft_ithaca_ifort_output.txt, the output file;

List of Routines:

• MAIN is the main program for FFT_OPENMP.
• CCOPY copies a complex vector.
• CFFT2 performs a complex Fast Fourier Transform.
• CFFTI sets up sine and cosine tables needed for the FFT calculation.
• GGL generates u(0,1) distributed random numbers.
• STEP carries out one step of the workspace version of CFFT2.
• TIMESTAMP prints the YMDHMS date as a timestamp.

You can go up one level to the FORTRAN77 source codes.