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Manuscript Title: MFFT: a package for two- and three-dimensional vectorized discrete Fourier transforms.
Authors: A. Nobile, V. Roberto
Program title: MFFT
Catalogue identifier: AALL_v1_0
Distribution format: gz
Journal reference: Comput. Phys. Commun. 42(1986)233
Programming language: Fortran.
Computer: CRAY X-MP 12.
Operating system: COS 1.14.
RAM: 27K words
Word size: 64
Keywords: Fast fourier transform, Parallel computations, Vector computations, General purpose, Fourier.
Classification: 4.6.

Revision history:
Type Tit le Reference
adaptation 0001 MFFT4 See below

Nature of problem:
Any problem requiring Fourier transforms.

Solution method:
The Discrete Fourier Transform (DFT) is calculated using the Fast Fourier Transform (FFT) algorithms implemented in place in a vectorized form. In particular the radix-2, radix-3, radix-5, and mixed-radix algorithms are implemented in two distinct versions: decimation-in-time (or Cooley-Tukey) and decimation-in-frequency (or Gentleman-Sande).

Restrictions:
In the data matrix to be tranformed each dimension has to be a product of integer powers of 2,3,5. In real transforms the first dimension in the input data has to be an even number.

Running time:
Top performances are reached for input data lengths which are powers of 2. The CPU time required by a complex DFT 64*64*64 is roughly 0.2 s, by a real DFT 512*512 is 0.12 s. If powers of 3 and 5 are present, then the typical running time is increased up to a 60%.

ADAPTATION SUMMARY
Manuscript Title: MFFT4: four dimensional vectorized fast Fourier transforms.
Authors: A. Nobile, V. Roberto, F. Saitta
Program title: 0001 MFFT4
Catalogue identifier: AALL_v1_0
Distribution format: gz
Journal reference: Comput. Phys. Commun. 48(1988)313
Programming language: Fortran.
Computer: CRAY X-MP 11-48.
RAM: 27K words
Word size: 64
Classification: 4.6.

Nature of problem:
To extend to four dimensions the vectorization scheme adopted to obtain very good performances for multidimensional fast Fourier transform (FFT) codes on Cray machines.

Solution method:
Classical FFT algorithms (decimation-in-time and decimation-in- frequency,) are vectorized and optimized.