RMFTL is a library of real and complex power-of-two multidimensional FFT (Fast Fourier Transform) routines that are faster and more accurate than iterative application of 1-dimensional transform routines employing Cooley-Tukey or Sande-Tukey methods.   Based on a proprietary algorithm, RMFTL affords the following significant advantages:
The number of complex multiplications for a D-dimensional transform is significantly less than required by interative application of 1-dimensional FFTs, the conventional method for forming multidimensional FFTs.   The relative number of multiplications goes approximately as 2/D, for D > 2.   See note below.
Fewer multiplications mean greater speed of execution and less roundoff error compared with iterative application of conventional 1-dimensional FFTs.
The transform can be taken along any subset of the dimensions of the multidimensional array.   Moreover, the transforms along the selected dimensions are formed simultaneously and do not require transposition or reordering of the multidimensional array, which affords another significant time savings.   See note below.
Transforms in any direction through the array are always developed by operating along the direction that the data are written.   Therefore, transposition of data is never required for arrays too large to fit into active memory, completely eliminating the additional, and sometimes prohibitive, I/O overhead associated with large external arrays.   See note below.
Transforms of real data, as well as complex data, are computed in place, regardless of the dimensionality of the transform, or the subset of directions along which the transform is taken. That is, real transform results always fit exactly within the space of the original real array, with no extra storage required.
A complete package of routines is included for converting between normally ordered, bit-reversed, and packed (real transform) data.

NOTE:   Further information on the number of complex multiplications and the number of external or row data accesses required by RMFTL is provided here in web page format.   To download this information in Adobe PDF (Acrobat Reader) format, click here.

Davis Associates, Inc. is currently in the process of porting RMFTL from its original real mode DOS version to Windows.   If you are interested and would like to be notified when the new version of RMFTL becomes available, please complete and submit the form below.

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Davis Associates, Inc. 43 Holden Road Newton, MA 02465-1909 U.S.A. 617-244-1450 FAX: 617-964-4917
RMFTL is a trademark of Davis Associates, Inc.

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