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Manuscript Title: Fast sine/cosine transform for periodic functions with reflection symmetry.
Authors: A. Besprozvannaya, D.J. Tannor
Program title: ROFT/REFT/COFT/CEFT
Catalogue identifier: ABTX_v1_0
Distribution format: gz
Journal reference: Comput. Phys. Commun. 63(1991)569
Programming language: Fortran.
Computer: STELLAR GS2000.
Operating system: STELLIX.
Keywords: General purpose, Fourier, Sine/cosine fast Transform, Periodic function, Real/complex, Odd/even symmetry, Inverse transform.
Classification: 4.6.

Nature of problem:
In many physical applications one is interested in obtaining a Fourier transform of a function having a particular reflection symmetry using only half of the grid points, thus saving both computation time and space without any loss of information.

Solution method:
The algorithm is based on fast sine/cosine transforms with some modifications which make it applicable to a wider class of real and complex functions.

The number of grid points should be a power of two in odd case and a power of two plus one in even case. We strongly recommend all the data to be double precision to achieve sufficient accuracy in the computations.

Running time:
It depends greatly on the computer type, the compiler optimization and the efficiency of the FFT routine used. For example, to perform 10**5 forward/inverse transform operations with an even data array of 33 elements using a highly-optimized Stellar FFT library, it took about 40 s for real and 80 s for complex double precision data.