Bit reversal on uniprocessors

SIAM Review

Volumn 38, Issue 1, 1996, Pages 1-26

  Karp, Alan H ^a  

^a HEWLETT PACKARD LABORATORIES   (United States)

Author keywords

Bit reversal; Fast Fourier transform; Hierarchical memory

Indexed keywords

ALGORITHMS; COMPUTER SYSTEMS; DATA STORAGE EQUIPMENT; FAST FOURIER TRANSFORMS; FORTRAN (PROGRAMMING LANGUAGE); HIERARCHICAL SYSTEMS;

BIT REVERSAL; HIERARCHICAL MEMORY; UNIPROCESSORS;

DATA HANDLING;

EID: 0030105461     PISSN: 00361445     EISSN: None     Source Type: Journal    
DOI: 10.1137/1038001     Document Type: Article

References (44)

1. D. BAILEY, private communication, 1989.
2. D. H. BAILEY, FFTs in external or hierarchical memory, J. Supercomputing, 4 (1990), pp. 23-35.
3. R. BELL, IBM RISC System/6000 NIC Tuning Guide for Fortran and C, Tech. report GG24-3611-01, IBM International Technical Support Center, Poughkeepsie, NY, July 1991.
4. A. BISWAS, Bit reversal in FFT from matrix viewpoint, IEEE Trans. Signal Proc., 39 (1991), pp. 1415-1418.
5. E. O. BRIGHAM, The Fast Fourier Transform, Prentice-Hall, Inc., Englewood Cliffs, NJ, 1974.
6. O. BUNEMAN, Conversion of FFT's to fast Hartley transforms, SIAM J. Sci. Statist. Comput., 7 (1986), pp. 624-638.
7. J. W. COOLEY, P. A. W. LEWIS, AND P. D. WELCH, The fast Fourier transform and its applications, IEEE Trans. Education, 12 (1969), pp. 27-34.
8. P. DUHAMEL, A connection between bit reversal and matrix transposition: Hardware and software consequences, IEEE Trans. Acoustics, Speech, Sig. Proc., 38 (1990), pp. 1893-1896.
9. A. EDELMAN, Optimal matrix transposition and bit reversal on hypercubes: All-to-all personalized communication, J. Parallel Distributed Computing, 11 (1991), pp. 328-331.
10. D. M. W. EVANS, An improved digit-reversal permutation algorithm for the fast Fourier and Hartley transforms, IEEE Trans. Acoustics, Speech, Sig. Proc., ASSP-35 (1987), pp. 1120-1125.
11. _, A second improved digit-reversal permutation algorithm for fast Fourier transforms, IEEE Trans. Acoustics, Speech, Sig. Proc., 37 (1989), pp. 1288-1291.
12. J. FERRANTE, V. SARKAR, AND W. THRASH, On estimating and enhancing cache effectiveness, Proc. 4th Workshop on Languages and Compilers for Parallel Computing, 1991; Lecture Notes in Computer Science series 589, Springer-Verlag.
13. D. FRASER, Bit-reversal and generalized sorting of multidimensional arrays, Signal Processing, 9 (1985), pp. 163-176.
14. S. HELLER AND A. EDELMAN, private communication, 1991.
15. C.-T. Ho AND M. T. RAGHUNATH, Efficient communication primitives on hypercubes, Tech. report RJ 7932, IBM Almaden Research Center, San Jose, CA, 1991.
16. R. W. HOCKNEY AND C. R. JESSHOPE, Parallel Computers 2, Adam Hilger, Bristol, England, 1988.
17. A. C. ELSTER, Fast Bit-Reversal Algorithms, Internat. Conf. Acoustics, Speech and Signal Processing, IEEE Press, May 1989, pp. 1099-1102.
18. J. JEONG AND W. J. WILLIAMS, A fast recursive bit-reversal algorithm, in Internat. Conf. Acoustics, Speech and Sig. Processing, IEEE, IEEE Press, April 1990.
19. S. L. JOHNSON AND C.-T. Ho, Algorithms for matrix transposition on Boolean N-cube configured ensemble architectures, SIAM J. Matrix Anal. Appl., 9 (1988), pp. 419-454.
20. _, Optimal communication channel utilizatio for matrix transposition and related permuations on Boolean cubes, Tech. report TMC-187, Thinking Machines Corp., Cambridge, MA, 1991.
21. F. I. KHAN, Another Fast Algorithm for Bit Reversal, preprint, 1992.
22. L. KOHN AND N. MARGULIS, The i860™ 64-bit supercomputing microprocessor, in Proc. Supercomputing '89, Los Alamitos, CA, November 1989, IEEE Computer Society Press, pp. 450-456.
23. D. G. KORN AND J. J. LAMBIOTTE, JR., Computing the fast Fourier transform on a vector computer, Math. Comp., 33 (1979), pp. 977-992.
24. J. MIDDLEDITCH, private communication, 1992.
25. b), IEEE Trans. Signal Processing, 40, (1992), pp. 1004-1008.
26. R. J. POLGE AND B. K. BHAGAVAN, Efficient fast Fourier transform programs for arbitrary factors with one step loop unscrambling, IEEE Trans. Computers, C25 (1976), pp. 534-539.
27. R. J. POLGE, B. K. BHAGAVAN, AND J. M. CARSWELL, Fast computational algorithms for bit reversal, IEEE Trans. Computers, C-23 (1974), pp. 1-9.
28. J. J. RODRIGUEZ, An improved bit-reversal algorithm for the fast Fourier transform, in IEEE Internat. Conf. Acoustics, Speech, Sig. Proc., 1988, pp. 1407-1410.
29. J. J. RODRIGUEZ, An improved FFT digit-reversal algorithm, IEEE Trans. Acoustics, Speech and Sig. Processing, 37 (1989), pp. 1298-1300.
30. P. RÖSEL, Timing of some bit reversal algorithms, Sig. Processing, 18 (1989), pp. 425-433.
31. U. RUTKOWSKA, A simple algorithm for the bit-reversal permutation, Sig. Processing, 23 (1991), pp. 313-317.
32. _, Fast recursive unscrambling algorithms, J. New Gener. Comput. Syst., 4 (1991), pp. 29-40.
33. J. SEQUEL, D. BELLMAN, AND J. FEO, Digit-index permuation algorithms for FFT computations: An applicative approach, in Proc. High-Performance Functional Computing Conf., Lawrence Livermore National Laboratory, Denver, CO, 1995, pp. 97-104.
34. R. C. SINGLETON, A method for computing the fast Fourier transform with auxiliary memory and limited high-speed storage, IEEE Trans. Audio Electroacoust., AU-15 (1967), pp. 91-97.
35. _, An algorithm for computing the mixed radix fast Fourier transform, IEEE Trans. Audio Electroacoust., AU-17 (1969), pp. 93-103.
36. A. J. SMITH, Cache memories, Computing Surveys, 14 (1982), pp. 473-530.
37. P. N. SWARZTRAUBER, FFT algorithms for vector computers, Parallel Computing, 1 (1984), pp. 45-63.
38. _, Multiprocessor FFTs, Parallel Computing, 5 (1987), pp. 197-210.
39. C. VAN LOAN, Computational Frameworks for the Fast Fourier Transform, Society for Industrial and Applied Mathematics, Philadelphia, PA, 1992.
40. V. VESELY, Fast cell-structured algorithm for digit reversal of arbitrary length, SIAM J. Sci. Statist. Comput., 12 (1991), pp. 298-310.
41. J. S. WALKER, A new bit reversal algorithm, IEEE Trans. Acoustics, Speech, Sig. Proc., 38 (1990), pp. 1472-1483.
42. H. H. WANG, On vectorizing the fast Fourier transform, BIT, 20 (1980), pp. 233-243.
43. A. A. YONG, A better FFT bit-reversal algorithm without tables, IEEE Trans. Signal Processing, 39 (1991), pp. 2365-2367.
44. H. YOON, K. Y. LEE, AND A. BAHIRI, On the modulo N translators for the prime memory system, J. Parallel Distrib. Comput., 8 (1990), pp. 72-76.