International
Tables for Crystallography Volume B Reciprocal space Edited by U. Shmueli © International Union of Crystallography 2006 
International Tables for Crystallography (2006). Vol. B, ch. 1.3, p. 58

In order to explore systematically all possible algorithms for carrying out a given DFT computation, and to pick the one best suited to a given machine, attempts have been made to develop:
Task (i) can be accomplished by systematic use of a tensor product notation to represent the various stages into which the DFT can be factored (reindexing, small transforms on subsets of indices, twiddle factors, digitreversal permutations).
Task (ii) may for instance use the Winograd CBA normal form for each small transform, then apply the rules governing the rearrangement of tensor product and ordinary product × operations on matrices. The matching of these rearrangements to the architecture of a vector and/or parallel computer can be formalized algebraically [see e.g. Chapter 2 of Tolimieri et al. (1989)].
Task (iii) is a complex search which requires techniques such as dynamic programming (Bellman, 1958).
Johnson & Burrus (1983) have proposed and tested such a scheme to identify the optimal tradeoffs between prime factor nesting and Winograd nesting of small Winograd transforms. In step (ii), they further decomposed the preaddition matrix A and postaddition matrix C into several factors, so that the number of design options available becomes very large: the Npoint DFT when N has four factors can be calculated in over 10^{12} distinct ways.
This large family of nested algorithms contains the prime factor algorithm and the Winograd algorithms as particular cases, but usually achieves greater efficiency than either by reducing the f.p. multiplication count while keeping the number of f.p. additions small.
There is little doubt that this systematic approach will be extended so as to incorporate all available methods of restructuring the DFT.
References
Bellman, R. (1958). Dynamic programming and stochastic control processes. Inf. Control, 1, 228–239.Johnson, H. W. & Burrus, C. S. (1983). The design of optimal DFT algorithms using dynamic programming. IEEE Trans. Acoust. Speech Signal Process. 31, 378–387.
Tolimieri, R., An, M. & Lu, C. (1989). Algorithms for discrete Fourier transform and convolution. New York: SpringerVerlag.