Adaptive Computation of Self Sorting In-Place FFTs on Hierarchical Memory Architectures

Computing "In-place and In-order" FFT poses a very difficult problem on hierarchical memory architectures where data movement can seriously degrade the performance. In this paper the authors present recursive formulation of a self sorting in-place FFT algorithm that adapts to the target architecture. For transform sizes where an in-place, in-order execution is not possible, the authors show how schedules can be constructed that use minimum work-space to perform the computation efficiently. In order to express and construct FFT schedules, they present a context free grammar that generates the FFT Schedule Specification Language.