Efficiency of radix-K transforms on computers with cache

The impact of the most critical part of the up-to-date computer memory hierarchy, the cache, on the efficiency of fast transform algorithms (e.g. FFT, DCT/DST, DWHT, including multidimensional generalizations) is analyzed. Cache misses can severely deteriorate the efficiency of a computer program, and indeed, it is shown that for large data vectors a modification of a fast transform algorithm realization may change their number dramatically. Several memory managing problems are pointed out, and suggestions for their amelioration are given. Formulae on the minimum number of data-related cache misses for radix-2 ^s transform realizations are given, s is an integer