A recursive implementation of the dimensionless FFT

A divide and conquer algorithm is presented for computing arbitrary multi-dimensional discrete Fourier transforms. In contrast to standard approaches such as the row-column algorithm, this algorithm allows an arbitrary decomposition, based solely on the size of the transform independent of the dimension of the transform. Only minor modifications are required to compute transforms with different dimension. These modifications were incorporated into the FFTW package so that the algorithm for computing onedimensional transforms can be used to compute arbitrary dimensional transforms. This reduced the runtime of many multi-dimensional transforms.