sFFT: a faster accurate computation of the p-value of the entropy score

We present sFFT, an algorithm for efficiently computing the p-value of the information content, or the entropy score of an alignment of DNA sequences. Applying the FFT algorithm to an exponentially shifted probability mass function allows us perform fast convolutions that do not suffer from the otherwise overwhelming effect of accumulated numerical roundoff errors. Through a rigorous analysis of the propagation of numerical errors across the various steps of sFFT, we provide a theoretical bound on the overall error of our computed p-value. The accuracy of the computed p-value, as well as the utility of the error bound, are empirically demonstrated. Although there are faster algorithms that would compute this p-value, they can err significantly; sFFT is the fastest reliable algorithm. Finally, we note that the basic algorithm is likely to be applicable in a wider context than the one considered here.