 However, these algorithms require too many additions to be practical, at least on modern computers with hardware multipliers (Duhamel, 1990; Frigo & Johnson, 2005).A tight lower bound is not known on the number of required additions, although lower bounds have been proved under some restrictive assumptions on the algorithms.In 1973, Morgenstern proved an Ω("N" log "N") lower bound on the addition count for algorithms where the multiplicative constants have bounded magnitudes (which is true for most but not all FFT algorithms).