The analysis assumes constant-time arithmetic for the Fourier transforms. This limits the size of the multiplicands, since the error terms eventually grow large

The analysis assumes constant-time arithmetic for the Fourier transforms. This limits the size of the multiplicands, since the error terms eventually grow large enough to affect the computed product. From the paper: "Note that this error is due to the limited precision in which we can represent numbers on computers, it does not occur in exact arithmetic." But of course, exact reals (twiddle factors aren't rational) are rife with undecidability if not uncomputability.