https://github.com/openai/math/blob/main/preprints/An-explic...

"We give a deterministic algorithm that computes the discrete Fourier transform at every length n in O ( n ( log ⁡ n ) ** (1 − 10 ** −13)) operations. The model uses exact complex arithmetic, unrestricted coefficients, specified Fourier roots, and unit-cost logarithmic-size indexing; scalar preparation and array organization are included."