Not only that, but DFT itself has many many different forms. There's DFT that is O(n)^3 and there's DFT that's O(n)^7 in time complexity, the wild variations are due to the different approximations (i.e. algorithm and parameters).
Saying "I used DFT" is like saying "I used a computer", its nowhere near enough info to reproduce the work
Saying "I used DFT" is like saying "I used a computer", its nowhere near enough info to reproduce the work