[amluto]

Traditionally they were done in FORTRAN or C or maybe bespoke DSP code, usually using ordinary boring complex numbers. Sometimes you’ll see FFTs over rings, called “number theoretic transforms”, used to multiply very large integers.

I suppose these days FFTs are used for highly power optimized, very much real-time OFDM transceivers. I’m guessing they’re done in carefully written assembly, possibly automatically generated (by conventional code, not LLMs, at least for existing solutions), possibly with a little bit of hardware help.