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> By scaling the numbers first by taking the log, multiplication becomes addition and addition becomes x + log1p(exp(y - x)).

Isn't this the same approach as in GF(2^x), which has been in use for decades? The only limitation that comes to mind is the field size.




Finite field log/antilog lookup tables are used for efficient-ish multiplication, similar to addition/subtraction tables used for logarithmic number systems.




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