I've managed to perform operations without taking the absolute value of the fraction, but I'm still xoring the exponents, only to xor them back when encoding. Since

a xor (0 | -1)

=

a * (1 | -1) + (0 | -1)

(where

(0 | -1)

and

(1 | -1)

denote the format of the sign for the operation), are there any algebraic manipulations that could be done to eliminate them?