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For example, if I know that I added something to 27 and got -32, reversibility means I should be able to uniquely determine what was added to 27; under the rules of linear addition, it would have to be -59, not any positive number. But with modular addition, it could be either of two numbers, -59 and ($MODULUS - 59), so modular addition isn't reversible like linear additon.
Yeah, but if you have the additional information that all "numbers" are in the range -2^31 to 2^31-1 inclusive, you can determine the unique value that was added to 27 to give -59.
I'm not saying fixnums are great, just that your example doesn't convince me that addition of fixnums is not reversible.
Regards, Alan -- Dr Alan Watson Centro de Radioastronomía y Astrofísica Universidad Astronómico Nacional de México