What would be a good hash function that will return a positive integer value, even if the key is an negative integer value? How do I pick a hash function? So what I would want is to associate negative numbers with some positive value so I can use them later.
UPDATE: (summary) I need to find a bijection $f: \mathbb{Z}\to\mathbb{N}$ which also has the property that: $$ f(x) + f(y) = f(x + y) $$