Bijection between integers and random output

[sethmachine]

Hi,

Suppose I have some function F that has random output on each call.

Now suppose I want to create a new function G, that given an integer, maps it exactly one of F's outputs every time.

e.g. suppose F outputs random powers of 2.

Then

G(0) = 0

G(1) = 2

G(2) = 4

etc.

This seems straightforward, but what if F doesn't output necessarily a number, but a data structure whose fields are random? Do I need to translate every single possible permutation of the data structure into a unique number in order to create G?

In the same sense, what I want to do is somehow save the random output of F into an integer, so I can always reconstruct that random output at anytime.

I would rather not want to enumerate F in order to create G--the only way I know would literally "list" out every possible output of F and then assign an integer to it. Not very efficient and not very fun.