When is hash(n) == n in Python?

Question

I\'ve been playing with Python\'s hash function. For small integers, it appears hash(n) == n always. However this does not extend to large numbers:

Answer 1

Hash function returns plain int that means that returned value is greater than -sys.maxint and lower than sys.maxint, which means if you pass sys.maxint + x to it result would be -sys.maxint + (x - 2).

hash(sys.maxint + 1) == sys.maxint + 1 # False
hash(sys.maxint + 1) == - sys.maxint -1 # True
hash(sys.maxint + sys.maxint) == -sys.maxint + sys.maxint - 2 # True

Meanwhile 2**200 is a n times greater than sys.maxint - my guess is that hash would go over range -sys.maxint..+sys.maxint n times until it stops on plain integer in that range, like in code snippets above..

So generally, for any n <= sys.maxint:

hash(sys.maxint*n) == -sys.maxint*(n%2) +  2*(n%2)*sys.maxint - n/2 - (n + 1)%2 ## True

Note: this is true for python 2.