Tim Peters <[email protected]> added the comment:
Jeroen, I understood the part about -2 from your initial report ;-) That's why
the last code I posted didn't use -2 at all (neither -1, which hashes to -2).
None of the very many colliding tuples contained -2 in any form. For example,
these 8 tuples all have the same hash now:
(-4, -4, -4, 40) (-4, -4, 4, -48)
( 4, 4, -4, 40) ( 4, 4, 4, -48)
(-4, 28, -28, -48) (-4, 28, 28, 40)
( 4, -28, -28, -48) ( 4, -28, 28, 40)
Your last example (with (3, -2) and (-3, 0)) also implicitly relies on that:
j is even implies (j ^ -3) == -(j ^ 3)
There are apparently piles of similar identities :-(
I appreciate that
a*M + C = b*M + C (mod N)
implies
a = b (mod N)
when M is coprime to N, and also that the theory of linear combinations modulo
2**K is far better known than the well-hidden theory FNV developed.
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<https://bugs.python.org/issue34751>
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