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Can you please explain this assertion? ;)

If I have a 32 bit current hash value-- for any possible 32 bit value I add, I get a different 32 bit value out.

XORing is effectively adding each bit and throwing away the carry bit. Adding just cascades carries to the left.

You know what, you're right. I made a knee-jerk comment but I didn't think it through all the way. From any arbitrary unsigned 32-bit integer, every other unsigned 32-bit integer is reachable with a single addition. Therefore addition works just fine here.

It still feels wrong to say this, it feels like since adding will effectively shove bits off the high end and drop them on the floor that you're losing information, but I can't actually justify that feeling with reasoning.

Adding is actually considerably better. For high quality hashes XOR is just as good; but if there's any distributional problems at all in the hash, adding mixes stuff more.

(XORing is effectively adding with all of the carry information lost/falling off).

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