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Date: Tue, 18 Apr 2023 19:29:37 +0200
From: Solar Designer <>
Subject: Re: Birthday paradox

On Tue, Apr 18, 2023 at 07:12:09PM +0200, magnum wrote:
> $ bc -l <<< '4096*(1-(4095/4096)^1024)'
> 906.12935699914074324992

I was using this same formula for these things.

> Background: I was amazed how an 4-level bitmap that "should" give 1/16 
> false positives, could end up as good as 1/43.  That was with 512 hashes 
> in a 4x1024 bitmap. Using this formula we end up with 1/41, so mystery 
> solved.
> In another test case, 1024 hashes in a 8x1024 bitmap would be "full" and 
> should give 1/1 false positives if we don't factor in the birthday 
> paradox.  But empirical tests showed an amazing 1/38 - actually good 
> enough to make an nvidia perform near its best!  This was again 
> explained with the birthday paradox (which says 1/39).

Now you need to compare efficiency of these multiple bitmaps against one
Bloom filter of their cumulative size.  And then against a Cuckoo filter
of the same size.


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