On Thu, 2013-04-18 at 19:05 +0200, Florian Pflug wrote:
> On Apr18, 2013, at 19:04 , Jeff Davis <pg...@j-davis.com> wrote:
> > On Wed, 2013-04-17 at 20:21 -0400, Greg Smith wrote:
> >> -Original checksum feature used Fletcher checksums. Its main problems,
> >> to quote wikipedia, include that it "cannot distinguish between blocks
> >> of all 0 bits and blocks of all 1 bits".
> >
> > That is fairly easy to fix by using a different modulus: 251 vs 255.
>
> At the expense of a drastic performance hit though, no? Modulus operations
> aren't exactly cheap.
Modulo is only necessary when there's a possibility of overflow, or at
the very end of the calculation. If we accumulate 32-bit integers into
64-bit sums, then it turns out that it can't overflow given the largest
input we support (32K page).
32K page = 8192 32-bit integers
1*(2^32-1) + 2*(2^32-1) + 3*(2^32-1) ... 8192*(2^32-1)
= (2^32-1) * (8192^2 - 8192)/2
= 144097595856261120 ( < 2^64-1 )
So, we only need to do the modulo at the end.
Regards,
Jeff Davis
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