Messages in this thread | | | From | Daniel Phillips <> | Subject | Re: [PATCH] [rmap] operator-sparse Fibonacci hashing of waitqueues | Date | Tue, 19 Feb 2002 02:01:24 +0100 |
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On February 19, 2002 01:34 am, William Lee Irwin III wrote: > On February 17, 2002 10:01 am, William Lee Irwin III wrote: > >> After distilling with hpa's help the results of some weeks-old > >> numerological experiments^W^Wnumber crunching, I've devised a patch > >> here for -rmap to make the waitqueue hashing somewhat more palatable > >> for SPARC and several others. > >> > >> This patch uses some operator-sparse Fibonacci hashing primes in order > >> to allow shift/add implementations of the hash function used for hashed > >> waitqueues. > >> > >> Dan, Dave, could you take a look here and please comment? > > On Mon, Feb 18, 2002 at 11:31:15PM +0100, Daniel Phillips wrote: > > Could you explain in very simple terms, suitable for Aunt Tillie (ok, not > > *that* simple) how the continued fraction works, how it's notated, and how > > the terms of the expansion relate to good performance as a hash? > > Do you want it just in a post or in-line? > > Here's the posted brief version: > > Numbers have "integer parts" and "fractional parts", for instance, if > you have a number such as 10 1/2 (ten and one half) the integer part > is 10 and the fractional part is 1/2. The fractional part of a number > x is written {x}. > > Now, there is something called the "spectrum" of a number, which for > a number x is the set of all the numbers of the form n * x, where n > is an integer. So we have {1*x}, {2*x}, {3*x}, and so on. > > If we want to measure how well a number distributes things we can try > to see how uniform the spectrum is as a distribution. There is a > theorem which states the "most uniform" distribution results from the > number phi = (sqrt(5)-1)/2, which is related to Fibonacci numbers. > > The continued fraction of phi is > > 0 + 1 > ----- > 1 + 1 > ----- > 1 + 1 > ----- > 1 + 1 > ----- > 1 + 1 > ... > > where it's 1's all the way down. Some additional study also revealed > that how close the continued fraction of a number is to phi is related > to how uniform the spectrum is. For brevity, I write continued fractions > in-line, for instance, 0,1,1,1,1,... for phi, or 0,1,2,3,4,... for > > 0 + 1 > ----- > 1 + 2 > ----- > 1 + 3 > ----- > 1 + 4 > .... > > One way to evaluate these is to "chop off" the fraction at some point > (for instance, where I put ...) and then reduce it like an ordinary > fraction expression. > > Fibonacci hashing considers the number p/2^n where n is BITS_PER_LONG > and p is a prime number, and this is supposed to have a relationship > to how evenly-distributed all the n-bit numbers multiplied by p in > n-bit arithmetic are. Which is where the hash functions come in, since > you want hash functions to evenly distribute things. There are reasons > why primes are better, too. > > And I think that covers most of what you had in mind.
Yes, it sure does, thanks a lot.
> In my own opinion, this stuff borders on numerology, but it seems to be > a convenient supply of hash functions that pass chi^2 tests on the > bucket distributions, so I sort of tolerate it. If I'm not using a strict > enough test then I'm all ears...
/me resolves to get back to htree hashing very soon.
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