On Mon, May 21, 2007 at 04:26:03AM -0700, William Lee Irwin III wrote:
> On Mon, May 21, 2007 at 01:08:13AM -0700, William Lee Irwin III wrote:
> >> Choosing k distinct integers (mem_map array indices) from the interval
> >> [0,n-1] results in k(n-k+1)/n non-adjacent intervals of contiguous
> >> array indices on average. The average interval length is
> >> (n+1)/(n-k+1) - 1/C(n,k). Alignment considerations make going much
> >> further somewhat hairy, but it should be clear that contiguity arising
> >> from random choice is non-negligible.
>
> On Mon, May 21, 2007 at 11:27:42AM +0200, Nick Piggin wrote:
> > That doesn't say anything about temporal locality, though.
>
> It doesn't need to. If what's in the cache is uniformly distributed,
> you get that result for spatial locality. From there, it's counting
> cachelines.
OK, so your 'k' is the number of struct pages that are in cache? Then
that's fine.
I'm not sure how many that is going to be, but I would be surprised if
it were a significant proportion of mem_map, even on not-so-large
memory systems.
> On Mon, May 21, 2007 at 01:08:13AM -0700, William Lee Irwin III wrote:
> >> In any event, I don't have all that much of an objection to what's
> >> actually proposed, just this particular cache footprint argument.
> >> One can motivate increases in sizeof(struct page), but not this way.
>
> On Mon, May 21, 2007 at 01:08:13AM -0700, William Lee Irwin III wrote:
> > Realise that you have to have a run of I think at least 7 or 8 contiguous
> > pages and temporally close references in order to save a single cacheline.
> > Then also that if the page being touched is not partially in cache from
> > an earlier access, then it is statistically going to cost more lines to
> > touch it (up to 75% if you touch the first and the last field, obviously 0%
> > if you only touch a single field, but that's unlikely given that you
> > usually take a reference then do at least something else like check flags).
> > I think the problem with the cache footprint argument is just whether
> > it makes any significant difference to performance. But..
>
> The average interval ("run") length is (n+1)/(n-k+1) - 1/C(n,k), so for
> that to be >= 8 you need (n+1)/(n-k+1) - 1/C(n,k) >= 8 which also happens
> when (n+1)/(n-k+1) >= 9 or when n >= (9/8)*k - 1 or k <= (8/9)*(n+1).
> Clearly a lower bound on k is required, but not obviously derivable.
> k >= 8 is obvious, but the least k where (n+1)/(n-k+1) - 1/C(n,k) >= 8
> is not entirely obvious. Numerically solving for the least such k finds
> that k actually needs to be relatively close to (8/9)*n. A lower bound
> of something like 0.87*n + O(1) probably holds.
Ah, you worked it out... yeah I'd guess this is going to be pretty difficult
a condition to satisfy (given that it isn't possible for a 4GB system, even
if you had 32MB of cache to fill entirely with struct pages).
> On Mon, May 21, 2007 at 01:08:13AM -0700, William Lee Irwin III wrote:
> >> Now that I've been informed of the ->_count and ->_mapcount issues,
> >> I'd say that they're grave and should be corrected even at the cost
> >> of sizeof(struct page).
>
> On Mon, May 21, 2007 at 11:27:42AM +0200, Nick Piggin wrote:
> > ... yeah, something like that would bypass
>
> Did you get cut off here?
Must have. I was going to say it would bypass the whole speed/size
discussion anyway :P
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