Re: [PATCH 05/18] writeback: per task dirty rate limit

[Wu Fengguang <fengguang.wu@intel.com>]

On Tue, Sep 06, 2011 at 11:47:10PM +0800, Peter Zijlstra wrote:
> On Sun, 2011-09-04 at 09:53 +0800, Wu Fengguang wrote:
> >  /*
> > + * After a task dirtied this many pages, balance_dirty_pages_ratelimited_nr()
> > + * will look to see if it needs to start dirty throttling.
> > + *
> > + * If dirty_poll_interval is too low, big NUMA machines will call the expensive
> > + * global_page_state() too often. So scale it near-sqrt to the safety margin
> > + * (the number of pages we may dirty without exceeding the dirty limits).
> > + */
> > +static unsigned long dirty_poll_interval(unsigned long dirty,
> > +                                        unsigned long thresh)
> > +{
> > +       if (thresh > dirty)
> > +               return 1UL << (ilog2(thresh - dirty) >> 1);
> > +
> > +       return 1;
> > +}
> 
> Where does that sqrt come from? 

Ideally if we know there are N dirtiers, it's safe to let each task
poll at (thresh-dirty)/N without exceeding the dirty limit.

However we neither know the current N, nor is sure whether it will
rush high at next second. So sqrt is used to tolerate larger N on
increased (thresh-dirty) gap:

irb> 0.upto(10) { |i| mb=2**i; pages=mb<<(20-12); printf "%4d\t%4d\n", mb, Math.sqrt(pages)}
   1      16
   2      22
   4      32
   8      45
  16      64
  32      90
  64     128
 128     181
 256     256
 512     362
1024     512

The above table means, given 1MB (or 1GB) gap and the dd tasks polling
balance_dirty_pages() on every 16 (or 512) pages, the dirty limit
won't be exceeded as long as there are less than 16 (or 512) concurrent
dd's.

Note that dirty_poll_interval() will mainly be used when (dirty < freerun).
When the dirty pages are floating in range [freerun, limit],
"[PATCH 14/18] writeback: control dirty pause time" will independently
adjust tsk->nr_dirtied_pause to get suitable pause time.

So the sqrt naturally leads to less overheads and more N tolerance for
large memory servers, which have large (thresh-freerun) gaps.

Thanks,
Fengguang