Re: [PATCH 06/11] Export fragmentation index via/proc/extfrag_index

[Mel Gorman]

On Thu, Mar 25, 2010 at 08:20:04PM +0900, KOSAKI Motohiro wrote:
> > On Thu, Mar 25, 2010 at 11:47:17AM +0900, KOSAKI Motohiro wrote:
> > > > On Tue, Mar 23, 2010 at 09:22:04AM +0900, KOSAKI Motohiro wrote:
> > > > > > > > +	/*
> > > > > > > > +	 * Index is between 0 and 1 so return within 3 decimal places
> > > > > > > > +	 *
> > > > > > > > +	 * 0 => allocation would fail due to lack of memory
> > > > > > > > +	 * 1 => allocation would fail due to fragmentation
> > > > > > > > +	 */
> > > > > > > > +	return 1000 - ( (1000+(info->free_pages * 1000 / requested)) / info->free_blocks_total);
> > > > > > > > +}
> > > > > > > 
> > > > > > > Dumb question.
> > > > > > > your paper (http://portal.acm.org/citation.cfm?id=1375634.1375641) says
> > > > > > > fragmentation_index = 1 - (TotalFree/SizeRequested)/BlocksFree
> > > > > > > but your code have extra '1000+'. Why?
> > > > > > 
> > > > > > To get an approximation to three decimal places.
> > > > > 
> > > > > Do you mean this is poor man's round up logic?
> > > > 
> > > > Not exactly.
> > > > 
> > > > The intention is to have a value of 968 instead of 0.968231. i.e.
> > > > instead of a value between 0 and 1, it'll be a value between 0 and 1000
> > > > that matches the first three digits after the decimal place.
> > > 
> > > Let's consider extream case.
> > > 
> > > free_pages: 1
> > > requested: 1
> > > free_blocks_total: 1
> > > 
> > > frag_index = 1000  - ((1000 + 1*1000/1))/1 = -1000
> > > 
> > > This is not your intension, I guess. 
> > 
> > Why not?
> > 
> > See this comment
> > 
> > /* Fragmentation index only makes sense when a request would fail */
> > 
> > In your example, there is a free page of the requested size so the allocation
> > would succeed. In this case, fragmentation index does indeed go negative
> > but the value is not useful.
> >
> > > Probably we don't need any round_up/round_down logic. because fragmentation_index
> > > is only used "if (fragindex >= 0 && fragindex <= 500)" check in try_to_compact_pages().
> > > +1 or -1 inaccurate can be ignored. iow, I think we can remove '1000+' expression.
> > > 
> > 
> > This isn't about rounding, it's about having a value that normally is
> > between 0 and 1 expressed as a number between 0 and 1000 because we
> > can't use double in the kernel.
> 
> Sorry, My example was wrong. new example is here.
> 
> free_pages: 4
> requested: 2
> free_blocks_total: 4
> 
> theory: 1 - (TotalFree/SizeRequested)/BlocksFree
>             = 1 - (4/2)/4 = 0.5
> 
> code : 1000 - ((1000 + 4*1000/2))/4 = 1000 - (1000 + 2000)/4 = 1000/4 = 250
> 
> I don't think this is three decimal picking up code. This seems might makes
> lots compaction invocation rather than theory.
> 

Ok, I cannot apologise for this enough.

Since that paper was published, further work showed that the equation could
be much improved. As part of that, I updated the equation to the following;

double index = 1    - ( (1    + ((double)info->free_pages        / requested)) / info->free_blocks_total);

or when approximated to three decimal places

int index =    1000 - ( (1000 + (        info->free_pages * 1000 / requested)) / info->free_blocks_total);

Your analysis of the paper is perfect. When slotted into a driver program
with your example figures, I get the following results

old equation = 0.500000
current equation = 0.250000
integer approximation = 250

The code as-is is correct and is what I intended. My explanation on the
other hand sucks and I should have remembered that I updated equation since
I published that paper 2 years ago.

Again, I am extremely sorry for misleading you.

-- 
Mel Gorman
Part-time Phd Student                          Linux Technology Center
University of Limerick                         IBM Dublin Software Lab
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