On Fri, 29 Jul 2005, Michal Schmidt wrote:
> Rafael J. Wysocki wrote:
> > On Friday, 29 of July 2005 21:46, Michal Schmidt wrote:
> >
> >>The function calc_nr uses an iterative algorithm to calculate the number
> >>of pages needed for the image and the pagedir. Exactly the same result
> >>can be obtained with a one-line expression.
> >
> >
> > Could you please post the proof?
> >
> > Rafael
>
> OK, attached is a proof-by-brute-force program. It compares the results
> of the original function and the simplified one.
Here's a more general proof.
As I understand it, calc_nr is given nr_copy, the number of data pages
that need to be written out, and it has to return the number of pages
needed to hold the image data plus a bunch of PBE pagedir indexes, where
each page gets one index (and pages containing PBEs need their own indexes
as well).
For brevity, let n = nr_copy, let p = PBES_PER_PAGE, and let x be the
number of pagdir pages needed. Since each page can hold p PBEs, there
will be room to store px PBEs. The total number of pages is n + x, so
the routine needs to find the smallest value of x for which
px >= n + x
or
(p-1)x >= n
or
x >= n / (p-1).
The obvious solution is
x = ceiling(n / (p-1)),
so calc_nr should return n + ceiling(n / (p-1)), which is exactly what
Michal's patch computes.
Alan Stern
-
To unsubscribe from this list: send the line "unsubscribe linux-kernel" in
the body of a message to [email protected]
More majordomo info at http://vger.kernel.org/majordomo-info.html
Please read the FAQ at http://www.tux.org/lkml/
[Index of Archives]
[Kernel Newbies]
[Netfilter]
[Bugtraq]
[Photo]
[Gimp]
[Yosemite News]
[MIPS Linux]
[ARM Linux]
[Linux Security]
[Linux RAID]
[Video 4 Linux]
[Linux for the blind]
| |
 |