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Message-ID: <20080214233759.GA30902@us.ibm.com>
Date: Thu, 14 Feb 2008 15:37:59 -0800
From: Nishanth Aravamudan <nacc@...ibm.com>
To: Mariusz Kozlowski <m.kozlowski@...land.pl>
Cc: Julia Lawall <julia@...u.dk>,
Pekka Enberg <penberg@...helsinki.fi>,
linux-kernel@...r.kernel.org, kernel-janitors@...r.kernel.org
Subject: Re: [PATCH 2/6] fs/direct-io.c: Use DIV_ROUND_UP
On 14.02.2008 [23:16:44 +0100], Mariusz Kozlowski wrote:
> Hello,
>
> > > > Is it just me, or does
> > > >
> > > > ((user_addr + iov[seg].iov_len + PAGE_SIZE - 1)/PAGE_SIZE - user_addr/PAGE_SIZE)
> > > >
> > > > not simplify to
> > > >
> > > > = ((iov[seg].iov_len + PAGE_SIZE - 1)/PAGE_SIZE + user_addr/PAGE_SIZE - user_addr/PAGE_SIZE)
> > > >
> > > > = ((iov[seg].iov_len + PAGE_SIZE - 1)/PAGE_SIZE)
> > > >
> > > > = DIV_ROUND_UP(iov[seg].iov_len, PAGE_SIZE)
> > > >
> > > > CMIIW.
> > >
> > > I double-checked this and I believe you're correct. It's simpler to
> > > see when you do:
> > >
> > > x = user_addr
> > > y = iov[seg].iov_len
> > > z = PAGE_SIZE
> > >
> > > So
> > >
> > > (x + y + z - 1)/z - x/z
> > >
> > > = [x + (y + z - 1)]/z - x/z
> > >
> > > = [xz + z(y + z - 1)]/z^2 - x/z
> > >
> > > = x/z + (y + z - 1)/z - x/z
> > >
> > > And the rest follows from your simplifications.
> >
> > It doesn't work:
> >
> > ((3+4+5-1)/5) - (3/5) = 2
> > ((4+5-1)/5) = 1
>
> Logic was wrong but conclusion was right :) and so was Nishanth:
<snip>
As I replied to Julia off-list -- the math I and others have given is
correct, but assumes we're dealing with real-typed values. However, we
only have integer types in the kernel, meaning the divisions truncate.
Thus, while mathematically equivalent, the simplification is not
computationally so.
Thanks,
Nish
--
Nishanth Aravamudan <nacc@...ibm.com>
IBM Linux Technology Center
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