Re: [PATCH 2/6] fs/direct-io.c: Use DIV_ROUND_UP

[Nishanth Aravamudan <nacc@us.ibm.com>]

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@us.ibm.com>
IBM Linux Technology Center