Date: Sun, 10 Jan 1999 16:37:17 -0700 (MST)
From: Colin Plumb <colin@nyx.net>
Message-Id: <199901102337.QAA05245@nyx10.nyx.net>
To: sct@redhat.com
Subject: Re: tiny patch, reduces kernel memory usage
Cc: linux-kernel@vger.rutgers.edu
Sender: owner-linux-kernel@vger.rutgers.edu
Content-Length: 1242
Lines: 43

Stephen Tweedie wrote:
> The unused field needs to go.  Fine.  The map_nr field is needed to
> avoid a division when we try to find a page number from a struct page.

Um, it's a division by a constant, which GCC optimizes to a multiply.
GCC also knows that the division must have no remainder, so it can do even
better than the usual case.)

For example,
struct x {
	unsigned c[13];
};

unsigned foo (struct x *p1, struct x *p2)
{
	return p2-p1;
}

On an x86 with egcc -O2 -fomit-frame-pointer produces:
foo:
	movl 8(%esp),%eax
	subl 4(%esp),%eax
	imull $-991146299,%eax,%eax
	sarl $2,%eax
	ret

A multiply is not a trivial cost, but it's cheaper than a divide.
(And depending on the multiplier, GCC can optimize it further into
a series of shifts and adds.)

Any odd number x has a multiplicative inverse y such that
(x*y) == 1 (mod 2^32).  Thus, (k*x)*y == k*(x*y) == k (mod 2^32).hC
and multiplying by y is the same as dividing by x.

And may number at all can be broken down into an odd number and
a power of two, where division is a simple shift.
-- 
	-Colin

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