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Date: Mon, 6 Jul 2020 18:01:54 -0400
From: Rich Felker <dalias@...c.org>
To: musl@...ts.openwall.com
Subject: Re: Superfluous shift in qsort()?
On Thu, Jul 02, 2020 at 04:44:47PM +0200, Markus Wichmann wrote:
> On Wed, Jul 01, 2020 at 11:23:09PM +0200, Valentin Ochs wrote:
> > On Wed, Jul 01, 2020 at 04:44:56PM -0400, Rich Felker wrote:
> > > On Wed, Jul 01, 2020 at 08:50:26PM +0200, Markus Wichmann wrote:
> > > > Hi all,
> > > >
> > > > I noticed something while reading code today: Near the end of qsort(),
> > > > we have this gem:
> > > >
> > > > shl(p, 2);
> > > > pshift -= 2;
> > > > p[0] ^= 7;
> > > > shr(p, 1);
> > > >
> > > > Now, I don't know if I am missing something, but don't the shl and the
> > > > shr partially cancel out? Isn't this the same as
> > > >
> > > > shl(p, 1);
> > > > p[0] ^= 3;
> > > >
> > > > As it is, it isn't wrong, just weird.
> > >
> > > Assuming non-overflow, I think they're equivalent (also assuming you
> > > keep the pshift-=2).
> >
> > Yes, it looks that way. I'm afraid I don't have any further insight -
> > it's been quite a while since I thought about the qsort code, and I've
> > not been doing much work on algorithms over the last couple of years.
> > The only thing I can think of is that one could figure out which
> > behaviour with regard to overflow in shl() should be the valid one. I
> > suspect that replacing it would be valid and this is some transformation
> > I did while implementing smoothsort without realizing that this can be
> > simplified.
> >
> > Cheers,
> > Valentin
> >
>
> Overflow on shl() is completely impossible. To overflow a shl(p, 2), we
> would need the penultimate bit in p to be set. Every bit in p stands in for
> a tree of that order, so if bit n is set, the heap contains a tree with
> a number of elements equal to the n'th Leonardo number.
>
> I don't know how big the Leonardo number corresponding to the
> penultimate bit is, but I do know that halfway through the upper word
> (wasn't the factor something like 1.44 or so?), the Leonardo numbers get
> too big to be contained in a machine word. Meaning that tree would be
> way too large to be addressed.
>
> I concur that this looks like a missed optimization opportunity, and not
> a deliberate design decision.
Indeed, I don't believe overflow is possible here; I just mentioned it
for completeness. I think the change proposed here is correct but I'll
hold off on touching it til after release since it's not fixing a bug,
just a minor missed simplification.
Rich
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