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From: "Randy Brukardt" <randy@rrsoftware.com>
Newsgroups: comp.lang.ada
Subject: Re: GNAT Optimization of Constant Expressions
Date: Fri, 18 May 2007 21:44:17 -0500
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Date: 2007-05-18T21:44:17-05:00
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"Adam Beneschan" <adam@irvine.com> wrote in message
news:1179528686.946797.189500@w5g2000hsg.googlegroups.com...
> On May 18, 10:40 am, "Randy Brukardt" <r...@rrsoftware.com> wrote:
....
> So I suspect Randy is right, but I'm not sure.  If the hardware keeps
> just one extra mantissa bit internally when it does the subtraction,
> and uses the extra bit when it shifts left to normalize the result,
> then I think the two expressions will always produce the same result.

No, I think you have it right. The point is that if you subtract 1.0, you
depend on the hardware to do the right thing to preserve the last bit (which
is shifted out, then back in), whereas if you subtract 0.5 twice, you always
get the most accurate possible answer without worrying about what the
hardware does. Thus hardcore numerical programs do things like this so that
they don't depend on the characteristics of the hardware. Assuming an
optimizer doesn't screw that up...

Of course, if the hardware takes pains to preserve that extra bit (and a lot
of it does), none of this matters that much. Since most optimizers are at
least partially machine independent, however, they need to be careful; and
in any case, they need to avoid any optmizations which have the potential of
losing more bits.

                               Randy.