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Re: The Inf type
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From:
TSa
Date:
June 3, 2008 03:57
Subject:
Re: The Inf type
HaloO,
John M. Dlugosz wrote:
> I don't know why he's calling it an "Int with non-uniform spacing"
> unless he is complaining about what happens when you store ints in
> floats: it rounds off to the mantissa size.
With uniform spacing you have
constant $step = 1;
and
$x++; # means $x = $x + $step
whereas non-uniform is
$x++; # means $x = $x + $x.step;
You can make the second to subsume the first with
multi method *step (Int) { 1 }
and optimize whenever you can prove that $x always
does Int. If you can't, you leave that to the runtime.
Going further with that you could define $a == $b to
actually mean abs($a-$b) < min($a.step, $b.step).
E.g. with the usual 64bit floats you have 0.5.step==2**-53
and (2**52).step==1. Then per definition
multi method *step (Real) { 0 }
essentially means a real object can't step away from itself
or some such.
Given the above, the optimizer can e.g. take a sub that claims to
achieve its business with two Reals in such a way that ++ is
considered a noop and taken out of the code. If the code is not
up to that it can hardly be a function that properly handles two
Reals. If your test suite manages to detect that failure is another
question. But a good enough optimizer makes bad enough programs
reveal their realness or lack thereof ;)
Regards, TSa.
--
"The unavoidable price of reliability is simplicity" -- C.A.R. Hoare
"Simplicity does not precede complexity, but follows it." -- A.J. Perlis
1 + 2 + 3 + 4 + ... = -1/12 -- Srinivasa Ramanujan
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