Re: Floating point inaccuracies

[David Kastrup <dak@...>]

Roberto Ierusalimschy <roberto@inf.puc-rio.br> writes:

>> On Tue, Nov 30, 2010 at 4:47 PM, Paul Hudson <phudson@pobox.com> wrote:
>> > Even more likely to trap the unwary, I'd have thought.
>> 
>> Yes, such weird implementation details will only postpone the point
>> when someone _really_ needs to understand floating-point!  The earlier
>> the better; when they taught us FORTRAN IV they hammered the
>> do-not-expect-floats-to-be-equal point home.
>
> YES!!!!  Lots of very bright people have been working with floating
> points for a very long time. Learn with them before trying to "solve"
> those problems.

I want transitivity for my comparison operators.

a==b and b==c => a==c
a<=b and b<=c => a<=c

And of course I want exactly one of the following to hold for any
definite pair of numbers:

a<b, a>b, a==b

And I want a<=b to be the same as (a<b or a==b) and as not (a>b).

Anything else is madness.  It's bad enough that floating point addition
and multiplication are not associative operators.  We should not mess
with more dependable properties than avoidable.

-- 
David Kastrup