On Wed, Oct 29, 2008 at 12:36 PM, Gabriel Dos Reis wrote:
> ...
> There is a huge ongoing debate in the Interval Computation community
> about the links between intervals and floating points.
>
> They are different systems trying to deal with computability with real
> numbers. The IEEE floating point systems are well defined algebraic
> systems. I'm not aware they are less correct or less mathematical
> than unspoken alternatives.
>
I'll take your word on that. :-)
> For use of signed zeros, it might be enlightening to read
>...
>For a mode in-depth, tutorial see Goldberg's classic paper
> ...
I really appreciate these references. Thanks.
>
> | However as I understand it, values in the domain FLOAT are
> | to be taken as exact rationals that approximate real numbers in
> | a well defined manner. Is this an accurate view? Are there specific
> | changes that should be made to these floating point domains that
> | would make their associated algebra more obvious?
>
> As far as I know all floating point systems define a subset of
> rational numbers as approximation to the reals; they come with
> projections (rounding mode) for delivering result of computations.
> Also, see Language Independent Arithmetic, part 1.
>
Well in the context of this thread a specific example might be -0. As
I understand it, the reason that this value is not included in the
domain Float is because the representation used there has no room for
it. Instead, the values in Float are *exactly* the numbers
mantissa*base^exponent
where base=2 and mantissa and exponent are values from domain Integer.
These rational values always have an exact representation in the
domain Fraction Integer and form a specific subset of the real
numbers. Among other things, this makes equality in Float fully
transitive, where as in some other floating point systems this might
not be the case. Simiarly, %plusInfinity and %minusInfinity are not
values in Float.
IEEE floats however are something different - wouldn't you agree? What
I was supposing is the maybe the domain DoubleFloat (which currently
looks more or less just like a fixed precision version of Float)
should be given semantics that more closely resembles IEEE 754-2008.
Regards,
Bill Page.
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