[Haskell-cafe] Re: Defaulting to Rational [was: Number overflow]

[Jon Fairbairn]

Henning Thielemann <lemming at henning-thielemann.de> writes:

> On Thu, 12 Jul 2007, Jon Fairbairn wrote:
> > (ie limited precision, but unbounded magnitude). If we were
> > to use BigFloat the base would need to be a power of ten to
> > get the desired results for things like Don's example)
> 
> People will be confused, that 'sin pi' won't lead to a result since the
> correct result is zero and it will need forever to normalize that number.

Surely the first few digits can be computed? I thought
sin pi was a computable numer, anyway. Note that in my
representation I didn't specify what form the small part
would take; I'm not sufficiently familiar with computing on
proper reals to know the best choice for that, but as I
undestand it, once we reach the point of showing a number to
a finite precision, we /can/ compute the necessary digits.

> They will be confused, that the result of 'sqrt 2 ^ 2' cannot be shown in
> usual decimal notation, since the formatting algorithm cannot decide
> between starting with 2.0000 and 1.9999.

Again, if it's being shown to finite precision, it can look
at the next digit after the last one to be shown and use
that to decide what to start with.  There's no reason why
show should be defined to truncate rather than defined to
round after the last digit, is there?

> In short, the Real number type will leed to all
> difficulties known from computable reals.

All the real ones, anyway :-).

-- 
Jón Fairbairn                                 Jon.Fairbairn at cl.cam.ac.uk