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

On Thu, 12 Jul 2007, Jon Fairbairn wrote:

Henning Thielemann writes:

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On Thu, 12 Jul 2007, Jon Fairbairn wrote:

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Now, a proper exact real type is doubtless very inefficient, but wouldn't it be possible to define something that had a fairly efficient head, and a lazy tail? So you'd have, say

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data Real = R {big::(Ratio !Int !Int), small:: More_Precision}

Interesting approach.

But flawed as I put it: the big part can't express big numbers! The big part needs to be either Rational (and the precision of that part limited during arithmetic) or BigFloat where

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Data BigFloat = BF {mantissa:: Int, exponent:: Integer}

(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. 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. However 'round (sqrt 2 ^ 2)' will work as expected. In short, the Real number type will leed to all difficulties known from computable reals.