Re: Integers and Mathematical Correctness

[Niklas Holsti <niklas.holsti@tidorum.invalid>]

On 14-09-26 12:07 , vincent.diemunsch@gmail.com wrote:
> Le vendredi 2 novembre 2001 02:40:08 UTC+1, Steven Deller a écrit :

[ a mess of unformatted text ]

> I thing there are two problems with the current Ada implementation :

...

> 2. The very existence of the 
>    
>    function "/" (Left, Right : Integer) return Integer; 
> 
> prevents the implementation and the use of Rational types in Ada,

False. Ada can overload operators on the result type, so you can very
well add

   function "/" (Left, Right : Integer) return Rational;

and have both"/" visible and used with in-fix notation.

> which are otherwise very simple to implement using a record type,
> just like complex numbers.

I beg to disagree. Rational numbers with Integer numerator and
denominator are not very useful, because after a relatively small number
of arithmetic operations, the numerator and denominator often become
very large and overflow the Integer range.

IMO rational numbers are useful only when the numerator and denominator
are "bignums", effectively unbounded integer types.

-- 
Niklas Holsti
Tidorum Ltd
niklas holsti tidorum fi
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