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Re: [Scheme-reports] Numeric towers

Ray Dillinger scripsit:

> For what it's worth, I consider it worthwhile to have a limited range 
> of exact ratios, where the results of (/) on exact arguments are exact 
> if both numerator and denominator are within a bounded integer range 
> and inexact otherwise.

Technically, systems without ratios already do this, but the denominator
is limited to 1.

> This provides "opportunistic" preservation of exactness where you could
> not ordinarily specify it due to the possibility of representation
> explosion.

It's an interesting idea, but AFAIK no Schemes provide it, so it is
not ripe for standardization.

> Type theorists objecting that they need to be able to statically
> determine the type of an operation without referent to the values 
> of the arguments will object to the exact/inexact conversion implicit 
> in bounded ratios.  

We already have such things with EXPT.

> It is also important to programs to know whether exact and inexact 
> numbers are interconvertible without changing numeric value.  IE, 
> whether the system supports the same precision in inexact numbers 
> as exact numbers.  

I don't know any systems that do this: it would require very artificial
restrictions on ratios to make them match IEEE flonums.

"Repeat this until 'update-mounts -v' shows no updates.         John Cowan
You may well have to log in to particular machines, hunt down   cowan@x
people who still have processes running, and kill them."        www.ccil.org/~cowan

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