Re: Smooth numeric upgrades?

[Mark Biggar]

Handling promotion (and demotion) between single and multi-precision 
integers is fairly easy.  And once you have that doing it for rationals 
is basically free. Likewise promoting an Integer up to rational is 
trivial and vice versa. But promotion (or demotion) between IEEE floats 
and rationals is really hard and I don't know of a language that even 
tries.  The major problem is that the demotion from rational to IEEE 
float is very lossy.  In general, there are many possible distinct 
rationals that convert into the same IEEE value and converting  IEEE 
float to the simplest rational out of that set is a very expensive 
operation..  Once you're in rationals you probably never want to demote 
back to IEEE (except possibly at the very end).  Every language that 
supports rationals, that I know of, leaves it up to the programmer to 
decide whether they will be doing computations in IEEE float or 
rationals and do not try to automatically convert back and forth.  I 
looked at thos and basically gave up when I was writing the perl 5 
Bigint and Bigrat packages.

Before you discuss implementations, you should define exactly what rules 
you are going to use for promotion and demotion between the various types.

--
Mark Biggar
Perl'sMaternal Uncle

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