> -----Original Message----- > From: Vincent St-Amour [mailto:stamo...@ccs.neu.edu] > Sent: 13 December 2010 17:01 > To: Jos Koot > Cc: 'Noel Welsh'; dev@racket-lang.org > Subject: Re: [racket-dev] (round), etc. in Typed Racket > > At Mon, 13 Dec 2010 16:43:58 +0100, > Jos Koot wrote: > > Would we not have the same problem with 'rational?'. > > All reals, both exact and inexact ones are rationals (for > the obvious > > reason that we cannot represent every irrational number in finite > > memory) Would we not need the same distinction between > > 'exact-rational?' and 'inexact-rational?'. May be > 'rational?' should > > mean 'exact-rational?' and 'real?' should mean > 'inexact-real?' or 'inexact-rational?'. > > I like that, it's consistent with exact-integer -> integer. > > > And how about exact and inexact 'complex?'? > > It's a bit more tricky, since there are potentially 4 kinds > of complexes, each part could be exact or inexact. However, > I'm not sure that complex numbers of the shape > exact+inexact*i are of any use, and apart from the special > case inexact+0i (inexact reals), I don't see much use for > inexact+exact*i either. > > > I have the feeling that the numeric tower is tilting like > that of Pisa. > > Sounds more like straightening it up to me. > > > When it comes to efficiency, flonums may be preferred, but > it is not > > difficult to enforce a function to do all its computations > with flonums. > > It can be tricky if you mix exacts and inexacts, the result > is not always inexact: > (* 3.4 0) -> 0 ; not 0.0
When multiplying any number (nan and inf excepted) by exact 0, should, of course produce exact 0. There are more problems though. How about: (let ((x 1.0)) (- x x)) Should it produce inexact or exact 0? Don't ask me, for I am not sure, yet. IIAR Racket produces 0.0. Evidently the problem is located in the simulation of truly REAL computations within a finite memory that necessarily must produce approximations for many computations. I am inclined to the idea that a programmer should be aware of when he or she is using exact numbers or approximations of them. Jos > > Vincent _________________________________________________ For list-related administrative tasks: http://lists.racket-lang.org/listinfo/dev
