>________________________________ > From: Quim Llimona <lemonz...@gmail.com> >To: pd-list <pd-list@iem.at> >Sent: Friday, March 9, 2012 1:18 PM >Subject: Re: [PD] Some more float weirdness/fun > > >It's well-known that floats can't be treated the same way as integers... but >since PD is aimed at non-engineers and non-scientists I think it would be a >good idea to implement the "good" comparison algorithms (i.e. checking against >a threshold, etc) inside [==] and so, just to make patching easier. Maybe it's >already supposed to behave this way...
How often do these problems happen for people? Or maybe there is a better example than [==], which let's face it isn't going to be used anyway when you're checking against a threshold value. -Jonathan > > As for the loss of integer precision issue, an object that detects "integer >overflow" (that is, when all integer digits of the number cannot be >represented) could be created, taking into account the floating point >precision (32-bit, 64-bit...) and so. > > >2012/3/9 Mathieu Bouchard <ma...@artengine.ca> > >Le 2012-03-09 à 09:39:00, Charles Henry a écrit : >> >>Martin a écrit : >>> >>> >>>For any floatX unless X is infinity the number of floats that are not >>>>exactly represented is always infinite. >>>> >>For a floatX format where X is the number of bits, every float is exact and >>there are at most pow(2,X) floats. >> >>You mean that there are an infinity of numbers that round to a finite number >>of floats. >> >> >> >>There is a countably infinite number of rational numbers and a uncountably >>infinite number of irrational numbers that cannot be represented. >>> >> >From a constructivist point of view, there's a countably infinite number of >irrationals that can be represented at all no matter how. For a certain >ontology useful to constructivism, it can be said that the uncountably many >irrationals that are inexpressible also don't exist. >> >>This leaves you with countably many rational numbers and countably many >>irrationals, that can't be represented in a finite format. >> >> >> >>We could also debate over whether infinity is exactly represented. >>>When some math operation overflows (exceeds the range of floats), the >>>result assigned is inf. >>> >> Every float represents a range of numbers. The difference with infinities is that they represent half-intervals, that is, a line bounded only on one side. >> >> >> >>That's not the definition of infinity either: Take the set of real numbers R >>and the ordering operation <, then add an additional point "infinity" such >>that for any x belonging to R, x < infinity. >>> >> You should know that there are several competing definitions of infinity for real numbers (not considering other number systems in which this definition doesn't work). >> >>There are three definitions of Real numbers (R) in common use : one without >>any infinite number, one with two infinite numbers as endpoints, and one with >>a single infinite number without a sign. There are different motivations for >>the use of each of those three sets. There's no definition that fits all >>purposes, though the one without infinite numbers at all is considered >>generally «cleaner» in the field of pure math. >> >> >> >>So, the inf in the float definition only represents "infinity" defined >>relative to the finitely countable set of numbers that can be represented as >>floats >>> >> Yes, except NaN. >> >>You'll also find out that certain definitions of infinity that applies to the >>whole set of Reals also are relative to just that set, and don't work as-is >>for all possible extensions of Reals ; for example, Complex numbers don't >>have a single coherent definition of less-than and greater-than anymore, >>because all you can do is extract features of Complex numbers and compare >>those features as Reals... thus you need more specific definitions (and there >>are more possibilities of them). >> >> >> >>not the actual infinity as represented in your head :) >>> >> How do you know what's in people's heads ? >> >> >> ______________________________________________________________________ >>| Mathieu BOUCHARD ----- téléphone : +1.514.383.3801 ----- Montréal, QC >>_______________________________________________ >>Pd-list@iem.at mailing list >>UNSUBSCRIBE and account-management -> >>http://lists.puredata.info/listinfo/pd-list >> >> > >_______________________________________________ >Pd-list@iem.at mailing list >UNSUBSCRIBE and account-management -> >http://lists.puredata.info/listinfo/pd-list > > > _______________________________________________ Pd-list@iem.at mailing list UNSUBSCRIBE and account-management -> http://lists.puredata.info/listinfo/pd-list
