>________________________________
> 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
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>>
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