2009/7/8 Hernan Wilkinson <[email protected]>: > it was just an example where you can "bind" as "late" as possible a > combination of symbols with its value... I like late binding :-) in this > example allows you to get rigth results... and of course > cosPiHalved is not the same as "a/b cos" where a is bound to pi and b to > 2... it is not only for literals. >
If you like the late binding, and if you are using a set of functions which having no side effects , then you can, instead of computing the result , store the numerical operations (in same fashion as Fraction stores division) and compute the exact value(s) only when you really need them. Then you can bring in the power of mathematical apparatus/trigonometry rules and use them at full scale. Think, how many things we can add (in parallel to Fraction) SquaredNumber SquaredRootNumber CosFn SinFn TanFn PiFraction and so on.. limited only by your own limits/knowledge... But again, all of this stuff is more related to predicting than exact computing , which is happens to be inexact because of hardware limitations :) > On Wed, Jul 8, 2009 at 3:59 PM, Igor Stasenko <[email protected]> wrote: >> >> 2009/7/8 Hernan Wilkinson <[email protected]>: >> > >> >> >> >> >> >> > [...] and if you write 1.3, the object that represents that number >> >> > is not going to be an instance of float but of scaledecimal or >> >> > fraction or whatever, but not float... >> >> >> >> That only solves the issue of representing literals because: >> >> >> >> >> >> > and all operations are made with exact representation. >> >> >> >> >> >> >> >> cannot be done for all operations: obvious ones like square root, log, >> >> sin, etc and less obvious ones like #squared where you run out of >> >> enough bits to maintain precision (in fixed-width implementations). >> > >> > not really... root, log, sin, etc could be messages that only inexact >> > numbers know how to answer , so you want "2 sqrt", do "2 asFloat sqrt", >> > but >> > for +, *, /, etc. they work as expected. >> > We can also have better representations for number like pi. Why pi is >> > instance of Float and not Pi? If pi is instance of Pi, then cos(pi/2) = >> > 0 >> > could be true... just a quick hack: >> > Pi>>/ aNumber >> > >> > ^ Fraction numerator: self denominator: aNumber "Or maybe an object >> > representing that Pi has been divided/multiplied, etc >> > >> > Fraction>>cos >> > >> > ^ numerator cosDividedWith: denominator >> > >> > Pi>>cosDividedWith: denominator >> > >> > ^denominator = 2 ifTrue: [ 0 ] ifFalse: [ ... ] >> > >> > and so on >> > >> >> >> don't forget to add >> Pi>>mantisOfLength: numBits >> >> to compute the Pi up to given precision. :) >> >> >> But your examples is not about computing a result, but rather predicting >> it. >> So why bother writing so much stuff , while you can just implement : >> >> Number>>cosPiHalved >> ^ 0 >> >> :) >> >> >> >> >> >> >> >> >> R >> >> - >> >> >> >> >> >> _______________________________________________ >> >> Pharo-project mailing list >> >> [email protected] >> >> http://lists.gforge.inria.fr/cgi-bin/mailman/listinfo/pharo-project >> > >> > >> > _______________________________________________ >> > Pharo-project mailing list >> > [email protected] >> > http://lists.gforge.inria.fr/cgi-bin/mailman/listinfo/pharo-project >> > >> >> >> >> -- >> Best regards, >> Igor Stasenko AKA sig. >> >> _______________________________________________ >> Pharo-project mailing list >> [email protected] >> http://lists.gforge.inria.fr/cgi-bin/mailman/listinfo/pharo-project > > _______________________________________________ > Pharo-project mailing list > [email protected] > http://lists.gforge.inria.fr/cgi-bin/mailman/listinfo/pharo-project > -- Best regards, Igor Stasenko AKA sig. _______________________________________________ Pharo-project mailing list [email protected] http://lists.gforge.inria.fr/cgi-bin/mailman/listinfo/pharo-project
