That's why we need BigRational <https://github.com/andrioni/BigRationals.jl> :)
Le lundi 9 juin 2014 12:52:48 UTC+2, Ivar Nesje a écrit : > > A float is a binary fraction, and can not represent most decimal fractions > exactly. 0.1 is a famous example of a decimal fraction that can not be > represented exactly in binary, just like 1/3 is impossible to represent in > decimal (0.333333333333333333333...) > > Rational can express many fractions exactly, but as soon as you start > working with irrational numbers there is no clear way to do rounding. > Rational also have a limited range compared to floating point, so you get > overflow (or underflow) much easier. > > kl. 11:13:06 UTC+2 mandag 9. juni 2014 skrev Stéphane Laurent følgende: >> >> A Float is a decimal number, hence it also is a rational number : >> >> *2.243423592592582385923 = 2243423592592582385923 / >> 1000000000000000000000* >> >> >> Hence, depending on the limitations about the sizes of the integers, the >> set Rational could be bigger than the set Float. In this case, the better >> approximation of an irrational is achieved by a Rational. >> >> >> >> Le lundi 9 juin 2014 02:16:24 UTC+2, Miguel Bazdresch a écrit : >>> >>> Thanks -- I wasn't aware that a^b is irrational in general in this case. >>> Now I wonder if a Float is a better approximation to an irrational number >>> than a Rational. >>> >>> Of course, one could say that sqrt(a) is complex in general for real a, >>> but Julia returns a real. As Stefan says, some of these cases have no good >>> solutions, only less worse ones. >>> >>> -- mb >>> >>> >>> On Sun, Jun 8, 2014 at 7:09 PM, 'Stéphane Laurent' via julia-users < >>> julia...@googlegroups.com> wrote: >>> >>>> If b is rational then a^b is irrational in general, even for a integer, >>>> so this output is quite expected, as well as >>>> >>>> julia> (10//1)^(2//1) >>>> >>>> 100.0 >>>> >>>> >>>> >>>> >>>> Le lundi 9 juin 2014 00:54:37 UTC+2, Miguel Bazdresch a écrit : >>>>> >>>>> I just tried this (on 0.2.1): >>>>> >>>>> julia> (10//1)^(-2//1) >>>>> 0.01 >>>>> >>>>> Is this expected? >>>>> >>>>> -- mb >>>>> >>>>> >>>>> >>>>> On Sun, Jun 8, 2014 at 6:36 PM, 'Stéphane Laurent' via julia-users < >>>>> julia...@googlegroups.com> wrote: >>>>> >>>>>> julia> (10//1)^(-2) >>>>>> >>>>>> 1//100 >>>>>> >>>>>> >>>>>> Would it be problematic to return a rational >>>>>> for (a::Integer)^(b::Integer) ? >>>>>> >>>>>> >>>>>> >>>>>> Le dimanche 8 juin 2014 21:53:45 UTC+2, Stefan Karpinski a écrit : >>>>>>> >>>>>>> There are three obvious options for (a::Integer)^(b::Integer): >>>>>>> >>>>>>> 1. Always return an integer ⟹ fails for negative b. >>>>>>> 2. Always return a float ⟹ a^2 is not the same as a*a. >>>>>>> 3. Return float for negative b, integer otherwise ⟹ not >>>>>>> type-stable. >>>>>>> >>>>>>> As you can see, all of these choices are problematic. The first one, >>>>>>> which is what we currently do, seems to be the least problematic. One >>>>>>> somewhat crazier option that has been proposed is making ^- as in a^-b >>>>>>> parse as a different operator and have a^b return an integer for >>>>>>> integer >>>>>>> arguments but a^-b return a float for integer arguments. This would >>>>>>> have >>>>>>> the unfortunate effect of making a^-b different from a^(-b). >>>>>>> >>>>>>> >>>>>>> On Sat, Jun 7, 2014 at 12:41 PM, Daniel Jones <daniel...@gmail.com> >>>>>>> wrote: >>>>>>> >>>>>>>> I'd definitely be in favor of '^' converting to float, like '/', >>>>>>>> having fallen for than recently >>>>>>>> <https://github.com/JuliaLang/Color.jl/commit/c3d05dd2b94f0d38b64ef86022accdfec886a673> >>>>>>>> . >>>>>>>> >>>>>>>> On Sat, Jun 7, 2014, at 12:53 AM, Ivar Nesje wrote: >>>>>>>> > >>>>>>>> > There has also been discussion on whether >>>>>>>> ^(a::Integer,b::Integer) should >>>>>>>> > return a Float64 by default, and defer to pow() like /(a::Integer, >>>>>>>> > b::Integer) defers to div(). The problem is that many people like >>>>>>>> the >>>>>>>> > 10^45 vs 1e45 notation for large integers vs float constants, and >>>>>>>> we can >>>>>>>> > make it a clean error instead of a silent bug. >>>>>>>> >>>>>>>> >>>>>>> >>>>>>> >>>>> >>>
