Thank you for the clarification. There is a method to set Rat precision at the scope of the program to apply to all *.Rat() cases?
On Mon, Jun 22, 2020 at 5:57 PM Tobias Boege <t...@taboege.de> wrote: > On Mon, 22 Jun 2020, Aureliano Guedes wrote: > > Hi all, > > > > First, I'm naive in Raku. Then let's go to my question. > > > > I'm trying to figure out why we got so different results here: > > > > > e.Rat()**(pi.Rat()*i) > > -0.9999999999999902-1.3942922582021257e-07i > > > e**(pi*i) > > -1+1.2246467991473532e-16i > > > e.Rat()**(pi.Rat()*i) == e**(pi*i) > > False > > > > I understand the Num actually have the traditional behavior which leads > > this: > > 0.1.Num() + 0.2.Num() != 0.3.Num() > > > > And Rat is awesome cos deal nice to the real world. > > > > Anyway, I do not expect so different results between Rat and Num. > > > > First, e and π are not rational numbers, so Num (IEEE 754 double) > and Rat (pair of bigint numerator and denominator) both will be only > approximations. > > The literals e and pi in Raku are typed as Num and when you call the > Rat method on them, you get a Rat back with the *default* precision > of 1e-6 [1]. That is a lot less precise than the Nums you started > with, hence the difference. Try supplying a large enough precision: > > > e.Rat(1e-200)**(pi.Rat(1e-200)*i) > -1+1.2246467991473532e-16i > > This is better than a default .Rat() but notice that you cannot get > past the limited precision in the source Nums, which is ca. 1e-16. > > Best, > Tobias > > [1] https://docs.raku.org/routine/Rat > > -- > "There's an old saying: Don't change anything... ever!" -- Mr. Monk > -- Aureliano Guedes skype: aureliano.guedes contato: (11) 94292-6110 whatsapp +5511942926110
