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
