in reply to Euler's identity in Raku

Why is the fancy part not 0?

Because the estimation used for "pi" is not exactly equal to pi.
For the imaginary part of the result to be zero, you need to multiply "i" by exactly pi.

Cheers,
Rob

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Re^2: Euler's identity in Raku
by tomasz (Acolyte) on Jun 03, 2021 at 05:41 UTC
    Wouldn't e have to be pure also?
[reply]
      Wouldn't e have to be pure also?

      You're correct - the inexactness of "e" is also influencing the result.


      UPDATE: BTW, in perl we can reproduce you're original result with: 
      >perl -MMath::Complex -le "print exp(1) ** (pi * i);"
-1+1.22460635382238e-16i

      [download]
      Oops ... hang on ... that's not exactly the same. (I'm not all that familiar with Raku, so I'm not sure what accounts for that difference.)

      Cheers,
      Rob
[reply]
[d/l]

        Copying Rob's one-liner into my system gives yet another answer: 

        -1+1.22464679914735e-16i

        Using perl -v, my perl is "

        This is perl 5, version 32, subversion 1 (v5.32.1) built for x86_64-linux-gnu-thread-multi
        ". Possibly different compilers or options used to build the executables. As somebody who has dealt with floating point issues, 10**(-16) in a operation return like this is frequently noise. I'd not expect perl to return exactly zero to sin(pi) and I don't get it, but 1.22464679914735e-16.

        That's hinting at something, but I'm not quite sure what.

        Tried (and hopefully succeeded) in fixing the formatting, so my reply isn't in my sig.

        Information about American English usage here and here. Floating point issues? Please read this before posting. — emc

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