in reply to Re^4: Euler's identity in Raku

in thread Euler's identity in Raku

*I'd not expect perl to return exactly zero to sin(pi) and I don't get it, but 1.22464679914735e-16*

The reliance on the sine and cosine trig functions can be seen at https://www.math.toronto.edu/mathnet/questionCorner/complexexp.html.

For the case under consideration in this thread, the imaginary component should be

`sin(3.1415926535897931 * log(2.7182818284590451))`

`log(2.7182818284590451)`is calculated to be exactly 1 and, as already noted,

`sin(3.1415926535897931)`is calculated to be 1.2246467991473532e-16.

I don't know how the MPC library is coming up with

`2.8954204500590832e-16`, but I'm about to ask them about that, and I'll update this post when I get the answer.

**UPDATE:**I've changed my mind - the value returned for these inputs is very sensitive to minute changes in the evaluation of those inputs. For example:

I don't see much point in investigating further when such a minute alteration to the arguments can make such a largesisyphus@sisyphus5-desktop:~$ perl -MMath::Complex -E "say sin(pi * 1) +;" 1.22464679914735e-16 sisyphus@sisyphus5-desktop:~$ perl -MMath::Complex -E "say sin(pi * 0. +99999999999999994);" 5.66553889764798e-16

**relative**difference, especially when we consider that the

**absolute**difference is so minute.

Cheers,

Rob

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