From @titsuki

See the following results

$ perl6 -e 'say -1 ** -0.1'
-1
$ perl6 -e 'say reduce * ** *, -1, (-0.1)'
NaN

My Perl 6 version is
$ perl6 --version
This is Rakudo version 2016.05-4-g7a4ca4d built on MoarVM version 2016.05
implementing Perl 6.c.

From @titsuki

Sorry

"negative integers with negative decimal exponents"

is the correct expression.

On 2016-7月-09 土 05​:19​:49, cookbook_000@​yahoo.co.jp wrote​:

See the following results

$ perl6 -e 'say -1 ** -0.1'
-1
$ perl6 -e 'say reduce * ** *, -1, (-0.1)'
NaN

My Perl 6 version is
$ perl6 --version
This is Rakudo version 2016.05-4-g7a4ca4d built on MoarVM version 2016.05
implementing Perl 6.c.

From @pmichaud

On Sat, Jul 09, 2016 at 05​:19​:49AM -0700, Itsuki Toyota wrote​:

See the following results

$ perl6 -e 'say -1 ** -0.1'
-1
$ perl6 -e 'say reduce * ** *, -1, (-0.1)'
NaN

This is not a bug in "reduce" itself. Exponentiation has higher
precedence than unary minus, so the first expression is being
parsed and executed as -(1 ** -0.1) and not (-1) ** -0.1.
From my rakudo (ver 2016.06-50-g5a4963f)​:

$ ./perl6 -e 'say -1 ** -0.1'
-1
$ ./perl6 -e 'say (-1) ** -0.1'
NaN

So, the reduce subroutine is doing exactly the same thing as &infix​:<**> here does with a negative base.

At the moment I'm inclined to believe that a negative integer with
negative exponent should return NaN, but someone with more mathematics
sense than I would have to make that call.

Pm

The RT System itself - Status changed from 'new' to 'open'

From @zoffixznet

First a bit of deconfusion​: negative exponents just mean x⁻² = 1/x². That works just fine and is not relevant to this ticket​:

  <ZoffixW> m​: say (-2) ** -2
  <camelia> rakudo-moar 605f27​: OUTPUT«0.25␤»

Fractional exponents mean the number is raised to the power of the numerator and then the denominator-th-root is taken from it. So raising to 0.1th power simply means we take 10th root​:

  <ZoffixW> m​: say 1024 ** .1
  <camelia> rakudo-moar 605f27​: OUTPUT«2␤»

So far so good for positive base numbers, but some stuff appears to be broken for roots of negatives. First, the NaN case described in this ticket​:

  <ZoffixW> m​: say (-1) ** .5
  <camelia> rakudo-moar 605f27​: OUTPUT«NaN␤»

We're taking a square root of a negative number which "doesn't exist", so we're dealing with Complex numbers.
The NaN result matches what we'd get from sqrt(), so this case is fine​:

  <ZoffixW> m​: say sqrt(-1)
  <camelia> rakudo-moar 605f27​: OUTPUT«NaN␤»

BUT, unlike sqrt(), if we request to deal with Complex numbers, the output from the infix​:<**> is incorrect​:

  <ZoffixW> m​: say sqrt(-1+0i)
  <camelia> rakudo-moar 605f27​: OUTPUT«0+1i␤»
  <ZoffixW> m​: say (-1+0i) ** .5
  <camelia> rakudo-moar 605f27​: OUTPUT«6.12323399573677e-17+1i␤»

Moreover, if we raise a negative number to an *odd* power, the result will be negative​:

  <ZoffixW> m​: say (-5)**3
  <camelia> rakudo-moar 605f27​: OUTPUT«-125␤»

This means that taking an *odd* root doesn't have anything to do with Complex numbers and should Just Work™, but Rakudo still gives us a NaN, instead of the original -5​:

  <ZoffixW> m​: say (-125)**(1/3)
  <camelia> rakudo-moar 605f27​: OUTPUT«NaN␤»

We can try using the "Complex mode", and that doesn't give NaN, but the result is wrong, so we can't use that to perform such a computation​:

  <ZoffixW> m​: say (-125+0i) ** (1/3)
  <camelia> rakudo-moar 605f27​: OUTPUT«2.5+4.33012701892219i␤»
  <ZoffixW> m​: say (-125+0i) ** ((1+0i)/(3+0i))
  <camelia> rakudo-moar 605f27​: OUTPUT«2.5+4.33012701892219i␤»

In summation, the buggy behaviour revealed by this ticket is​:
  (a) odd roots (rational powers with odd denominators) produce NaN instead of actual non-complex result
  (b) rational powers on complex numbers produce wrong results

On Sat Jul 09 09​:51​:38 2016, pmichaud wrote​:

On Sat, Jul 09, 2016 at 05​:19​:49AM -0700, Itsuki Toyota wrote​:

See the following results

$ perl6 -e 'say -1 ** -0.1'
-1
$ perl6 -e 'say reduce * ** *, -1, (-0.1)'
NaN

This is not a bug in "reduce" itself. Exponentiation has higher
precedence than unary minus, so the first expression is being
parsed and executed as -(1 ** -0.1) and not (-1) ** -0.1.
From my rakudo (ver 2016.06-50-g5a4963f)​:

$ ./perl6 -e 'say -1 ** -0.1'
-1
$ ./perl6 -e 'say (-1) ** -0.1'
NaN

So, the reduce subroutine is doing exactly the same thing as
&infix​:<**> here does with a negative base.

At the moment I'm inclined to believe that a negative integer with
negative exponent should return NaN, but someone with more mathematics
sense than I would have to make that call.

Pm