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This problem is present in C pow and powf functions. So, this issue is related with standard math library of C [1], which is in the bones of Lua ;-)

[1] says: pow(base, exponent) returns NaN and raises FE_INVALID if base is finite and negative and exponent is finite and non-integer

On Thu, 14 Apr 2016 at 12:30 Christopher Kappe <> wrote:

I just noticed that it is not possible to compute the cubic root of a
negative number. See e.g.
print( math.pow( -27, 1/3 ) ) --> -nan instead of -3
The same is true for the ^ operator (not surprising).

This probably stems from the fact that the result of the n-th root of a
negative number is not real if n is even (e.g. sqrt(-1) = (-1)^(1/2) =
i). However, (-3)^3 = -27 and likewise should hold that (-27)^(1/3) = -3.
This works by the way with Google (try googling f(x) = x^(1/3) and you
will see the graph of the function also for the negative x-axis).

If such a correct behavior is not easy to implement in the generic
math.pow function, I would suggest offering a math.cbrt function as
exists e.g. in C, C++ or Octave.

The least one should do, is document the fact that exponentiation only
works for a non-negative base argument.


Pako ZM :)