(^^) is not correct for Double and Float

[daniel.is.fischer]

Consider

Prelude> 2 ^^ (-1024)
0.0
Prelude> 0.5 ^^ 1024
5.562684646268003e-309

The cause is

x ^^ n          =  if n >= 0 then x^n else recip (x^(negate n))

If we change it to

x ^^ n          =  if n >= 0 then x^n else ((recip x)^(negate n))

it'll do the right thing for Double and Float, and I don't know of any type where it would produce incorrect results.

Does it need a library proposal or can the change be made without?

[igloo]

I'm not sure I see why this is necessarily more correct in general.

[daniel.is.fischer]

It produces correct (in the sense of "if the real result of xⁿ is a finite nonzero number, so is x ^^ n, and the value of x ^^ n differs only very little from each of the real value, x ** n and fromRational (toRational x ^^ n)") results for more inputs. When abs(x) > 1, n < 0 and x ^ (-n) gives Infinity, so x ^^ n yields 1/Infinity = 0, (1/x) ^ (-n) can, as in the example, yield a nonzero (subnormal) number.