possible bug in awk's x^y

[John Wheeler]

I found in evaluating e = lim_{n-> inf} (1+1/n)^n
for n = 2^m
that gawk
1. became slow
2. failed to be accurate at about single precision arithmetic.
When I instead calculated exp(n*log(1+1/n))
it ran much faster and attained full double precision arithmetic.
When I tried
x = n + sqrt(3)
it ran fast, but again only produced single precision reliability.
This leads me to suspect there is a bug in the implementation of gawk's x^y.
Comments?
John Wheeler
address@hidden
858-699-2585