Some words of wisdom like the following need to be added to the
definition of the exponentiation operator (as well as the complex
and imag cases being documented):
This operator is unlike other mathematical operators for floating
point data which are correctly rounded, i.e. have a rounding error
which is not greater than 0.5 ULP (1). At best, exponentiation of
a floating point number achieves a rounding error which is for a
floating point exponent is guaranteed to not exceed 1 ULP(1)
with an underlying robust mathematical library. For the optimized
cases of integral exponents of floating point data, the rounding
error in most cases does not exceed several ULPs, although that
is not guaranteed.
A more succinct version of the above would be better which could
reference the above would be good.
Summary of Problem
Description:
This was reported by Damian in our mailing list. He said there: