Some years ago I noticed that the Power operator ** won't always give
exactly the same result as repeated multiplication, as described in 10.2.1.
"For calculating the power, the number is multiplied by itself for the
number of times expressed by the power."
Indeed; the power operator is 'hard'. Multiplying by itself is accurate
but too slow for large powers, and doesn't work well for non-integer powers.
The IEEE 754 committee spent many meetings arguing whether a 'correctly
rounded' power operator was even possible. After five years, and much
research, a group came up with a proof that a correctly rounded result was,
in fact, always possible.
Unfortunately, they were unable to prove that such a result could always be
calculated in finite time.
So the standard just 'recommends' that a correctly rounded result be given
... :-)
Mike
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