For
, the function fails owing to danger of setting overflow in calculating
. The result returned for such calls is
, i.e., it returns the result for the nearest valid argument. The value of machine-dependent constant
may be given in the
Users' Note for your implementation.
If
and
are the relative errors in the argument and result, respectively, then in principle
That is, the relative error in the argument,
, is amplified by a factor, at least
. The equality should hold if
is greater than the
machine precision (
is due to data errors etc.) but if
is simply a result of round-off in the machine representation of
then it is possible that an extra figure may be lost in internal calculation round-off.
The behaviour of the error amplification factor is shown by the following graph:
Figure 1
It should be noted that near
where this amplification factor tends to zero the accuracy will be limited eventually by the
machine precision. Also for
where
is the absolute error in the argument
.
Not applicable.
None.