Since
and
are less than or equal to
in magnitude, it is possible that
may overflow although
or
does not. In this case the alternative formula
is used for the real part of the result, and
for the imaginary part. If either part of the result still overflows, a warning is returned through parameter
IFAIL.
If
is too large, precision may be lost in the evaluation of
and
. Again, a warning is returned through
IFAIL.
None.
If on entry
or
, explanatory error messages are output on the current error message unit (as defined by
X04AAF).
Accuracy is limited in general only by the accuracy of the standard functions in the computation of
,
and
, where
,
. As
gets larger, precision will probably be lost due to argument reduction in the evaluation of the sine and cosine functions, until the warning error
occurs when
gets larger than
, where
is the
machine precision. Note that on some machines, the intrinsic functions SIN and COS will not operate on arguments larger than about
, and so
IFAIL can never return as
.
None.