Upon further thought, it's not clear that specifying a NaN error-object
is necessary or desirable; as in all cases it would appear preferable to
signal a recoverable exception, upon which a default most-likely-useful
value based on the context of the calculation is returned, or optional
alternative action (potentially inclusive of a halting error) may be
invoked if specified. Thereby alleviating any explicit need for a
non-numerical error object itself.

Where then default most-likely-useful numeral results may be specified if
desired, or left implementation specific (whereby then an implementation
may choose to explicitly represent a NaN error-object it so chooses,
however not mandated to do so by the standard).

Where then, an error-object may be independently specified as a proposed
srfi independently, where by then such an object (such as <void> for the
sake of argument), may be returned in lieu of an otherwise valid object as
a result of any calculation, numeral or otherwise, as may be desired in lieu
of a recoverable exception handler returning an otherwise more useful value.

As just a thought.