The Allen and Greenough is still under construction;
so some links may not work quite the way you would expect.
THE PERIPHRASTIC CONJUGATIONS.
193. A Periphrastic form, as the name indicates, is
a ``roundabout way of speaking.'' In the widest sense, all verb-phrases
consisting of participles and sum are Periphrastic Forms. The Present
Participle is, however, rarely so used, and the Perfect Participle with
sum is included in the regular conjugation (amátus sum, eram, etc.). Hence the term
Periphrastic Conjugation is usually restricted to verb-phrases consisting
of the Future Active Participle or the Gerundive with sum.
NOTE: The Future Passive Infinitive, as amátum írí, formed from
the infinitive passive of eó,
go, used impersonally with the supine in -um, may also be classed as a periphrastic form
(§ 203. a).