terminology - What is a gerund? A noun or a verb? 'His smoking upset me’

I've been studying the Huddleston and Pullum book for four months now. So far only one thing confuses me: the identity of gerund. Is it a noun or a verb?

1. His constant smoking upset me. smoking seems noun because of adjective constant.


2. Him/His constantly smoking upset me. smoking seems to be verb because of adverb constantly.


3. Him/His smoking cigars upset me. smoking seems to be a verb because of object cigars.

"His smoking upset me." So is this smoking gerund a noun or verb? Because there is no differentiation, is it both verb and noun? Maybe it's new word category?

Also his seems to be both sometimes a subject and at other times a possessive determiner. Is that correct?