USAGE: "Laughingly":What part of speech is it?

I'd like to know a little more about the grammar of a gerund that is
changed into an adverb . I'm going to make a gender changer that changes
a root or infinitive verb to a corresponding adverb for vector tense.
I want to say things like,

He goes walkingly to the store.

Obviously this isn't great english, but for some reason,

He said laughingly that he didn't mean it.

seems ok.

Any information about these  gerund-adverbs would help me.
Thanks,

Jerry

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