In a giant-like manner; with the size, strength, or grandiosity characteristic of a giant; in an enormously large or impressive way.
From 'giant' + '-ly' (a suffix forming adverbs from adjectives). The '-ly' suffix comes from Old English '-lice' meaning 'in the manner of' and became the standard English adverb-forming suffix.
Very rarely used, 'giantly' is an interesting case of English's adverb-forming productivity—even though we don't normally say it, the structure is perfectly valid, much like how 'sleepily' or 'hungrily' work.
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