Is "fastly" a correct word?

Solution 1:

There is no need for "fastly" because "fast" is both an adjective and an adverb. So, "I ran fast" is completely correct.

The existence of "fast" as an adverb does not preclude the future development of a word "fastly", but it does hinder it.

One might note that the corresponding adjective "slow" does take the -ly suffix, but this has no impact on the behavior of "fast". (There is also no real reason why, for example, we have warm/warmth, but cool/coolness. Semantically related things sometimes have similar morphological patterns, and sometimes not.)

One interesting thing worth noting (that was brought up in a comment by Jimi Oke) is that there are cases of adjectives with identical adverbs that also have an -ly form; for example, we have "right" and "wrong" as adjectives and adverbs, but we also have "rightly" and "wrongly". In such cases, the -ly form has carved out its own semantic niche; the adverb "right" and the adverb "rightly" cannot be used interchangeably in every situation. I can say "turn right" and "rightly so", but I can't exchange them in either sentence.

With normal adjectives that cannot become adverbs without -ly, usually the -ly just transparently makes the adjective adverbial — it doesn't have its own separate semantic nuances (e.g. "quickly" simply means "in a quick manner").

Solution 2:

The adverb form of fast is irregular. It is one of several exceptions, as is "well" as mentioned by Dena A.

a fast runner   /    run fast
a hard worker   /    work hard
a bad smell     /    smell bad

etc. etc. etc.

About work hard: 'he works hard', in contrast to 'he is hardly working'. Two different meanings.

Solution 3:

Fast is an adverb as well as an adjective, so you wouldn't use fastly. Another common adverb that doesn't follow the pattern of ending in ly is well, not the expected goodly, which is actually an adjective and means a large quantity, e.g. a goodly sum.