Does the entire blockchain have to be recomputed to validate a transaction?

Does the entire blockchain have to be recomputed to validate a transaction?

Are transactions validated by recomputing the entire blockchain? If not, how else can it be confirmed that a bitcoin I'm attempting to transact is one that I actually had come into acquisition of previously and still have?

If yes on the other hand, how long does that recomputation typically take in practice, and does that pose a scalability risk in the potential for Bitcoin usage (and hence the length of the blockchain) to outpace Moore's law?

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