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If we are talking about CPU cache. Is Ln synonym for saying 'TLB (translation lookaside buffer) of type Ln' or does Ln include also somethin else than just TLB?

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Ln identifies the level of a particular type of storage (or more generally "resource"). It can be applied to memory caches (including separately for instruction and data caches), TLBs, branch prediction structures, hardware instruction schedulers, etc.

An Ln cache is specifically the cache for memory and is distinct from the TLB.

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