A true set-associative cache tests all the possible ways simultaneously, using something like a content addressable memory. A pseudo-associative cache tests each possible way one at a time. A hash-rehash cache is one kind of pseudo-associative cache.
In the common case of finding a hit in the first way tested, a pseudo-associative cache is as fast as a direct-mapped cache. But it has a much lower conflict miss rate than a direct-mapped cache, closer to the miss rate of a fully associative cache
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