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In relational algebra, a rename is a unary operation written as / where: . R is a relation; a and b are attribute names; b is an attribute of R; The result is identical to R except that the b attribute in all tuples is renamed to a. [1]
Early out-of-order machines did not separate the renaming and ROB/PRF storage functions. For that matter, some of the earliest, such as Sohi's RUU or the Metaflow DCAF, combined scheduling, renaming, and storage all in the same structure. Most modern machines do renaming by RAM indexing a map table with the logical register number.
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The finite form typically occurs only for the gamma and related functions, for which the identity follows from a p-adic relation over a finite field. For example, the multiplication theorem for the gamma function follows from the Chowla–Selberg formula, which follows from the theory of complex multiplication.
Drawing up a comprehensive list of words in English is important as a reference when learning a language as it will show the equivalent words you need to learn in the other language to achieve fluency. A big list will constantly show you what words you don't know and what you need to work on and is useful for testing yourself.