Execution of Regular Do Loops On Asynchronous Multiprocessors
Execution of Regular Do Loops On Asynchronous Multiprocessors
Pei Ouyang
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proof. U k = [ky, . . . , kn] is in 7, we show that it is impossible that it depends on any other iterations in the iteration space S. Suppose on the contrary that it depends on some other iteration, then there must exist an iteration k' = [k[, . . . , k'„] such that k = k' + d, for some fixed s. Since k £ fli^i U?=i ^>] ' ^ must be in /, ( for some fixed t. Since k = k' + d, v/e have Jt( = k[ + d, t. However, • if d, t > 0, then k[ - ki - d„ 0, then d, j
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