Mapping Nested Loop Algorithms Into Multi Dimensional Systolic Arrays

P Lee

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S). In general, the time hyperplane H and the space hyperplane S must satisfy certain constraints which we will state next.
3 Necessary and SufRcient Conditions Let l array Ar must preserve data-dependence relations, the right tokens must be in the right place at the right time, and in addition, data tokens must not collide in data links.
3. 1 Necessary Conditions We now consider conditions to be satisfied by (H. S) in order to assure a correct construction. There are four necessary conditions ...for (H, S).
1. H has to preserve the data-dependence relation, that is, if h - I\ = d, and rf, ^ Op (Op = (0, 0, . .. , 0)', a p-tuple zero vector) for all two indices /j and I2, then I2 must be executed after I\. That is, H/2 - H/i > 0. Or, H(/2 - /j ) = Hf/, > 0. (In the following report, we also assume 3 NECESSARY AND SUFFICIENT CONDITIONS 6 /i ^ I2 if we do not mention it. ) Condition 1 : HJ, > must be true for all nonzero data-dependence vectors d, (^ Op).

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