A major problem in executing algorithms in array processors is the implementation of broadcasts without unnecessary speed-up factor degradation. We discuss when and how broadcasts can be eliminated or reduced to easily implementable sequences of reduced local broadcasts. Algorithms are modelled as a structured set of indexed computations which operate on variables associated with a referencing or indexing function. The discussion is restricted to variables with linear indexing functions and to algorithms linearly scheduled for execution in array processors. Linear indexing functions are represented as affine matricial functions of the index set of the algorithm. The linear part of such representation is a coefficient matrix denoted the indexing matrix. Linear schedules are defined as linear time-space allocation functions mapping the computations of an algorithm into time and processors. We discuss necessary and sufficient conditions for the occurrence of broadcasts in a linearly scheduled algorithm. Necessary and sufficient conditions and constructive criteria are given for selecting linear schedules for which all broadcasts are eliminated or reduced to sequences of small local broadcasts.
在阵列处理器中执行算法的主要问题是广播的实现,而没有不必要的提速因子降低。我们讨论何时以及如何消除广播或将广播减少为易于实施的减少本地广播的序列。算法被建模为索引计算的结构化集合,该索引计算对与引用或索引函数关联的变量进行操作。讨论仅限于具有线性索引功能的变量以及线性计划在数组处理器中执行的算法。线性索引函数表示为算法索引集的仿射矩阵函数。这种表示的线性部分是表示为索引矩阵的系数矩阵。线性时间表定义为线性时空分配函数,将算法的计算映射到时间和处理器中。我们讨论了在线性调度算法中发生广播的必要条件和充分条件。给出了选择线性广播时间表的必要和充分条件,并提出了建设性的标准,对于这些线性时间表,所有广播都将被消除或减少为小型本地广播的序列。 P>
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机译:在内存处理器阵列上优化数据调度
机译:在线性阵列和网格上广播。