Generation for A ne Subscripts inData - Parallel

This paper presents an eecient compilation technique to generate the local memory access sequences for block-cyclically distributed array references with aane subscripts in data-parallel programs. For the memory accesses of an array reference with aane subscript within a two-nested loop, there exist repetitive patterns both at the outer and inner loops. We use tables to record the memory accesses of repetitive patterns. According to these tables, a new start-computation algorithm is proposed to compute the starting elements on a processor for each outer loop iteration. The complexities of the table constructions are O(k + s 2), where s 2 is the access stride for the inner loop. After tables are constructed, generating each starting element for each outer loop iteration can run in O(1) time. For the repetitive pattern of outer loop, Moreover, we also discover that the repetitive iterations for outer loop are Pk= gcd(P k; s 1) instead of Pk, where s 1 is the access stride for the outer loop. Therefore, the total complexity to generate the local memory access sequences for a block-cyclically distributed array with aane subscript in a two-nested loop is O(Pk gcd(P k;s1) + k + s 2).