# Compiling Parallel Loops for High Performance Computers: by David E. Hudak, Santosh G. Abraham

By David E. Hudak, Santosh G. Abraham

4. 2 Code Segments . . . . . . . . . . . . . . . ninety six four. three selecting communique Parameters . ninety nine four. four Multicast communique Overhead · 103 four. five Partitioning . . . . . . · 103 four. 6 Experimental effects . 117 four. 7 end. . . . . . . · 121 five COLLECTIVE PARTITIONING AND REMAPPING FOR a number of LOOP NESTS one hundred twenty five five. 1 advent. . . . . . . . . one hundred twenty five five. 2 software Enclosure timber. . 128 five. three The CPR set of rules . . 132 five. four Experimental effects. . 141 five. five end. . 146 BIBLIOGRAPHY. 149 INDEX . . . . . . . . 157 record OF FIGURES determine 1. 1 The Butterfly structure. . . . . . . . . . five 1. 2 instance of an iterative data-parallel loop . . 7 1. three Contiguous tiling and task of an new release house. thirteen 2. 1 conversation alongside a line phase. . . 24 2. 2 entry development for the entry offset, (3,2). 25 2. three Decomposing an entry vector alongside an orthogonal foundation set of vectors. . . . . . . . . . . . . . . . . . . 26 2. four An research of conversation styles. 29 2. five Decomposing a vector alongside separate foundation units of vectors. 31 2. 6 Cache traces aligning with borders. 33 2. 7 Cache traces now not aligned with borders. 34 2. eight nh is the variation of nd and nb. forty two 2. nine nh is the sum of nd and nb. forty two 2. 10 The ADAPT process. forty four 2. eleven Code phase utilized in experiments. . forty six 2. 12 Execution premiums for numerous walls. forty seven 2. thirteen Execution time of walls on Multimax. forty eight 2. 14 functionality bring up as processing strength raises. forty nine 2. 15 percent leave out ratios for varied point ratios and line sizes.

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Since loops can have widely differing computational requirements and communication patterns, a single partition may not provide adequate performance for every loop. , alter the loop partition when the computational requirements or communication patterns vary greatly between loops. However, remapping introduces additional interprocessor communication, so remapping must be applied selectively. We developed the Collective Partitioning and Remapping (CPR) algorithm with three distinct phases. The first phase, remapping, aggressively inserts remapping points between data-parallel loops whenever there is a potential for improving processor utilization or reducing interprocessor communication.

Proof: Without loss of generality, assume that the head of an access vector for a point located on the boundary of Ii lies outside the part. 2: Access pattern for the access offset, (3,2). of dimensions Land q sin B, as illustrated in Fig. 1. The statement of the theorem follows from Definition 1. 0 Now, consider the access vector associated with the access offset (3,2). The decomposition q sin B along the horizontal axis gives the amount of extra communication incurred for every data point along a vertical partition border, which is two.

Define m. 2) i=l Proof: Each pair of line segments accounts for nil. communication by Theorem 1. Therefore, the total communication for all m line segment pairs is as above. However, some data points near the corners of the part may be counted twice in this analysis; hence the approximate nature of the result. We will carry out a more exact analysis of rectangles and show that the term is only a function of the access offsets and independent of the dimensions of the part. 0 Consider a rectangular partitioning scheme, where each rectangle has dimensions h and v along the horizontal and vertical directions.