By David E. Hudak, Santosh G. Abraham

4. 2 Code Segments . . . . . . . . . . . . . . . ninety six four. three picking conversation Parameters . ninety nine four. four Multicast verbal exchange 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 checklist OF FIGURES determine 1. 1 The Butterfly structure. . . . . . . . . . five 1. 2 instance of an iterative data-parallel loop . . 7 1. three Contiguous tiling and project of an generation house. thirteen 2. 1 conversation alongside a line phase. . . 24 2. 2 entry trend 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 communique styles. 29 2. five Decomposing a vector alongside separate foundation units of vectors. 31 2. 6 Cache strains aligning with borders. 33 2. 7 Cache traces now not aligned with borders. 34 2. eight nh is the adaptation of nd and nb. forty two 2. nine nh is the sum of nd and nb. forty two 2. 10 The ADAPT method. forty four 2. eleven Code phase utilized in experiments. . forty six 2. 12 Execution premiums for varied walls. forty seven 2. thirteen Execution time of walls on Multimax. forty eight 2. 14 functionality elevate as processing energy raises. forty nine 2. 15 percent omit ratios for numerous element ratios and line sizes.

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Assume A(i, j+1) is also within the same part as A(i,j), and the second access vector requires that A(i + 1, (j + 1) + 2), which is really A( i + 1, j + 3) be brought into the local cache. The first method for constructing communication weights given r access vectors treats all accesses as distinct 3 and is called additive construction. The procedure assumes that every access vector contributes to bus traffic. The additive construction gives an upper bound on the worst case communication. Theorem 3 Given k access vectors S = {ml' m2, ...

9, the real plane has been subdivided into eight numbered semiquadrants. These semiquadrants are partitioned into two sets, {I, 4, 5, 8} and {2, 3, 6, 7}. For semiquadrants in the first set an access vector's projections along the B-Axis and the D-Axis lie on opposite sides of the H-Axis, as in Fig. 8. 24) For semiquadrants in the second set, an access vector's projections along the B-Axis and the D-Axis lie on the same side of the H-Axis, as in Fig. 9. 8: nh is the difference of nd and nb. 9: nh is the sum of nd and nb.

Each processor executes the chunk located at a fixed position within each tile. The aspect ratio of the tiles is optimized by a tradeoff of row and column multicast communication. The size of the chunks is determined by a tradeoff between load balancing and false sharing. A small chunk size reduces load imbalance by distributing the work finely between processors. Similar classes of partitions have been previously proposed [GB90] [ACF+87] but this work presents a methodology to choose the right partition for a particular program running on a particular machine.

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