David E. Hudak

4. 2 Code Segments . . . . . . . . . . . . . . . 96 4. 3 Determining Communication Parameters . 99 4. 4 Multicast Communication Overhead · 103 4. 5 Partitioning . . . . . . · 103 4. 6 Experimental Results . 117 4. 7 Conclusion. . . . . . . · 121 5 COLLECTIVE PARTITIONING AND REMAPPING FOR MULTIPLE LOOP NESTS 125 5. 1 Introduction. . . . . . . . . 125 5. 2 Program Enclosure Trees. . 128 5. 3 The CPR Algorithm . . 132 5. 4 Experimental Results. . 141 5. 5 Conclusion. . 146 BIBLIOGRAPHY. 149 INDEX . . . . . . . . 157 LIST OF FIGURES Figure 1. 1 The Butterfly Architecture. . . . . . . . . . 5 1. 2 Example of an iterative data-parallel loop . . 7 1. 3 Contiguous tiling and assignment of an iteration space. 13 2. 1 Communication along a line segment. . . 24 2. 2 Access pattern for the access offset, (3,2). 25 2. 3 Decomposing an access vector along an orthogonal basis set of vectors. . . . . . . . . . . . . . . . . . . 26 2. 4 An analysis of communication patterns. 29 2. 5 Decomposing a vector along two separate basis sets of vectors. 31 2. 6 Cache lines aligning with borders. 33 2. 7 Cache lines not aligned with borders. 34 2. 8 nh is the difference of nd and nb. 42 2. 9 nh is the sum of nd and nb. 42 2. 10 The ADAPT system. 44 2. 11 Code segment used in experiments. . 46 2. 12 Execution rates for various partitions. 47 2. 13 Execution time of partitions on Multimax. 48 2. 14 Performance increase as processing power increases. 49 2. 15 Percentage miss ratios for various aspect ratios and line sizes.

4. 2 Code Segments . . . . . . . . . . . . . . . 96 4. 3 Determining Communication Parameters . 99 4. 4 Multicast Communication Overhead · 103 4. 5 Partitioning . . . . . . · 103 4. 6 Experimental Results . 117 4. 7 Conclusion. . . . . . . · 121 5 COLLECTIVE PARTITIONING AND REMAPPING FOR MULTIPLE LOOP NESTS 125 5. 1 Introduction. . . . . . . . . 125 5. 2 Program Enclosure Trees. . 128 5. 3 The CPR Algorithm . . 132 5. 4 Experimental Results. . 141 5. 5 Conclusion. . 146 BIBLIOGRAPHY. 149 INDEX . . . . . . . . 157 LIST OF FIGURES Figure 1. 1 The Butterfly Architecture. . . . . . . . . . 5 1. 2 Example of an iterative data-parallel loop . . 7 1. 3 Contiguous tiling and assignment of an iteration space. 13 2. 1 Communication along a line segment. . . 24 2. 2 Access pattern for the access offset, (3,2). 25 2. 3 Decomposing an access vector along an orthogonal basis set of vectors. . . . . . . . . . . . . . . . . . . 26 2. 4 An analysis of communication patterns. 29 2. 5 Decomposing a vector along two separate basis sets of vectors. 31 2. 6 Cache lines aligning with borders. 33 2. 7 Cache lines not aligned with borders. 34 2. 8 nh is the difference of nd and nb. 42 2. 9 nh is the sum of nd and nb. 42 2. 10 The ADAPT system. 44 2. 11 Code segment used in experiments. . 46 2. 12 Execution rates for various partitions. 47 2. 13 Execution time of partitions on Multimax. 48 2. 14 Performance increase as processing power increases. 49 2. 15 Percentage miss ratios for various aspect ratios and line sizes.