Parallel Java A Unified API for Shared Memory and Cluster Parallel Programming in 100% Java Lecture Notes Prof. Alan Kaminsky Department of Computer Science B. Thomas Golisano College of Computing and Information Sciences Rochester Institute of Technology Rochester, NY, USA Presented at the 9th International Workshop on Java and Components for Parallelism, Distribution and Concurrency International Parallel and Distributed Processing Symposium (IPDPS 2007) Long Beach, CA, USA March 26, 2007 Overview Parallel Computer Architectures   Motivations for Parallel Java   Programming with Parallel Java -- Example 1   Parallel Java Performance -- Example 1   Programming with Parallel Java -- Example 2   Parallel Java Performance -- Example 2   Parallel Java Architecture   Status   Future Plans   For Further Information   Running Time Data -- Example 1   Running Time Data -- Example 2 Parallel Computer Architectures Shared memory multiprocessor (SMP) parallel computers Even consumer desktop machines are starting to look like this     Cluster parallel computers Soon you won't even be able to build these any more     Hybrid SMP cluster parallel computers Soon all clusters will look like this     The RIT CS Department's parallel computers, used for teaching parallel computing courses:   SMP parallel computers paradise.cs.rit.edu -- Four Sun UltraSPARC-IV dual-core CPUs, eight processors, 1.35 GHz clock, 16 GB main memory parasite.cs.rit.edu -- Four Sun UltraSPARC-IV dual-core CPUs, eight processors, 1.35 GHz clock, 16 GB main memory paradox.cs.rit.edu -- Four Sun UltraSPARC-II CPUs, four processors, 450 MHz clock, 4 GB main memory paragon.cs.rit.edu -- Four Sun UltraSPARC-II CPUs, four processors, 450 MHz clock, 4 GB main memory   Cluster parallel computer Frontend computer -- paranoia.cs.rit.edu -- UltraSPARC-II CPU, 296 MHz clock, 192 MB main memory 32 backend computers -- thug01 through thug32 -- each an UltraSPARC-IIi CPU, 440 MHz clock, 256 MB main memory 100-Mbps switched Ethernet backend interconnection network Aggregate 14 GHz clock, 8 GB main memory   Hybrid SMP cluster parallel computer Frontend computer -- tardis.cs.rit.edu -- UltaSPARC-IIe CPU, 650 MHz clock, 512 MB main memory 10 backend computers -- dr00 through dr09 -- each with two AMD Opteron 2218 dual-core CPUs, four processors, 2.6 GHz clock, 8 GB main memory 1-Gbps switched Ethernet backend interconnection network Aggregate 104 GHz clock speed, 80 GB main memory Motivations for Parallel Java Parallel computing is moving into nontraditional domains Graphics, animation, data mining, informatics, . . . Applications tend to be written in newer languages like Java, not Fortran or C   Java is becoming the language of choice for learning programming ACM Java Task Force resources for teaching introductory programming in Java -- http://jtf.acm.org/   Soon everyone's desktop or laptop PC will be an SMP parallel computer That is, will have a multicore CPU chip Every computing student will have to learn how to write parallel programs, not just computational scientists   Standard parallel programming libraries have not caught up to the multicore revolution OpenMP addresses only SMP parallel programming MPI addresses only cluster parallel programming Programming a hybrid SMP cluster computer requires mastering two large and intricate APIs and their interactions   Hence: Parallel Java A single unified API . . . For thread-based SMP parallel programming, with features inspired by OpenMP . . . And for message-passing cluster parallel programming, with features inspired by MPI . . . And for hybrid SMP cluster parallel programming . . . In 100% Java   For instructors and students: Teach and learn parallel programming in the language of choice, Java   For developers: Master just one API whose SMP and cluster programming features are designed to work well together   For me: Explore just how much you can do with Java for high performance computing Both functionality-wise and performance-wise Programming with Parallel Java -- Example 1 Example: Cryptanalysis using exhaustive key search     Advanced Encryption Standard (AES) Plaintext block (128 bits) goes in Encrypted ciphertext block (128 bits) comes out Uses a 256-bit secret key   Known plaintext attack Plaintext block is known Corresponding ciphertext block is known Key is not known Problem: Discover the key Once you have the key, you can decrypt everything (that was encrypted with that key)   Exhaustive key search For every key from 0 to 2256-1, encrypt the given plaintext with that key, and see if you get the given ciphertext   Partial exhaustive key search 256-N bits of the key are known, N bits of the key are unknown For every combination of unknown key bits from 0 to 2N-1, encrypt the given plaintext with that key, and see if you get the given ciphertext   Sequential program -- Class FindKeySeq   SMP parallel program -- Class FindKeySmp3   Cluster parallel program -- Class FindKeyClu   Hybrid SMP cluster parallel program -- Class FindKeyHyb Parallel Java Performance -- Example 1 Running time measurements on the tardis.cs.rit.edu machine 10 backend processors, each with two dual-core CPU chips N = Problem size = number of keys searched = 32M, 64M, 128M, 256M K = Number of processors T = Running time (msec)   SMP parallel program -- Class FindKeySmp3 -- 1 process, 1 to 4 threads   Cluster parallel program -- Class FindKeyClu -- 1 to 4 processes, each with 1 thread   Hybrid SMP cluster parallel program -- Class FindKeyHyb -- 1 to 4 processes, each with 4 threads Programming with Parallel Java -- Example 2 Floyd's Algorithm Calculates the length of the shortest path from each node to every other node in a network of N nodes, given the distance from each node to its adjacent nodes On input, D is a distance matrix An NxN matrix where D[i,j] is the distance from node i to adjacent node j If node j is not adjacent to node i, then D[i,j] = infinity (The distance matrix need not be symmetric) On output, D[i,j] has been replaced by the length of the shortest path from node i to node j If there is no path from node i to node j, then D[i,j] = infinity Algorithm: for i = 0 to N-1 for r = 0 to N-1 for c = 0 to N-1 D[r,c] = min (D[r,c], D[r,i] + D[i,c]) Running time = O(N3)   Example input distance matrix (N = 10) 0.000 0.213 ∞ ∞ ∞ ∞ ∞ 0.248 0.240 ∞ 0.213 0.000 ∞ ∞ ∞ ∞ ∞ ∞ ∞ ∞ ∞ ∞ 0.000 ∞ ∞ ∞ ∞ ∞ 0.103 0.137 ∞ ∞ ∞ 0.000 0.212 ∞ ∞ 0.188 ∞ ∞ ∞ ∞ ∞ 0.212 0.000 0.077 ∞ ∞ ∞ ∞ ∞ ∞ ∞ ∞ 0.077 0.000 ∞ ∞ ∞ ∞ ∞ ∞ ∞ ∞ ∞ ∞ 0.000 ∞ ∞ ∞ 0.248 ∞ ∞ 0.188 ∞ ∞ ∞ 0.000 ∞ ∞ 0.240 ∞ 0.103 ∞ ∞ ∞ ∞ ∞ 0.000 0.043 ∞ ∞ 0.137 ∞ ∞ ∞ ∞ ∞ 0.043 0.000 Example output distance matrix 0.000 0.213 0.344 0.436 0.648 0.726 ∞ 0.248 0.240 0.284 0.213 0.000 0.557 0.649 0.861 0.939 ∞ 0.461 0.453 0.497 0.344 0.557 0.000 0.780 0.992 1.069 ∞ 0.592 0.103 0.137 0.436 0.649 0.780 0.000 0.212 0.289 ∞ 0.188 0.677 0.720 0.648 0.861 0.992 0.212 0.000 0.077 ∞ 0.400 0.888 0.932 0.726 0.939 1.069 0.289 0.077 0.000 ∞ 0.477 0.966 1.009 ∞ ∞ ∞ ∞ ∞ ∞ 0.000 ∞ ∞ ∞ 0.248 0.461 0.592 0.188 0.400 0.477 ∞ 0.000 0.488 0.532 0.240 0.453 0.103 0.677 0.888 0.966 ∞ 0.488 0.000 0.043 0.284 0.497 0.137 0.720 0.932 1.009 ∞ 0.532 0.043 0.000 Sequential program -- Class FloydSeq   SMP parallel program -- Class FloydSmpRow   Cluster parallel program -- Class FloydClu   Hybrid SMP cluster parallel program -- Class FloydHyb Parallel Java Performance -- Example 2 Running time measurements on the tardis.cs.rit.edu machine 10 backend processors, each with two dual-core CPU chips N = Problem size = number of network nodes = 2000, 2500, 3200, 4000 K = Number of processors T = Running time (msec) for computation only (not file I/O)   SMP parallel program -- Class FloydSmpRow -- 1 process, 1 to 4 threads   Cluster parallel program -- Class FloydClu -- 1 to 4 processes, each with 1 thread   Hybrid SMP cluster parallel program -- Class FloydHyb -- 1 to 4 processes, each with 4 threads Parallel Java Architecture Parallel Java on a cluster     Job Scheduler Daemon runs on the frontend processor Web interface for monitoring cluster status   SSH Daemon runs on each backend processor (not part of Parallel Java per se)   User runs a Java program with Parallel Java calls on the frontend processor   Parallel Java middleware, using SSH, runs a job backend process on each backend processor   Processes communicate using TCP sockets plus Parallel Java's own message passing layer Status Shared memory parallel programming features largely complete   Message passing parallel programming features partially complete Some of the more esoteric collective communication operations are not implemented   I use Parallel Java in my Parallel Computing I and Parallel Computing II classes Taught using Parallel Java for two years now   I started writing a parallel programming textbook using Parallel Java Building Parallel Programs: SMPs, Clusters, and Java Future Plans Continue work on the Parallel Java Library Continue improving performance of the parallel loop classes Continue improving performance of the message passing classes Implement remaining collective communication operations Add parallel file I/O as in MPI-2.0   Continue teaching the Parallel Computing I and II classes with Parallel Java   Finish writing the textbook To be published by Thomson Course Technology Tentative publication date January 2009   Accumulate more performance measurements on standard parallel benchmarks   Compare performance of Parallel Java programs with Fortran/C/OpenMP/MPI programs   Work on solving scientific computing problems with Parallel Java programs Computational medicine: MRI spin relaxometry -- done with mpiJava, need to redo with Parallel Java Computational biology: Maximum parsimony phylogenetic tree construction For Further Information Parallel Java Library (downloads) -- http://www.cs.rit.edu/~ark/pj.shtml   Parallel Java documentation -- http://www.cs.rit.edu/~ark/pj/doc/   Draft textbook Building Parallel Programs: SMPs, Clusters, and Java Draft chapters: http://www.cs.rit.edu/~ark/bpp/   Course web sites -- many more examples Parallel Computing I course web site -- http://www.cs.rit.edu/~ark/531/ Parallel Computing II course web site -- http://www.cs.rit.edu/~ark/532/ Running Time Data -- Example 1 Running time measurements on the tardis.cs.rit.edu machine 10 backend processors, each with two dual-core CPU chips N = Problem size = number of keys searched K = Number of processors T = Running time (msec)   SMP parallel program -- Class FindKeySmp3 -- 1 process, 1 to 4 threads   Raw running time data (msec) N K Run 1 Run 2 Run 3 Run 4 Run 5 Run 6 Run 7 ----------------------------------------------------------------- 32M seq 57554 55888 55898 55373 56628 55466 56340 32M 1 55132 55108 55118 55109 55129 55129 55127 32M 2 27855 27882 27886 27793 27847 27898 27886 32M 3 20052 18514 19598 18516 18604 20037 19846 32M 4 13990 13989 13997 14014 13878 14878 13912 ----------------------------------------------------------------- 64M seq 110613 113153 112272 112494 111997 112042 114074 64M 1 110039 110060 110025 110059 110042 110043 110027 64M 2 55582 55572 55771 55642 55620 54017 55401 64M 3 37193 37079 36896 39464 36797 36855 36879 64M 4 28687 27670 27641 27989 27892 29947 29670 ----------------------------------------------------------------- 128M seq 223830 221114 226464 228439 224009 223579 224229 128M 1 219907 219938 219931 219912 219917 219913 220055 128M 2 111108 111160 110978 111151 110973 110681 111162 128M 3 73943 73636 73723 74341 78368 74586 78434 128M 4 55627 58625 55239 56407 59402 55622 55232 ----------------------------------------------------------------- 256M seq 448199 447639 448544 447489 452227 442963 443627 256M 1 439946 439657 439669 439669 439954 439776 439911 256M 2 226232 236317 221227 221153 221355 221173 222203 256M 3 148458 147751 147751 147918 147928 156770 147808 256M 4 117842 117915 110956 117778 111206 111822 111150 Performance data based on median running time of 7 runs N K T Spdup Eff | N K T Spdup Eff --------------------------------+--------------------------------- 32M seq 55898 | 128M seq 224009 32M 1 55127 1.014 1.014 | 128M 1 219917 1.019 1.019 32M 2 27882 2.005 1.002 | 128M 2 111108 2.016 1.008 32M 3 19598 2.852 0.951 | 128M 3 74341 3.013 1.004 32M 4 13990 3.996 0.999 | 128M 4 55627 4.027 1.007 --------------------------------+--------------------------------- 64M seq 112272 | 256M seq 447639 64M 1 110042 1.020 1.020 | 256M 1 439776 1.018 1.018 64M 2 55582 2.020 1.010 | 256M 2 221355 2.022 1.011 64M 3 36896 3.043 1.014 | 256M 3 147918 3.026 1.009 64M 4 27989 4.011 1.003 | 256M 4 111822 4.003 1.001 Cluster parallel program -- Class FindKeyClu -- 1 to 4 processes, each with 1 thread   Raw running time data (msec) N K Run 1 Run 2 Run 3 Run 4 Run 5 Run 6 Run 7 ----------------------------------------------------------------- 32M seq 56093 55433 55370 56598 55677 57116 57020 32M 1 56063 55864 56534 56432 55866 56282 56238 32M 2 28629 28224 28486 28301 28358 28385 28486 32M 3 19273 19049 19527 19091 18901 19007 19182 32M 4 14512 14258 14283 14267 14169 14307 14381 ----------------------------------------------------------------- 64M seq 111259 111406 113811 110616 112279 113315 113414 64M 1 112703 111003 111514 111164 111070 111114 111162 64M 2 56778 56018 56169 56606 57202 56040 55746 64M 3 38011 37852 38100 37942 38543 37876 37868 64M 4 28414 28288 28515 28278 28855 28879 28776 ----------------------------------------------------------------- 128M seq 223911 226603 221868 221101 228810 224519 223992 128M 1 230116 225962 223623 221852 227974 224528 223135 128M 2 111652 110914 112747 113791 111568 112976 114307 128M 3 74977 76833 76514 75105 76936 76526 75448 128M 4 56364 56716 57856 57604 56099 56268 56511 ----------------------------------------------------------------- 256M seq 446635 458383 448998 443373 447317 447569 452077 256M 1 447636 447304 449702 449063 447011 449932 447347 256M 2 223405 223451 225417 225791 226536 227557 224497 256M 3 150542 152181 150320 154115 153313 153034 151609 256M 4 112367 114819 112454 113711 114548 112209 112854 Performance data based on median running time of 7 runs N K T Spdup Eff | N K T Spdup Eff --------------------------------+--------------------------------- 32M seq 56093 | 128M seq 223992 32M 1 56238 0.997 0.997 | 128M 1 224528 0.998 0.998 32M 2 28385 1.976 0.988 | 128M 2 112747 1.987 0.993 32M 3 19091 2.938 0.979 | 128M 3 76514 2.927 0.976 32M 4 14283 3.927 0.982 | 128M 4 56511 3.964 0.991 --------------------------------+--------------------------------- 64M seq 112279 | 256M seq 447569 64M 1 111162 1.010 1.010 | 256M 1 447636 1.000 1.000 64M 2 56169 1.999 0.999 | 256M 2 225417 1.986 0.993 64M 3 37942 2.959 0.986 | 256M 3 152181 2.941 0.980 64M 4 28515 3.938 0.984 | 256M 4 112854 3.966 0.991 Hybrid SMP cluster parallel program -- Class FindKeyHyb -- 1 to 4 processes, each with 4 threads   Raw running time data (msec) N K Run 1 Run 2 Run 3 Run 4 Run 5 Run 6 Run 7 ----------------------------------------------------------------- 32M seq 56310 56128 56463 56264 56297 56040 55573 32M 4 14200 14100 14781 14922 14873 13997 14036 32M 8 7539 7207 7333 7091 7484 7196 7129 32M 12 5029 5031 5058 4861 4765 5069 5049 32M 16 3855 3683 3790 3621 3727 4025 3678 ----------------------------------------------------------------- 64M seq 111439 112733 112808 112144 111382 112339 110704 64M 4 27727 28071 27888 29518 27851 27803 28046 64M 8 14840 14007 14619 14822 14068 14741 14826 64M 12 9790 10128 9433 9842 9787 9899 10047 64M 16 7478 7470 7476 7146 7516 7428 7502 ----------------------------------------------------------------- 128M seq 221286 224377 228848 222893 224856 225697 222933 128M 4 55762 55189 55828 58887 55336 55734 55534 128M 8 27851 29526 28043 28960 29603 29462 29371 128M 12 19910 19650 19239 19691 18703 19874 19768 128M 16 14720 15769 14002 15034 14833 14041 14849 ----------------------------------------------------------------- 256M seq 451873 450527 452347 449579 454331 442091 448688 256M 4 110538 110776 117559 117530 110952 110463 111017 256M 8 55601 58826 55502 55651 55464 58885 55661 256M 12 37335 37196 37572 39284 39341 39518 39157 256M 16 29658 29492 27955 29479 29177 27864 29530 Performance data based on median running time of 7 runs N K T Spdup Eff | N K T Spdup Eff ---------------------------------+---------------------------------- 32M seq 56264 | 128M seq 224377 32M 4 14200 3.962 0.991 | 128M 4 55734 4.026 1.006 32M 8 7207 7.807 0.976 | 128M 8 29371 7.639 0.955 32M 12 5031 11.183 0.932 | 128M 12 19691 11.395 0.950 32M 16 3727 15.096 0.944 | 128M 16 14833 15.127 0.945 ---------------------------------+---------------------------------- 64M seq 112144 | 256M seq 450527 64M 4 27888 4.021 1.005 | 256M 4 110952 4.061 1.015 64M 8 14741 7.608 0.951 | 256M 8 55651 8.096 1.012 64M 12 9842 11.394 0.950 | 256M 12 39157 11.506 0.959 64M 16 7476 15.001 0.938 | 256M 16 29479 15.283 0.955 Running Time Data -- Example 2 Running time measurements on the tardis.cs.rit.edu machine 10 backend processors, each with two dual-core CPU chips N = Problem size = number of network nodes K = Number of processors T = Running time (msec) for computation only (not file I/O)   SMP parallel program -- Class FloydSmpRow -- 1 process, 1 to 4 threads   Raw running time data (msec) N K Run 1 Run 2 Run 3 Run 4 Run 5 Run 6 Run 7 ----------------------------------------------------------------- 2000 seq 97113 99085 98948 93671 94408 97140 96513 2000 1 67057 67670 64367 67563 67373 67526 65576 2000 2 34662 35782 36223 36414 36784 34158 37070 2000 3 24532 26125 27204 24710 23798 26082 25952 2000 4 21260 20669 21822 21593 21700 23701 20447 ----------------------------------------------------------------- 2500 seq 186063 217191 217615 191590 189348 190165 180123 2500 1 131027 129526 126603 132528 127296 129003 133174 2500 2 69734 67110 69780 67836 68175 70753 68435 2500 3 47995 47582 48740 47389 53106 52267 49738 2500 4 47511 38973 38829 43564 41002 37614 38511 ----------------------------------------------------------------- 3200 seq 394730 598482 379841 382651 382114 395578 392587 3200 1 274454 281809 274050 281935 272110 273204 269594 3200 2 146226 151452 146754 139883 150754 150534 147635 3200 3 109583 99601 103254 108057 104460 109318 109124 3200 4 96488 90686 80469 92404 92076 99219 97737 ----------------------------------------------------------------- 4000 seq 731069 732866 730051 759480 745603 792375 767126 4000 1 532354 533930 546589 533816 537893 531977 531226 4000 2 272714 277347 290291 287493 298268 299514 283927 4000 3 212327 207476 200459 208415 202730 190989 203084 4000 4 164552 165455 152348 178772 169537 165960 189851 Performance data based on median running time of 7 runs N K T Spdup Eff | N K T Spdup Eff ---------------------------------+--------------------------------- 2000 seq 97113 | 3200 seq 392587 2000 1 67373 1.441 1.441 | 3200 1 274050 1.433 1.433 2000 2 36223 2.681 1.340 | 3200 2 147635 2.659 1.330 2000 3 25952 3.742 1.247 | 3200 3 108057 3.633 1.211 2000 4 21593 4.497 1.124 | 3200 4 92404 4.249 1.062 ---------------------------------+--------------------------------- 2500 seq 190165 | 4000 seq 745603 2500 1 129526 1.468 1.468 | 4000 1 533816 1.397 1.397 2500 2 68435 2.779 1.389 | 4000 2 287493 2.593 1.297 2500 3 48740 3.902 1.301 | 4000 3 203084 3.671 1.224 2500 4 38973 4.879 1.220 | 4000 4 165960 4.493 1.123 Cluster parallel program -- Class FloydClu -- 1 to 4 processes, each with 1 thread   Raw running time data (msec) N K Run 1 Run 2 Run 3 Run 4 Run 5 Run 6 Run 7 ----------------------------------------------------------------- 2000 seq 95829 93626 97073 119715 93656 93963 96778 2000 1 76081 76612 76153 76761 76043 76131 120483 2000 2 38891 38608 38782 39367 39265 39194 38972 2000 3 26409 26409 26377 25965 26470 26426 26445 2000 4 20069 22724 19723 20111 19732 20167 20060 ----------------------------------------------------------------- 2500 seq 188945 278582 181498 192093 186893 271585 192097 2500 1 148169 148301 148775 147408 148472 148149 146089 2500 2 75189 73653 74360 75181 74290 74998 74843 2500 3 50756 50044 50605 50554 50481 50308 50350 2500 4 38169 38160 38141 38128 38270 38034 38119 ----------------------------------------------------------------- 3200 seq 379428 395100 378885 379657 395567 391628 384953 3200 1 307701 303635 303056 305669 307553 305448 307532 3200 2 153887 155461 154936 154351 154607 247483 154256 3200 3 103526 104033 101934 103090 102651 103705 101656 3200 4 77603 78591 79202 77175 77797 78921 78390 ----------------------------------------------------------------- 4000 seq 730375 767507 756481 905333 753473 760107 770087 4000 1 583924 579399 586376 941518 584101 584242 588733 4000 2 300765 298561 299811 296489 293777 297021 292867 4000 3 198491 199893 197299 199329 198110 201843 195711 4000 4 149874 149214 150304 150631 150831 150422 151087 Performance data based on median running time of 7 runs N K T Spdup Eff | N K T Spdup Eff ---------------------------------+--------------------------------- 2000 seq 95829 | 3200 seq 384953 2000 1 76153 1.258 1.258 | 3200 1 305669 1.259 1.259 2000 2 38972 2.459 1.229 | 3200 2 154607 2.490 1.245 2000 3 26409 3.629 1.210 | 3200 3 103090 3.734 1.245 2000 4 20069 4.775 1.194 | 3200 4 78390 4.911 1.228 ---------------------------------+--------------------------------- 2500 seq 192093 | 4000 seq 760107 2500 1 148169 1.296 1.296 | 4000 1 584242 1.301 1.301 2500 2 74843 2.567 1.283 | 4000 2 297021 2.559 1.280 2500 3 50481 3.805 1.268 | 4000 3 198491 3.829 1.276 2500 4 38141 5.036 1.259 | 4000 4 150422 5.053 1.263 Hybrid SMP cluster parallel program -- Class FloydHyb -- 1 to 4 processes, each with 4 threads   Raw running time data (msec) N K Run 1 Run 2 Run 3 Run 4 Run 5 Run 6 Run 7 ----------------------------------------------------------------- 2000 seq 95376 97130 96306 96309 96578 95076 98759 2000 4 23503 21650 20597 22375 24933 21825 20539 2000 8 12369 12867 11351 12885 13802 12850 12954 2000 12 9874 9600 10517 10592 9814 9984 10092 2000 16 7817 7780 7754 7947 7775 7656 7888 ----------------------------------------------------------------- 2500 seq 278491 188900 190663 189832 192424 189394 188200 2500 4 42337 43052 41499 46714 36733 46795 44571 2500 8 26495 24024 24359 24170 23485 25513 26596 2500 12 18453 18362 18426 18293 18639 18341 18433 2500 16 14597 14538 14780 14839 14396 14758 14661 ----------------------------------------------------------------- 3200 seq 382824 394215 381224 382087 393131 394416 380780 3200 4 80895 95277 89185 96307 87662 93239 91036 3200 8 44654 56366 49481 49506 50378 49746 46708 3200 12 37511 37625 37959 31491 37458 38274 39091 3200 16 30133 29728 27584 29385 28692 30015 29608 ----------------------------------------------------------------- 4000 seq 751262 768429 741521 760933 761249 733081 767620 4000 4 175165 189191 192225 182727 173654 171494 165932 4000 8 102282 111787 96570 93923 89797 111533 106312 4000 12 70304 73596 65165 75121 64560 67690 76289 4000 16 54833 56919 55561 54969 55687 56324 56447 Performance data based on median running time of 7 runs N K T Spdup Eff | N K T Spdup Eff ----------------------------------+---------------------------------- 2000 seq 96309 | 3200 seq 382824 2000 4 21825 4.413 1.103 | 3200 4 91036 4.205 1.051 2000 8 12867 7.485 0.936 | 3200 8 49506 7.733 0.967 2000 12 9984 9.646 0.804 | 3200 12 37625 10.175 0.848 2000 16 7780 12.379 0.774 | 3200 16 29608 12.930 0.808 ----------------------------------+---------------------------------- 2500 seq 189832 | 4000 seq 760933 2500 4 43052 4.409 1.102 | 4000 4 175165 4.344 1.086 2500 8 24359 7.793 0.974 | 4000 8 102282 7.440 0.930 2500 12 18426 10.302 0.859 | 4000 12 70304 10.823 0.902 2500 16 14661 12.948 0.809 | 4000 16 55687 13.664 0.854 Alan Kaminsky • Department of Computer Science • Rochester Institute of Technology • 4486 + 1980 = 6466 Home Page Copyright © 2007 Alan Kaminsky. All rights reserved. Last updated 24-Mar-2007. Please send comments to ark­@­cs.rit.edu.