ZU064-05-FPR main. 7th January 2018. 18:35. Under consideration for publication in J. Functional Programming. 1. Arrows for Parallel Computation.
ZU064-05-FPR
main
7th January 2018
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Under consideration for publication in J. Functional Programming
1
Arrows for Parallel Computation Supplementary Material M A RT I N B R AU N University Bayreuth, 95440 Bayreuth, Germany O L E G L O BAC H E V University Bayreuth, 95440 Bayreuth, Germany and P H I L T R I N D E R Glasgow University, Glasgow, G12 8QQ, Scotland
Abstract
This is supplementary material to our paper ‘Arrows for parallel computation’. It shows the speedup and mean overhead plots for all benchmarks.
Contents 1
2
Shared-Memory Plots
2
1.1
Rabin–Miller test
2
1.2
Sudoku
6
1.3 Gentleman Distributed Plots
8 9
2.1
Rabin–Miller test
9
2.2
Jacobi sum test
10
2.3
Gentleman
11
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M. Braun, O. Lobachev, and P. Trinder 1 Shared-Memory Plots 1.1 Rabin–Miller test 1.1.1 Speedup Speedup of Rabin–Miller test ‘11213 32’ linear Eden CP GpH Par Monad
16
Speedup
12
8
4
0 0
4
8
12
16
Threads Speedup of Rabin–Miller test ‘11213 64’ linear Eden CP GpH Par Monad
16
12 Speedup
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4
0 0
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8 Threads
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Arrows for Parallel Computation 1.1.2 Overhead ·10−2
Mean Overhead for shared-memory Rabin–Miller test 11213 32 vs Eden CP
4 Mean Overhead 3 2 Overhead
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1 0 −1 −2 −3 −4
0
4
8
12
16
Threads Mean Overhead for shared-memory Rabin–Miller test 11213 64 vs Eden CP −2 ·10 3 Mean Overhead 2.25 1.5 Overhead
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0.75 0 −0.75 −1.5 −2.25 −3
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4
8 Threads
12
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M. Braun, O. Lobachev, and P. Trinder Mean Overhead for shared-memory Rabin–Miller test 11213 32 vs GpH 0.2 Mean Overhead 0.15
Overhead
0.1 5 · 10−2 0 −5 · 10−2 −0.1 −0.15 −0.2
0
·10−2
4
8
12
16
Threads Mean Overhead for shared-memory Rabin–Miller test 11213 64 vs GpH
5 Mean Overhead 3.75 2.5 Overhead
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1.25 0 −1.25 −2.5 −3.75 −5
0
4
8 Threads
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Arrows for Parallel Computation Mean Overhead for shared-memory Rabin–Miller test 11213 32 vs Par Monad 0.2 Mean Overhead 0.15 0.1 Overhead
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5 · 10−2 0 −5 · 10−2 −0.1 −0.15 −0.2
0
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8 12 16 Threads Mean Overhead for shared-memory Rabin–Miller test 11213 64 vs Par Monad
0.2 Mean Overhead 0.15 0.1 Overhead
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5 · 10−2 0 −5 · 10−2 −0.1 −0.15 −0.2
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4
8 Threads
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M. Braun, O. Lobachev, and P. Trinder 1.2 Sudoku 1.2.1 Speedup Parallel speedup of Sudoku ‘1000’ linear Eden CP GpH Par Monad
16
Speedup
12
8
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0 0
4
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Threads
1.2.2 Overhead ·10−2
Mean Overhead for shared-memory Sudoku 1000 vs Eden CP
5 Mean Overhead 3.75 2.5 Overhead
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1.25 0 −1.25 −2.5 −3.75 −5
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Arrows for Parallel Computation
·10−2
Mean Overhead for shared-memory Sudoku 1000 vs GpH
5 Mean Overhead 3.75 2.5 Overhead
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1.25 0 −1.25 −2.5 −3.75 −5
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·10−2
4
8
12
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Threads Mean Overhead for shared-memory Sudoku 1000 vs Par Monad
5 Mean Overhead 3.75 2.5 Overhead
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1.25 0 −1.25 −2.5 −3.75 −5
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8 Threads
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M. Braun, O. Lobachev, and P. Trinder 1.3 Gentleman 1.3.1 Speedup Parallel speedup of Sudoku ‘512’ linear Eden CP GpH Par Monad
16
Speedup
12
8
4
0 0
4
8
12
16
Threads
1.3.2 Overhead ·10−2
Mean Overhead for shared-memory Gentleman 512 vs Eden CP
8 Mean Overhead 6 4 Overhead
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2 0 −2 −4 −6 −8
0
4
8 Threads
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Arrows for Parallel Computation 2 Distributed Plots 2.1 Rabin–Miller test 2.1.1 Speedup Speedup of distributed Rabin–Miller test ‘44497 256’ linear PArrows Eden
256 224 192 Speedup
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160 128 96 64 32 0
0
32
64
96
128 160 Threads
192
224
256
2.1.2 Overhead ·10−2
Mean Overhead for distributed Rabin–Miller test 44497 256
4 Mean Overhead 3 2 Overhead
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1 0 −1 −2 −3 −4
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32
64
96
128
160 Threads
192
224
256
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M. Braun, O. Lobachev, and P. Trinder 2.2 Jacobi sum test 2.2.1 Speedup Speedup of distributed Jacobi sum test ‘3217’ 32
Speedup
linear PArrows Eden
0 0
32
64
96
128
160 Threads
192
224
256
2.2.2 Overhead ·10−2
Mean Overhead for distributed Jacobi sum test 3217
4 Mean Overhead 3 2 Overhead
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1 0 −1 −2 −3 −4
0
32
64
96
128
160 Threads
192
224
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Arrows for Parallel Computation 2.3 Gentleman Mean Overhead for distributed Gentleman 4096
·10−2 4
Mean Overhead 3 2 Overhead
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1 0 −1 −2 −3 −4
0
32
64
96
128
160 Threads
192
224
256
2.3.1 Speedup Speedup of distributed Gentleman ‘4096’ 160 linear PArrows Eden 128
