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PORole of cores in Parallel GMP-Chudnovsky using OpenMP with factorization
 

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  1. PORole of cores in Parallel GMP-Chudnovsky using OpenMP with factorization
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    <p>I recently found this implementation of Chudnovsky's algorithm for calculating pi: <a href="http://gmplib.org/list-archives/gmp-discuss/2008-November/003444.html" rel="nofollow">Parallel GMP-Chudnovsky using OpenMP with factorization</a></p> <p>I have compiled it for various numbers from 1o^3 to 10^8 with the default 1 core option. However, I have noticed that as I increase the number of cores, the time it takes to calculate the result takes longer for both cpu and wall clock time. Why does the higher number of cores increase the time needed for computation? Shouldn't it speed up the calculation and result in better performance? </p> <p>here is a sample output: </p> <pre><code>~/Desktop$ ./pgmp-chudnovsky 7500000 0 1 #terms=528852, depth=21, cores=1 sieve cputime = 0.120 ................................................... bs cputime = 30.300 wallclock = 30.313 gcd cputime = 6.380 div cputime = 3.800 sqrt cputime = 2.140 mul cputime = 1.420 total cputime = 37.800 wallclock = 37.838 P size=10919784 digits (1.455971) Q size=10919777 digits (1.455970) ~/Desktop$ ./pgmp-chudnovsky 7500000 0 2 #terms=528852, depth=21, cores=2 sieve cputime = 0.120 ................................................... bs cputime = 30.890 wallclock = 17.661 gcd cputime = 12.930 div cputime = 3.790 sqrt cputime = 2.130 mul cputime = 1.420 total cputime = 38.380 wallclock = 25.153 P size=10919611 digits (1.455948) Q size=10919605 digits (1.455947) ~/Desktop$ ./pgmp-chudnovsky 7500000 0 3 #terms=528852, depth=21, cores=3 sieve cputime = 0.120 ................................................... bs cputime = 31.400 wallclock = 14.266 gcd cputime = 21.640 div cputime = 3.810 sqrt cputime = 2.130 mul cputime = 1.410 total cputime = 38.900 wallclock = 21.784 P size=10726889 digits (1.430252) Q size=10726883 digits (1.430251) ~/Desktop$ ./pgmp-chudnovsky 7500000 0 4 #terms=528852, depth=21, cores=4 sieve cputime = 0.130 ................................................... bs cputime = 32.480 wallclock = 11.771 gcd cputime = 27.770 div cputime = 3.800 sqrt cputime = 2.130 mul cputime = 1.410 total cputime = 39.980 wallclock = 19.284 P size=10920859 digits (1.456115) Q size=10920852 digits (1.456114) ~/Desktop$ ./pgmp-chudnovsky 7500000 0 5 #terms=528852, depth=21, cores=5 sieve cputime = 0.130 ................................................... bs cputime = 33.010 wallclock = 15.496 gcd cputime = 28.500 div cputime = 3.790 sqrt cputime = 2.130 mul cputime = 1.420 total cputime = 40.510 wallclock = 23.000 P size=10605102 digits (1.414014) Q size=10605096 digits (1.414013) ~/Desktop$ ./pgmp-chudnovsky 7500000 0 10 #terms=528852, depth=21, cores=10 sieve cputime = 0.130 ................................................... bs cputime = 33.210 wallclock = 14.311 gcd cputime = 29.640 div cputime = 3.780 sqrt cputime = 2.140 mul cputime = 1.420 total cputime = 40.720 wallclock = 21.822 P size=10607304 digits (1.414307) Q size=10607297 digits (1.414306) ~/Desktop$ ./pgmp-chudnovsky 7500000 0 100 #terms=528852, depth=21, cores=100 sieve cputime = 0.120 ................................................... bs cputime = 33.080 wallclock = 13.412 gcd cputime = 17.630 div cputime = 3.780 sqrt cputime = 2.130 mul cputime = 1.420 total cputime = 40.570 wallclock = 20.912 P size=12169347 digits (1.622580) Q size=12169341 digits (1.622579) ~/Desktop$ ./pgmp-chudnovsky 7500000 0 200 #terms=528852, depth=21, cores=200 sieve cputime = 0.130 ................................................... bs cputime = 34.080 wallclock = 13.942 gcd cputime = 15.620 div cputime = 3.760 sqrt cputime = 2.110 mul cputime = 1.420 total cputime = 41.530 wallclock = 21.401 P size=12642316 digits (1.685642) Q size=12642309 digits (1.685641) </code></pre>
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