c - 使用 OpenMP 进行分解的并行 GMP-Chudnovsky 中内核的作用

Question

我最近发现了用于计算 pi 的 Chudnovsky 算法的实现:Parallel GMP-Chudnovsky using OpenMP with factorization

我使用默认的 1 核心选项将其编译为从 1o^3 到 10^8 的各种数字。然而，我注意到，随着核心数量的增加，计算结果所需的时间对于 cpu 和挂钟时间来说都需要更长的时间。为什么更多的核心会增加计算所需的时间？难道它不应该加快计算速度并带来更好的性能吗？

这是一个示例输出:

~/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)

Answer 1

从结果来看，您拥有一个 4 核系统。在此之后增加使用的线程数将损害性能，因为您会获得线程上下文切换的开销，而无需完成任何更多的同步工作。

Cores    Total Time
1        37.838
2        25.153
3        21.784
4        19.284    *Best*
5        23.000
10       21.822
100      20.912