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

Question

I recently found this implementation of Chudnovsky's algorithm for calculating pi: Parallel GMP-Chudnovsky using OpenMP with factorization

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?

here is a sample output:

~/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

From the looks of the results, you have a 4-core system. Increasing the number of threads used will hurt performance after this point, because you gain the overhead of thread context-switching, without any more simultaneous work being done.

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