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Factorial Benchmark
Timings (seconds)
MPIR Factorial Benchmark (2011)
CPU: AMD Athlon II X4 640, 3.0 GHz, RAM: 4.0 GB, OS: Win 7 (64 bit)
MPIR-2.4.0 Factorial Benchmark (Jun 14 2011)
| (N x 10^6) ! | 1 | 2 | 4 | 8 | 16 | 32 | 64 | 100 |
| ParallelPrimeSwing | 0.25 | 0.58 | 1.70 | 3.81 | 7.85 | 16.69 | 35.86 | 56.92 |
| ParallelPrimeSchoenhage | 0.25 | 0.62 | 1.83 | 4.10 | 8.50 | 18.21 | 38.86 | 62.03 |
| PrimeSwing | 0.28 | 0.66 | 1.92 | 4.21 | 8.81 | 18.86 | 41.62 | 65.01 |
| PrimeSchoenhage | 0.27 | 0.66 | 1.92 | 4.24 | 8.89 | 18.95 | 40.67 | 65.33 |
| MPIR-Library | 0.27 | 0.66 | 1.90 | 4.26 | 8.89 | 19.06 | 41.03 | 66.16 |
You can download the source code here.
MPIR Factorial Benchmark (2010)
CPU: AMD 64 X2 Dual Core 4400, 2.31 GHz, RAM: 2.0 GB, OS: Win XP (32 bit)
MPIR-1.3.0 Factorial Benchmark (Jan 29 2010)
| (N x 10^6) ! | 1 | 2 | 4 | 8 | 16 | 32 | 64 | 100 |
| ParallelPrimeSwing | 0.9 | 1.9 | 4.2 | 9.2 | 20.6 | 45.5 | 101.8 | 181.1 |
| ParallelPrimeSchoenhage | 0.9 | 2.1 | 4.6 | 10.2 | 22.6 | 50.2 | 112.1 | 197.4 |
| PrimeSwing | 1.0 | 2.1 | 4.8 | 10.7 | 23.9 | 53.1 | 118.9 | 209.0 |
| PrimeSchoenhage | 1.0 | 2.1 | 4.8 | 10.7 | 23.9 | 53.2 | 119.0 | 209.2 |
| MPIR-Library | 1.0 | 2.2 | 4.8 | 10.7 | 24.1 | 53.4 | 119.3 | 209.6 |
GMP-5.0.1 Factorial Benchmark (Feb 07 2010)
| (N x 10^6) ! | 1 | 2 | 4 | 8 | 16 | 32 | 64 | 100 |
| ParallelPrimeSwing | 0.8 | 1.9 | 4.6 | 10.9 | 25.0 | 58.1 | 129.7 | 218.5 |
| ParallelPrimeSchoenhage | 0.9 | 2.2 | 5.1 | 11.9 | 27.1 | 62.9 | 140.3 | 237.1 |
| PrimeSwing | 0.9 | 2.2 | 5.2 | 12.4 | 28.3 | 65.5 | 146.9 | 249.5 |
| PrimeSchoenhage | 0.9 | 2.2 | 5.3 | 12.4 | 28.4 | 65.8 | 147.2 | 249.7 |
| GMP-Library | 1.6 | 3.7 | 9.3 | 21.8 | 51.2 | 117.9 | 276.9 | 468.7 |
Note that this benchmark only compares a tiny fraction of the two multiple precision libraries. It compares the factorial function as provided by the libraries and it compares how some factorial functions implemented on the more basic functions of the libraries perform. So basically only the multiplication algorithms are tested. GMP 5.0.1 performs relatively poor compared to MPIR-1.3.0. It might be the case that earlier versions of GMP perform better. However, I did not test this. (I know that the developers of GMP are hard working to improve things.)
The following plot sums our findings up. It shows in units of [dd/ms] (decimal digit per millisecond) the performance of ParallelPrimeSwing (red) with MPIR 1.3.0 and the GMP library function (blue) in the region tested (higher figures are better here).
PPSMPIR := listplot([[1,6472],[2,6157],[4,5935],[8,5624],[16,5256],[32,4970],[64,4635],[100,4178]],color=red): LIBGMP := listplot([[1,3525],[2,3142],[4,2663],[8,2376],[16,2114],[32,1920],[64,1705],[100,1615]],color=blue):
You might also be interested to compare different implementations of the double factorial function. On that page you can also find the source code (see the class diagram below) of the above benchmark. Benchmark yourself on your favorite system!
MPIR Binomial Benchmark (2011)
CPU: AMD Athlon II X4 640, 3.0 GHz, RAM: 4.0 GB, OS: Win 7 (64 bit)
MPIR-2.4.0 Factorial Benchmark (Jun 14 2011)
Testing binomial: 100000, 33333 ParallelBinomial: 0.001 sec PrimeBinomial: 0.001 sec MPIR-Binomial: 0.037 sec Testing binomial: 200000, 66666 ParallelBinomial: 0.003 sec PrimeBinomial: 0.003 sec MPIR-Binomial: 0.177 sec Testing binomial: 400000, 133333 ParallelBinomial: 0.005 sec PrimeBinomial: 0.006 sec MPIR-Binomial: 0.710 sec Testing binomial: 800000, 266666 ParallelBinomial: 0.010 sec PrimeBinomial: 0.014 sec MPIR-Binomial: 2.842 sec Testing binomial: 1600000, 533333 ParallelBinomial: 0.022 sec PrimeBinomial: 0.033 sec MPIR-Binomial: 11.39 sec Testing binomial: 3200000, 1066666 ParallelBinomial: 0.051 sec PrimeBinomial: 0.076 sec MPIR-Binomial: 45.57 sec Testing binomial: 6400000, 2133333 ParallelBinomial: 0.117 sec PrimeBinomial: 0.179 sec MPIR-Binomial: 333.4 sec
You can download the source code here.
Java Factorial Benchmark (2011)
Java 1.6.0_25 Sun VM server (64 bit)
Arithmetic: Apfloat Library 1.6.2
by Mikko Tommila
CPU: AMD Athlon II X4 640, 3.0 GHz, RAM: 4.0 GB, OS: Win 7 (64 bit)
You can download the source code here.
Timings (seconds)
| (N x 10^6)! | 1 | 2 | 4 | 8 | 16 | 32 |
| ParallelPrimeSwing | 2,3 | 3,4 | 6,8 | 14,4 | 30,4 | 61,7 |
| ParallelPrimeSplit | 1,8 | 3,4 | 7,0 | 14,5 | 29,8 | 63,4 |
| PrimeSchoenhage | 1,9 | 4,2 | 8,7 | 18,1 | 37,6 | 79,6 |
| PrimeSwingList | 1,9 | 4,4 | 8,7 | 19,1 | 38,3 | 80,7 |
| PrimeSwing | 2,1 | 4,6 | 8,8 | 19,3 | 40,2 | 84,5 |
| PrimeVardi | 2,0 | 4,5 | 9,0 | 19,9 | 40,1 | 82,8 |
| ParallelSplit | 3,8 | 8,1 | 17,2 | 38,0 | 72,8 | 149,1 |
| ParallelSwing | 4,0 | 8,9 | 18,3 | 39,5 | 77,8 | 158,8 |
| Split | 6,0 | 13,4 | 27,5 | 90,5 | 121,9 | 234,3 |
| Swing | 6,6 | 14,4 | 31,3 | 69,4 | 134,4 | 255,9 |
Ranking relative to PrimeSwing
| (N x 10^6)! | 1 | 2 | 4 | 8 | 16 | 32 |
| ParallelPrimeSwing | 1,1 | 0,7 | 0,8 | 0,7 | 0,8 | 0,7 |
| ParallelPrimeSplit | 0,9 | 0,7 | 0,8 | 0,8 | 0,7 | 0,8 |
| PrimeSchoenhage | 0,9 | 0,9 | 1,0 | 0,9 | 0,9 | 0,9 |
| PrimeSwingList | 1,0 | 1,0 | 1,0 | 1,0 | 1,0 | 1,0 |
| PrimeSwing | 1,0 | 1,0 | 1,0 | 1,0 | 1,0 | 1,0 |
| PrimeVardi | 1,0 | 1,0 | 1,0 | 1,0 | 1,0 | 1,0 |
| ParallelSplit | 1,8 | 1,8 | 1,9 | 2,0 | 1,8 | 1,8 |
| ParallelSwing | 2,0 | 1,9 | 2,1 | 2,0 | 1,9 | 2,0 |
| Split | 2,9 | 2,9 | 3,1 | 4,7 | 3,0 | 2,8 |
| Swing | 3,2 | 3,1 | 3,5 | 3,6 | 3,3 | 3,0 |
Timing: Red = first, blue = second.
Ranking: The smaller the value the better.
Values p <= 1 (red) indicate excellent performance,
values p <= 2 (blue) indicate good performance.
Java Factorial Benchmark (2009)
Java 1.7.0 Sun VM server (32 bit)
Arithmetic: Apfloat Library 1.5.2
(int32-based) by Mikko Tommila
CPU: AMD 64 X2 Dual, 2.3 GHz, RAM: 2.0 GB, OS: Win XP (32 bit)
Timings (seconds)
| (N x 10^6) ! | 1 | 2 | 4 | 8 | 16 | 32 |
| ParallelPrimeSwing | 4,2 | 8,5 | 18,1 | 39,1 | 84,5 | 174,7 |
| ParallelPrimeSplit | 4,3 | 9,1 | 18,8 | 40,0 | 101,1 | 180,1 |
| PrimeSwing | 4,3 | 9,5 | 20,1 | 49,0 | 106,8 | 192,2 |
| PrimeSchoenhage | 4,3 | 9,6 | 20,6 | 43,5 | 104,0 | 197,4 |
| PrimeVardi | 4,4 | 9,8 | 20,7 | 43,8 | 102,6 | 195,0 |
| PrimeSwingList | 4,4 | 9,8 | 20,7 | 44,1 | 104,0 | 199,4 |
| ParallelSplit | 6,9 | 15,0 | 33,3 | 80,2 | 188,2 | 366,8 |
| ParallelSwing | 8,8 | 18,7 | 40,6 | 88,2 | 224,6 | 425,0 |
| Split | 9,5 | 20,8 | 44,8 | 97,1 | 211,0 | 460,1 |
Ranking relative to PrimeSwing
| (N x 10^6) ! | 1 | 2 | 4 | 8 | 16 | 32 |
| ParallelPrimeSwing | 0,9 | 0,9 | 0,9 | 0,9 | 0,9 | 0,9 |
| ParallelPrimeSplit | 1,0 | 0,9 | 0,9 | 0,9 | 0,9 | 0,9 |
| PrimeSwing | 1,0 | 1,0 | 1,0 | 1,0 | 1,0 | 1,0 |
| PrimeSchoenhage | 1,0 | 1,0 | 1,0 | 1,0 | 1,0 | 1,0 |
| PrimeVardi | 1,0 | 1,0 | 1,0 | 1,0 | 1,0 | 1,0 |
| PrimeSwingList | 1,0 | 1,0 | 1,0 | 1,0 | 1,0 | 1,0 |
| ParallelSplit | 1,7 | 1,6 | 1,6 | 1,7 | 1,9 | 1,9 |
| ParallelSwing | 2,0 | 2,0 | 2,0 | 2,1 | 2,2 | 2,2 |
| Split | 2,2 | 2,2 | 2,2 | 2,2 | 2,4 | 2,4 |
