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A Tour of NTL: Some Performance Data


Here are some timing figures from using NTL. They were obtained using NTL 9.9.0 compiled with g++ 4.8.5 and with GMP 6.1 on a 2.3GHz Intel Haswell processor (E5-2698 v3) running Linux.

All times are ins seconds. The times were obtained using the program Timing included in the distribution. The data was generated using NTL's random number generator, but running this on a different machine should (in theory) generate the same data.

NOTE: that the PRG changed in v9.4.0, so there may be some inconsistencies.


multiply 1000-bit ints: 1.76284e-07
remainder 2000/1000-bit ints: 3.60535e-07
gcd 1000-bit ints: 2.87045e-06
multiply degree-1000 poly mod 1000-bit prime: 0.00432981
remainder degree-2000/1000 poly mod 1000-bit prime: 0.0125583
preconditioned remainder degree-2000/1000 poly mod 1000-bit prime: 0.00443356
gcd degree-1000 poly mod 1000-bit prime: 0.122722
multiply degree-1000 int poly with 1000-bit coeffs: 0.00812543

factoring degree-1000 poly mod 1000-bit prime...
square-free decomposition...0.122685
factoring multiplicity 1, deg = 1000
computing X^p...7.23809
computing DDF...generating baby steps...+++++++++++++++++++++6.21623
generating giant steps...++++++++++++++++++++++6.49462
giant refine...++++split 1 1
split 2 26
*++++*++++*++++*++++*++*split 0 973
giant refine time: 4.8139
baby refine...split 1 1
split 26 26
split 973 973
baby refine time: 3.3e-05
DDF time: 17.5262
...total time = 24.8965

multiply 500-bit GF2Xs: 5.54208e-08
remainder 1000/500-bit GF2Xs: 8.40658e-07
gcd 500-bit GF2Xs: 3.60963e-06

factoring degree-500 GF2X: 0.00015574
gcd 500-bit GF2X: 3.61365e-06
multiply degree-500 poly mod 500-bit GF2X: 0.00251375
remainder degree-1000/500 poly mod 500-bit GF2X: 0.00905957
preconditioned remainder degree-1000/500 poly mod 500-bit GF2X: 0.00505149
gcd degree-500 poly mod 500-bit GF2X: 0.0478557

factoring degree-500 poly mod 500-bit GF2X...
square-free decomposition...0.004635
factoring multiplicity 1, deg = 250
computing X^p...0.488941
computing DDF...generating baby steps...++++++++++0.332162
generating giant steps...+++++++++++0.357681
giant refine...++++split 1 9
split 2 13
split 4 44
*++++split 7 73
*split 0 111
giant refine time: 0.233787
baby refine...split 9 9
split 13 13
split 44 44
split 73 73
split 111 111
baby refine time: 0.001275
DDF time: 0.924938

...total time = 1.41792



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