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A Tour of NTL: Some Performance Data


Here are some timing figures from using NTL. They were obtained using NTL 11.0.0 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.


multiply 1000-bit ints: 1.77435e-07
square 1000-bit ints: 1.07467e-07
remainder 2000/1000-bit ints: 3.60989e-07
gcd 1000-bit ints: 2.85212e-06
xgcd 1000-bit ints: 4.39055e-06
power mod 1000-bit ints: 0.000424867
multiply degree-1000 poly mod 1000-bit prime: 0.00409039
remainder degree-2000/1000 poly mod 1000-bit prime: 0.0119471
preconditioned remainder degree-2000/1000 poly mod 1000-bit prime: 0.00417065
gcd degree-1000 poly mod 1000-bit prime: 0.118674
multiply degree-1000 int poly with 1000-bit coeffs: 0.00582299

factoring degree-1000 poly mod 1000-bit prime...
square-free decomposition...0.118535
factoring multiplicity 1, deg = 1000
computing X^p...6.87595
computing DDF...generating baby steps...+++++++++++++++++++++2.72866
generating giant steps...++++++++++++++++++++++2.82147
giant refine...++++split 1 18
*++++*++++*++++*++++split 17 355
*split 0 627
giant refine time: 4.10968
baby refine...split 1 1
split 8 8
split 9 9
split 355 355
split 627 627
baby refine time: 0.036778
DDF time: 9.70113
...total time = 16.7036

multiply 500-bit GF2Xs: 5.35842e-08
remainder 1000/500-bit GF2Xs: 8.24988e-07
gcd 500-bit GF2Xs: 3.55214e-06

factoring degree-500 GF2X: 0.000149589
gcd 500-bit GF2X: 3.54077e-06
multiply degree-500 poly mod 500-bit GF2X: 0.0024216
remainder degree-1000/500 poly mod 500-bit GF2X: 0.00871277
preconditioned remainder degree-1000/500 poly mod 500-bit GF2X: 0.00488511
gcd degree-500 poly mod 500-bit GF2X: 0.0447275

factoring degree-500 poly mod 500-bit GF2X...
square-free decomposition...0.00438
factoring multiplicity 1, deg = 250
computing X^p...0.466925
computing DDF...generating baby steps...++++++++++0.319649
generating giant steps...+++++++++++0.344317
giant refine...++++split 1 9
split 2 13
split 4 44
*++++split 7 73
*split 0 111
giant refine time: 0.224187
baby refine...split 9 9
split 13 13
split 44 44
split 73 73
split 111 111
baby refine time: 0.001257
DDF time: 0.889446

...total time = 1.36354


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