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A Tour of NTL: Some Performance Data


Here are some timing figures from using NTL. They were obtained using NTL 8.1 compiled with g++ 4.2.1 and with GMP 5.1 on a 2.8GHz Intel Core 2 Duo running on Max OSX 10.6.8.

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: 4.47942e-07
remainder 2000/1000-bit ints: 8.3923e-07
gcd 1000-bit ints: 1.07981e-05
multiply degree-1000 poly mod 1000-bit prime: 0.0140632
remainder degree-2000/1000 poly mod 1000-bit prime: 0.0386337
preconditioned remainder degree-2000/1000 poly mod 1000-bit prime: 0.0143691
gcd degree-1000 poly mod 1000-bit prime: 0.338774
multiply degree-1000 int poly with 1000-bit coeffs: 0.0162582

factoring degree-1000 poly mod 1000-bit prime...
square-free decomposition...0.339693
factoring multiplicity 1, deg = 1000
computing X^p...22.9192
computing DDF...generating baby steps...+++++++++++++++++++++16.9463
generating giant steps...++++++++++++++++++++++17.695
giant refine...++++split 1 43
split 2 38
split 3 64
*++++split 5 108
*++++split 11 237
split 12 510
*giant refine time: 8.19123
baby refine...split 3 6
split 6 6
split 9 9
split 22 22
split 38 38
split 64 64
split 108 108
split 237 237
split 248 248
split 262 262
baby refine time: 0.611474
DDF time: 43.4528
computing EDF(3,2)...+0.077447
...total time = 66.8182

multiply 500-bit GF2Xs: 1.03529e-06
remainder 1000/500-bit GF2Xs: 6.06942e-06
gcd 500-bit GF2Xs: 1.19302e-05

factoring degree-500 GF2X: 0.0010868
gcd 500-bit GF2X: 1.18877e-05
multiply degree-500 poly mod 500-bit GF2X: 0.024646
remainder degree-1000/500 poly mod 500-bit GF2X: 0.0884258
preconditioned remainder degree-1000/500 poly mod 500-bit GF2X: 0.049274
gcd degree-500 poly mod 500-bit GF2X: 0.555096

factoring degree-500 poly mod 500-bit GF2X...
square-free decomposition...0.038657
factoring multiplicity 1, deg = 250
computing X^p...4.93964
computing DDF...generating baby steps...++++++++++3.51054
generating giant steps...+++++++++++3.78422
giant refine...++++*++++split 6 59
split 7 68
*split 0 123
giant refine time: 2.59123
baby refine...split 59 59
split 68 68
split 123 123
baby refine time: 3.4e-05
DDF time: 9.88619

...total time = 14.879


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