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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: 4.48334e-07
remainder 2000/1000-bit ints: 8.40397e-07
gcd 1000-bit ints: 1.05831e-05
multiply degree-1000 poly mod 1000-bit prime: 0.0188591
remainder degree-2000/1000 poly mod 1000-bit prime: 0.0526041
preconditioned remainder degree-2000/1000 poly mod 1000-bit prime: 0.0191026
gcd degree-1000 poly mod 1000-bit prime: 0.42031
multiply degree-1000 int poly with 1000-bit coeffs: 0.0159478

factoring degree-1000 poly mod 1000-bit prime...
square-free decomposition...0.419396
factoring multiplicity 1, deg = 1000
computing X^p...30.7268
computing DDF...generating baby steps...+++++++++++++++++++++19.005
generating giant steps...++++++++++++++++++++++19.883
giant refine...++++split 1 43
split 2 38
split 3 64
*++++split 5 108
*++++split 11 237
split 12 510
*giant refine time: 10.8346
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: 0.782315
DDF time: 50.5169
computing EDF(3,2)...+0.076398
...total time = 81.7783

multiply 500-bit GF2Xs: 1.02539e-06
remainder 1000/500-bit GF2Xs: 6.08515e-06
gcd 500-bit GF2Xs: 1.18188e-05

factoring degree-500 GF2X: 0.00108608
gcd 500-bit GF2X: 1.18323e-05
multiply degree-500 poly mod 500-bit GF2X: 0.0246272
remainder degree-1000/500 poly mod 500-bit GF2X: 0.0883986
preconditioned remainder degree-1000/500 poly mod 500-bit GF2X: 0.0492956
gcd degree-500 poly mod 500-bit GF2X: 0.555426

factoring degree-500 poly mod 500-bit GF2X...
square-free decomposition...0.038173
factoring multiplicity 1, deg = 250
computing X^p...4.93404
computing DDF...generating baby steps...++++++++++3.50859
generating giant steps...+++++++++++3.78156
giant refine...++++*++++split 6 59
split 7 68
*split 0 123
giant refine time: 2.58798
baby refine...split 59 59
split 68 68
split 123 123
baby refine time: 3.4e-05
DDF time: 9.87834

...total time = 14.8648

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