A Tour of NTL: Some Performance Data

Here are some timing figures from using NTL. They were obtained using NTL 6.2 compiled with g++ 4.2.1 and with GMP 5.1 on a 2.4GHz Intel Core 2 Duo running on Max OSX 10.7.2.

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: 5.31027e-07
remainder 2000/1000-bit ints: 1.01566e-06
gcd 1000-bit ints: 1.4682e-05
multiply degree-1000 poly mod 1000-bit prime: 0.0264952
remainder degree-2000/1000 poly mod 1000-bit prime: 0.076708
preconditioned remainder degree-2000/1000 poly mod 1000-bit prime: 0.0266063
gcd degree-1000 poly mod 1000-bit prime: 0.565005
multiply degree-1000 int poly with 1000-bit coeffs: 0.0273532

factoring degree-1000 poly mod 1000-bit prime...
square-free decomposition...0.558535
factoring multiplicity 1, deg = 1000
computing X^p...42.0216
computing DDF...generating baby steps...+++++++++++++++++++++24.69
generating giant steps...++++++++++++++++++++++25.3912
giant refine...++++split 1 43
split 2 38
split 3 64
*++++split 5 108
*++++split 11 237
split 12 510
*giant refine time: 15.1859
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: 1.0758
DDF time: 66.3546
computing EDF(3,2)...+0.028255
...total time = 109.019

multiply 500-bit GF2Xs: 1.33614e-06
remainder 1000/500-bit GF2Xs: 7.95517e-06
gcd 500-bit GF2Xs: 1.55201e-05

factoring degree-500 GF2X: 0.00137361
gcd 500-bit GF2X: 1.56605e-05
multiply degree-500 poly mod 500-bit GF2X: 0.0324352
remainder degree-1000/500 poly mod 500-bit GF2X: 0.114726
preconditioned remainder degree-1000/500 poly mod 500-bit GF2X: 0.0641071
gcd degree-500 poly mod 500-bit prime: 0.710028

factoring degree-500 poly mod 500-bit prime...
square-free decomposition...0.048244
factoring multiplicity 1, deg = 250
computing X^p...6.35723
computing DDF...generating baby steps...++++++++++4.55756
generating giant steps...+++++++++++4.92042
giant refine...++++*++++