A Tour of NTL: Some Performance Data

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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: 1.77903e-07
    square 1000-bit ints: 1.08537e-07
    remainder 2000/1000-bit ints: 3.58799e-07
    gcd 1000-bit ints: 2.86069e-06
    xgcd 1000-bit ints: 4.27161e-06
    power mod 1000-bit ints: 0.000424325
    multiply degree-1000 poly mod 1000-bit prime: 0.0041019
    remainder degree-2000/1000 poly mod 1000-bit prime: 0.0119166
    preconditioned remainder degree-2000/1000 poly mod 1000-bit prime: 0.00418589
    gcd degree-1000 poly mod 1000-bit prime: 0.122145
    multiply degree-1000 int poly with 1000-bit coeffs: 0.00467749

    factoring degree-1000 poly mod 1000-bit prime...
    square-free decomposition...0.119126
    factoring multiplicity 1, deg = 1000
    computing X^p...6.89619
    computing DDF...generating baby steps...+++++++++++++++++++++2.72505
    generating giant steps...++++++++++++++++++++++2.82554
    giant refine...++++split 1 18
    *++++*++++*++++*++++split 17 355
    *split 0 627
    giant refine time: 4.09811
    baby refine...split 1 1
    split 8 8
    split 9 9
    split 355 355
    split 627 627
    baby refine time: 0.037111
    DDF time: 9.6903
    ...total time = 16.7138

    multiply 500-bit GF2Xs: 5.3414e-08
    remainder 1000/500-bit GF2Xs: 8.19842e-07
    gcd 500-bit GF2Xs: 3.57209e-06

    factoring degree-500 GF2X: 0.000154251
    gcd 500-bit GF2X: 3.55401e-06
    multiply degree-500 poly mod 500-bit GF2X: 0.00247313
    remainder degree-1000/500 poly mod 500-bit GF2X: 0.00889548
    preconditioned remainder degree-1000/500 poly mod 500-bit GF2X: 0.00498747
    gcd degree-500 poly mod 500-bit GF2X: 0.0451361

    factoring degree-500 poly mod 500-bit GF2X...
    square-free decomposition...0.004369
    factoring multiplicity 1, deg = 250
    computing X^p...0.478202
    computing DDF...generating baby steps...++++++++++0.329912
    generating giant steps...+++++++++++0.355037
    giant refine...++++split 1 9
    split 2 13
    split 4 44
    *++++split 7 73
    *split 0 111
    giant refine time: 0.230542
    baby refine...split 9 9
    split 13 13
    split 44 44
    split 73 73
    split 111 111
    baby refine time: 0.001228
    DDF time: 0.916753

    ...total time = 1.39667