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A Tour of NTL: Some Performance Data

Here are some timing figures from using NTL. They were obtained using NTL 9.6.0 compiled with `g++` 4.2.1 and with GMP 6.1 on a 2.4GHz Intel Core 2 Duo running on Max OSX 10.7.5.

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.

NOTE: that the PRG changed in v9.4.0, so there may be some inconsistencies.

    multiply 1000-bit ints: 5.01944e-07
    remainder 2000/1000-bit ints: 1.00661e-06
    gcd 1000-bit ints: 1.4468e-05
    multiply degree-1000 poly mod 1000-bit prime: 0.0135032
    remainder degree-2000/1000 poly mod 1000-bit prime: 0.0384725
    preconditioned remainder degree-2000/1000 poly mod 1000-bit prime: 0.0138238
    gcd degree-1000 poly mod 1000-bit prime: 0.349662
    multiply degree-1000 int poly with 1000-bit coeffs: 0.0225321

    factoring degree-1000 poly mod 1000-bit prime...
    square-free decomposition...0.350224
    factoring multiplicity 1, deg = 1000
    computing X^p...22.542
    computing DDF...generating baby steps...+++++++++++++++++++++18.1148
    generating giant steps...++++++++++++++++++++++18.8901
    giant refine...++++split 1 1
    split 2 26
    *++++*++++*++++*++++*++*split 0 973
    giant refine time: 14.757
    baby refine...split 1 1
    split 26 26
    split 973 973
    baby refine time: 0.000113
    DDF time: 51.7706
    ...total time = 74.6882

    multiply 500-bit GF2Xs: 1.30174e-06
    remainder 1000/500-bit GF2Xs: 8.41598e-06
    gcd 500-bit GF2Xs: 1.53247e-05

    factoring degree-500 GF2X: 0.00129122
    gcd 500-bit GF2X: 1.52925e-05
    multiply degree-500 poly mod 500-bit GF2X: 0.0314531
    remainder degree-1000/500 poly mod 500-bit GF2X: 0.111864
    preconditioned remainder degree-1000/500 poly mod 500-bit GF2X: 0.0625321
    gcd degree-500 poly mod 500-bit GF2X: 0.692733

    factoring degree-500 poly mod 500-bit GF2X...
    square-free decomposition...0.047487
    factoring multiplicity 1, deg = 250
    computing X^p...6.22461
    computing DDF...generating baby steps...++++++++++4.43465
    generating giant steps...+++++++++++4.78364
    giant refine...++++split 1 9
    split 2 13
    split 4 44
    *++++split 7 73
    *split 0 111
    giant refine time: 2.96613
    baby refine...split 9 9
    split 13 13
    split 44 44
    split 73 73
    split 111 111
    baby refine time: 0.0194
    DDF time: 12.204

    ...total time = 18.4939