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 9.9.0 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.

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

    multiply 1000-bit ints: 1.76284e-07
    remainder 2000/1000-bit ints: 3.60535e-07
    gcd 1000-bit ints: 2.87045e-06
    multiply degree-1000 poly mod 1000-bit prime: 0.00432981
    remainder degree-2000/1000 poly mod 1000-bit prime: 0.0125583
    preconditioned remainder degree-2000/1000 poly mod 1000-bit prime: 0.00443356
    gcd degree-1000 poly mod 1000-bit prime: 0.122722
    multiply degree-1000 int poly with 1000-bit coeffs: 0.00812543

    factoring degree-1000 poly mod 1000-bit prime...
    square-free decomposition...0.122685
    factoring multiplicity 1, deg = 1000
    computing X^p...7.23809
    computing DDF...generating baby steps...+++++++++++++++++++++6.21623
    generating giant steps...++++++++++++++++++++++6.49462
    giant refine...++++split 1 1
    split 2 26
    *++++*++++*++++*++++*++*split 0 973
    giant refine time: 4.8139
    baby refine...split 1 1
    split 26 26
    split 973 973
    baby refine time: 3.3e-05
    DDF time: 17.5262
    ...total time = 24.8965

    multiply 500-bit GF2Xs: 5.54208e-08
    remainder 1000/500-bit GF2Xs: 8.40658e-07
    gcd 500-bit GF2Xs: 3.60963e-06

    factoring degree-500 GF2X: 0.00015574
    gcd 500-bit GF2X: 3.61365e-06
    multiply degree-500 poly mod 500-bit GF2X: 0.00251375
    remainder degree-1000/500 poly mod 500-bit GF2X: 0.00905957
    preconditioned remainder degree-1000/500 poly mod 500-bit GF2X: 0.00505149
    gcd degree-500 poly mod 500-bit GF2X: 0.0478557

    factoring degree-500 poly mod 500-bit GF2X...
    square-free decomposition...0.004635
    factoring multiplicity 1, deg = 250
    computing X^p...0.488941
    computing DDF...generating baby steps...++++++++++0.332162
    generating giant steps...+++++++++++0.357681
    giant refine...++++split 1 9
    split 2 13
    split 4 44
    *++++split 7 73
    *split 0 111
    giant refine time: 0.233787
    baby refine...split 9 9
    split 13 13
    split 44 44
    split 73 73
    split 111 111
    baby refine time: 0.001275
    DDF time: 0.924938

    ...total time = 1.41792