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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: 1.77435e-07
    square 1000-bit ints: 1.07467e-07
    remainder 2000/1000-bit ints: 3.60989e-07
    gcd 1000-bit ints: 2.85212e-06
    xgcd 1000-bit ints: 4.39055e-06
    power mod 1000-bit ints: 0.000424867
    multiply degree-1000 poly mod 1000-bit prime: 0.00409039
    remainder degree-2000/1000 poly mod 1000-bit prime: 0.0119471
    preconditioned remainder degree-2000/1000 poly mod 1000-bit prime: 0.00417065
    gcd degree-1000 poly mod 1000-bit prime: 0.118674
    multiply degree-1000 int poly with 1000-bit coeffs: 0.00582299

    factoring degree-1000 poly mod 1000-bit prime...
    square-free decomposition...0.118535
    factoring multiplicity 1, deg = 1000
    computing X^p...6.87595
    computing DDF...generating baby steps...+++++++++++++++++++++2.72866
    generating giant steps...++++++++++++++++++++++2.82147
    giant refine...++++split 1 18
    *++++*++++*++++*++++split 17 355
    *split 0 627
    giant refine time: 4.10968
    baby refine...split 1 1
    split 8 8
    split 9 9
    split 355 355
    split 627 627
    baby refine time: 0.036778
    DDF time: 9.70113
    ...total time = 16.7036

    multiply 500-bit GF2Xs: 5.35842e-08
    remainder 1000/500-bit GF2Xs: 8.24988e-07
    gcd 500-bit GF2Xs: 3.55214e-06

    factoring degree-500 GF2X: 0.000149589
    gcd 500-bit GF2X: 3.54077e-06
    multiply degree-500 poly mod 500-bit GF2X: 0.0024216
    remainder degree-1000/500 poly mod 500-bit GF2X: 0.00871277
    preconditioned remainder degree-1000/500 poly mod 500-bit GF2X: 0.00488511
    gcd degree-500 poly mod 500-bit GF2X: 0.0447275

    factoring degree-500 poly mod 500-bit GF2X...
    square-free decomposition...0.00438
    factoring multiplicity 1, deg = 250
    computing X^p...0.466925
    computing DDF...generating baby steps...++++++++++0.319649
    generating giant steps...+++++++++++0.344317
    giant refine...++++split 1 9
    split 2 13
    split 4 44
    *++++split 7 73
    *split 0 111
    giant refine time: 0.224187
    baby refine...split 9 9
    split 13 13
    split 44 44
    split 73 73
    split 111 111
    baby refine time: 0.001257
    DDF time: 0.889446

    ...total time = 1.36354