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 8.1 compiled with `g++` 4.2.1 and with GMP 5.1 on a 2.8GHz Intel Core 2 Duo running on Max OSX 10.6.8.

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: 4.48334e-07
    remainder 2000/1000-bit ints: 8.40397e-07
    gcd 1000-bit ints: 1.05831e-05
    multiply degree-1000 poly mod 1000-bit prime: 0.0188591
    remainder degree-2000/1000 poly mod 1000-bit prime: 0.0526041
    preconditioned remainder degree-2000/1000 poly mod 1000-bit prime: 0.0191026
    gcd degree-1000 poly mod 1000-bit prime: 0.42031
    multiply degree-1000 int poly with 1000-bit coeffs: 0.0159478

    factoring degree-1000 poly mod 1000-bit prime...
    square-free decomposition...0.419396
    factoring multiplicity 1, deg = 1000
    computing X^p...30.7268
    computing DDF...generating baby steps...+++++++++++++++++++++19.005
    generating giant steps...++++++++++++++++++++++19.883
    giant refine...++++split 1 43
    split 2 38
    split 3 64
    *++++split 5 108
    *++++split 11 237
    split 12 510
    *giant refine time: 10.8346
    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: 0.782315
    DDF time: 50.5169
    computing EDF(3,2)...+0.076398
    ...total time = 81.7783

    multiply 500-bit GF2Xs: 1.02539e-06
    remainder 1000/500-bit GF2Xs: 6.08515e-06
    gcd 500-bit GF2Xs: 1.18188e-05

    factoring degree-500 GF2X: 0.00108608
    gcd 500-bit GF2X: 1.18323e-05
    multiply degree-500 poly mod 500-bit GF2X: 0.0246272
    remainder degree-1000/500 poly mod 500-bit GF2X: 0.0883986
    preconditioned remainder degree-1000/500 poly mod 500-bit GF2X: 0.0492956
    gcd degree-500 poly mod 500-bit GF2X: 0.555426

    factoring degree-500 poly mod 500-bit GF2X...
    square-free decomposition...0.038173
    factoring multiplicity 1, deg = 250
    computing X^p...4.93404
    computing DDF...generating baby steps...++++++++++3.50859
    generating giant steps...+++++++++++3.78156
    giant refine...++++*++++split 6 59
    split 7 68
    *split 0 123
    giant refine time: 2.58798
    baby refine...split 59 59
    split 68 68
    split 123 123
    baby refine time: 3.4e-05
    DDF time: 9.87834

    ...total time = 14.8648