#

A Tour of NTL: Some Performance Data

Here are some timing figures from using NTL. They were obtained using NTL 9.6.3 compiled with `g++` 4.9.2 and with GMP 6.1 on a 2.5GHz Intel Haswell processor 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: 2.09304e-07
    remainder 2000/1000-bit ints: 3.85453e-07
    gcd 1000-bit ints: 3.16825e-06
    multiply degree-1000 poly mod 1000-bit prime: 0.00492108
    remainder degree-2000/1000 poly mod 1000-bit prime: 0.0142035
    preconditioned remainder degree-2000/1000 poly mod 1000-bit prime: 0.00498239
    gcd degree-1000 poly mod 1000-bit prime: 0.138828
    multiply degree-1000 int poly with 1000-bit coeffs: 0.00919382

    factoring degree-1000 poly mod 1000-bit prime...
    square-free decomposition...0.139174
    factoring multiplicity 1, deg = 1000
    computing X^p...8.18452
    computing DDF...generating baby steps...+++++++++++++++++++++7.24814
    generating giant steps...++++++++++++++++++++++7.57509
    giant refine...++++split 1 1
    split 2 26
    *++++*++++*++++*++++*++*split 0 973
    giant refine time: 5.43868
    baby refine...split 1 1
    split 26 26
    split 973 973
    baby refine time: 3.5e-05
    DDF time: 20.2627
    ...total time = 28.596

    multiply 500-bit GF2Xs: 6.07628e-08
    remainder 1000/500-bit GF2Xs: 2.605e-06
    gcd 500-bit GF2Xs: 4.00145e-06

    factoring degree-500 GF2X: 0.000177292
    gcd 500-bit GF2X: 3.99635e-06
    multiply degree-500 poly mod 500-bit GF2X: 0.0027215
    remainder degree-1000/500 poly mod 500-bit GF2X: 0.00981861
    preconditioned remainder degree-1000/500 poly mod 500-bit GF2X: 0.00547851
    gcd degree-500 poly mod 500-bit GF2X: 0.0526317

    factoring degree-500 poly mod 500-bit GF2X...
    square-free decomposition...0.004987
    factoring multiplicity 1, deg = 250
    computing X^p...0.528441
    computing DDF...generating baby steps...++++++++++0.361397
    generating giant steps...+++++++++++0.389211
    giant refine...++++split 1 9
    split 2 13
    split 4 44
    *++++split 7 73
    *split 0 111
    giant refine time: 0.253624
    baby refine...split 9 9
    split 13 13
    split 44 44
    split 73 73
    split 111 111
    baby refine time: 0.001397
    DDF time: 1.00566

    ...total time = 1.5405