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A Tour of NTL: Some Performance Data

Here are some timing figures from using NTL. They were obtained using NTL 9.5.0 compiled with `g++` 4.2.1 and with GMP 6.0 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.

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

    multiply 1000-bit ints: 4.27453e-07
    remainder 2000/1000-bit ints: 8.48588e-07
    gcd 1000-bit ints: 1.04784e-05
    multiply degree-1000 poly mod 1000-bit prime: 0.0116206
    remainder degree-2000/1000 poly mod 1000-bit prime: 0.0334745
    preconditioned remainder degree-2000/1000 poly mod 1000-bit prime: 0.0119743
    gcd degree-1000 poly mod 1000-bit prime: 0.306743
    multiply degree-1000 int poly with 1000-bit coeffs: 0.0183048

    factoring degree-1000 poly mod 1000-bit prime...
    square-free decomposition...0.30792
    factoring multiplicity 1, deg = 1000
    computing X^p...19.3247
    computing DDF...generating baby steps...+++++++++++++++++++++15.6532
    generating giant steps...++++++++++++++++++++++16.3381
    giant refine...++++split 1 1
    split 2 26
    *++++*++++*++++*++++*++*split 0 973
    giant refine time: 12.7031
    baby refine...split 1 1
    split 26 26
    split 973 973
    baby refine time: 7.9e-05
    DDF time: 44.7023
    ...total time = 64.357

    multiply 500-bit GF2Xs: 1.03056e-06
    remainder 1000/500-bit GF2Xs: 7.05941e-06
    gcd 500-bit GF2Xs: 1.19136e-05

    factoring degree-500 GF2X: 0.00109245
    gcd 500-bit GF2X: 1.19024e-05
    multiply degree-500 poly mod 500-bit GF2X: 0.0246636
    remainder degree-1000/500 poly mod 500-bit GF2X: 0.0886752
    preconditioned remainder degree-1000/500 poly mod 500-bit GF2X: 0.0493821
    gcd degree-500 poly mod 500-bit GF2X: 0.556096

    factoring degree-500 poly mod 500-bit GF2X...
    square-free decomposition...0.038475
    factoring multiplicity 1, deg = 250
    computing X^p...4.94318
    computing DDF...generating baby steps...++++++++++3.51545
    generating giant steps...+++++++++++3.79071
    giant refine...++++split 1 9
    split 2 13
    split 4 44
    *++++split 7 73
    *split 0 111
    giant refine time: 2.34984
    baby refine...split 9 9
    split 13 13
    split 44 44
    split 73 73
    split 111 111
    baby refine time: 0.015533
    DDF time: 9.67169

    ...total time = 14.6677