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A Tour of NTL: Some Performance Data


Here are some timing figures from using NTL. They were obtained using NTL 9.6.3 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


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