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A Tour of NTL: Some Performance Data


Here are some timing figures from using NTL. They were obtained using NTL 10.0.0 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: 1.77738e-07
square 1000-bit ints: 1.13905e-07
remainder 2000/1000-bit ints: 3.56371e-07
gcd 1000-bit ints: 2.86527e-06
xgcd 1000-bit ints: 4.48244e-06
power mod 1000-bit ints: 0.000424936
multiply degree-1000 poly mod 1000-bit prime: 0.00429163
remainder degree-2000/1000 poly mod 1000-bit prime: 0.012531
preconditioned remainder degree-2000/1000 poly mod 1000-bit prime: 0.0043504
gcd degree-1000 poly mod 1000-bit prime: 0.121598
multiply degree-1000 int poly with 1000-bit coeffs: 0.00625419

factoring degree-1000 poly mod 1000-bit prime...
square-free decomposition...0.121691
factoring multiplicity 1, deg = 1000
computing X^p...7.19641
computing DDF...generating baby steps...+++++++++++++++++++++6.26664
generating giant steps...++++++++++++++++++++++6.55775
giant refine...++++split 1 1
split 2 26
*++++*++++*++++*++++*++*split 0 973
giant refine time: 4.7865
baby refine...split 1 1
split 26 26
split 973 973
baby refine time: 4.1e-05
DDF time: 17.6118
...total time = 24.9393

multiply 500-bit GF2Xs: 5.50964e-08
remainder 1000/500-bit GF2Xs: 8.44805e-07
gcd 500-bit GF2Xs: 3.55114e-06

factoring degree-500 GF2X: 0.000155
gcd 500-bit GF2X: 3.54746e-06
multiply degree-500 poly mod 500-bit GF2X: 0.00246963
remainder degree-1000/500 poly mod 500-bit GF2X: 0.00886708
preconditioned remainder degree-1000/500 poly mod 500-bit GF2X: 0.00497244
gcd degree-500 poly mod 500-bit GF2X: 0.0459971

factoring degree-500 poly mod 500-bit GF2X...
square-free decomposition...0.004514
factoring multiplicity 1, deg = 250
computing X^p...0.476309
computing DDF...generating baby steps...++++++++++0.3256
generating giant steps...+++++++++++0.350459
giant refine...++++split 1 9
split 2 13
split 4 44
*++++split 7 73
*split 0 111
giant refine time: 0.2289
baby refine...split 9 9
split 13 13
split 44 44
split 73 73
split 111 111
baby refine time: 0.001253
DDF time: 0.906253

...total time = 1.38865

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