A Tour of NTL: Some Performance Data
Here are some timing figures from using NTL. They were obtained using NTL 9.9.0 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.
NOTE: that the PRG changed in v9.4.0, so there may be some inconsistencies.
multiply 1000-bit ints: 1.76284e-07 remainder 2000/1000-bit ints: 3.60535e-07 gcd 1000-bit ints: 2.87045e-06 multiply degree-1000 poly mod 1000-bit prime: 0.00432981 remainder degree-2000/1000 poly mod 1000-bit prime: 0.0125583 preconditioned remainder degree-2000/1000 poly mod 1000-bit prime: 0.00443356 gcd degree-1000 poly mod 1000-bit prime: 0.122722 multiply degree-1000 int poly with 1000-bit coeffs: 0.00812543 factoring degree-1000 poly mod 1000-bit prime... square-free decomposition...0.122685 factoring multiplicity 1, deg = 1000 computing X^p...7.23809 computing DDF...generating baby steps...+++++++++++++++++++++6.21623 generating giant steps...++++++++++++++++++++++6.49462 giant refine...++++split 1 1 split 2 26 *++++*++++*++++*++++*++*split 0 973 giant refine time: 4.8139 baby refine...split 1 1 split 26 26 split 973 973 baby refine time: 3.3e-05 DDF time: 17.5262 ...total time = 24.8965 multiply 500-bit GF2Xs: 5.54208e-08 remainder 1000/500-bit GF2Xs: 8.40658e-07 gcd 500-bit GF2Xs: 3.60963e-06 factoring degree-500 GF2X: 0.00015574 gcd 500-bit GF2X: 3.61365e-06 multiply degree-500 poly mod 500-bit GF2X: 0.00251375 remainder degree-1000/500 poly mod 500-bit GF2X: 0.00905957 preconditioned remainder degree-1000/500 poly mod 500-bit GF2X: 0.00505149 gcd degree-500 poly mod 500-bit GF2X: 0.0478557 factoring degree-500 poly mod 500-bit GF2X... square-free decomposition...0.004635 factoring multiplicity 1, deg = 250 computing X^p...0.488941 computing DDF...generating baby steps...++++++++++0.332162 generating giant steps...+++++++++++0.357681 giant refine...++++split 1 9 split 2 13 split 4 44 *++++split 7 73 *split 0 111 giant refine time: 0.233787 baby refine...split 9 9 split 13 13 split 44 44 split 73 73 split 111 111 baby refine time: 0.001275 DDF time: 0.924938 ...total time = 1.41792