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