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A Tour of NTL: Some Performance Data
Here are some timing figures from using NTL. They were obtained using NTL 11.6.0 compiled with Apple clang version 17.0.0 (clang-1700.3.19.1) and with GMP 6.3 on an Apple M1 Max running macOS.
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: 1.2862e-07 square 1000-bit ints: 7.99998e-08 remainder 2000/1000-bit ints: 3.0913e-07 gcd 1000-bit ints: 3.44037e-06 xgcd 1000-bit ints: 4.18556e-06 power mod 1000-bit ints: 0.000251588 multiply degree-1000 poly mod 1000-bit prime: 0.00241779 remainder degree-2000/1000 poly mod 1000-bit prime: 0.00662264 preconditioned remainder degree-2000/1000 poly mod 1000-bit prime: 0.00243341 gcd degree-1000 poly mod 1000-bit prime: 0.0706218 multiply degree-1000 int poly with 1000-bit coeffs: 0.00293567 factoring degree-1000 poly mod 1000-bit prime... square-free decomposition...0.071287 factoring multiplicity 1, deg = 1000 computing X^p...4.07509 computing DDF...generating baby steps...+++++++++++++++++++++1.47373 generating giant steps...++++++++++++++++++++++1.53734 giant refine...++++split 1 18 *++++*++++*++++*++++split 17 355 *split 0 627 giant refine time: 2.45511 baby refine...split 1 1 split 8 8 split 9 9 split 355 355 split 627 627 baby refine time: 0.02605 DDF time: 5.49543 ...total time = 9.64638 multiply 1000x1000 matrices mod 1000-bit prime: 6.01712 multiply 500-bit GF2Xs: 1.82301e-08 remainder 1000/500-bit GF2Xs: 4.12932e-07 gcd 500-bit GF2Xs: 2.95696e-06 factoring degree-500 GF2X: 8.74958e-05 gcd 500-bit GF2X: 2.9557e-06 multiply degree-500 poly mod 500-bit GF2X: 0.000861831 remainder degree-1000/500 poly mod 500-bit GF2X: 0.0030675 preconditioned remainder degree-1000/500 poly mod 500-bit GF2X: 0.00169757 gcd degree-500 poly mod 500-bit GF2X: 0.019063 factoring degree-500 poly mod 500-bit GF2X... square-free decomposition...0.00218 factoring multiplicity 1, deg = 250 computing X^p...0.170542 computing DDF...generating baby steps...++++++++++0.120979 generating giant steps...+++++++++++0.135235 giant refine...++++split 1 9 split 2 13 split 4 44 *++++split 7 73 *split 0 111 giant refine time: 0.084774 baby refine...split 9 9 split 13 13 split 44 44 split 73 73 split 111 111 baby refine time: 0.000523 DDF time: 0.341556 ...total time = 0.507704