A Tour of NTL: Some Performance Data
Here are some timing figures from using NTL. They were obtained using NTL 9.6.2 compiled with g++ 4.2.1 and with GMP 6.1 on a 2.4GHz Intel Core 2 Duo running on Max OSX 10.7.5.
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: 5.02504e-07 remainder 2000/1000-bit ints: 1.00513e-06 gcd 1000-bit ints: 1.4485e-05 multiply degree-1000 poly mod 1000-bit prime: 0.0131606 remainder degree-2000/1000 poly mod 1000-bit prime: 0.0381163 preconditioned remainder degree-2000/1000 poly mod 1000-bit prime: 0.0135755 gcd degree-1000 poly mod 1000-bit prime: 0.345835 multiply degree-1000 int poly with 1000-bit coeffs: 0.0225677 factoring degree-1000 poly mod 1000-bit prime... square-free decomposition...0.346712 factoring multiplicity 1, deg = 1000 computing X^p...22.2213 computing DDF...generating baby steps...+++++++++++++++++++++18.0226 generating giant steps...++++++++++++++++++++++18.8124 giant refine...++++split 1 1 split 2 26 *++++*++++*++++*++++*++*split 0 973 giant refine time: 14.5554 baby refine...split 1 1 split 26 26 split 973 973 baby refine time: 0.000109 DDF time: 51.3992 ...total time = 73.9925 multiply 500-bit GF2Xs: 1.29482e-06 remainder 1000/500-bit GF2Xs: 8.38771e-06 gcd 500-bit GF2Xs: 1.54409e-05 factoring degree-500 GF2X: 0.00131092 gcd 500-bit GF2X: 1.54394e-05 multiply degree-500 poly mod 500-bit GF2X: 0.030962 remainder degree-1000/500 poly mod 500-bit GF2X: 0.111182 preconditioned remainder degree-1000/500 poly mod 500-bit GF2X: 0.0622763 gcd degree-500 poly mod 500-bit GF2X: 0.690277 factoring degree-500 poly mod 500-bit GF2X... square-free decomposition...0.047294 factoring multiplicity 1, deg = 250 computing X^p...6.20889 computing DDF...generating baby steps...++++++++++4.41372 generating giant steps...+++++++++++4.75237 giant refine...++++split 1 9 split 2 13 split 4 44 *++++split 7 73 *split 0 111 giant refine time: 2.94889 baby refine...split 9 9 split 13 13 split 44 44 split 73 73 split 111 111 baby refine time: 0.019359 DDF time: 12.1345 ...total time = 18.4086