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Productivity
Comparative characteristic of various algorithms realized today.
The formula is approximate to the experimental data and computed on a Intel Core2Duo T8300 processor clocked at 2.40 GHz.

Older data computed on Pentium II-400 can be found here.

Legend Fast algorithm N<95bit Classical multiplication Montgomery multiplication FFT multiplication Mixed CPU/GPU GPU implementation

 

Average value k/sec for 25 < n < 51

n=24283236404448
mmff.exe1,900,000,0001,820,000,0001,600,000,0001,000,000,000900,000,000800,000,000
Fermat.exe29,750,00025,000,00021,600,00018,700,00016,750,00013,500,0002,700,000
GMP-Fermat30,000,00028,000,00026,000,00024,000,00022,500,00021,000,00020,000,000
FermFact+PFGW50,00050,00045,000
Ppsieve+PFGW50,00060,00065,00070,00065,000

Compare relative speed of different processors with this Excel file.
George Woltman's mmff.exe works for 27<N<174 and k>224.

 

Average value k/sec for 50 < n < 1000

n=546080100150200300400600800
mmff.exe750,000,000650,000,000350,000,000300,000,000130,000,000
Fermat.exe2,400,0002,100,0001,130,0001,000,000430,000300,000140,00077,00031,20015,700
GMP-Fermat18,300,00017,000,00016,900,0007,250,0003,000,0002,625,000750,000450,000152,00054,000
FermFact+PFGW40,00035,00030,00025,00015,00014,00012,0006,0002,5002,000
Ppsieve+PFGW50,00045,00040,00033,00022,00021,00020,00015,0007,5003,500

Note. For small N, Proth and PFGW are not efficient.
George Woltman's mmff.exe works for 27<N<174 and k>224.

 

Average value k/sec for n > 1000

n=1000106020003000500010 00020 00030 00050 000100 000
Fermat.exe9,0007,8001,650550150152,30.84
GMP-Fermat31,00025,0005,2001,5503254350.84
Proth.exe55537017651157
FermFact+PFGW1,3001,2006004502418943215.11
Ppsieve+PFGW1,7001,600770530255102502561.2

Note. For n > 1000, Fermat.exe becomes inefficient.


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