who knows Ryan Propper?

[xilman]

Originally Posted by ryanp

This thread is.. strange.

[firejuggler]

*Acoustic guitar mode on*

[ryanp]

Originally Posted by bsquared

Sparing me the build process to figure it out for myself, does GWNUM provide a speedup even for "small" inputs like 2^1277-1? How about 2^941-1? Wondering where the cutoff is to normal mulmod methods.

(Small, of course, relative to where prime95 usually operates.)

Attempting to get something useful out of this thread, here are some timings on a 2Ghz Skylake VM. Without GWNUM:

$ echo "2^1277-1" | ./ecm -c 5 11e6
GMP-ECM 7.0.4 [configured with GMP 6.2.0, --enable-asm-redc] [ECM]
Input number is 2^1277-1 (385 digits)
Using B1=11000000, B2=35133391030, polynomial Dickson(12), sigma=0:15382913345576557885
Step 1 took 63126ms
Step 2 took 28310ms
Run 2 out of 5:
Using B1=11000000, B2=35133391030, polynomial Dickson(12), sigma=0:2472923556820086104
Step 1 took 63697ms
Step 2 took 28330ms
Run 3 out of 5:
Using B1=11000000, B2=35133391030, polynomial Dickson(12), sigma=0:13772778279637613489
Step 1 took 63532ms
Step 2 took 28339ms
Run 4 out of 5:
Using B1=11000000, B2=35133391030, polynomial Dickson(12), sigma=0:4149983287909296098
Step 1 took 65040ms
Step 2 took 28394ms
Run 5 out of 5:
Using B1=11000000, B2=35133391030, polynomial Dickson(12), sigma=0:3089621796835281869
Step 1 took 65407ms
Step 2 took 28430ms

With GWNUM linked:

$ echo "2^1277-1" | ./ecm -c 5 11e6
GMP-ECM 7.0.4 [configured with GMP 6.2.0, GWNUM 29.8, --enable-asm-redc] [ECM]
Due to incompatible licenses, this binary file must not be distributed.
Input number is 2^1277-1 (385 digits)
Using B1=11000000, B2=35133391030, polynomial Dickson(12), sigma=0:1133017334638497343
Step 1 took 52939ms
Step 2 took 28574ms
Run 2 out of 5:
Using B1=11000000, B2=35133391030, polynomial Dickson(12), sigma=0:16936162798099609109
Step 1 took 52935ms
Step 2 took 28488ms
Run 3 out of 5:
Using B1=11000000, B2=35133391030, polynomial Dickson(12), sigma=0:4745769159583183902
Step 1 took 52719ms
Step 2 took 28706ms
Run 4 out of 5:
Using B1=11000000, B2=35133391030, polynomial Dickson(12), sigma=0:14575819613407288447
Step 1 took 52688ms
Step 2 took 28512ms
Run 5 out of 5:
Using B1=11000000, B2=35133391030, polynomial Dickson(12), sigma=0:7117923393329265041
Step 1 took 52795ms
Step 2 took 28585ms

So, a decent speedup in stage 1.

[bsquared]

Thanks, that's unexpected but neat. Wonder where the crossover is...

[ryanp]

Originally Posted by bsquared

Thanks, that's unexpected but neat. Wonder where the crossover is...

With larger inputs and B1's, the speedup is even more dramatic:

$ echo "2^2267-1" | ./ecm -c 5 43e6
GMP-ECM 7.0.4 [configured with GMP 6.2.0, --enable-asm-redc] [ECM]
Input number is 2^2267-1 (683 digits)
Using B1=43000000, B2=198654756318, polynomial Dickson(12), sigma=0:12068850290356100037
Step 1 took 546568ms
Step 2 took 163563ms

vs.

$ echo "2^2267-1" | ./ecm -c 5 43e6
GMP-ECM 7.0.4 [configured with GMP 6.2.0, GWNUM 29.8, --enable-asm-redc] [ECM]
Due to incompatible licenses, this binary file must not be distributed.
Input number is 2^2267-1 (683 digits)
Using B1=43000000, B2=198654756318, polynomial Dickson(12), sigma=0:16623107045151173302
Step 1 took 250555ms
Step 2 took 163852ms

Over twice as fast in B1!

[bbb120]

Originally Posted by ryanp

This thread is.. strange.

not strange，
I take Great curiosity on primality and integer factorization.

[ryanp]

Originally Posted by bbb120

not strange，
I take Great curiosity on primality and integer factorization.

Me, too!