M1061... - Page 12

thomasn · 2004-11-29, 12:33

Quote:

Originally Posted by Xyzzy

I haven't been keeping track of the 55 digit stuff I've posted, but hopefully thomasn will continue to keep stats for us!

I will do that, and I am sure ET_ will be able to take over if neccessary.

Thomas

thomasn · 2004-11-30, 13:23

[Fri Nov 26 01:50:15 2004]
M1061 completed 200 ECM curves, B1=44000000, B2=4290000000
[Sun Nov 28 23:05:16 2004]
M1061 completed 200 ECM curves, B1=44000000, B2=4290000000

Thomas

thomasn · 2004-11-30, 14:00

Code:

Name		Curves		Multiplier	B2		Message No	Line total
Xyzzy		5		?		?		#49		5
Xyzzy		50		1		680270182898	#76		50
Marc		1		1		680270182898	#82		1
Xyzzy		1		1		680270182898	#88		1
Xyzzy		105		1		680270182898	#94		105
Xyzzy		17		1		680270182898	#100		17
										
										
Grand total										179

Here is the list of work done for B1=110M. As you can see we have a long way to go if we want to complete that level.

Also: Please remember that we still need about 2000 curves to finish B1=44M.

Thomas

Mystwalker · 2004-11-30, 20:43

Is the multiplier really 1? After all, these curves have been done with gmp-ecm and higher bounds than 100 * B1...

Xyzzy · 2004-12-01, 14:35

243 curves using B1=110000000 & B2=680270182898...

Note the interesting time differences:

64-bit install:
Step 1 took 2050755ms
Step 2 took 2291610ms

32-bit install:
Step 1 took 3586745ms
Step 2 took 3287874ms

I installed a 32-bit version of Debian just to test this, and the time difference is pretty amazing... I let both run for several days to make sure that the numbers were stable...

ET_ · 2004-12-01, 14:42

Quote:

Originally Posted by Xyzzy

243 curves using B1=110000000 & B2=680270182898...

Note the interesting time differences:

64-bit install:
Step 1 took 2050755ms
Step 2 took 2291610ms

32-bit install:
Step 1 took 3586745ms
Step 2 took 3287874ms

I installed a 32-bit version of Debian just to test this, and the time difference is pretty amazing... I let both run for several days to make sure that the numbers were stable...

Amazing!

Now there's a good reason to exchange S.O.

Luigi

Xyzzy · 2004-12-01, 16:33

To be fair, the 32-bit install was using the i386 kernel and not a 686 or K7 kernel... I'm not sure how much of a difference is from the kernel and how much is from having the package compiled with a 64-bit only compiler... The 64-bit install was a pure 64-bit install...

Maybe I'll run a quick benchmark with the k7 kernel installed...

Xyzzy · 2004-12-01, 21:34

Quote:

Originally Posted by Xyzzy

Maybe I'll run a quick benchmark with the k7 kernel installed...

Code:

GMP-ECM 5.0.3 [powered by GMP 4.1.4] [ECM]
Input number is 24707306311927565716857342128774085333197833223161879682238935306082805123046306993647507776054336486228891340858985829027076261887914242781617846672453431386903982455635542158748401823985988322905245077938567513252198179128990807936780194781391547404884040101606295111368825026273254703636026307207764436438929167613951 (320 digits)
Using B1=110000000, B2=680270182898, polynomial Dickson(30), sigma=1217266501
Step 1 took 3578186ms
Step 2 took 3293512ms
Run 2 out of 0:
Using B1=110000000, B2=680270182898, polynomial Dickson(30), sigma=3163474637
Step 1 took 3567709ms
Step 2 took 3284253ms

Nope, it is just as slow with the K7 kernel...

Edit: Oh yeah, I got 3 more curves done... Same bounds as all the others...

geoff · 2004-12-01, 22:16

Quote:

Originally Posted by Xyzzy

Nope, it is just as slow with the K7 kernel...

It is probably the libgmp that makes it slow, the pure 64 bit install will have a well optimised libgmp whereas the 32 bit install will have a generic one.

akruppa · 2004-12-01, 22:52

I think it's the other way round: in 32 bit mode, gmp uses the 32 bit K7 optimized code, whereas in 64 bit mode it uses the generic C code with 64 bit types. For small numbers GMP uses the basecase (grammar-school) multiplication code whose time is quadratic in the number of machine words, so 64 bit mode has a factor 4 advantage there. That Xyzzy sees "only" a factor <2 speedup probably comes from lower mul-per-clock throughput the C code gets. That the relative speedup in stage 2 is smaller probably comes from the higher ratio of O(n) opertaions (adds, shifts) over muls in stage 2 compared to stage 1.

Torbjorn Granlund once mentioned that the Hammer (as it was called back then) could in theory get twice the mul throughput of the K7, for a total eightfold speedup when multiplying small numbers. I don't know how optimistic this estimate is, but AMD64 seems to make a good architecture for GMP related work either way - wish I had one. Unfortunately, full AMD64 support in GMP is scheduled only for late 2005.

Alex

garo · 2004-12-02, 08:11

Gentlemen, give this man a cigar..... Umm an AMD64

2004-11-30, 14:00	#124
thomasn Jun 2003 166₈ Posts	Code: Name Curves Multiplier B2 Message No Line total Xyzzy 5 ? ? #49 5 Xyzzy 50 1 680270182898 #76 50 Marc 1 1 680270182898 #82 1 Xyzzy 1 1 680270182898 #88 1 Xyzzy 105 1 680270182898 #94 105 Xyzzy 17 1 680270182898 #100 17 Grand total 179 Here is the list of work done for B1=110M. As you can see we have a long way to go if we want to complete that level. Also: Please remember that we still need about 2000 curves to finish B1=44M. Thomas

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2004-11-30, 13:23	#123
thomasn Jun 2003 2×59 Posts	[Fri Nov 26 01:50:15 2004] M1061 completed 200 ECM curves, B1=44000000, B2=4290000000 [Sun Nov 28 23:05:16 2004] M1061 completed 200 ECM curves, B1=44000000, B2=4290000000 Thomas

2004-11-30, 20:43	#125
Mystwalker Jul 2004 Potsdam, Germany 3×277 Posts	Is the multiplier really 1? After all, these curves have been done with gmp-ecm and higher bounds than 100 * B1...

2004-12-01, 14:35	#126
Xyzzy "Mike" Aug 2002 5×17×97 Posts	243 curves using B1=110000000 & B2=680270182898... Note the interesting time differences: 64-bit install: Step 1 took 2050755ms Step 2 took 2291610ms 32-bit install: Step 1 took 3586745ms Step 2 took 3287874ms I installed a 32-bit version of Debian just to test this, and the time difference is pretty amazing... I let both run for several days to make sure that the numbers were stable...

2004-12-01, 16:33	#128
Xyzzy "Mike" Aug 2002 5×17×97 Posts	To be fair, the 32-bit install was using the i386 kernel and not a 686 or K7 kernel... I'm not sure how much of a difference is from the kernel and how much is from having the package compiled with a 64-bit only compiler... The 64-bit install was a pure 64-bit install... Maybe I'll run a quick benchmark with the k7 kernel installed...

2004-12-01, 22:52	#131
akruppa "Nancy" Aug 2002 Alexandria 2467₁₀ Posts	I think it's the other way round: in 32 bit mode, gmp uses the 32 bit K7 optimized code, whereas in 64 bit mode it uses the generic C code with 64 bit types. For small numbers GMP uses the basecase (grammar-school) multiplication code whose time is quadratic in the number of machine words, so 64 bit mode has a factor 4 advantage there. That Xyzzy sees "only" a factor <2 speedup probably comes from lower mul-per-clock throughput the C code gets. That the relative speedup in stage 2 is smaller probably comes from the higher ratio of O(n) opertaions (adds, shifts) over muls in stage 2 compared to stage 1. Torbjorn Granlund once mentioned that the Hammer (as it was called back then) could in theory get twice the mul throughput of the K7, for a total eightfold speedup when multiplying small numbers. I don't know how optimistic this estimate is, but AMD64 seems to make a good architecture for GMP related work either way - wish I had one. Unfortunately, full AMD64 support in GMP is scheduled only for late 2005. Alex

2004-12-02, 08:11	#132
garo Aug 2002 Termonfeckin, IE ACC₁₆ Posts	Gentlemen, give this man a cigar..... Umm an AMD64