Raspberry Pi - Page 2

xilman · 2016-10-16, 16:55

My health is slowly returning to what passes for normal so now making progress with the Pi-3 hardware. Downloaded NOOBS and installed Raspbian Lite. Feels like a nice snappy system without all that GUI crap getting in the way, despite being only a 32-bit OS. Who needs X11 or Wayland when the curses version of aptitude is so friendly?

GMP and GMP-ECM is a task for tomorrow. After that, perhaps, 64-bit Arch Linux and then on to Gentoo. More micro-SD needs to be purchased before I'm happy with burning multiple operating systems.

xilman · 2016-10-16, 17:18

Anyone here have experience with Snappy Ubuntu Core ?

Looks like it might be another light-weight option but I'm not so familiar with that environment.

Hmm. Perhaps this thread should be moved elsewhere.

xilman · 2016-10-17, 17:32

Quote:

Originally Posted by henryzz

The raspberry pi 2 ran fine with gmp-ecm. The main issues I had with it were its speed was 1/20th of a Q6600 core and it had 1 GB of memory to share between 4 cores.
You should get a bit more speed on the pi 3 but I believe it still only has 1gb of memory.

First look results. This with the Debian released GMP and GMP-ECM:

Code:

pi@raspberrypi:~ $ ecm -v 1000000
GMP-ECM 6.4.4 [configured with GMP 6.0.0] [ECM]
Running on raspberrypi
533052935812724471841380849020536310747376222877714764551452418611323101581424711043443478661689064895630882238466804976175445143564101669576617833008137571
Input number is 533052935812724471841380849020536310747376222877714764551452418611323101581424711043443478661689064895630882238466804976175445143564101669576617833008137571 (156 digits)
Using MODMULN [mulredc:0, sqrredc:0]
Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=1121907350
dF=4096, k=6, d=39270, d2=13, i0=13
Expected number of curves to find a factor of n digits:
35	40	45	50	55	60	65	70	75	80
910	8615	97096	1281819	1.9e+07	3.1e+08	6.2e+09	1.7e+11	2.3e+16	3.1e+21
Step 1 took 45020ms
Using 37 small primes for NTT
Estimated memory usage: 14M
Initializing tables of differences for F took 110ms
Computing roots of F took 770ms
Building F from its roots took 880ms
Computing 1/F took 620ms
Initializing table of differences for G took 100ms
Computing roots of G took 660ms
Building G from its roots took 890ms
Computing roots of G took 660ms
Building G from its roots took 890ms
Computing G * H took 330ms
Reducing  G * H mod F took 350ms
Computing roots of G took 660ms
Building G from its roots took 890ms
Computing G * H took 340ms
Reducing  G * H mod F took 350ms
Computing roots of G took 660ms
Building G from its roots took 890ms
Computing G * H took 340ms
Reducing  G * H mod F took 360ms
Computing roots of G took 660ms
Building G from its roots took 890ms
Computing G * H took 330ms
Reducing  G * H mod F took 350ms
Computing roots of G took 660ms
Building G from its roots took 890ms
Computing G * H took 340ms
Reducing  G * H mod F took 350ms
Computing polyeval(F,G) took 1830ms
Computing product of all F(g_i) took 10ms
Step 2 took 17170ms
Expected time to find a factor of n digits:
35	40	45	50	55	60	65	70	75	80
15.72h	6.20d	69.89d	2.53y	37.82y	621.07y	12157y	335755y	4e+10y	6e+15y

The corresponding snippet from a 3.2GHz AMD PhenomII X6 1090T is

Code:

pcl@anubis ~/nums/msieve-code/trunk $ ecm -v 1000000
GMP-ECM 7.0.1-dev [configured with GMP 6.0.0, --enable-asm-redc, --enable-gpu] [ECM]
Running on anubis.home.brnikat.com
533052935812724471841380849020536310747376222877714764551452418611323101581424711043443478661689064895630882238466804976175445143564101669576617833008137571
Input number is 533052935812724471841380849020536310747376222877714764551452418611323101581424711043443478661689064895630882238466804976175445143564101669576617833008137571 (156 digits)
Using MODMULN [mulredc:0, sqrredc:1]
Computing batch product (of 1442099 bits) of primes up to B1=1000000 took 49ms
Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=1:3702621647
dF=4096, k=6, d=39270, d2=13, i0=13
Expected number of curves to find a factor of n digits:
35	40	45	50	55	60	65	70	75	80
1071	10283	118226	1565171	2.4e+07	3.9e+08	7.7e+09	2.9e+11	5.6e+16	7.6e+21
Step 1 took 4608ms
Using 20 small primes for NTT
Estimated memory usage: 21.59MB
Initializing tables of differences for F took 14ms
Computing roots of F took 140ms
Building F from its roots took 163ms
Computing 1/F took 120ms
Initializing table of differences for G took 7ms
Computing roots of G took 60ms
Building G from its roots took 83ms
Computing roots of G took 61ms
Building G from its roots took 82ms
Computing G * H took 35ms
Reducing  G * H mod F took 35ms
Computing roots of G took 61ms
Building G from its roots took 82ms
Computing G * H took 35ms
Reducing  G * H mod F took 35ms
Computing roots of G took 61ms
Building G from its roots took 82ms
Computing G * H took 35ms
Reducing  G * H mod F took 35ms
Computing roots of G took 61ms
Building G from its roots took 82ms
Computing G * H took 35ms
Reducing  G * H mod F took 34ms
Computing roots of G took 61ms
Building G from its roots took 82ms
Computing G * H took 34ms
Reducing  G * H mod F took 36ms
Computing polyeval(F,G) took 222ms
Computing product of all F(g_i) took 2ms
Step 2 took 1899ms
Expected time to find a factor of n digits:
35	40	45	50	55	60	65	70	75	80
1.94h	18.59h	8.90d	117.88d	4.88y	80.21y	1592y	60480y	1e+10y	2e+15y

The number is a c156 and the smallest composite in the GCW tables and it is now undergoing a GNFS run. The timings for the 60-digit level above suggest that the AMD is 621.07 / 80.21 = 7.75 times faster. This is vastly better than 1/20 of a Q6600 core!

This is not entirely fair as the latter is running code as optimized as I can make it on a 64-bit OS, whereas the Pi is hobbled by 32-bit arithmetic. When scaled by the clock frequency and a factor of 2 or so for the word size the two are comparable --- as I would expect.

Assuming that a 64-bit system can be installed, and the signs are very promising, the price-performance, both capital and running, also seem competitive --- admittedly with a now elderly AMD system. In time I'll make more detailed measurements.

xilman · 2016-10-17, 17:48

This is amusing.

A 3.2GHz AMD 1090 core is 6428.18 bogomips according to /proc/cpuinfo. The Pi-3 claims 38.40 bogomips per core.

Bogo indeed!

Mark Rose · 2016-10-17, 18:22

Quote:

Originally Posted by xilman

This is amusing.

A 3.2GHz AMD 1090 core is 6428.18 bogomips according to /proc/cpuinfo. The Pi-3 claims 38.40 bogomips per core.

Bogo indeed!

https://en.wikipedia.org/wiki/BogoMips

henryzz · 2016-10-17, 21:18

That is about what I would expect for the pi 3 as it's CPU should be twice as fast per core as the pi 2.

Mark Rose · 2016-10-17, 21:41

https://www.raspberrypi.org/blog/acc...using-its-gpu/

henryzz · 2016-10-17, 22:07

Quote:

Originally Posted by Mark Rose

https://www.raspberrypi.org/blog/acc...using-its-gpu/

404 error on the pi webpage.
edit: Just needs separating.
https://www.raspberrypi.org/blog/acc...using-the-gpu/
https://petewarden.com/2014/08/07/ho...using-its-gpu/

henryzz · 2016-10-17, 22:12

It looks like there may be issues with accuracy. The size of the ffts is also limited by the fact that is only uses single precision. Not likely to be very useful here. Nice idea though.

Mark Rose · 2016-10-18, 02:49

Quote:

Originally Posted by henryzz

404 error on the pi webpage.
edit: Just needs separating.
https://www.raspberrypi.org/blog/acc...using-the-gpu/
https://petewarden.com/2014/08/07/ho...using-its-gpu/

My bad. Thank you.

ET_ · 2016-10-18, 08:43

Quote:

Originally Posted by xilman

First look results. This with the Debian released GMP and GMP-ECM:

The number is a c156 and the smallest composite in the GCW tables and it is now undergoing a GNFS run. The timings for the 60-digit level above suggest that the AMD is 621.07 / 80.21 = 7.75 times faster. This is vastly better than 1/20 of a Q6600 core!

This is not entirely fair as the latter is running code as optimized as I can make it on a 64-bit OS, whereas the Pi is hobbled by 32-bit arithmetic. When scaled by the clock frequency and a factor of 2 or so for the word size the two are comparable --- as I would expect.

Assuming that a 64-bit system can be installed, and the signs are very promising, the price-performance, both capital and running, also seem competitive --- admittedly with a now elderly AMD system. In time I'll make more detailed measurements.

Did you also test PI with multiple instances of gmp-ecm? I suspect that a memory bottleneck may appear sooner there .

2016-10-17, 21:18	#17
henryzz Just call me Henry "David" Sep 2007 Liverpool (GMT/BST) 3×23×89 Posts	That is about what I would expect for the pi 3 as it's CPU should be twice as fast per core as the pi 2. Last fiddled with by henryzz on 2016-10-17 at 21:18

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2016-10-16, 16:55	#12
xilman Bamboozled! "𒉺𒌌𒇷𒆷𒀭" May 2003 Down not across 2²·3·983 Posts	My health is slowly returning to what passes for normal so now making progress with the Pi-3 hardware. Downloaded NOOBS and installed Raspbian Lite. Feels like a nice snappy system without all that GUI crap getting in the way, despite being only a 32-bit OS. Who needs X11 or Wayland when the curses version of aptitude is so friendly? GMP and GMP-ECM is a task for tomorrow. After that, perhaps, 64-bit Arch Linux and then on to Gentoo. More micro-SD needs to be purchased before I'm happy with burning multiple operating systems.

2016-10-16, 17:18	#13
xilman Bamboozled! "𒉺𒌌𒇷𒆷𒀭" May 2003 Down not across 2²·3·983 Posts	Anyone here have experience with Snappy Ubuntu Core ? Looks like it might be another light-weight option but I'm not so familiar with that environment. Hmm. Perhaps this thread should be moved elsewhere.

2016-10-17, 17:48	#15
xilman Bamboozled! "𒉺𒌌𒇷𒆷𒀭" May 2003 Down not across 2²×3×983 Posts	This is amusing. A 3.2GHz AMD 1090 core is 6428.18 bogomips according to /proc/cpuinfo. The Pi-3 claims 38.40 bogomips per core. Bogo indeed!

2016-10-17, 21:41	#18
Mark Rose "/X\(‘-‘)/X\" Jan 2013 https://pedan.tech/ 2⁴×199 Posts	https://www.raspberrypi.org/blog/acc...using-its-gpu/

2016-10-17, 22:12	#20
henryzz Just call me Henry "David" Sep 2007 Liverpool (GMT/BST) 3·23·89 Posts	It looks like there may be issues with accuracy. The size of the ffts is also limited by the fact that is only uses single precision. Not likely to be very useful here. Nice idea though.