mersenneforum.org  

Go Back   mersenneforum.org > Great Internet Mersenne Prime Search > Hardware

Reply
 
Thread Tools
Old 2019-01-25, 20:18   #34
kriesel
 
kriesel's Avatar
 
"TF79LL86GIMPS96gpu17"
Mar 2017
US midwest

11100110001102 Posts
Default

Quote:
Originally Posted by ewmayer View Post
I'll be interested to see your "baby, it's cold outside" timings, as well.
Likewise. I have some choice weather for such tests too. (Almost wrote "prime weather" ;) Today's high out is comparable to the kitchen's freezer compartment. Bringing in more firewood shortly to augment the silicon space heaters.
kriesel is offline   Reply With Quote
Old 2019-01-25, 21:42   #35
M344587487
 
M344587487's Avatar
 
"Composite as Heck"
Oct 2017

3·311 Posts
Default

1024K temperature test. Started at ambient ~20C with no airflow until ~14:02, then by an open window ~14C with airflow, then sandwiched between two ice blocks until ~15:30, then back to ~20C ambient no airflow. Attached is a graph of SoC temperature sensors, looks like the ones near the cores were bouncing between 40C and 70C during the ice block challenge.

tl;dr
Code:
   20C no airflow primary timings ~0.0524, secondary timings ~0.0582
       14C airflow primary timings ~0.0475, secondary timings  ~0.0482
       ice blocks primary timings ~0.04     secondary timings  ~0.037
Which gives combined synthetic iteration times of ~27.6 ms/it, ~23.9 ms/it and ~19.2 ms/it respectively. What's odd is that the secondary cluster performed much better than the first as temps dropped, to the point where it ended up faster.

0,1,2,3:
Code:
INFO: no restart file found...starting run from scratch.
M20000047: using FFT length 1024K = 1048576 8-byte floats.
 this gives an average   19.073531150817871 bits per digit
Using complex FFT radices        16         8        16        16        16
[Jan 25 13:35:29] M20000047 Iter# = 10000 [ 0.05% complete] clocks = 00:08:38.680 [  0.0519 sec/iter] Res64: 9A2AF744DE060296. AvgMaxErr = 0.220879008. MaxErr = 0.312500000.
[Jan 25 13:44:13] M20000047 Iter# = 20000 [ 0.10% complete] clocks = 00:08:44.009 [  0.0524 sec/iter] Res64: D99B4D255F5C0C74. AvgMaxErr = 0.221481918. MaxErr = 0.312500000.
[Jan 25 13:52:58] M20000047 Iter# = 30000 [ 0.15% complete] clocks = 00:08:44.485 [  0.0524 sec/iter] Res64: 284DC13397AAE4DB. AvgMaxErr = 0.221543568. MaxErr = 0.312500000.
[Jan 25 14:01:43] M20000047 Iter# = 40000 [ 0.20% complete] clocks = 00:08:44.671 [  0.0525 sec/iter] Res64: C3ECAE145A41D57D. AvgMaxErr = 0.221724329. MaxErr = 0.296875000.
[Jan 25 14:10:25] M20000047 Iter# = 50000 [ 0.25% complete] clocks = 00:08:42.245 [  0.0522 sec/iter] Res64: 39BDD0E9AB6C5ACB. AvgMaxErr = 0.221664849. MaxErr = 0.312500000.
[Jan 25 14:18:20] M20000047 Iter# = 60000 [ 0.30% complete] clocks = 00:07:54.824 [  0.0475 sec/iter] Res64: A159C329415881C9. AvgMaxErr = 0.221609130. MaxErr = 0.312500000.
[Jan 25 14:26:15] M20000047 Iter# = 70000 [ 0.35% complete] clocks = 00:07:54.622 [  0.0475 sec/iter] Res64: 1204AAA78EC90606. AvgMaxErr = 0.221570026. MaxErr = 0.312500000.
[Jan 25 14:33:59] M20000047 Iter# = 80000 [ 0.40% complete] clocks = 00:07:43.799 [  0.0464 sec/iter] Res64: 2A44C89CB15BEF6C. AvgMaxErr = 0.221480947. MaxErr = 0.312500000.
[Jan 25 14:40:29] M20000047 Iter# = 90000 [ 0.45% complete] clocks = 00:06:30.099 [  0.0390 sec/iter] Res64: 1D7337E424D1D000. AvgMaxErr = 0.221663247. MaxErr = 0.312500000.
[Jan 25 14:47:03] M20000047 Iter# = 100000 [ 0.50% complete] clocks = 00:06:33.219 [  0.0393 sec/iter] Res64: 5EAA63BE1B9FA238. AvgMaxErr = 0.221479401. MaxErr = 0.312500000.
[Jan 25 14:53:34] M20000047 Iter# = 110000 [ 0.55% complete] clocks = 00:06:30.607 [  0.0391 sec/iter] Res64: DA8DD536ABDE47CB. AvgMaxErr = 0.221367128. MaxErr = 0.312500000.
[Jan 25 15:00:17] M20000047 Iter# = 120000 [ 0.60% complete] clocks = 00:06:42.765 [  0.0403 sec/iter] Res64: 642F5B6BC7CEB0D0. AvgMaxErr = 0.221727658. MaxErr = 0.312500000.
[Jan 25 15:07:07] M20000047 Iter# = 130000 [ 0.65% complete] clocks = 00:06:50.504 [  0.0411 sec/iter] Res64: E3553A51D6F6A365. AvgMaxErr = 0.221800594. MaxErr = 0.312500000.
[Jan 25 15:13:54] M20000047 Iter# = 140000 [ 0.70% complete] clocks = 00:06:46.294 [  0.0406 sec/iter] Res64: 56F4FCB4CCCC033B. AvgMaxErr = 0.221403671. MaxErr = 0.312500000.
[Jan 25 15:20:42] M20000047 Iter# = 150000 [ 0.75% complete] clocks = 00:06:48.604 [  0.0409 sec/iter] Res64: 0282DBDDEFF571C8. AvgMaxErr = 0.221367624. MaxErr = 0.296875000.
[Jan 25 15:27:37] M20000047 Iter# = 160000 [ 0.80% complete] clocks = 00:06:54.258 [  0.0414 sec/iter] Res64: 2847475575162412. AvgMaxErr = 0.221594595. MaxErr = 0.312500000.
[Jan 25 15:34:55] M20000047 Iter# = 170000 [ 0.85% complete] clocks = 00:07:18.160 [  0.0438 sec/iter] Res64: 6E883290AB4FE5DD. AvgMaxErr = 0.221736798. MaxErr = 0.312500000.
[Jan 25 15:43:07] M20000047 Iter# = 180000 [ 0.90% complete] clocks = 00:08:11.718 [  0.0492 sec/iter] Res64: D82A2BD113598640. AvgMaxErr = 0.221641509. MaxErr = 0.312500000.
[Jan 25 15:51:48] M20000047 Iter# = 190000 [ 0.95% complete] clocks = 00:08:40.463 [  0.0520 sec/iter] Res64: E13B981CABF386C0. AvgMaxErr = 0.221472874. MaxErr = 0.312500000.
[Jan 25 16:00:32] M20000047 Iter# = 200000 [ 1.00% complete] clocks = 00:08:43.504 [  0.0524 sec/iter] Res64: 99047F27A64C5119. AvgMaxErr = 0.221815586. MaxErr = 0.312500000.
[Jan 25 16:09:16] M20000047 Iter# = 210000 [ 1.05% complete] clocks = 00:08:43.702 [  0.0524 sec/iter] Res64: ABA0B0711FFFACFC. AvgMaxErr = 0.221564638. MaxErr = 0.312500000.
[Jan 25 16:17:59] M20000047 Iter# = 220000 [ 1.10% complete] clocks = 00:08:42.884 [  0.0523 sec/iter] Res64: F3CA77307D4583D2. AvgMaxErr = 0.221703177. MaxErr = 0.312500000.
[Jan 25 16:26:43] M20000047 Iter# = 230000 [ 1.15% complete] clocks = 00:08:43.929 [  0.0524 sec/iter] Res64: BF99A6EF10473797. AvgMaxErr = 0.221476924. MaxErr = 0.312500000.
[Jan 25 16:35:27] M20000047 Iter# = 240000 [ 1.20% complete] clocks = 00:08:43.595 [  0.0524 sec/iter] Res64: 91744165C085E55A. AvgMaxErr = 0.221551273. MaxErr = 0.312500000.
[Jan 25 16:44:12] M20000047 Iter# = 250000 [ 1.25% complete] clocks = 00:08:45.098 [  0.0525 sec/iter] Res64: CCC040796FAF88D2. AvgMaxErr = 0.221474659. MaxErr = 0.312500000.
[Jan 25 16:52:56] M20000047 Iter# = 260000 [ 1.30% complete] clocks = 00:08:43.309 [  0.0523 sec/iter] Res64: 071133B7D2BD4F31. AvgMaxErr = 0.221562684. MaxErr = 0.312500000.
4,5:
Code:
INFO: no restart file found...starting run from scratch.
M20000047: using FFT length 1024K = 1048576 8-byte floats.
 this gives an average   19.073531150817871 bits per digit
Using complex FFT radices        32        16        32        32
[Jan 25 13:36:06] M20000047 Iter# = 10000 [ 0.05% complete] clocks = 00:09:16.868 [  0.0557 sec/iter] Res64: 9A2AF744DE060296. AvgMaxErr = 0.247842553. MaxErr = 0.375000000.
[Jan 25 13:45:47] M20000047 Iter# = 20000 [ 0.10% complete] clocks = 00:09:40.720 [  0.0581 sec/iter] Res64: D99B4D255F5C0C74. AvgMaxErr = 0.248834183. MaxErr = 0.375000000.
[Jan 25 13:55:31] M20000047 Iter# = 30000 [ 0.15% complete] clocks = 00:09:43.547 [  0.0584 sec/iter] Res64: 284DC13397AAE4DB. AvgMaxErr = 0.248772266. MaxErr = 0.375000000.
[Jan 25 14:05:11] M20000047 Iter# = 40000 [ 0.20% complete] clocks = 00:09:39.651 [  0.0580 sec/iter] Res64: C3ECAE145A41D57D. AvgMaxErr = 0.248787216. MaxErr = 0.375000000.
[Jan 25 14:14:09] M20000047 Iter# = 50000 [ 0.25% complete] clocks = 00:08:57.896 [  0.0538 sec/iter] Res64: 39BDD0E9AB6C5ACB. AvgMaxErr = 0.248659808. MaxErr = 0.375000000.
[Jan 25 14:22:09] M20000047 Iter# = 60000 [ 0.30% complete] clocks = 00:07:59.679 [  0.0480 sec/iter] Res64: A159C329415881C9. AvgMaxErr = 0.248328552. MaxErr = 0.375000000.
[Jan 25 14:30:11] M20000047 Iter# = 70000 [ 0.35% complete] clocks = 00:08:02.419 [  0.0482 sec/iter] Res64: 1204AAA78EC90606. AvgMaxErr = 0.248587927. MaxErr = 0.343750000.
[Jan 25 14:36:56] M20000047 Iter# = 80000 [ 0.40% complete] clocks = 00:06:44.080 [  0.0404 sec/iter] Res64: 2A44C89CB15BEF6C. AvgMaxErr = 0.248547253. MaxErr = 0.375000000.
[Jan 25 14:42:40] M20000047 Iter# = 90000 [ 0.45% complete] clocks = 00:05:43.846 [  0.0344 sec/iter] Res64: 1D7337E424D1D000. AvgMaxErr = 0.249011792. MaxErr = 0.375000000.
[Jan 25 14:48:23] M20000047 Iter# = 100000 [ 0.50% complete] clocks = 00:05:42.716 [  0.0343 sec/iter] Res64: 5EAA63BE1B9FA238. AvgMaxErr = 0.248647055. MaxErr = 0.375000000.
[Jan 25 14:54:21] M20000047 Iter# = 110000 [ 0.55% complete] clocks = 00:05:57.899 [  0.0358 sec/iter] Res64: DA8DD536ABDE47CB. AvgMaxErr = 0.248535843. MaxErr = 0.375000000.
[Jan 25 15:00:28] M20000047 Iter# = 120000 [ 0.60% complete] clocks = 00:06:07.018 [  0.0367 sec/iter] Res64: 642F5B6BC7CEB0D0. AvgMaxErr = 0.248928904. MaxErr = 0.375000000.
[Jan 25 15:06:42] M20000047 Iter# = 130000 [ 0.65% complete] clocks = 00:06:13.814 [  0.0374 sec/iter] Res64: E3553A51D6F6A365. AvgMaxErr = 0.248515112. MaxErr = 0.375000000.
[Jan 25 15:12:46] M20000047 Iter# = 140000 [ 0.70% complete] clocks = 00:06:04.361 [  0.0364 sec/iter] Res64: 56F4FCB4CCCC033B. AvgMaxErr = 0.248713062. MaxErr = 0.375000000.
[Jan 25 15:19:12] M20000047 Iter# = 150000 [ 0.75% complete] clocks = 00:06:24.898 [  0.0385 sec/iter] Res64: 0282DBDDEFF571C8. AvgMaxErr = 0.249065100. MaxErr = 0.375000000.
[Jan 25 15:25:31] M20000047 Iter# = 160000 [ 0.80% complete] clocks = 00:06:19.361 [  0.0379 sec/iter] Res64: 2847475575162412. AvgMaxErr = 0.248730342. MaxErr = 0.375000000.
M20000047 Roundoff warning on iteration   166998, maxerr =   0.437500000000
[Jan 25 15:31:59] M20000047 Iter# = 170000 [ 0.85% complete] clocks = 00:06:27.822 [  0.0388 sec/iter] Res64: 6E883290AB4FE5DD. AvgMaxErr = 0.248881311. MaxErr = 0.437500000.
[Jan 25 15:40:11] M20000047 Iter# = 180000 [ 0.90% complete] clocks = 00:08:11.603 [  0.0492 sec/iter] Res64: D82A2BD113598640. AvgMaxErr = 0.248942981. MaxErr = 0.343750000.
[Jan 25 15:49:26] M20000047 Iter# = 190000 [ 0.95% complete] clocks = 00:09:14.533 [  0.0555 sec/iter] Res64: E13B981CABF386C0. AvgMaxErr = 0.248550307. MaxErr = 0.375000000.
[Jan 25 15:59:05] M20000047 Iter# = 200000 [ 1.00% complete] clocks = 00:09:39.335 [  0.0579 sec/iter] Res64: 99047F27A64C5119. AvgMaxErr = 0.248845004. MaxErr = 0.375000000.
[Jan 25 16:08:45] M20000047 Iter# = 210000 [ 1.05% complete] clocks = 00:09:39.636 [  0.0580 sec/iter] Res64: ABA0B0711FFFACFC. AvgMaxErr = 0.248549252. MaxErr = 0.375000000.
[Jan 25 16:18:21] M20000047 Iter# = 220000 [ 1.10% complete] clocks = 00:09:35.614 [  0.0576 sec/iter] Res64: F3CA77307D4583D2. AvgMaxErr = 0.248690302. MaxErr = 0.375000000.
[Jan 25 16:27:57] M20000047 Iter# = 230000 [ 1.15% complete] clocks = 00:09:35.461 [  0.0575 sec/iter] Res64: BF99A6EF10473797. AvgMaxErr = 0.248809814. MaxErr = 0.375000000.
[Jan 25 16:37:34] M20000047 Iter# = 240000 [ 1.20% complete] clocks = 00:09:37.210 [  0.0577 sec/iter] Res64: 91744165C085E55A. AvgMaxErr = 0.248753148. MaxErr = 0.375000000.
[Jan 25 16:47:11] M20000047 Iter# = 250000 [ 1.25% complete] clocks = 00:09:36.814 [  0.0577 sec/iter] Res64: CCC040796FAF88D2. AvgMaxErr = 0.248809012. MaxErr = 0.375000000.
  [Jan 25 16:56:51] M20000047 Iter# = 260000 [ 1.30% complete] clocks = 00:09:39.912 [  0.0580 sec/iter] Res64: 071133B7D2BD4F31. AvgMaxErr = 0.248568909. MaxErr = 0.375000000.
I wouldn't recommend running too cold, I tried the test again at 2560K but I don't think the SoC ramped up to compensate as the phone errored out and stopped execution saying it was too cold for the battery. When it warmed up it started executing again.


Quote:
Originally Posted by ewmayer View Post
Are you able to edit /proc/cpuinfo? I don't know how the OS exposes/hides cores from Joe User, but it might be worth a shot to see if simply exposing them via that system file allows a user app to use them. I would need to send you a little hack of the Mlucas util.c file to test this - one of the pending changes in v18 is to work around portability issues by having the program read the relevant data directly from that file rather than relying on the ABI for it. I would be surprised if said hack actually worked in terms of giving you access to cores 6:7, but it's easy enough to try.
That would be a hilarious solution if it worked, unfortunately not. It let me edit and save the file but it was instantly overwritten. It's a virtual file created by the kernel to advertise the hardware, I'm guessing that even if the edit stuck it would only trick userland programs that used cpuinfo not the kernel itself. A custom kernel is required, hopefully it exists.


BTW 1024k powered unlocked -cpu 0:5 failed to produce any results, it was busy but I think a process cannot be on both clusters at the same time so it was probably busy juggling threads (over half an hour with no results, when there should have been at least 3). There appear to be a few different ways big.little works which might explain it: https://community.arm.com/processors...out-big-little
Attached Thumbnails
Click image for larger version

Name:	1024k.temp.test.png
Views:	243
Size:	118.9 KB
ID:	19756  

Last fiddled with by M344587487 on 2019-01-25 at 22:12 Reason: Reason for Editing
M344587487 is offline   Reply With Quote
Old 2019-01-26, 04:38   #36
ewmayer
2ω=0
 
ewmayer's Avatar
 
Sep 2002
Repรบblica de California

2DEB16 Posts
Default

M344587487: Those are some very nice speedups due to cooling - so the obvious 'production' issue is to open the case so as to be able to stick mini-cooling-fin squares atop just the CPUs and get some airflow running parallel to the cooling channels in the fins.

By way of reference, my Odroid C2 needs ~40 msec/iter @1024K and 120 msec/iter @2560K, it's doing DCs at the latter runlength. Your timings-with-cooling extrapolate to only little less total throughput across both CPUs. Not bad, methinks.
ewmayer is offline   Reply With Quote
Old 2019-01-26, 11:00   #37
M344587487
 
M344587487's Avatar
 
"Composite as Heck"
Oct 2017

3·311 Posts
Default

Adding a direct heatsink looks to be a pain at least for the S7 Edge: https://www.ifixit.com/Teardown/Sams...Teardown/56845

You open the phone from the back, but the SoC is on the wrong side of the motherboard facing the screen. To put a heatsink directly on the SoC you need to keep everything splayed out if the connections between boards even allows for that.

Quote:
Originally Posted by masser View Post
I may have an iPhone 5S to donate to the cause. Is it too old? Would any one be able to provide a link to instructions for wiping all personal data from a phone?
Wikipedia says it has the first 64 bit ARM chip used in phones, but it's only a 1.3GHz quad core on a 28nm process, probably raspberry pi 3 levels of performance. It's in the grey area of technically being usable if it can be bent to our will but not really being worth bothering with IMO, YMMV.
M344587487 is offline   Reply With Quote
Old 2019-01-26, 20:24   #38
ewmayer
2ω=0
 
ewmayer's Avatar
 
Sep 2002
Repรบblica de California

267538 Posts
Default

Quote:
Originally Posted by M344587487 View Post
Adding a direct heatsink looks to be a pain at least for the S7 Edge: https://www.ifixit.com/Teardown/Sams...Teardown/56845

You open the phone from the back, but the SoC is on the wrong side of the motherboard facing the screen. To put a heatsink directly on the SoC you need to keep everything splayed out if the connections between boards even allows for that.
Is there any kind of thermal heat-spreading between the 'wrong side' - or between either side - of the CPUs and the metal parts of the case? If not, that means that your cooling efforts yesterday were all indirect through-the-case. The fact that such gave good speedups suggests that simply opening the back of the case and getting air flowing over the guts of the phone might give similar timings to the best ones you got yesterday.

Oh, also I misspoke re. the Odroid C2 comparison - if your best timings @1024k are ~40 msec/iter for each of the 2 per-CPU jobs that is in fact roughly 2x the throughput of the C2, which is pretty good.
ewmayer is offline   Reply With Quote
Old 2019-01-26, 22:46   #39
M344587487
 
M344587487's Avatar
 
"Composite as Heck"
Oct 2017

3×311 Posts
Default

There's a heatpipe connected to the metal frame, looks like a decent attempt at cooling: https://d3nevzfk7ii3be.cloudfront.ne...JN3FQhjVl.huge


I won't dismantle this one to investigate further as it'll probably kill the screen.
M344587487 is offline   Reply With Quote
Old 2019-01-26, 23:55   #40
kriesel
 
kriesel's Avatar
 
"TF79LL86GIMPS96gpu17"
Mar 2017
US midwest

1CC616 Posts
Default

Quote:
Originally Posted by M344587487 View Post
There's a heatpipe connected to the metal frame, looks like a decent attempt at cooling: https://d3nevzfk7ii3be.cloudfront.ne...JN3FQhjVl.huge

I won't dismantle this one to investigate further as it'll probably kill the screen.
Bonding a heat sink to the outside of the case other side of the case wall from the heat pipe may help. It's better than mere natural convection off a limited surface area. A little cpu cooler fan, on the heat sink, even more so, though that ups cost and power a bit.

Last fiddled with by kriesel on 2019-01-26 at 23:55
kriesel is offline   Reply With Quote
Old 2019-01-27, 04:04   #41
ewmayer
2ω=0
 
ewmayer's Avatar
 
Sep 2002
Repรบblica de California

5×2,351 Posts
Default

Quote:
Originally Posted by M344587487 View Post
There's a heatpipe connected to the metal frame, looks like a decent attempt at cooling: https://d3nevzfk7ii3be.cloudfront.ne...JN3FQhjVl.huge

I won't dismantle this one to investigate further as it'll probably kill the screen.
It stands to reason that getting some airflow over the heatpipe or the surface it spreads the heat to should help - can you also post a pic of the other half of the phone, the one that mates with the half-clamshell shown in yor pic? I'm trying to get a sense of the 3D structure of things. Best would be a shot laid out the same way. Thanks!
ewmayer is offline   Reply With Quote
Old 2019-01-27, 09:21   #42
M344587487
 
M344587487's Avatar
 
"Composite as Heck"
Oct 2017

3·311 Posts
Default

It's all detailed in the ifixit teardown link a few posts up, here's the side of the motherboard that sits on the copper pipe. The red square is the SoC with RAM above it: https://d3nevzfk7ii3be.cloudfront.ne...QQXRVyoHT.huge
M344587487 is offline   Reply With Quote
Old 2019-01-27, 19:37   #43
ewmayer
2ω=0
 
ewmayer's Avatar
 
Sep 2002
Repรบblica de California

101101111010112 Posts
Default

Quote:
Originally Posted by M344587487 View Post
It's all detailed in the ifixit teardown link a few posts up, here's the side of the motherboard that sits on the copper pipe. The red square is the SoC with RAM above it: https://d3nevzfk7ii3be.cloudfront.ne...QQXRVyoHT.huge
Thanks - so if I'm mentally fitting that together properly, that row of various subsystem-processors including the SoC sits atop the heatpipe, whihc distributes the heat to metal back of the case?
ewmayer is offline   Reply With Quote
Old 2019-01-27, 20:03   #44
xilman
Bamboozled!
 
xilman's Avatar
 
"๐’‰บ๐’ŒŒ๐’‡ท๐’†ท๐’€ญ"
May 2003
Down not across

3·132·23 Posts
Default

Quote:
Originally Posted by M344587487 View Post
1024K temperature
:woot: That's bloody hot!
xilman is offline   Reply With Quote
Reply

Thread Tools


Similar Threads
Thread Thread Starter Forum Replies Last Post
Official GIMPS 2019 fundraiser thread Prime95 GIMPS Board of Directors News 46 2019-11-22 06:01
GIMPS wiki account request thread ixfd64 mersennewiki 169 2018-09-21 05:43
Cuda and a cluster efiGeek Msieve 17 2015-12-06 14:31
GPUs vs. Cellphone GSM Rodrigo GPU Computing 2 2011-07-14 07:48
Cluster @ MSRC smh NFSNET Discussion 1 2003-08-12 08:52

All times are UTC. The time now is 02:13.


Sun Feb 5 02:13:14 UTC 2023 up 170 days, 23:41, 1 user, load averages: 1.32, 1.22, 1.04

Powered by vBulletin® Version 3.8.11
Copyright ©2000 - 2023, Jelsoft Enterprises Ltd.

This forum has received and complied with 0 (zero) government requests for information.

Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version published by the Free Software Foundation.
A copy of the license is included in the FAQ.

โ‰  ยฑ โˆ“ รท ร— ยท โˆ’ โˆš โ€ฐ โŠ— โŠ• โŠ– โŠ˜ โŠ™ โ‰ค โ‰ฅ โ‰ฆ โ‰ง โ‰จ โ‰ฉ โ‰บ โ‰ป โ‰ผ โ‰ฝ โŠ โŠ โŠ‘ โŠ’ ยฒ ยณ ยฐ
โˆ  โˆŸ ยฐ โ‰… ~ โ€– โŸ‚ โซ›
โ‰ก โ‰œ โ‰ˆ โˆ โˆž โ‰ช โ‰ซ โŒŠโŒ‹ โŒˆโŒ‰ โˆ˜ โˆ โˆ โˆ‘ โˆง โˆจ โˆฉ โˆช โจ€ โŠ• โŠ— ๐–• ๐–– ๐–— โŠฒ โŠณ
โˆ… โˆ– โˆ โ†ฆ โ†ฃ โˆฉ โˆช โŠ† โŠ‚ โŠ„ โŠŠ โŠ‡ โŠƒ โŠ… โŠ‹ โŠ– โˆˆ โˆ‰ โˆ‹ โˆŒ โ„• โ„ค โ„š โ„ โ„‚ โ„ต โ„ถ โ„ท โ„ธ ๐“Ÿ
ยฌ โˆจ โˆง โŠ• โ†’ โ† โ‡’ โ‡ โ‡” โˆ€ โˆƒ โˆ„ โˆด โˆต โŠค โŠฅ โŠข โŠจ โซค โŠฃ โ€ฆ โ‹ฏ โ‹ฎ โ‹ฐ โ‹ฑ
โˆซ โˆฌ โˆญ โˆฎ โˆฏ โˆฐ โˆ‡ โˆ† ฮด โˆ‚ โ„ฑ โ„’ โ„“
๐›ข๐›ผ ๐›ฃ๐›ฝ ๐›ค๐›พ ๐›ฅ๐›ฟ ๐›ฆ๐œ€๐œ– ๐›ง๐œ ๐›จ๐œ‚ ๐›ฉ๐œƒ๐œ— ๐›ช๐œ„ ๐›ซ๐œ… ๐›ฌ๐œ† ๐›ญ๐œ‡ ๐›ฎ๐œˆ ๐›ฏ๐œ‰ ๐›ฐ๐œŠ ๐›ฑ๐œ‹ ๐›ฒ๐œŒ ๐›ด๐œŽ๐œ ๐›ต๐œ ๐›ถ๐œ ๐›ท๐œ™๐œ‘ ๐›ธ๐œ’ ๐›น๐œ“ ๐›บ๐œ”