gpuOwL: an OpenCL program for Mersenne primality testing

Originally Posted by preda

Both should be fixed now. If you encounter other exponents with errors caused by too-small default FFT size, please report and I'll have a look to further tune the default.

Good morning,
FFT selection is fixed for me, further tests coming soon.


I have upgraded CLANG and LLVM on my system, same result as before.

Originally Posted by preda

Thanks for the investigation. Interesting, I don't see the same (see below). I think maybe some driver difference or something else, e.g. different precision in sin/cos implementation on the GPU, may be the reason. But a slight relaxation of FFT size may be granted.

2018-10-22 21:59:05 vega0 gpuowl 4.6-9b7ff7b-mod
2018-10-22 21:59:05 vega0 FFT 4608K: Width 512 (64x8), Height 512 (64x8), Middle 9; 18.37 bits/word
2018-10-22 21:59:05 vega0 Note: using short carry kernels
2018-10-22 21:59:07 vega0 gfx900-64x1630-@67:0.0 Vega [Radeon RX Vega]
2018-10-22 21:59:10 vega0 OpenCL compilation in 3774 ms, with "-DEXP=86700001u -DWIDTH=512u -DSMALL_HEIGHT=512u -DMIDDLE=9u -I. -cl-fast-relaxed-math -cl-std=CL2.0 "
2018-10-22 21:59:11 vega0 PRP M(86700001), FFT 4608K, 18.37 bits/word, B1 0
2018-10-22 21:59:12 vega0 OK loaded: 0/86700001, B1 0, blockSize 400, 0000000000000003 (expected 0000000000000003)
2018-10-22 21:59:12 vega0 Selected 0 P-1 trial points
2018-10-22 21:59:15 vega0 OK 800/86700001 [ 0.00%], 2.15 ms/it [2.15, 2.16]; ETA 2d 03:54; 16460e4280156eaa (check 1.11s)
2018-10-22 21:59:35 vega0 10000/86700001 [ 0.01%], 2.16 ms/it [2.16, 2.16]; ETA 2d 04:02; 82759ed0ecd6fc95
2018-10-22 21:59:57 vega0 20000/86700001 [ 0.02%], 2.16 ms/it [2.16, 2.16]; ETA 2d 04:04; d5075945f4b2b972
2018-10-22 22:00:18 vega0 30000/86700001 [ 0.03%], 2.16 ms/it [2.16, 2.16]; ETA 2d 04:04; 41a8bb8b01bf4633
2018-10-22 22:00:40 vega0 40000/86700001 [ 0.05%], 2.16 ms/it [2.16, 2.16]; ETA 2d 04:04; ee0734f60d7b1db3
2018-10-22 22:01:01 vega0 50000/86700001 [ 0.06%], 2.16 ms/it [2.16, 2.16]; ETA 2d 04:03; f6a660fe2b783ce6
2018-10-22 22:01:23 vega0 60000/86700001 [ 0.07%], 2.16 ms/it [2.16, 2.16]; ETA 2d 04:04; 4274d66af0efb8f4
2018-10-22 22:01:45 vega0 70000/86700001 [ 0.08%], 2.16 ms/it [2.16, 2.16]; ETA 2d 04:03; 750a4f4758744c06
2018-10-22 22:02:06 vega0 80000/86700001 [ 0.09%], 2.16 ms/it [2.16, 2.16]; ETA 2d 04:03; c711dd998fe2f029
2018-10-22 22:02:28 vega0 90000/86700001 [ 0.10%], 2.16 ms/it [2.16, 2.16]; ETA 2d 04:02; 6a0a2c5b2353d680
2018-10-22 22:02:50 vega0 100000/86700001 [ 0.12%], 2.16 ms/it [2.16, 2.17]; ETA 2d 04:02; 8cdc89078250d440
2018-10-22 22:03:11 vega0 110000/86700001 [ 0.13%], 2.16 ms/it [2.16, 2.16]; ETA 2d 04:01; 17bab91f2ac31b34
2018-10-22 22:03:33 vega0 120000/86700001 [ 0.14%], 2.16 ms/it [2.16, 2.16]; ETA 2d 04:01; 4b09dcf722c21e76
2018-10-22 22:03:55 vega0 130000/86700001 [ 0.15%], 2.16 ms/it [2.16, 2.16]; ETA 2d 04:02; 9a5730be57db997f
2018-10-22 22:04:16 vega0 140000/86700001 [ 0.16%], 2.16 ms/it [2.16, 2.16]; ETA 2d 04:01; 1f4140f6971a3fc8
2018-10-22 22:04:38 vega0 150000/86700001 [ 0.17%], 2.16 ms/it [2.16, 2.16]; ETA 2d 04:01; db1014b1d4121f4c
2018-10-22 22:05:01 vega0 OK 160000/86700001 [ 0.18%], 2.16 ms/it [2.16, 2.16]; ETA 2d 04:01; a6afed696697b5c4 (check 1.21s)
2018-10-22 22:05:22 vega0 170000/86700001 [ 0.20%], 2.16 ms/it [2.16, 2.16]; ETA 2d 03:59; 9bfc2eae15121eeb
2018-10-22 22:05:44 vega0 180000/86700001 [ 0.21%], 2.16 ms/it [2.16, 2.16]; ETA 2d 03:59; fac14bff3c6daa15
2018-10-22 22:06:06 vega0 190000/86700001 [ 0.22%], 2.16 ms/it [2.16, 2.16]; ETA 2d 03:59; bed36466316f8442
2018-10-22 22:06:27 vega0 200000/86700001 [ 0.23%], 2.16 ms/it [2.16, 2.16]; ETA 2d 03:59; b332138d2e641277
2018-10-22 22:06:49 vega0 210000/86700001 [ 0.24%], 2.16 ms/it [2.16, 2.16]; ETA 2d 03:59; c74057dc770ba4b7
2018-10-22 22:07:11 vega0 220000/86700001 [ 0.25%], 2.16 ms/it [2.16, 2.16]; ETA 2d 03:58; c03b5a734225ab6c
2018-10-22 22:07:32 vega0 230000/86700001 [ 0.27%], 2.16 ms/it [2.16, 2.16]; ETA 2d 03:57; 46160146db97217f
2018-10-22 22:07:54 vega0 240000/86700001 [ 0.28%], 2.16 ms/it [2.16, 2.17]; ETA 2d 03:58; 001f3c4bc2e3107e
2018-10-22 22:08:16 vega0 250000/86700001 [ 0.29%], 2.16 ms/it [2.16, 2.16]; ETA 2d 03:56; 3d01711945270baf
2018-10-22 22:08:37 vega0 260000/86700001 [ 0.30%], 2.16 ms/it [2.16, 2.16]; ETA 2d 03:57; 9bc0aa6cb0bfac3b
2018-10-22 22:08:59 vega0 270000/86700001 [ 0.31%], 2.16 ms/it [2.16, 2.16]; ETA 2d 03:56; ce0b50a6de9e3293
2018-10-22 22:09:21 vega0 280000/86700001 [ 0.32%], 2.16 ms/it [2.16, 2.16]; ETA 2d 03:55; b99f827733e4ec3d
2018-10-22 22:09:42 vega0 290000/86700001 [ 0.33%], 2.16 ms/it [2.16, 2.16]; ETA 2d 03:55; 9827be481aba3805
2018-10-22 22:10:04 vega0 300000/86700001 [ 0.35%], 2.16 ms/it [2.16, 2.16]; ETA 2d 03:55; f33b6414738221e7
2018-10-22 22:10:25 vega0 310000/86700001 [ 0.36%], 2.16 ms/it [2.16, 2.16]; ETA 2d 03:55; 5f6c14ec328abdee
2018-10-22 22:10:48 vega0 OK 320000/86700001 [ 0.37%], 2.16 ms/it [2.16, 2.16]; ETA 2d 03:54; 2bbfb6c8f24890d2 (check 1.11s)
2018-10-22 22:11:10 vega0 330000/86700001 [ 0.38%], 2.16 ms/it [2.15, 2.16]; ETA 2d 03:53; 8d1b60211b94ac90
2018-10-22 22:11:32 vega0 340000/86700001 [ 0.39%], 2.16 ms/it [2.16, 2.16]; ETA 2d 03:53; 05590b87a9ddfafa
2018-10-22 22:11:53 vega0 350000/86700001 [ 0.40%], 2.16 ms/it [2.16, 2.16]; ETA 2d 03:53; 1f3a102e8771564d
2018-10-22 22:12:15 vega0 360000/86700001 [ 0.42%], 2.16 ms/it [2.16, 2.16]; ETA 2d 03:53; 9f0890f84be5d70e
2018-10-22 22:12:36 vega0 370000/86700001 [ 0.43%], 2.16 ms/it [2.16, 2.16]; ETA 2d 03:53; bf5bb13efebafbae
2018-10-22 22:12:58 vega0 380000/86700001 [ 0.44%], 2.16 ms/it [2.16, 2.16]; ETA 2d 03:52; eadd1ee5a31802f5
2018-10-22 22:13:20 vega0 390000/86700001 [ 0.45%], 2.16 ms/it [2.16, 2.16]; ETA 2d 03:52; d398a7819315a916
2018-10-22 22:13:41 vega0 400000/86700001 [ 0.46%], 2.16 ms/it [2.16, 2.16]; ETA 2d 03:51; b8450226874b2ef6
2018-10-22 22:14:03 vega0 410000/86700001 [ 0.47%], 2.16 ms/it [2.16, 2.17]; ETA 2d 03:51; 75d4ceed1067a7f4
2018-10-22 22:14:25 vega0 420000/86700001 [ 0.48%], 2.16 ms/it [2.16, 2.16]; ETA 2d 03:50; 8cf582cfb8566ad5
2018-10-22 22:14:46 vega0 430000/86700001 [ 0.50%], 2.16 ms/it [2.16, 2.16]; ETA 2d 03:50; ca456c850b7640d5
2018-10-22 22:15:08 vega0 440000/86700001 [ 0.51%], 2.16 ms/it [2.16, 2.16]; ETA 2d 03:50; bb6a2381b36d8890
2018-10-22 22:15:30 vega0 450000/86700001 [ 0.52%], 2.16 ms/it [2.16, 2.16]; ETA 2d 03:49; f5f83bb8aefe41de
2018-10-22 22:15:51 vega0 460000/86700001 [ 0.53%], 2.16 ms/it [2.16, 2.16]; ETA 2d 03:49; 9d36032d12489b80
2018-10-22 22:16:13 vega0 470000/86700001 [ 0.54%], 2.16 ms/it [2.16, 2.16]; ETA 2d 03:49; 399fdd68854c4d92
2018-10-22 22:16:36 vega0 OK 480000/86700001 [ 0.55%], 2.16 ms/it [2.16, 2.16]; ETA 2d 03:48; ceac25548f3e21f7 (check 1.10s)
2018-10-22 22:16:57 vega0 490000/86700001 [ 0.57%], 2.16 ms/it [2.16, 2.16]; ETA 2d 03:47; 28371927276164f3

You have exceptional performance with the Vega board, I should buy one.

[preda]

Originally Posted by SELROC

You have exceptional performance with the Vega board, I should buy one.

My Vega64 GPU is down-clocked to 1401MHz (for temperature & noise reasons), and at that point it takes exactly 150W, not bad. Part of the performance comes from the better compiler in ROCm (compared to amdgpu-pro), but I think amdgpu-pro would gradually follow the same improvements a couple of months behind ROCm.

I'm looking forward to what GPU AMD brings next. Vega64 are mostly retired from sale now, from what I see.

Originally Posted by preda

My Vega64 GPU is down-clocked to 1401MHz (for temperature & noise reasons), and at that point it takes exactly 150W, not bad. Part of the performance comes from the better compiler in ROCm (compared to amdgpu-pro), but I think amdgpu-pro would gradually follow the same improvements a couple of months behind ROCm.

I'm looking forward to what GPU AMD brings next. Vega64 are mostly retired from sale now, from what I see.

Now there are the Radeon Pro WX Series


https://www.amd.com/en/graphics/workstations-wx-series

Originally Posted by preda

My Vega64 GPU is down-clocked to 1401MHz (for temperature & noise reasons), and at that point it takes exactly 150W, not bad. Part of the performance comes from the better compiler in ROCm (compared to amdgpu-pro), but I think amdgpu-pro would gradually follow the same improvements a couple of months behind ROCm.

I hope they release the amdgpu driver for Debian too.

[preda]

PRP-1 (AKA "PRP,P-1") is a technique for doing a variant of P-1 during a PRP test, see https://mersenneforum.org/showthread.php?t=23628

1. How to enable PRP-1 in GpuOwl.
By default GpuOwl does a normal PRP test. To enable PRP-1 prepend a B1 value specification to a normal worktodo line, e.g.:
B1=1000000;82252003
B1=2000000;PRP=AID,1,2,82252003,-1,76,0

Such lines that contain a B1 together with a PRP test will start a PRP-1.

The work of PRP-1 is:
- do a P-1 first-stage to the indicated B1. This takes about 1.4 * B1 iterations. (note: right now this "P-1 first stage" is not saved while ongoing, so don't interrupt it before the PRP proper starts)
- compute a set of iteration points that will be P-1 tested during the PRP. The cost of each such "test point" is about one iteration (a bit larger than one iteration).

After the "P-1 first stage", and periodically during the PRP, GCDs are computed on the CPU looking for a factor. If a factor is found (this is rare), the PRP stops early.

2. B2
How are the points to be P-1-tested during the PRP selected? By default, for a given exponent E, a set of points is selected such as to cover a B2=E, (where B2 is the "second stage" bound in classic P-1). As an example, for E=82252003 that I'm testing now, such a default B2=E results in 3314921 points to be tested.

If we know the B1, and the number of "points" selected based on B2, we can estimate the cost:
for B1=2000000, first-stage P-1 takes about 2.8M iterations.
for B2=E=82252003, 3.3M points are selected, so 3.3M additional iterations during the PRP.

There is control over B2 in worktodo.txt like this:
B1=2000000,B2=40000000;PRP=AID,1,2,82252003,-1,76,0

This would require a B2 of only 40M instead of the default B2==E. Because B2 is smaller, the cost of the "second stage" (the number of P-1 points selected) is less.

It is also possible to set B2 in worktodo to a value larger than the exponent. But the primes can be covered in a compact manner (as needed for a B2 bound) only up to E. Beyond E, only part of the primes can be covered during the PRP.

Setting the B2 to a value larger than E will include the primes up to B2 that happen to be testable in iterations up to E. But the B2 bound that will be reported in the results.txt will still be equal to E. More points are tested during the PRP, the factor probability increases a bit, but cost increases too, but the reported B2 stays at most E.

3. The cost of the PRP-1 during the PRP proper (after the preliminary "first-stage") is accounted in the iteration cost. The ms/it value becomes a bit larger than for simple PRP because, for each "test point", an additional multiplication is done. Because the "test points" are not uniformly distributed over the PRP, this results in a slight variation of ms/it over the test.

All this being new, please report problems and suggestions. (and questions)

[preda]

I call "kset", or "test points", the set of iteration numbers to be P-1 tested during the PRP test; and I'll try to explain simply the selection procedure ("kselect") of these points.

This can be read in source here:
https://github.com/preda/gpuowl/blob...d/Gpu.cpp#L623

For every prime p in the interval [B1, B2]:
compute z = z(p) = znorder(Mod(2,p))
This means that 2^z == 1 (modulo p), i.e. p is a factor of 2^z - 1, so the prime p can be tested in iteration z at the earliest. p can also be tested in any iteration that's a multiple of z.

Iterating over the primes p in [B1, B2], if z(p)<E, mark z(p) as a test-point -- unless some other prime q in [B1, B2] has a z(q) that is a multiple of z(p), in which case z(q) "wins" and z(p) is not tested. (because z(q) covers both p and q).

This procedure does not produce the absolute smallest number of test points covering all the primes in [B1, B2], but it has the nice property of testing many primes "early" (at small iterations); in the [unlikely] event that a factor is found, this stops the PRP earlier.

[preda]

The best exponents for PRP-1 testing are the ones that didn't have any P-1 done yet. One way to get such exponents is to ask for P-1 assignments (and run PRP-1 on them).

[kriesel]

#update mingw/msys2 (twice; once for base system, again for packages including gcc-8.20; third says nothing to do ;)
pacman -Syu
pacman -Syu

$ g++ --version
g++.exe (Rev3, Built by MSYS2 project) 8.2.0
Copyright (C) 2018 Free Software Foundation, Inc.
This is free software; see the source for copying conditions.  There is NO
warranty; not even for MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.

ken@condorella MINGW64 ~/gpuowl-compile/v4.7
$ g++ -std=c++17 -O2 -DREV=\"5b01b65\" Worktodo.cpp Result.cpp common.cpp gpuowl.cpp Gpu.cpp clwrap.cpp Task.cpp checkpoint.cpp timeutil.cpp Args.cppGCD.cpp Primes.cpp Stats.cpp state.cpp Signal.cpp -o openowl -lOpenCL -lgmp -pthread -L/c/Windows/System32 -L.
C:/msys64/mingw64/bin/../lib/gcc/x86_64-w64-mingw32/8.2.0/../../../../x86_64-w64-mingw32/bin/ld.exe: d000034.o:(.idata$5+0x0): multiple definition of`__imp___C_specific_handler'; d000028.o:(.idata$5+0x0): first defined here
C:/msys64/mingw64/bin/../lib/gcc/x86_64-w64-mingw32/8.2.0/../../../../x86_64-w64-mingw32/bin/ld.exe: C:/msys64/mingw64/bin/../lib/gcc/x86_64-w64-mingw32/8.2.0/../../../../x86_64-w64-mingw32/lib/../lib/crt2.o: in function `pre_c_init':
C:/repo/mingw-w64-crt-git/src/mingw-w64/mingw-w64-crt/crt/crtexe.c:146: undefined reference to `__p__fmode'
C:/msys64/mingw64/bin/../lib/gcc/x86_64-w64-mingw32/8.2.0/../../../../x86_64-w64-mingw32/bin/ld.exe: C:/msys64/mingw64/bin/../lib/gcc/x86_64-w64-mingw32/8.2.0/../../../../x86_64-w64-mingw32/lib/../lib/crt2.o: in function `__tmainCRTStartup':
C:/repo/mingw-w64-crt-git/src/mingw-w64/mingw-w64-crt/crt/crtexe.c:290: undefined reference to `_set_invalid_parameter_handler'
C:/msys64/mingw64/bin/../lib/gcc/x86_64-w64-mingw32/8.2.0/../../../../x86_64-w64-mingw32/bin/ld.exe: C:/repo/mingw-w64-crt-git/src/mingw-w64/mingw-w64-crt/crt/crtexe.c:299: undefined reference to `__p__acmdln'
C:/msys64/mingw64/bin/../lib/gcc/x86_64-w64-mingw32/8.2.0/../../../../x86_64-w64-mingw32/bin/ld.exe: C:\msys64\tmp\ccCBiz5C.o:common.cpp:(.text+0x4cb): undefined reference to `__imp___acrt_iob_func'
C:/msys64/mingw64/bin/../lib/gcc/x86_64-w64-mingw32/8.2.0/../../../../x86_64-w64-mingw32/bin/ld.exe: C:\msys64\tmp\ccRlimfO.o:Args.cpp:(.text+0x29): undefined reference to `__imp___acrt_iob_func'
C:/msys64/mingw64/bin/../lib/gcc/x86_64-w64-mingw32/8.2.0/../../../../x86_64-w64-mingw32/bin/ld.exe: C:/msys64/mingw64/bin/../lib/gcc/x86_64-w64-mingw32/8.2.0/../../../../x86_64-w64-mingw32/lib/../lib/libmingw32.a(lib64_libmingw32_a-merr.o): in function `_matherr':
C:/repo/mingw-w64-crt-git/src/mingw-w64/mingw-w64-crt/crt/merr.c:72: undefined reference to `__acrt_iob_func'
C:/msys64/mingw64/bin/../lib/gcc/x86_64-w64-mingw32/8.2.0/../../../../x86_64-w64-mingw32/bin/ld.exe: C:/msys64/mingw64/bin/../lib/gcc/x86_64-w64-mingw32/8.2.0/../../../../x86_64-w64-mingw32/lib/../lib/libmingw32.a(lib64_libmingw32_a-pseudo-reloc.o): in function `__report_error':
C:/repo/mingw-w64-crt-git/src/mingw-w64/mingw-w64-crt/crt/pseudo-reloc.c:149: undefined reference to `__acrt_iob_func'
C:/msys64/mingw64/bin/../lib/gcc/x86_64-w64-mingw32/8.2.0/../../../../x86_64-w64-mingw32/bin/ld.exe: C:/repo/mingw-w64-crt-git/src/mingw-w64/mingw-w64-crt/crt/pseudo-reloc.c:150: undefined reference to `__acrt_iob_func'
C:/msys64/mingw64/bin/../lib/gcc/x86_64-w64-mingw32/8.2.0/../../../../x86_64-w64-mingw32/bin/ld.exe: C:/msys64/mingw64/bin/../lib/gcc/x86_64-w64-mingw32/8.2.0/../../../../x86_64-w64-mingw32/lib/../lib/libmingwex.a(lib64_libmingwex_a-wassert.o): in function `_wassert':
C:/repo/mingw-w64-crt-git/src/mingw-w64/mingw-w64-crt/misc/wassert.c:35: undefined reference to `__acrt_iob_func'
C:/msys64/mingw64/bin/../lib/gcc/x86_64-w64-mingw32/8.2.0/../../../../x86_64-w64-mingw32/bin/ld.exe: C:/msys64/mingw64/bin/../lib/gcc/x86_64-w64-mingw32/8.2.0/../../../../x86_64-w64-mingw32/lib/../lib/libmingwex.a(lib64_libmingwex_a-mingw_vfprintf.o): in function `__mingw_vfprintf':
C:/repo/mingw-w64-crt-git/src/mingw-w64/mingw-w64-crt/stdio/mingw_vfprintf.c:53: undefined reference to `_lock_file'
C:/msys64/mingw64/bin/../lib/gcc/x86_64-w64-mingw32/8.2.0/../../../../x86_64-w64-mingw32/bin/ld.exe: C:/repo/mingw-w64-crt-git/src/mingw-w64/mingw-w64-crt/stdio/mingw_vfprintf.c:55: undefined reference to `_unlock_file'
collect2.exe: error: ld returned 1 exit status

[kriesel]

Originally Posted by SELROC

Ok so the timings are:
v4.0, 4.8 ms/it
v4.6, 4.4 ms/it

with FFT 5120K

I haven't gotten any commit of v4.6 or v4.7 that I've tried to compile and link for Windows yet, so no 4.x timing on my RX480. However, for 3.x, I found 3.3 and 3.9 were not as fast as the following which were essentially equal: v3.5 v3.6 v3.8. A sparsely populated table vs. 3.x and fft length choices is available as the second attachment of https://www.mersenneforum.org/showpo...35&postcount=2

[preda]

Originally Posted by kriesel

$ g++ --version
g++.exe (Rev3, Built by MSYS2 project) 8.2.0

I don't know what causes the errors you see. Can you build some other version (3.x) in the same setup successfully? (i.e. are the errors caused by a difference in GpuOwl, or by the setup)