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drummerslowrise

1)
Message boards :
Number crunching :
Rtx 30 series
(Message 143424)
Posted 9 days ago by Yves Gallot
Also, the FP64 units are removed from Ampere RTX GPUs.
I hadn't noticed this in all the gaming hype. Interesting... does that mean you can't run FP64 at all, or is there some software emulation perhaps at even lower performance?
FP64 is slightly slower on the RTX 3080
AIDA64 GPGPU Benchmark
Model Freq Mem Read Mem Write Mem Copy FP32 FP64 INT32 INT64
RTX 2080 Ti 1635 12.4 GB/s 12.2 GB/s 499 GB/s 16496 507 15556 3486
RTX 3080 1710 12.4 GB/s 12.2 GB/s 643 GB/s 32513 516 16854 3998
507 * 1710 / 1635 = 530

2)
Message boards :
Number crunching :
Rtx 30 series
(Message 143393)
Posted 10 days ago by Yves Gallot
Some may consider a used 2080ti with its lower power consumption a better buy.
Did you check power consumption?
Because of the 8 nm process and as FP32, RTX and Tensor Cores are not used, power usage may be lower than TPD = 320W.
Thanks for benchmarks. As expected, the real number of cores is 4352 and not 8704. 8704 is the number of ALUs. With similar reasoning, the i99900K is not an octacore but a 32core processor!
Since both RTX 2080 and RTX 3080 have the same clock speed, we can easily compare core speed. RTX30 cores seem to be similar to RTX20 cores (expect the new FP32 unit) and the speed improvement for GFN22 (per core) must come from GDDR6X bandwidth.
Now, I have to find how to exploit these useless FP32 and Tensor Cores...

3)
Message boards :
Number crunching :
Rtx 30 series
(Message 143368)
Posted 10 days ago by Yves Gallot
No, all of them use INT32.
Each Pascal core is a single INT32+FP32 unit. Turing has two separate units: INT32 and FP32. Each RTX30 Ampere core has two units: INT32+FP32 and FP32. Then RTX30 can perform 2x FP32 but 1x INT32.
So that means no big improvement can be expected compared to the 2xxxseries, since the INT32 is used by PG?
It is unclear, I can just say that the GeForce 30 series may not be faster than the 20 series per core.
GA102/104 is different from GA100. The same name for both but it's clearly two different architectures.
Only half of the cores of the RTX30 are true cores. It's a new CUDA compute capability: 8.6 (GA100 is 8.0) and this version is still undocumented. With CUDA (or OpenCL) each core executes the same code, I don't see how it is possible with half of the cores that are not able to execute INT32 instructions.
I think that the RTX 3080 doesn't have 8704 cores but 4352 cores with two FP32 units per core. There is probably a new set of SIMD instructions able to execute two FP32 operations (?).
Then for PrimeGrid applications the comparison is RTX 2080 Ti: 4352 cores @ 1545MHz and RTX 3080: 4352 cores @ 1700MHz + faster memory and larger cache.

4)
Message boards :
Number crunching :
Rtx 30 series
(Message 143265)
Posted 15 days ago by Yves Gallot
They claim 2x FP32 performance among other things, which sounds really good for now...
Yes, 2x FP32 since 2x FP32 compute units.
PG softwares use FP32 right?
No, all of them use INT32.
Each Pascal core is a single INT32+FP32 unit. Turing has two separate units: INT32 and FP32. Each RTX30 Ampere core has two units: INT32+FP32 and FP32. Then RTX30 can perform 2x FP32 but 1x INT32.

5)
Message boards :
Generalized Fermat Prime Search :
Generalized Fermat with odd base?
(Message 142748)
Posted 31 days ago by Yves Gallot
Yves, thanks for the link, is it doing LLR or PRP? I assume LLR? Will it be possible to include a PRP test?
Neither LLR nor PRP but Proth's theorem.
For numbers of the form k·2^{n} + 1, k < 2^{n}, Proth's test is as fast as a prp test and is a primality proof. proth20 implements this test with Gerbicz error checking.
Gerbicz algorithm doesn't work with LLR because of the 2 term. Then if you want to search for primes of the form k·2^{n}  1 and implement Gerbicz error checking, you must do a PRP test to eliminate composite numbers. Only the final primality proof on prp numbers will be LLR test.

6)
Message boards :
Generalized Fermat Prime Search :
Generalized Fermat with odd base?
(Message 142710)
Posted 33 days ago by Yves Gallot
One last idea, is there a GPU software for Proth primes? I couldn't find any though.
Yes, proth20 binaries and proth20 sources.

7)
Message boards :
Generalized Fermat Prime Search :
Generalized Fermat with odd base?
(Message 142705)
Posted 33 days ago by Yves Gallot
For primes of the form b^2^n + 2 it's also not easy to prove their primality?
No, see Finding primes & proving primality.

8)
Message boards :
General discussion :
Mathematical Properties of Infinity
(Message 142515)
Posted 43 days ago by Yves Gallot
whether infinity is prime.
If the infinite is prime, add one to it and you will find another infinite which is composite :)
The infinite is not an element of the set of natural numbers then it is neither prime nor composite.

9)
Message boards :
General discussion :
Generalized Fermat Progression Search
(Message 142438)
Posted 46 days ago by Yves Gallot
GFP is great, because it can be Generalized or Gallot ;)
If we read Fermat's letter, this progression is in the same vein.
He built the sequence 2^{1}, 2^{2}, 2^{3}, ... and added one. He proved that they are composite if the exponent is not in the sequence (i.e. a power of two) and he thought that the other ones were primes because he didn't find their divisors.
Here the sequence is b^{1}, b^{2}, b^{3}, ... Similarly b^{n} + 1 is composite is n is not a power of two. We try to replace 3, 5, 17, 257 with a longer sequence of primes.

10)
Message boards :
Generalized Fermat Prime Search :
Gaps between GF primes
(Message 142322)
Posted 53 days ago by Yves Gallot
Still loving how high the W_{1}(2210) value is (~4.2559). This makes me curious if it is possible to calculate the limit for the maximum W_{1}(a) value, or if there is a theoretical maximum value at all.
Edit: I suppose that W_{1}(64090) is also a candidate for having a higher value. With 5, 13 and 17 in 2210 I just had Fermat primes on the brain, but 29 works too :)
Yes 64090 = 2 * 5 * 13 * 17 * 29 and let's continue:
If a = 2 * p_{1} * p_{2} * ... p_{n}, where p_{i} are the primes of the form 4 k + 1, we have w_{1}(p_{i}, a) = 2.
Then W_{1}(a) >= prod _{pi} (1  2/p_{i}) / (1  4/p_{i}) ~ 1.25357 log p_{n}.
The constant can be computed with Dirichlet series but the most important is that the product is divergent. Then W_{1}(a) is unbounded.

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