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Forum: Miscellaneous Math 2020-08-28, 04:07
Replies: 56
Views: 3,129
Posted By bsquared
Looks like you still have some work to do at...

Looks like you still have some work to do at higher offsets though:

primesieve-7.4 10^14 to 10^14+10^11
6.08 sec

twinprimes_ssoz.rs, 10^14 to 10^14+10^11
13.2 sec

primesieve-7.4 10^16 to...
Forum: Miscellaneous Math 2020-08-28, 03:06
Replies: 56
Views: 3,129
Posted By bsquared
I'm afraid I'm running into problems, probably...

I'm afraid I'm running into problems, probably because of my ignorance of the rust build process. I tried running cargo.exe build in the top level of the SSoZ repository and got this
...
Forum: Miscellaneous Math 2020-08-27, 20:08
Replies: 56
Views: 3,129
Posted By bsquared
I've downloaded the code from...

I've downloaded the code from https://github.com/jzakiya/SSoZ, but I don't know how to compile it. Any pointers?
Forum: Miscellaneous Math 2020-08-27, 19:11
Replies: 56
Views: 3,129
Posted By bsquared
I've just compared the java version of ssojz that...

I've just compared the java version of ssojz that Till provided with primesieve and yafu and I'm indeed impressed.

Counting twin primes to 10^11 with 16 threads:
ssojz: 3.34 sec

Counting twin...
Forum: Factoring 2020-08-26, 22:03
Replies: 6
Views: 615
Posted By bsquared
Saves registers. The goal of unrolling is to...

Saves registers. The goal of unrolling is to minimize loop overhead (comparing against loop condition, jumps). But unrolling increases the code size. A sweet spot occurs if all variables in the...
Forum: Factoring 2020-08-26, 21:10
Replies: 5
Views: 421
Posted By bsquared
If your interest is limited to factoring Mersenne...

If your interest is limited to factoring Mersenne numbers, then the practical advice is probably: never. Unless you represent a small government or large research collaboration? Only they have the...
Forum: Factoring 2020-08-26, 20:22
Replies: 6
Views: 615
Posted By bsquared
Also, usually people initialize the sieve byte...

Also, usually people initialize the sieve byte values to a cutoff:

for (i=0; i < sieve_length; i++) {
sieve[i] = cutoff;
}

Then sieve just like normal, but subtract instead of add.
...
Forum: Factoring 2020-08-26, 20:17
Replies: 6
Views: 615
Posted By bsquared
For small-ish primes you could unroll it. log...

For small-ish primes you could unroll it. log changes slowly and will be the same for 4 adjacent primes. I don't know how to to re-work this code exactly given that currentPosition, prime, log,...
Forum: Miscellaneous Math 2020-08-26, 20:03
Replies: 56
Views: 3,129
Posted By bsquared
When have I said that it doesn't have value? In...

When have I said that it doesn't have value? In fact I said that your work is to be commended. And that I will experiment to see if there are any benefits I can apply for my own code. I'm glad you...
Forum: Miscellaneous Math 2020-08-26, 19:18
Replies: 56
Views: 3,129
Posted By bsquared
I would argue the opposite: people have been...

I would argue the opposite: people have been building on the ideas behind that particular sieve for almost 20 years now. The point is that sieving by residues, wheel factorization and wheel sieving...
Forum: Miscellaneous Math 2020-08-26, 16:17
Replies: 56
Views: 3,129
Posted By bsquared
Your SSoZ is not new; sieving over residue...

Your SSoZ is not new; sieving over residue classes has been done for a long time. An early example is the (IMO lovely named) black-key sieve (https://www.qsl.net/w2gl/blackkey.html) in 1993. (It is...
Forum: Lounge 2020-08-25, 18:35
Replies: 82
Views: 2,977
Posted By bsquared
I didn't know mine, but apparently I'm Erdös=4...

I didn't know mine, but apparently I'm Erdös=4 and Dijkstra=5, according to that site.
Forum: Alberico Lepore 2020-08-18, 15:04
Replies: 70
Views: 4,748
Posted By bsquared
Well, he has been trying to factor N=91 since at...

Well, he has been trying to factor N=91 since at least May of 2017 (https://www.mersenneforum.org/showpost.php?p=459615&postcount=20). Now, apparently working on 1375 (?). That's 3 years for a 2...
Forum: Msieve 2020-08-18, 13:15
Replies: 23
Views: 4,665
Posted By bsquared
After 1% elasped, the ETA is: -np 2 1x2...

After 1% elasped, the ETA is:


-np 2 1x2 -t 20: 3 hrs 9 min
-np 4 1x4 -t 10: 2 hrs 48 min
-np 5 1x5 -t 8: 3 hrs 49 min
-np 8 1x8 -t 5: 2 hrs 50 min


The 1x5 time is not surprising as one...
Forum: Puzzles 2020-08-06, 20:42
Replies: 28
Views: 1,798
Posted By bsquared
I see that you are finding a short addition chain...

I see that you are finding a short addition chain using the x^(2^k) elements that will be computed anyway during the test. That's a very nice approach. As mentioned, the short addition chain...
Forum: Puzzles 2020-08-06, 18:59
Replies: 28
Views: 1,798
Posted By bsquared
Maybe also relevant to mention that the problem...

Maybe also relevant to mention that the problem of finding the shortest addition chain for a given binary string is known to be NP-hard (section 14.102 in HOAC). But you'd only have to do it once...
Forum: Puzzles 2020-08-06, 18:44
Replies: 28
Views: 1,798
Posted By bsquared
I'm just looking for ways to minimize the number...

I'm just looking for ways to minimize the number of multiplications in a modular exponentiation x^N mod M.
In the handbook of applied cryptography (http://cacr.uwaterloo.ca/hac/about/chap14.pdf),...
Forum: Hardware 2020-08-06, 18:13
Replies: 31
Views: 1,486
Posted By bsquared
Maybe not as cheap as you think :smile:. If...

Maybe not as cheap as you think :smile:.

If the sand is mosly quartz with a density of 2.65 g/cm^3, then you have around 9433 cm^3 of sand. With a 250 micron grain size you'd only have around 600...
Forum: Puzzles 2020-08-06, 17:11
Replies: 28
Views: 1,798
Posted By bsquared
If it is possible/cheap to compute 3^-1 mod M,...

If it is possible/cheap to compute 3^-1 mod M, then it is possible to do even a little better by first recoding the exponent in signed representation {-1, 0, 1}.


powersmooth(1000000) has 1442080...
Forum: Lounge 2020-07-27, 15:03
Replies: 46
Views: 1,923
Posted By bsquared
I ran into this luna moth while camping last...

I ran into this luna moth while camping last month. I'd never seen one this close up before.
It was pretty big - maybe 5 inches wingtip to wingtip.
Forum: Lounge 2020-07-23, 12:44
Replies: 91
Views: 6,579
Posted By bsquared
Congratulations, and nice pictures! I hope to do...

Congratulations, and nice pictures! I hope to do that also someday.
Forum: Programming 2020-07-23, 02:42
Replies: 14
Views: 1,153
Posted By bsquared
Agreed, it's not a good benchmark. The OP asked...

Agreed, it's not a good benchmark. The OP asked for a way to multiply 64-bit unsigned ints and he now has several things to try. I assumed he will use them in his application to figure out which is...
Forum: Programming 2020-07-22, 15:48
Replies: 14
Views: 1,153
Posted By bsquared
As far as I can see from objdump, yes (except the...

As far as I can see from objdump, yes (except the one usage of mulx).
Forum: Programming 2020-07-22, 14:56
Replies: 14
Views: 1,153
Posted By bsquared
Yeah, macros may integrate better into the rest...

Yeah, macros may integrate better into the rest of the code.

However, for this simple benchmark loop:

for (i = 0; i < 1000000000; i++)
{
c = mulx64(a, b, &d);
a = c;
b = d;
}
Forum: Programming 2020-07-22, 13:25
Replies: 14
Views: 1,153
Posted By bsquared
Try: __inline uint64_t mul64(uint64_t x,...

Try:
__inline uint64_t mul64(uint64_t x, uint64_t y, uint64_t* hi) {
__asm__(
"mulq %3 \n\t"
: "=&a"(x), "=&d"(y)
: "0"(x), "1"(y)
: "cc"
);

*hi...
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