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Forum: Puzzles 2020-08-06, 20:42
Replies: 27
Views: 850
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: 27
Views: 850
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: 27
Views: 850
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: 596
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: 27
Views: 850
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: 13
Views: 317
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: 5,805
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: 583
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: 583
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: 583
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: 583
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...
Forum: YAFU 2020-07-10, 01:14
Replies: 2
Views: 269
Posted By bsquared
Yes, use -pretest

Yes, use -pretest
Forum: Factoring 2020-06-29, 23:11
Replies: 10
Views: 783
Posted By bsquared
For the C100, this is not true; or at least, it...

For the C100, this is not true; or at least, it is close enough to be worth discussing. For the others, of course you're right. But everyone discussing here knows that already; we are optimizing...
Forum: Factoring 2020-06-29, 14:10
Replies: 10
Views: 783
Posted By bsquared
Thanks! I have also been tinkering with the...

Thanks!

I have also been tinkering with the three large prime variation during this pandemic. I've mostly been focused on seeing if I can make QS faster in the upper end of the size range where...
Forum: Factoring 2020-06-28, 03:06
Replies: 10
Views: 783
Posted By bsquared
Congratulations, that's quite a feat! Can...

Congratulations, that's quite a feat!

Can you give a few more details? What were the large prime bounds? Do you have any more statistics on the cycles, e.g., the percentage that used a TLP? ...
Forum: Puzzles 2020-06-25, 19:21
Replies: 16
Views: 1,653
Posted By bsquared
It is yafu starting from a r381 (wip-branch).

It is yafu starting from a r381 (wip-branch).
Forum: Puzzles 2020-06-25, 13:25
Replies: 16
Views: 1,653
Posted By bsquared
>> x=2^7* 5 * 23 * 127 * 659 * 53323 * 1876187 *...

>> x=2^7* 5 * 23 * 127 * 659 * 53323 * 1876187 * 97544836889 * 665320793909
7998766649128898059663516612687535453720960
>> totient(x)
3031634148236289733373855928919180891127808
>> sigma(x,1)-x...
Forum: Miscellaneous Math 2020-06-23, 20:48
Replies: 59
Views: 1,290
Posted By bsquared
I agree with the first but my take on his...

I agree with the first but my take on his "explanation" so far is that BillyB(x,0) = x. i.e., a thing of size x cut zero times remains size x. So BillyB(0,0) = 0 by that definition.

[edit]
but...
Forum: Msieve 2020-06-16, 19:52
Replies: 2
Views: 222
Posted By bsquared
Yeah, I ran across this and came up with this...

Yeah, I ran across this and came up with this fix:
https://www.mersenneforum.org/showpost.php?p=540947&postcount=81

I suspect the problem comes about because of this from the gmp changelog:

...
Forum: YAFU 2020-06-16, 16:08
Replies: 14
Views: 1,025
Posted By bsquared
The CADO-as-a-black-box approach might not be too...

The CADO-as-a-black-box approach might not be too bad to add to yafu... I really don't want to have to deal with param files, managing different stages, etc. But if someone already has good params...
Forum: Factoring 2020-06-15, 20:28
Replies: 22
Views: 1,283
Posted By bsquared
Yes, exactly. But I'm using 16-bit containers...

Yes, exactly. But I'm using 16-bit containers for everything so overflow is a little trickier to handle. There are actually several different k's used in the p/2^k approximations as primes grow in...
Forum: YAFU 2020-06-15, 19:04
Replies: 14
Views: 1,025
Posted By bsquared
I saw this too. I think it has to do with blank...

I saw this too. I think it has to do with blank lines in the .ini. I changed the ReadINI function to ignore these but the writeINI function that is called as part of tune did not get changed and...
Forum: YAFU 2020-06-15, 18:51
Replies: 14
Views: 1,025
Posted By bsquared
In my mind, the .ini file should be used to set...

In my mind, the .ini file should be used to set *permanent* parameters. Things that you always need (for example the ecm path, ggnfs binary folder, and ecm pretesting preferences). Anything in the...
Forum: Factoring 2020-06-15, 17:14
Replies: 22
Views: 1,283
Posted By bsquared
By the way, I would recommend ignoring most of...

By the way, I would recommend ignoring most of the optimization stuff I talked about until you address other things. I posted them mostly for reference. Till's list of things in post 15 and 16 are...
Forum: Factoring 2020-06-15, 16:14
Replies: 22
Views: 1,283
Posted By bsquared
Yafu uses a similar method, with the following...

Yafu uses a similar method, with the following optimizations:

1) small primes (less than 256) are not sieved. A "zeroth" pass trial divides candidates by these small primes and there is a second...
Showing results 1 to 25 of 1000

 
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