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Forum: Computer Science & Computational Number Theory 2019-08-05, 01:16
Replies: 45
Views: 17,242
Posted By Happy5214
I forgot to mention that Brent's version is what...

I forgot to mention that Brent's version is what yafu uses, so it's the basis for my earlier tests.

Speed is not really measured by iterations. As Brent established, it's measured by the number of...
Forum: Computer Science & Computational Number Theory 2019-08-04, 04:36
Replies: 45
Views: 17,242
Posted By Happy5214
The rho algorithm is basically dependent on the...

The rho algorithm is basically dependent on the size of the prime [$]p[/$] it finds. The tail length and the cycle length both have expected values of [$]\sqrt{\pi N/8}[/$], where [$]N[/$] is the...
Forum: Computer Science & Computational Number Theory 2019-07-21, 11:29
Replies: 45
Views: 17,242
Posted By Happy5214
Can you post some result comparisons between the...

Can you post some result comparisons between the "[$]z^2[/$]" and "[$]-z^2[/$]" versions of your code? I'm particularly interested in the difference in iterations between the two, if any, because I...
Forum: Computer Science & Computational Number Theory 2019-07-21, 10:00
Replies: 45
Views: 17,242
Posted By Happy5214
[$](p - z^2)^2 = p^2 - 2pz^2 + z^4 \equiv z^4...

[$](p - z^2)^2 = p^2 - 2pz^2 + z^4 \equiv z^4 \pmod{p}[/$], since [$]p^2 - 2pz^2 = p(p - 2z^2) \equiv 0 \pmod{p}[/$].
Forum: Computer Science & Computational Number Theory 2019-07-21, 05:56
Replies: 45
Views: 17,242
Posted By Happy5214
I compared your code to the yafu version with...

I compared your code to the yafu version with [$]p = 135241[/$], where [$]p - 1 = 2^3 \cdot 3 \cdot 5 \cdot 7^2 \cdot 23[/$], and [$]q[/$] an arbitrary 37-digit prime I found in my aliquot logs. Here...
Forum: Computer Science & Computational Number Theory 2019-07-19, 22:49
Replies: 45
Views: 17,242
Posted By Happy5214
Not exactly. The "ending index" is the last index...

Not exactly. The "ending index" is the last index of the sequence the algorithm touches, which is twice the number of iterations for the Floyd family of algorithms. I can't figure out why the last...
Forum: Computer Science & Computational Number Theory 2019-07-19, 21:38
Replies: 45
Views: 17,242
Posted By Happy5214
With those fixes, here are the updated times: ...

With those fixes, here are the updated times:

happy5214@happy5214-desktop:~/rps/progs/test/rho$ time ./restricted -Icomposites.res.txt -c 0 -i 2000 -l 1000
Factor: 3228341
Ending index: 280
...
Forum: Computer Science & Computational Number Theory 2019-07-19, 02:42
Replies: 45
Views: 17,242
Posted By Happy5214
Multipliers don't work if you don't already know...

Multipliers don't work if you don't already know the prime factor. When I multiplied [$]n[/$] by a constant (I chose 32), it consistently found factors of 32 before the desired prime factors of the...
Forum: Computer Science & Computational Number Theory 2019-07-18, 19:23
Replies: 45
Views: 17,242
Posted By Happy5214
Logs from my local GMP-based copies of your...

Logs from my local GMP-based copies of your algorithm (minus the constant scaling) and the yafu algorithm:

happy5214@happy5214-desktop:~/rps/progs/test/rho$ time ./restricted -Icomposites.res.txt...
Forum: Computer Science & Computational Number Theory 2019-07-17, 23:03
Replies: 45
Views: 17,242
Posted By Happy5214
yafu's Brent-based traditional rho algorithm can...

yafu's Brent-based traditional rho algorithm can factor this number in roughly 200k cycle indices (or 7k iterations based on yafu's count), which is significantly faster than the algorithm given here.
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