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Old 2010-09-29, 04:30   #4
R.D. Silverman
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Nov 2003

22×5×373 Posts

Originally Posted by R.D. Silverman View Post
I just realized that there are other problms as well.

We hope that norm(c + d alpha) is smooth. Let v1, v2 be the reduced
lattice row vectors for some special_q. Then (c,d) = i*v1 + j*v2
where (i,j) is a point in the reduced lattice. i and j are bounded by
the size of the sieve region, but for large special_q, it is possible that
eiither i*v1 or j*v2 (or both) may overflow, giving a wrong value for
c and/or d when they are defined as signed 32-bit ints.

I will need to deal with this as well.

Does anyone know if GGNFS uses 64-bits for any/all of these variables?

For 2,2166L, I am now sieving special_q near 250 million. The average yield
is now only about 3 relations/q. A fair fraction of the q's produce no relation
at all. I may need to fix my code, and go back and RESIEVE a large
set of q's that I have already done.
I've been trying to get to sleep without success..... I've been too busy
thinking about the difficulties.

It is clear that I need to fix the lattice reduction. However, the problem
with (c,d) possibly overflowing still remains. It would take a MAJOR
rewrite to allow (c,d) to exceed 32 bits. And the CWI tools can only
handle 30-bit (c,d) as well.

It is also how to proceed with my current effort. I can let the siever
keep running, on ever-larger special q's. But the yield rate will only
get worse. At the current rate I will need to sieve another 6 million
special q's. I have already sieved through 14 million of them.

Or I can fix the latred problems (which will take time) and go back and
resieve q's that have already been done.

I have reserved 2,1870L, but may have to release it until I can fix my
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