Parameter Underestimation

[R.D. Silverman]

I am currently sieving 2,2166L.

I have been slowed down somewhat by electrical system
shutdowns and network shutdowns for maintenence.

However, my biggest slowdown has been a mis-estimate for
the input parameters.

I am using factor base bounds of 86million and 14million for the
rational and algebraic polynomials respectively. I am using 30 bit
large primes for both, and a sieve region of 8K x 16K for each special
q. I had orginally estimated that I would need about 12 million
special q's. I am already at 14 million and have only about 77% of
the needed relations. Further, the yield rate is now quite low: only
about 3.2 relations per q. I am going to have to do quite a bit more
sieving that I anticipated. YECH.

[R.D. Silverman]

I just found an interesting bug in my siever. I discovered it while
making some improvements, including a larger sieve region.

Here is one instance. For special_q = 256300217 with root 137499035,
my lattice reduction routine returned (36738082, 6593) (137499035, 1)

This is not correct. The problem, of course is integer overflow. The
routine uses signed ints.

Of course, since the reduced lattice is wrong, everything that follows is
wrong and no relations get produced.

I had been getting a very low relation yield rate for the larger special q's
on my current factorization. This explains it. I've been losing valid
relations.

I am going to have to change the latred routine to use 64 bit ints.

[R.D. Silverman]

Originally Posted by R.D. Silverman

I just found an interesting bug in my siever. I discovered it while
making some improvements, including a larger sieve region.

Here is one instance. For special_q = 256300217 with root 137499035,
my lattice reduction routine returned (36738082, 6593) (137499035, 1)

This is not correct. The problem, of course is integer overflow. The
routine uses signed ints.

Of course, since the reduced lattice is wrong, everything that follows is
wrong and no relations get produced.

I had been getting a very low relation yield rate for the larger special q's
on my current factorization. This explains it. I've been losing valid
relations.

I am going to have to change the latred routine to use 64 bit ints.

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.

[R.D. Silverman]

Originally Posted by R.D. Silverman

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
siever.

[Batalov]

In redu2.c, the GGNFS/Franke siever uses double in the variant of the code that is used by practically everyone. However, the very latest version has the gmp mpz_t version:
int reduce2(i32_t*,i32_t*,i32_t*,i32_t*,i64_t,i64_t,i64_t,i64_t,double);
int reduce2gmp(i64_t*,i64_t*,i64_t*,i64_t*,mpz_t,mpz_t,double);

@ Note that we dont use lattice reduction to organize sieving with the factor
base primes which are larger than the line length. Instead, we use a method
based on the relation with continued fractions and diophantine approximations.
Therefore, the code contained in this file is not time crtitical.
@(redu2.h@>=
int reduce2(i32_t*,i32_t*,i32_t*,i32_t*,i64_t,i64_t,i64_t,i64_t,double);
int reduce2gmp(i64_t*,i64_t*,i64_t*,i64_t*,mpz_t,mpz_t,double);
 
@ This is done in the straigthforward way. A basis is given by
the fifth to eighth argument (|a0|,|b0|), (|a1|,|b1|). The
reduced basis is written to the addresses given by the first four arguments.
The ninth argument will often be larger than 1 an punishes large |b|.
As a safeguard against numerical instability, the scalar products
are recalculated from the modified vectors after each reduction step and
not updated in a way which would save multiplications. Note again that this
function is not likely time critical for lattice sieving.
The scalar products of the two vector with themselves are called
|a0sq| and |a1sq|. Their scalar product is called |s|.

[jrk]

Originally Posted by R.D. Silverman

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.

At least until you get your siever fixed properly, have you thought about using composite special-q in the range which still works (assuming you've used only prime special-q)?

Assuming you are sieving the special-q on the rational side, I think it should not be too difficult to allow composite special-q's (on the algebraic side it would take more work). Might be worth doing as a quick measure to finish your current job.

[R.D. Silverman]

Originally Posted by jrk

At least until you get your siever fixed properly, have you thought about using composite special-q in the range which still works (assuming you've used only prime special-q)?

Assuming you are sieving the special-q on the rational side, I think it should not be too difficult to allow composite special-q's (on the algebraic side it would take more work). Might be worth doing as a quick measure to finish your current job.

It won't work. Almost all relations found with composite q will be duplicates.
If norm(a + balpha)/(pq) is smooth, it will have been found with either
special_q = p, or special_q = q (or both!)

[R.D. Silverman]

Originally Posted by R.D. Silverman

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
siever.

Does msieve handle lattice points whose coordinates are larger than
single precision ints?

Even if I fix the latred problem, I am still faced with losing valid relations
(c,d) = i * V1 + j * V2, when the multiplications overflow 32 (signed) bits.

[jasonp]

Msieve doesn't have a lattice sieve at all. Both the line sieve and the postprocessing can handle 63-bit signed 'a' and 32-bit 'b' values.

Perhaps the most expedient solution is to use the Kleinjung siever to resieve enough, then postprocess the generated relations into CWI format (which is easy).

[R.D. Silverman]

Originally Posted by jasonp

Msieve doesn't have a lattice sieve at all. Both the line sieve and the postprocessing can handle 63-bit signed 'a' and 32-bit 'b' values.

Perhaps the most expedient solution is to use the Kleinjung siever to resieve enough, then postprocess the generated relations into CWI format (which is easy).

I fixed the latred bug. I need to rebuild my code, and re-install it.

[R.D. Silverman]

Originally Posted by R.D. Silverman

I fixed the latred bug. I need to rebuild my code, and re-install it.

I rebuilt my code. Sort-of. For some &*(@#@& reason, my copy
of Visual Studio at work produces code that seg-faults with
a release (non-debug) version. The debug version runs just fine,
albeit slower. I will need to rebuild everything on my home PC.

I have encountered (and reported on) this problem before.