Thread: Reservations
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Old 2010-11-07, 13:55   #3
Raman's Avatar
"Mr. Tuch"
Dec 2007
Chennai, India

23518 Posts

I am putting it in another way, it is not sieving, but linear algebra,
that takes up with much longer time. For example for 5,415+ sieving
took only 30 days, but that linear algebra took upto 40 days of time.
By the time linear algebra was going on for 5,415+ I finished off with
that sieving activity for three numbers (2,1910M 2,2226L 2,2238L). 5,415+
sieving required upto 190M range of special-q in order to build up with that
14.3M sized matrix. 2,1910M 2,2226L 2,2238L on the whole required upto
290M range of special-q with that help of gnfs-lasieve4I15e lattice
siever from that GGNFS suite.

This longer Linear Algebra time is because of the fact that I parallelize
sieving with upto 150 cores, but I make use of only 4 cores for Linear
Algebra, anything more than that would be wasteful, since it hardly
improves up with that Linear Algebra speed. Instead, I could make use
of rest of resources for sieving with some other number. I make use of
that msieve hyperthreading facility, of course, with that msieve version
1.43 for that Linear Algebra.

I am sure that Linear Algebra would be much faster enough upon a
core i7 processor, but all processors that I make use of are only Core 2
Duo, Core 2 Quad processors. For future jobs, I will make use of that
msieve MPI interface for that linear algebra, but for current linear algebra
jobs, it is not needed up. The duration of linear algebra will strongly
depend upon that utilization of MPI interface, but I would hope that it
would be certainly be much faster enough than mere hyperthreading
upon four cores. That 4 core hyperthreading with msieve v1.43 requires
upto 19 days for a 10M sized matrix, 38 days for that of a 14.14M matrix,
expecting around 76 days for that of a matrix with 20M dimensions.

I wish to say that I reserve numbers depending only upon my resources.
There have been instances when 2 or 3 linear algebra jobs have run in
parallel, each utilizing only upto 4 cores. Suppose that each sieving takes
only upto 20 days, every 20 days I have to reserve one number, instead
I could do so with some collectively. Please understand that it is a rather
big enough pipelining for that tasks of factoring with numbers.

The numbers that I work upon, quartics, had not been in demand before.
I see that the low hanging fruits, numbers, in 2010 (SNFS sextic difficulty
< 270, SNFS quartic difficulty < 230, that for GNFS difficulty < 180) have
been exhaustively reserved and then factored. Is it due to my Wiki tables?
Let me add that I consulted with you and then left some numbers for you.
It is someone else who actually picked up all those other numbers. Please
don't blame me. I decided to do so with that smaller-but-needed number
2,1910M at first, before 2,2226L 2,2238L, that's why it takes up with much
longer time for Linear Algebra. If it was so that other way, then certainly
that 2,2226L 2,2238L would have been finished off by now itself. It is a
13.6M matrix for that number 2,1910M, by using SNFS quartic of difficulty
size 229, of course.

Finally, I wish to say that the quartics are not as hard as you expect. For
example, for 2,2334M (snfs quartic difficulty = 234 digits) according to that
number size, for sieving, I would anticipate around 220M range of rational side
special-q. This can be done so within about 30 days; then expect about
16M matrix for that linear algebra (just a prediction, simply). Similar to that
of a sextic 256. Sieving for that number 2,2334M is being half-way done up through,
within around 20 days, I should rather start up with my next number for that sieving
exercise. Wouldn't you mind to receive a new factor with a gap for every
20 days (2,1910M by mid-November, 2,2226L 2,2238L by late November or
early December, rather that way)... Why is it that you actually attack up with
only about my current set of reservations, but not previous cases at all? I have
been rather reserving up with about 4 or 5 numbers everytime, since the
start of this year 2010. These current five numbers are my ultimate targets,
thus they will be my last set of reservations.

Why should you get so serious about all these things? After all, this is
actually being done only for fun. It is an exciting hobby, this factoring
numbers have provided me up with lot of fun during past 3 years. It is
neither being any type of commercial work, as well, nor any sort of academic
project with some deadline, that is to be published, that kind it is up so,
thus is that this type of work that is being done.

Last fiddled with by Raman on 2010-11-07 at 14:43
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