Commit 9f039a3b authored by GAUDRY Pierrick's avatar GAUDRY Pierrick
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polyselect for dlp240

parent 96779fe8
......@@ -16,9 +16,54 @@ commands as well.
## Searching for a polynomial pair
TODO: complete here...
We searched for a polynomial pair ``à la Joux-Lercier'', using the
program `dlpolyselect` of `cado-nfs`, with parameters `-bound 150`,
`-degree 4` and `-modm 1000003`. We tried also to use search for a skewed
pair of polynomials with the `-skewed` option, but this did not seem to
give a better polynomial for a fixed amount of time compared to plain
flat polynomials.
A typical command line for an individual work unit was:
$CADO_BUILD/polyselect/dlpolyselect -N 124620366781718784065835044608106590434820374651678805754818788883289666801188210855036039570272508747509864768438458621054865537970253930571891217684318286362846948405301614416430468066875699415246993185704183030512549594371372159029285303 -df 4 -dg 3 -area 2.0890720927744e+20 -Bf 34359738368.0 -Bg 34359738368.0 -bound 150 -modm 1000003 -modr 42 -t 8
where `-modr 42` gives the index of the task, and all tasks between 0 and
1000002 have been run.
And the winner is the [`dlp240.poly`](dlp240.poly) file:
A ranking between all the computed pairs was based on MurphyE as computed
by `dlpolyselect` with the parameters
which are the default parameters automatically computed by the server
script `` that we used for distributing the computation. These
are perhaps imprecise, but the ranking is pretty stable when parameters
are changed.
This polynomial selection took place on a variety of computer resources,
but more than half of it was done on the `grvingt` cluster that we take
as a reference. The program was improved during the computation, so it
makes little sense to report the total number of CPU-years really used.
The calendar time was 18 days.
When a node of `grvingt` is fully charged with 8 jobs of 8 threads, then
one task as above takes 1200 wall clock seconds on average to be
processed. This must be multiplied by the 4 physical cores it uses to get
the number of core-seconds per modr value. And we have 10^6 of them to
process. This adds-up to 152 core.years for the whole polynomial selection.
Some sample-sieving was done on the top-100 polynomials according to
MurphyE. Although there is a clear correlation between the efficiency of
a polynomial pairs and it MurphyE, the ranking is definitely not perfect.
In particular, the number-one polynomial pair according to MurphyE finds
10% less relations than the best ones.
Additional sample-sieving was performed on the few best candidates. With
a test on 128,000 special-q, 3 polynomials could not be separated.
We ended-up using the following [`dlp240.poly`](dlp240.poly):
cat > dlp240.poly <<EOF
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