Skip to content
GitLab
Menu
Projects
Groups
Snippets
Help
Help
Support
Community forum
Keyboard shortcuts
?
Submit feedback
Contribute to GitLab
Sign in
Toggle navigation
Menu
Open sidebar
cado-nfs
records
Commits
9f039a3b
Commit
9f039a3b
authored
May 27, 2020
by
GAUDRY Pierrick
Browse files
polyselect for dlp240
parent
96779fe8
Changes
1
Hide whitespace changes
Inline
Side-by-side
dlp240/README.md
View file @
9f039a3b
...
...
@@ -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
```
Bf=3.436e+10
Bg=3.436e+10
area=2.089e+20
```
which are the default parameters automatically computed by the server
script `cado-nfs.py` 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
...
...
Write
Preview
Supports
Markdown
0%
Try again
or
attach a new file
.
Attach a file
Cancel
You are about to add
0
people
to the discussion. Proceed with caution.
Finish editing this message first!
Cancel
Please
register
or
sign in
to comment