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Old 2007-02-27, 19:33   #3
Thomas11's Avatar
Feb 2003

3·5·127 Posts

The final one is a bit different.
Since the Nash algorithm is quite slow when computing large ranges (e.g. millions) of k, one needs a faster tool. Therefore I implemented an ordinary sieve for p up to 512 and a smaller n range of only 1-1000. Due to precomputation of the "reversed orders of n" the whole calculation can be done in cache memory and is therefore really fast (e.g. about 3000 k/sec on a 1.7 GHz P4).

So one can use multi5 for a fast pre-scanning of a k-range and then do some sorting on the results and run the "good ones" through nash.

For some historic reason it is written in Fortran (and lacks any comments) and there are no command line options. Therefore you need to edit the steer.txt file for specifying the k-range and a print condition. The latter is necessary since otherwise the sieve would produce hundreds of megabytes of output within minutes...

The example steer.txt file reads:
32000000025             KMIN
32001000000             KMAX
30                      KSTEP
600                     minimum weight for printing
You may skip the text comments at the right. The printing condition means, that the k is only printed when the weight is higher or equal to the specified value (e.g. weight>=600 in the example). Note, that we use a smaller n-range (1-1000), therefore 600 is a rather high weight. The weights are roughly one tenth of the Nash weights. Also note the restriction of k<2^63 (signed long).

Usage is simply:
for the example steer.txt file you will get:
        32000060235  609
        32000107425  622
        32000193225  612
        32000315325  605
        32000497485  640
        32000553585  618
        32000703735  674
        32000816445  601
        32000982585  622
If you want to store the results, you can simply redirect the output to a file, e.g.:
multi5 > my_ks.txt
Of course it works the some way for nash and mnash...
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Last fiddled with by Thomas11 on 2007-02-27 at 19:48
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