handle permutations in S_n with n > 2^16

[edgarcosta]

This resolves #39998, as the issue is gap having small and large permutations:
https://github.com/gap-system/gap/blob/f0b438db8fa5786d19975e6040076fd46b08bd85/src/permutat.h#L18-L26

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• The description explains in detail what this PR is about.
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• I have created tests covering the changes.
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[saraedum]

I guess the failing tests have nothing to do with these changes. If so, feel free to set this to positive review.

[tscrim]

LGTM except I have one question: did you look at the memory usage of your doctest? Does it require a lot of memory?

[edgarcosta]

In theory it just needs to allocate an array 2**17 of int32_t, but something else is going on behind the scenes.
Nonetheless, in practice the memory usage jumps by 112 MB

>>> (310099968 - 192577536)/1024.**2
112.078125

via:

/usr/bin/time -lh ./sage -c ""                                                                                                                                                          
           192577536  maximum resident set size
                   0  average shared memory size
                   0  average unshared data size
                   0  average unshared stack size
               36503  page reclaims
                 110  page faults
                   0  swaps
                   0  block input operations
                   0  block output operations
                   0  messages sent
                   0  messages received
                   0  signals received
                  10  voluntary context switches
                 158  involuntary context switches
           116133618  instructions retired
            47630290  cycles elapsed
             1458488  peak memory footprint

vs

/usr/bin/time -lh ./sage -c "SymmetricGroup(2**17)((2**16,2**17-1))._libgap_()" 
	1.00s real		0.52s user		0.25s sys
           310099968  maximum resident set size
                   0  average shared memory size
                   0  average unshared data size
                   0  average unshared stack size
               48026  page reclaims
                 114  page faults
                   0  swaps
                   0  block input operations
                   0  block output operations
                   0  messages sent
                   0  messages received
                   0  signals received
                  13  voluntary context switches
                7762  involuntary context switches
           116675395  instructions retired
            46895391  cycles elapsed
             1491280  peak memory footprint

[dimpase]

should this extreme high RAM test be marked as # long time ?

[edgarcosta]

I added # long time (100 mb)

and tried to make the example less memory intensive, but didn't succeed on that front:

sage: from resource import *
sage: print(getrusage(RUSAGE_SELF)[2]/1024.**2)
220.046875000000
sage: SymmetricGroup(2**16+1)((2**16,2**16+1))._libgap_()
(65536,65537)
sage: print(getrusage(RUSAGE_SELF)[2]/1024.**2)
319.703125000000

[dimpase]

can't you make sparse permutations in GAP? (probably not, as I vaguely recall). If not, then any test is bound to be RAM-expensive.

[edgarcosta]

There are small and large permutations, both stored in the one line representation, see
https://github.com/gap-system/gap/blob/master/src/permutat.h

[dimpase]

OK

[edgarcosta]

Thank you