A point shared by at least 2 groups has 2 positions in the internal communicator

[Algiane]

Issue description

When build in debug mode, ParMmg fails with the following error message:

## Error: PMMG_check_intNodeComm: rank <n>:
       A point shared by at least 2 groups has 2 positions  (<k1> and <k2>) in the internal communicator (dist = <dist>):
  ...

Steps to reproduce the issue

• environment:
  • ubuntu:22.04 or ubuntu:20.04
  • openMPI:4.0.3 (bug has also been reproduced with mpich)
  • gcc-9.4.0
  • x86_64 or aarch64 architecture
• checkout the commit c7549f120 of ParMmg. It should use the commit 2263f92c of Mmg;
• build ParMmg in Debug mode (-DCMAKE_BUILD_TYPE=Debug) with USE_POINTMAP enabled (default behaviour) and USE_SCOTCH disabled; ⚠️ Enabling Scotch solves the issue!
• enable the continuous integration tests (-DBUILD_TESTING=ON`)
• run the multidom_wave-8 test (that succeed), then the multidom_wave-8-rerun test that should fail.

Investigation

The error is linked to inconsistencies when sorting the coor_list array that contains the list of the coordinates of the points stored in the internal communicators and when travelling this sorted array to remove the duplicated points (https://github.com/MmgTools/ParMmg/blob/beb4147b7b29a2891e1a55745ff95863e93bcc0d/src/communicators_pmmg.c#L1788-L1811):

• the compare function provided to qsort compares the values to within a epsilon thus, x may me evaluated as equal to x+ε and x+ε evaluated equal to x+2ε, leading to an erroneous sort: x < x+2ε < x+ε. When travelling the array to delete the duplicated point, as the comparison function evaluates x as different from x+2ε, the point x+ε is not deleted, even if it should be evaluated as a duplication of x. In practice, we found values exactly identics separated by other values in the sorted array...
• using exact comparisons inside qsort (and approximated comparisons for the duplication detection) doesn't work either:
  • as we compare double precision values, 2 values with the same x-coordinate mais be evaluated as differents due to the epsilon machine (noted ε_m) leading, again, to an erroenous sort. Lets take 3 points with the following coordinates : A ( x,y); B(x,y_2>>y) and C (x+ε_m,y). C is a duplication of A while B is a different point (y is greater). We end up with the following order : A, B, C
  • as B is different from A, again, the duplication removal fails