Non-repeatable results when using OpenMP

[mancellin]

First, thank you very much for sharing your code, it is very helpful to me!

I ran into some issues when using your module in parallel with OpenMP (on Ubuntu 22.04 with gfortran 11).
Here is a minimal example: capytaine@fc0547e
Running this program leads to different results each time:

$ ./test_program
  -16.555834740387333       -15.476963986365671       -14.412503912173607       -13.369515798080531       -7.6451963635261464       -11.375288243750948       -10.437096348107897       -9.5463680118490171       -1.1665022407159018       -7.9295866320209587
$ ./test_program
  -17.991076320788107       -14.013290014374100       -12.149123395809470       -9.0501859811610483       -7.5840537209765362       -5.4395058216609842       -4.2437142185190195       -2.9313920411413523       -6.4453993960240510       -7.3892014684943774E-002

unless, the OpenMP parallelization is turned off:

$ OMP_NUM_THREADS=1 ./test_program
  -20.365766434529149       -15.476963986365671       -12.149123395809470       -9.5052157061777596       -7.2962058749427481       -5.4395058216609842       -3.9409000581548979       -2.9313920411413523       -2.9948334814816207       -9.6354549626564303
$ OMP_NUM_THREADS=1 ./test_program
  -20.365766434529149       -15.476963986365671       -12.149123395809470       -9.5052157061777596       -7.2962058749427481       -5.4395058216609842       -3.9409000581548979       -2.9313920411413523       -2.9948334814816207       -9.6354549626564303

A possible explanation for this issue is the use of global variables (GF_alpha, GF_beta, etc.) which might be shared between OpenMP threads. I will test that.

[mancellin]

A possible explanation for this issue is the use of global variables (GF_alpha, GF_beta, etc.) which might be shared between OpenMP threads. I will test that.

Indeed, it seems to fix the issue: capytaine@7e9f925