Performance improvement by using private declaration for gfortran

[hiker]

During our training, one of my team members added a private declaration for all module-inlined kernel, and got a significant speedup. I verified this, so we have now this confirmed for gfortran 8.4, 11.4, and 14-something. Timing (of my game-of-life test in the training):

No inlining (-O3):                                      38.933 seconds
(module) inlining:                                      27.603 seconds
(module) inlining + private declaration of all kernels: 10.159 seconds

Looking at the assembly output indicates that without the private declaration only two of four kernels are inlined. Without private:

~/work/psyclone/tutorial/training/gocean/2.6-GameOfLife-fuse/solution$ gfortran -S  -c -O3 -I/home/joerg/work/psyclone/tutorial/training/gocean/gol-lib -I/home/joerg/work/psyclone/external/dl_esm_inf/finite_difference/src time_step_alg_mod_psy.f90
~/work/psyclone/tutorial/training/gocean/2.6-GameOfLife-fuse/solution$ grep call time_step_alg_mod_psy.s 
	call	__psy_time_step_alg_mod_MOD_compute_die_code
	call	__psy_time_step_alg_mod_MOD_count_neighbours_code
~/work/psyclone/tutorial/training/gocean/2.6-GameOfLife-fuse/solution$ 

So there are still two calls left. Adding the private directive (details below):

~/work/psyclone/tutorial/training/gocean/2.6-GameOfLife-fuse/solution$ gfortran -S  -c -O3 -I/home/joerg/work/psyclone/tutorial/training/gocean/gol-lib -I/home/joerg/work/psyclone/external/dl_esm_inf/finite_difference/src time_step_alg_mod_psy.f90
~/work/psyclone/tutorial/training/gocean/2.6-GameOfLife-fuse/solution$ grep call time_step_alg_mod_psy.s 
~/work/psyclone/tutorial/training/gocean/2.6-GameOfLife-fuse/solution$ 

Test case: https://github.com/stfc/PSyclone/tree/1623_add_training/tutorial/training/gocean/2.6-GameOfLife-fuse/solution
(just modify the Makefile to use inline.py instead of fuse_loops.py).
Then manually add:

    private:: count_neighbours_code, compute_born_code, compute_die_code, combine_code

When also using fuse, it gets even worse: fusing the first three loops (the fourth one can't) with inlining results in a runtime of 30 seconds. Adding the above private declarations brings down the runtime to 7.5 seconds.