fixes for NAG natfor

[dimpase]

this is resolving a part of issues in scipy/scipy#13222

[ThemosTsikas]

The =unifyprecision tool in nagfor can do these automatically but it will not work on files needing preprocessing. One way through is to have all the preprocessing in a simple file that Includes a foo_ser.f90 or a foo_par.f90. To create those you start with just a preprocessing step:
nagfor foo.f -fpp -otype=F -openmp -o foo_par.f
and then
nagfor =unifyprecision -openmp -dcfuns foo_par.f -o foo_par.f90

For the serial file
nagfor -otype=F -fpp foo.f -Wp,-U_OPENMP,-P -o foo_ser.f
and then
nagfor =unifyprecision -dcfuns foo_ser.f -o foo_ser.f90

Might need some small fix up after that for Complex-returning functions (eliminate COMPLEX*16 in favour of Complex(Kind=wp))

[dimpase]

@ThemosTsikas - can you comment on the last commit: removing second() in order to avoid dealing with non-strandard etime, and assuming second() is available on Lapack. Is this sound?

[ThemosTsikas]

@ThemosTsikas - can you comment on the last commit: removing second() in order to avoid dealing with non-strandard etime, and assuming second() is available on Lapack. Is this sound?

Yes, provided the subroutine second(t) in Lapack takes a default real argument.

[mckib2]

Removing the second.F files causes 32-bit builds to segfault and best case propagate lots of NaNs (tested on Ubuntu 16 i386 VM), so I'm not sure if we're going to be able to remove those completely

[dimpase]

What blas/lapack are you using on Ubuntu 16 i386 VM ?

[mckib2]

I get the following warning:

/venvs/scipy38/lib/python3.8/site-packages/numpy/distutils/system_info.py:2026: UserWarning: 
    Optimized (vendor) Blas libraries are not found.
    Falls back to netlib Blas library which has worse performance.
    A better performance should be easily gained by switching
    Blas library.

I believe that means I'm using Netlib BLAS/LAPACK?

[dimpase]

I believe that means I'm using Netlib BLAS/LAPACK?

Perhaps you're using an obsolete version of BLAS/LAPCK (Lapack 3.6.0, I suppose)? One way or another, Ubuntu 16 is past EOL, and its gfortran (4.5 or so) is long past EOL, too. Surely one can find an even older system on which this will break...