specialfunctions: generalize gamma precision

[perazz]

Fix #964.

gamma functions always require quad-precision even when not WITH_QP.

Propose to: instead of hard-coded, the KINDs are taken from the lists of available ones.
Because they're sorted with increasing accuracy, generate all accuracies except the last one

• for single precision: the i+1-th accuracy is used.
• for all others: the maximum available accuracy is used (because when xdp is available, it is not enough to guarantee accuracy for dp evaluation: qp is always needed if present).

This is a more generalized version than #967.

cc: @jvdp1 @jalvesz @loiseaujc @osada-yum

[perazz]

The CI builds have an issue in complex gamma functions, they have a relative error ~1e-12 with the requested tolerance of ~1e-13. This does not happen on my local setup, it may be related to using extended precision internally rather than quadruple-precision

[jvdp1]

Thank you @perazz . I like this solution. Smart approach IMO.

[osada-yum]

fpm build fails without --with_qp in my environment

There is something wrong with calling l_gamma using 1.0_dp.

Console

(...) denotes unnecessary lines

 $ python3 config/fypp_deployment.py
 $ /usr/bin/gfortran --version
GNU Fortran (Ubuntu 12.3.0-1ubuntu1~22.04) 12.3.0
Copyright (C) 2022 Free Software Foundation, Inc.
This is free software; see the source for copying conditions.  There is NO
warranty; not even for MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.
 $ LANG=C fpm build --compiler="/usr/bin/gfortran" --flag="" --verbose
(...)
[ 12%] stdlib_specialfunctions_gamma.
 + /usr/bin/gfortran -c ././src/temp/stdlib_specialfunctions_gamma.f90  -cpp -Wall -Wextra -fPIC -fmax-errors=1 -g -fcheck=bounds -fcheck=array-temps -fbacktrace -fcoarray=single -fimplicit-none -Werror=implicit-interface -ffree-form -DMAXRANK=7 -I././include -J build/gfortran_128FBD428609BDB6 -Ibuild/gfortran_128FBD428609BDB6 -o build/gfortran_128FBD428609BDB6/stdlib/src_temp_stdlib_specialfunctions_gamma.f90.o
././src/temp/stdlib_specialfunctions_gamma.f90:1380:25:

 1380 |                     a = (1 - p - n / 2) * x
      |                         1
Warning: Possible change of value in conversion from INTEGER(8) to REAL(4) at (1) [-Wconversion]
(Warnings...)
././src/temp/stdlib_specialfunctions_gamma.f90:809:18:

  809 |             res = l_gamma(n + 1, 1.0_dp)
      |                  1
Error: There is no specific function for the generic 'l_gamma' at (1)
compilation terminated due to -fmax-errors=1.
[ 12%] stdlib_specialfunctions_gamma.  done.

././src/temp/stdlib_specialfunctions_gamma.f90:1380:25:

 1380 |                     a = (1 - p - n / 2) * x
      |                         1
Warning: Possible change of value in conversion from INTEGER(8) to REAL(4) at (1) [-Wconversion]
././src/temp/stdlib_specialfunctions_gamma.f90:1409:25:

 1409 |             b = x + 1 - p
      |                         1
Warning: Possible change of value in conversion from INTEGER(8) to REAL(4) at (1) [-Wconversion]
(Warnings...)
././src/temp/stdlib_specialfunctions_gamma.f90:809:18:

  809 |             res = l_gamma(n + 1, 1.0_dp)
      |                  1
Error: There is no specific function for the generic 'l_gamma' at (1)
compilation terminated due to -fmax-errors=1.
<ERROR> Compilation failed for object " src_temp_stdlib_specialfunctions_gamma.f90.o "
<ERROR> stopping due to failed compilation
STOP 1

[perazz]

Yes @osada-yum: I did not notice log_gamma would internally use the default real, log_factorial would use real(dp) (that requires qp available).

I have now generalized them too.

[osada-yum]

Thank you @perazz.
I can now compile stdlib_specialfunctions_gamma.f90 without issues.
However, I'm encountering errors related to complex(dp) in both example_gamma.f90 and example_log_gamma.f90.
Without quad precision, functions gamma and log_gamma do not have kinds about complex(dp) :: z1(e.g. print *, gamma(z1) and print *, log_gamma(z1)).
Please remove those lines about z1.
Once those lines are removed, everything builds successfully. Thank you!

build log in example/specialfunctions_gamma/example_gamma.f90

 + /usr/bin/gfortran -c example/specialfunctions_gamma/example_gamma.f90  -cpp -Wall -Wextra -fPIC -fmax-errors=1 -g -fcheck=bounds -fcheck=array-temps -fbacktrace -fcoarray=single -fimplicit-none -Werror=implicit-interface -ffree-form -DMAXRANK=7 -I././include -J build/gfortran_128FBD428609BDB6 -Ibuild/gfortran_128FBD428609BDB6 -o build/gfortran_128FBD428609BDB6/stdlib/example_specialfunctions_gamma_example_gamma.f90.o
example/specialfunctions_gamma/example_gamma.f90:35:10:

   35 |   print *, gamma(z1)
      |          1
Error: Generic function 'gamma' at (1) is not consistent with a specific intrinsic interface
[ 30%]              example_gamma.f90  done.

example/specialfunctions_gamma/example_gamma.f90:35:10:

   35 |   print *, gamma(z1)
      |          1
Error: Generic function 'gamma' at (1) is not consistent with a specific intrinsic interface

build log in example/specialfunctions_gamma/example_log_gamma.f90 after removing those lines

 + /usr/bin/gfortran -c example/specialfunctions_gamma/example_log_gamma.f90  -cpp -Wall -Wextra -fPIC -fmax-errors=1 -g -fcheck=bounds -fcheck=array-temps -fbacktrace -fcoarray=single -fimplicit-none -Werror=implicit-interface -ffree-form -DMAXRANK=7 -I././include -J build/gfortran_128FBD428609BDB6 -Ibuild/gfortran_128FBD428609BDB6 -o build/gfortran_128FBD428609BDB6/stdlib/example_specialfunctions_gamma_example_log_gamma.f90.o
example/specialfunctions_gamma/example_log_gamma.f90:32:10:

   32 |   print *, log_gamma(z1)
      |          1
Error: Generic function 'log_gamma' at (1) is not consistent with a specific intrinsic interface
[  1%]          example_log_gamma.f90  done.

example/specialfunctions_gamma/example_log_gamma.f90:32:10:

   32 |   print *, log_gamma(z1)
      |          1
Error: Generic function 'log_gamma' at (1) is not consistent with a specific intrinsic interface

[osada-yum]

Thank you @perazz.
I can now build stdlib without quadruple precision.

[jalvesz]

LGTM @perazz

[perazz]

Thank you @jvdp1 @jalvesz, let us wait a bit longer, and then we can merge imho.