Migrate off GSL onto fortnum

[krystophny]

Migrate MEPHIT off GSL onto fortnum, the single numerical core. Consumers depend
on fortnum directly (not the libneo math-kit). This supersedes the
libneo-routed PR #26.

What changed

Fortran (src/mephit_pert.f90)

• Drop the bind(C) interface to gsl_sf_bessel_In_array and call
  fortnum_special bessel_in_array in kilca_vacuum_fourier.
• fortnum fills I_n(0:nmax), so the order |pol_mode|-1 (which is -1 when
  pol_mode = 0) is recovered via I_{-n}(x) = I_n(x). Call-site values are
  unchanged.

C

• hyper1F1.c: gsl_integration_qag (rule GSL_INTEG_GAUSS21) becomes
  fortnum_integrate_qag(..., key=21, ..., ctx=&qp), threading the quadrature
  parameters through the C ABI context pointer; gsl_sum_levin_u_* becomes
  fortnum_levin_u_accel. Adds #include <float.h> for DBL_EPSILON,
  formerly pulled in transitively by the GSL headers.
• mephit_fem.c: gsl_integration_glfixed_* becomes
  fortnum_gauss_legendre_ab(order, 0.0, 1.0, ...).
• mephit_util.c / mephit_run.c: remove the GSL error-handler plumbing
  (gsl_errno_msg, gsl_set_error_handler); fortnum reports status via return
  codes.

Build

• Drop find_package(GSL) and the FGSL pickup from CMakeLists.txt /
  cmake/SetupCODE.cmake.
• Fetch fortnum with FetchContent from git@github.com:lazy-fortran/fortnum.git
  (GIT_TAG main), guarded by if(NOT TARGET fortnum) so a transitive pull
  through libneo does not redeclare the target. Link the fortnum target; add
  ${fortnum_SOURCE_DIR}/include to the C/C++ include path for fortnum.h.

FFTW (src/fftw3.f90) and the netlib zeroin / d1mach routines are not GSL
and are untouched. GSL is fully removed: no find_package(GSL), no GSL::gsl,
no gsl/* includes, no gsl_ symbols in libmephit.so.

This migration required forwarding an opaque user context through fortnum's
callback-driven C ABI (the header documented it as forwarded but the wrappers
hardcoded NULL). Fixed upstream in fortnum
(lazy-fortran/fortnum@dc277b5) and verified there before consuming it here.

Verification

GSL fully removed from the source and the linked library:

$ rg -n -i 'gsl' src/ CMakeLists.txt cmake/SetupCODE.cmake | grep -vi fgsl
CMakeLists.txt:102:### fortnum: numerical core replacing the former GSL routines. ...
$ ldd lib/libmephit.so | rg -i gsl        # no match
$ nm -D lib/libmephit.so | rg -i gsl      # no match

Full CMake configure (fortnum fetched over SSH, no GSL):

$ cmake -S . -B build -G Ninja
...
-- === Dependency Detection Complete ===
-- Performing Test FORTNUM_HAVE_HEAP_TRAMPOLINES - Success
-- Configuring done (13.8s)
-- Generating done (0.1s)
-- Build files have been written to: build

Full build (library + all executables), green:

$ cmake --build build -j$(nproc)
...
[86/91] Linking Fortran static library lib/libneo.a
[88/91] Linking CXX shared library lib/libmephit.so
[89/91] Linking Fortran executable bin/mephit_test.x
[90/91] Linking C executable bin/mephit_run.x
[91/91] Linking Fortran executable bin/mephit_post.x
$ ls bin/
mephit_post.x  mephit_run.x  mephit_test.x
$ nm -D lib/libmephit.so | rg 'fortnum_integrate_qag|fortnum_gauss_legendre_ab|fortnum_levin_u_accel'
0000000000115940 T fortnum_gauss_legendre_ab
0000000000115680 T fortnum_integrate_qag
0000000000115740 T fortnum_levin_u_accel
$ ./bin/mephit_test.x
ERROR STOP expected path to config file as first parameter   # loads, then exits on missing arg

Numerical equivalence of the migrated routines:

1F1(1;b;z) via the fortnum QAG path vs an independent Kummer-series reference
(b = 2 + 0.5i, z = 0.3 - 0.2i):

quad 1F1(1;b;z) = 1.11595703944 + -0.151544119902i      # fortnum_integrate_qag
series 1F1(1;b;z) = 1.11595703944 + -0.151544119902i    # independent reference

Bessel index logic in kilca_vacuum_fourier vs scipy iv, including the
pol_mode = 0 case that needs I_{-1} = I_1:

pol_mode=0  I_{m-1,m,m+1}=  0.797329314979  1.469277797944  0.797329314979
pol_mode=1  I_{m-1,m,m+1}=  1.469277797944  0.797329314979  0.242617313361
pol_mode=2  I_{m-1,m,m+1}=  0.797329314979  0.242617313361  0.050814504638
# scipy.special.iv reference, x = 1.3:
pol_mode= 0 I_{m-1,m,m+1}= 0.7973293149792691 1.469277797944251 0.7973293149792691
pol_mode= 1 I_{m-1,m,m+1}= 1.469277797944251 0.7973293149792691 0.2426173133607603
pol_mode= 2 I_{m-1,m,m+1}= 0.7973293149792691 0.2426173133607603 0.05081450463846809

5-point Gauss-Legendre on [0,1] from fortnum_gauss_legendre_ab integrates
1, x, x^2 exactly (matching the former GSL glfixed rule):

int 1 = 1.000000000000 (exp 1)
int x = 0.500000000000 (exp 0.5)
int x^2 = 0.333333333333 (exp 0.333333333333)

Upstream fortnum test suite after the ctx-ABI fix, including the C smoke test:

$ ctest --output-on-failure
100% tests passed, 0 tests failed out of 67
Total Test time (real) =   0.42 sec

Supersedes #26.

[krystophny]

This monolithic migration is superseded by an atomic, stacked re-cut off main, with the FFTW migration added. One PR per dependency or concern, each individually reviewable; merged in order they compose to the full migration:

• Replace GSL Bessel I_n with fortnum (1/5) #29 Replace GSL Bessel I_n with fortnum (1/5) - base: main. Drops gsl_sf_bessel_In_array; wires fortnum via FetchContent at tag a7faa3c.
• Replace GSL quadrature and Levin sum in hyper1F1 with fortnum (2/5) #30 Replace GSL quadrature and Levin sum in hyper1F1 with fortnum (2/5) - base: Replace GSL Bessel I_n with fortnum (1/5) #29. Drops gsl_integration_qag and gsl_sum_levin_u_*.
• Replace GSL fixed-rule quadrature and error handler with fortnum (3/5) #31 Replace GSL fixed-rule quadrature and error handler with fortnum (3/5) - base: Replace GSL quadrature and Levin sum in hyper1F1 with fortnum (2/5) #30. Drops gsl_integration_glfixed_* and the GSL error handler; after this no source references GSL.
• Replace FFTW with fortnum fft_c2c and drop the FFTW dependency (4/5) #32 Replace FFTW with fortnum fft_c2c and drop the FFTW dependency (4/5) - base: Replace GSL fixed-rule quadrature and error handler with fortnum (3/5) #31. Drops src/fftw3.f90, cmake/FindFFTW.cmake, and the FFTW link; fixes the executable link that was broken on main by the empty FFTW_LIBRARIES.
• Drop the GSL find_package, the fgsl path, and d1mach (5/5) #33 Drop the GSL find_package, the fgsl path, and d1mach (5/5) - base: Replace FFTW with fortnum fft_c2c and drop the FFTW dependency (4/5) #32. Removes find_package(GSL), the GSL::gsl link, the fgsl hint, and src/external/d1mach.f (d1mach(4) becomes epsilon(1.0d0)).

The stack tip builds clean: libmephit.so plus all three executables link, with zero GSL, FFTW, AMOS, and SLATEC symbols in the library and no GSL or FFTW dynamic dependency in the binaries. fortnum's own suite (68 tests) passes at tag a7faa3c. PRs 1 to 3 are drafts because their tips do not link the executables standalone (the empty FFTW_LIBRARIES link, also broken on main, is fixed in PR 4). Leaving this PR open for a human to close.

[krystophny]

Split into atomic per-aspect PRs #29-#33 (bessel, 1F1, C-quadrature, FFTW, plumbing). Closing in favor of the atomic stack.