Fortran function like

[isaacaka]

Add Fortran enzyme_function_like support

Summary

This adds two ways to register a Fortran function as behaving like a
mathematical function known to Enzyme.

use enzyme, only: enzyme_function_like, enzyme_log1p

call enzyme_function_like(log1p_like_function, enzyme_log1p)

The declaration-style alternative is closer to C's static registration:

procedure(log1p_like_function), pointer, private :: &
  fn__enzyme_function_like__log1p => log1p_like_function

This declaration creates a module global that points at
log1p_like_function. Because Fortran cannot construct the equivalent of C’s
statically initialized {function pointer, string pointer} struct the function whose rule is being copied is instead encoded in the global’s name. PreserveNVVM searches for __enzyme_function_like__ and reads log1p from its
suffix.

Trade-offs

• Call-style registration, such as
  call enzyme_function_like(target, enzyme_log1p), simpler and clearer.
  However, every math function name needs a global binding such as
  integer(c_int), bind(C, name="enzyme_math_log1p") :: enzyme_log1p.
  Users can declare missing bindings themselves.

• Procedure-pointer registration doesn't need a binding per function. Its
  less simple and the marker name must be unique, and the rule name
  must fit a Fortran identifier. Names containing punctuation etc won't work

Other things I tried

C-compatible static record

The closest translation of C's { function pointer, string pointer } global
didn't work:

type, bind(C) :: function_like_record
  type(c_funptr) :: target
  type(c_ptr) :: name
end type function_like_record

type(function_like_record), bind(C, name="__enzyme_function_like") :: &
  registration = function_like_record( &
    c_funloc(log1p_like_function), c_loc(log1p_name))

Flang rejects the initialiser because c_funloc and c_loc are not valid
constant initialisation expressions here:

error: Must be a constant value
c_funloc(log1p_like_function), c_loc(log1p_name)

C is able to handle things like the above but Fortran cannot

Passing "log1p" directly

call enzyme_function_like(log1p_like_function, "log1p")

does not lower to a direct constant-string argument. Flang copies the literal through a stack temporary variable

Tests

• End-to-end Fortran differentiation through the call-style registration.
• End-to-end differentiation through an independently registered
  procedure-pointer marker.
• IR checks that the declaration form adds "enzyme_math"="log1p"
• Add a warning for Conflicting registrations while retaining current behaviour

[joewallwork]

This looks great so far. I left a few comments and suggestions on the Fortran side of things.

I was wondering: is there any particular reason you use double precision rather than real in the test and docs here?

[isaacaka]

This looks great so far. I left a few comments and suggestions on the Fortran side of things.

I was wondering: is there any particular reason you use double precision rather than real in the test and docs here?

Both work, I think it was left over from when I was trying out different things. I've changed it to use real.

[joewallwork]

Thanks for your work on this @isaacaka. I have a concern about including procedures that don't belong to programs or modules because it's considered bad practice.

[joewallwork]

I'm happy with this now, thanks @isaacaka!