Add low-level wrappers for BLAS and LAPACK

[amontoison]

@ViralBShah I was at the Householder Symposium last week and had a discussion with Julien Langou (@langou), the main maintainer of reference-LAPACK, about what we’re doing in Julia for BLAS / LAPACK and our nice LBT feature.

Some feedback I got is that Julien doesn’t understand why we don’t expose all the arguments of the BLAS / LAPACK routines, and why we took the liberty of fusing om* / un* routines but not sy* / he*.

What I concluded with Julien is that we should maybe expose the low-level wrappers directly and call them from our higher-level interfaces.
This would make it easier to update with new releases and would also give users the ability to reuse buffers, which is currently a significant limitation of our API.
I also think it would help Julien interact more easily with us.
He’s starting to get interested in using Julia for unit testing reference-LAPACK and teaching!

A few months ago, I wrote a script to generate wrappers for Fortran routines implemented in F77 (for HSL), and I was able to adapt it for BLAS / LAPACK.
It is similar to what we obtain with Clang.jl from the C header files.
I open the PR as a draft for now to get feedback.

[ViralBShah]

This is something I have always wanted to do myself as well.

Is there a noticeable impact on system image size?

[ViralBShah]

It would be great if this PR could be a branch on this repo (easier to work on than a fork). Possibly needs these fixes:

diff --git a/src/blas.jl b/src/blas.jl
index 15c6467..3ebe212 100644
--- a/src/blas.jl
+++ b/src/blas.jl
@@ -1417,7 +1417,7 @@ Return the updated `C`.
 """
 function gemmt! end
 
-for (gemmt, elty) in
+for (fname, elty) in
         ((:dgemmt,:Float64),
          (:sgemmt,:Float32),
          (:zgemmt,:ComplexF64),
@@ -1488,7 +1488,7 @@ Update `C` as `alpha*A*B + beta*C` or the other three variants according to
 """
 function gemm! end
 
-for (gemm, elty) in
+for (fname, elty) in
         ((:dgemm,:Float64),
          (:sgemm,:Float32),
          (:zgemm,:ComplexF64),
@@ -1595,9 +1595,9 @@ for (mfname, elty) in ((:dsymm,:Float64),
             chkstride1(A)
             chkstride1(B)
             chkstride1(C)
-            $fname(side, uplo, m, n,
-                   alpha, A, max(1,stride(A,2)), B,
-                   max(1,stride(B,2)), beta, C, max(1,stride(C,2)))
+            $mfname(side, uplo, m, n,
+                    alpha, A, max(1,stride(A,2)), B,
+                    max(1,stride(B,2)), beta, C, max(1,stride(C,2)))
             C
         end
         function symm(side::AbstractChar, uplo::AbstractChar, alpha::($elty), A::AbstractMatrix{$elty}, B::AbstractMatrix{$elty})

[amontoison]

I wanted to create a branch but it seems that I don't have the rights on this repo.
It is why I did a fork.

Thanks for the patch, I also need to find how to use @blasfunc with a @ccall.

[ViralBShah]

I didn't realize you don't have access. Just invited.