backends/openblas Design

Responsibilities

• Provide a concrete native-only matrix backend that can participate in the public @algebra trait ecosystem.
• Keep the backend's owned public type local to this repository as BlasMatrix[T].
• Use OpenBLAS GEMM for matrix multiplication while keeping the rest of the first-pass matrix surface implemented locally in MoonBit.
• Hide OpenBLAS layout and binding details behind a repository-owned API.

Why This Is A Wrapper Backend

This package is a trait-compatible backend wrapper.

It is not:

• a runtime backend selector
• a global backend enum
• a direct trait implementation on the foreign OpenBLAS binding types

The wrapper exists so the package owns the concrete matrix type and can attach @algebra trait implementations without running into MoonBit's foreign trait / foreign type restriction.

Type And Target Decide Behavior

Backend choice is now determined by two things:

• type choice @immut.Matrix[T] and @default.ImmutableDenseMatrix[T] use the repository's existing dense implementations, while @openblas.BlasMatrix[T] uses the OpenBLAS-backed multiplication path
• target choice backends/openblas only participates in native builds

There is no runtime API for asking @immut.Matrix to switch to a different backend.

Scalar Strategy

BLASInnerType is intentionally backend-local. It captures the scalar-specific pieces this wrapper needs:

• dispatch to the correct GEMM kernel
• provide a tolerance value for backend validation

The repository currently implements this trait only for Float and Double. That matches the current OpenBLAS-backed matrix surface and avoids exposing a misleading generic type story.

Operation Split

• Mul delegates to OpenBLAS GEMM
• shape, transpose, +, -, neg stay as local MoonBit implementations for the first version

This split keeps the API complete enough for trait-oriented generic code without pretending that every matrix operation must already be backed by a BLAS routine.