[FEATURE REQUEST] `gemm` CuTe kernel implementation

[LoserCheems]

Problem statement

The BLAS level-3 gemm kernel has no CuTe backend implementation in this project. The README BLAS table lists an empty CuTe column for gemm, even though GEMM is the primary workload that CuTe/CUTLASS is designed to optimize.

Without a CuTe gemm kernel:

• users cannot see how GEMM is expressed using CuTe’s layout and tiling abstractions,
• there is no CuTe GEMM baseline for performance comparison with PyTorch and Triton,
• CuTe-based examples are missing the most important building block for many workloads.

Proposed solution

Implement a CuTe-based gemm kernel that matches the Python reference semantics and aligns with the project’s backend structure.

Concretely:

• Add a CuTe gemm kernel in the appropriate CuTe backend directory, implementing $C = \alpha A B + \beta C$.
• Use CuTe primitives to describe matrix layouts, threadblock tiling, and memory movement.
• Align the public API with other backends so callers can dispatch to CuTe GEMM uniformly.

Alternatives considered

Alternatives such as omitting CuTe gemm or relying on other backends would:

• significantly reduce the educational and practical value of including CuTe as a backend,
• leave the CuTe column incomplete in the README BLAS table for the most important BLAS-3 kernel,
• limit opportunities to demonstrate high-performance GEMM implementation details in CuTe.

Implementation details

• Establish file layout and build integration for CuTe kernels.
• Implement GEMM using CuTe abstractions tuned for GPU execution, potentially leveraging CUTLASS patterns.
• Ensure numerical equivalence with the Python reference and harmonize with PyTorch/Triton semantics.
• Integrate with planned tests and benchmarks for GEMM.

Use case

The CuTe gemm kernel will:

• demonstrate a high-performance GEMM implementation in CuTe,
• enable rich performance comparisons across backends,
• act as a cornerstone for Transformer modules and other large-scale linear algebra workloads.

Related work

• CuTe/CUTLASS GEMM examples and reference kernels.
• Standard BLAS gemm implementations.

Additional context

This issue complements the gemm Python/PyTorch/Triton feature requests and aims to make CuTe a first-class backend for the project’s most important BLAS-3 operation.