This directory contains operation-tag backend adapters that route dense linalg operations to BLAS. These adapters sit above the BLAS descriptor layer, which owns mdspan-to-BLAS descriptor construction and direct provider calls.

The native backend adapters are GEMM and GEMV. They delegate try_kernel(BlasBackend, operation, ...) to the corresponding direct uni20::linalg::blas::try_* wrapper. Direct representability failures return structured KernelAttempt decline reasons; provider failures remain terminal errors. Tensor contraction is an operation-specific strategy backend above this layer and delegates its projected rank-two operands through gemm_op.

When MPLAPACK MPFR is configured, gemm.hpp also includes mpfr.hpp, whose BlasBackend specialization packs logical mpreal/complex<mpreal> values and passes an explicit working precision to the provider. This specialization is available even when native BLAS is disabled. Exact GEMM declines without touching operands so the CPU reference kernel can perform rational arithmetic.

binary80.hpp supplies binary80 real/complex GEMM under the same BlasBackend, including when native BLAS is disabled. Provider representation conversion stays in the compiled MPLAPACK adapter.

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