This directory covers dense mdspan lowering, BLAS/LAPACK provider adapters, optional multiprecision support, and linear-algebra design background.
Implemented Layers And Forward Work
- Scalar Configuration separates optional scalar families from numerical-backend selection.
- Generic Precision defines the shared fixed/runtime precision API used by products, square solves, LU, and logarithmic determinants and dense decompositions.
- Dense Operation Contracts explains fixed outputs, matrix norms, destructive eigensystems, and Schur block reordering.
- Square Linear Solves describes strict and recoverable frontends, pivot policy, workspace ownership, and backend diagnostics.
- Least Squares describes preserving full-rank QR and minimum-norm SVD solves, rank/cutoff diagnostics, residual norms and generic precision.
- Numerical Infrastructure Plan sequences rank-aware solving, conditioning, mixed-precision refinement for dense and matrix-free problems, and complex Gamma/Barnes extraction.
- Reusable LU, Conditioning and Logarithmic Determinants describes owning factors, repeated solves, reciprocal condition estimates and signed or complex-phase log determinants.
- Three-Precision LU Refinement separates factor, working and residual arithmetic, with backward-error diagnostics and recoverable stops.
- Mdspan Linear Algebra Dispatch tracks implemented operation-tag vertical slices and the remaining dense-operation sequence.
- BLAS/LAPACK Mdspan Wrappers describes the provider-ready operand layer below dispatch.
- Dense BLAS/LAPACK Wrapper Coverage inventories active dispatched dependencies and the quarantined experimental wrapper survey separately from Krylov algorithm behavior.
- MPLAPACK Binary80 covers native extended-precision GEMM, square solves, reusable LU and dense decompositions through the standard BLAS/LAPACK families.
- MPLAPACK Binary128 is the build and validation guide for optional binary128 provider support.
- MPLAPACK MPFR/MPC covers explicit-precision matrix products, LU solves and dense decompositions through the BLAS/LAPACK families, tensor defaults and per-call provider context in async execution. Its roadmap separates completed integration from further routine coverage.
- Tensor Contraction defines the fixed-output dense contraction contract, current CPU reference path, and backend strategy hierarchy.
The adapter documents contain both implemented checkpoints and future work. For the current user-facing Tensor operation matrix, use Tensor Operations; tests remain the implementation evidence for exact backend coverage.
Design And Background
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