Merge branch 'feature/multidual' into 'master'

    when: manual

    allow_failure: true

# Manual pipeline - generates website with docs and coverage (triggered manually)

# Deploy docs and coverage to GitLab Pages — runs automatically on tagged releases

pages:

  stage: pages

  script:

    paths:

    - public/

  rules:

  - if: $CI_COMMIT_TAG

  - if: $CI_COMMIT_BRANCH == $CI_DEFAULT_BRANCH

    when: manual

    allow_failure: true

#

cmake_minimum_required (VERSION 3.14)

project (cppduals

  VERSION 0.7.4

  VERSION 0.8.0

  LANGUAGES C CXX

  )

include (GNUInstallDirs)

# Multivariate Dual — Remaining Work

## Phase 2: Drop-in replacement for `dual<T>`

Merge the `duals/multidual` implementation into `duals/dual` so that the

existing `dual<T>` becomes `dual<T, int N=1>`.  All existing code

compiles unchanged (N=1 default).

1. Replace the `dual<T>` class in `duals/dual` with `dual<T, int N=1>`

   from `duals/multidual`.  Remove `duals/partials` and

   `duals/multidual` as separate headers.

2. Update `duals/dual_eigen` — add `int N` template parameter to

   `NumTraits`, `ScalarBinaryOpTraits`, and the unary functors

   (`rpart`, `dpart`).  Guard SIMD packet specializations to `N=1`.

3. Update `duals/dual_fmt.h` — add `int N` template parameter.

   N=1 formatting unchanged; N>1 shows partials array.

4. Update SIMD headers (`duals/arch/{SSE,AVX,NEON}/Dual.h`,

   `ComplexDual.h`) — specialize for `dual<T,1>` only.

5. Run full existing test suite — must pass unchanged.

6. Update equivalency tests to compile against the unified header.

### Verification gate

```bash

make clangr && make test   # all existing tests pass

make cov                   # coverage report

```

## Phase 3: Eigen integration for N>1

Enable `Eigen::Matrix<dual<T,N>>` for N>1.  This allows multivariate

differentiation of matrix operations (gemm, LU solve, matrix

exponential) in a single evaluation pass.

1. Provide `NumTraits<dual<T,N>>` for arbitrary N.

2. Add `ScalarBinaryOpTraits` for mixed `dual<T,N>` / `T` operations.

3. Add `rpart(MatrixBase)` and `dpart(MatrixBase, int i)` unary

   functors returning component matrices.

4. Benchmark: compare N-pass `padm(Matrix<dual<T>>)` against

   1-pass `padm(Matrix<dual<T,N>>)` for matrix exponential

   derivatives.  This should show the multivariate advantage

   (compute f' once, multiply by N seeds) at the matrix level.

5. No SIMD for N>1 (Eigen falls back to scalar loops).

## Phase 4: Non-x86 vectorization

- CUDA kernel support for `dual<T>` and `dual<T,N>`.

- AltiVec / HIP packet specializations.

## Open questions

- Should `duals/multidual` remain as a convenience header that

  simply includes `duals/dual` after Phase 2?

- I/O format for N>1: `(3+{0,1,0}_e)` vs `(3; 0, 1, 0)` —

  settle on a format before Phase 2.

- Whether to add runtime-sized N (e.g. `dual<T, Eigen::Dynamic>`)

  for cases where the number of variables isn't known at compile time.