Add multivariate forward-mode AD: dual<T, int N=1>

Michael Teschrequested to merge
feature/multidual into master

Summary

  • New dual<T, int N=1> carries N independent partial derivatives, computing the full gradient in a single evaluation pass. With N=1 (default), behavior is identical to the existing dual<T>.
  • New headers: duals/partials (lightweight std::array<T,N> wrapper) and duals/multidual (complete implementation with all ~40 math functions, complex overloads, I/O, type traits).
  • Equivalency tests verify bit-exact match between duals/dual and duals/multidual for N=1. Benchmarks show 1-pass N=3 is ~2.4x faster than 3x N=1 passes for gradient computation.
  • Updated README with multivariate examples, updated duals/dual header docs, GitLab Pages auto-deploys on tagged releases.

Phase 1 of the multivariate plan

This is the standalone multidual header proving the design. Phase 2 (converging into duals/dual as a drop-in replacement) is future work.

Test plan

  • CI build passes (C++20 and C++17)
  • test_multidual — correctness for N=1,2,3, gradient verification
  • test_multidual_equiv — diff output of old vs new targets (should be empty)
  • bench_multidual — verify N=1 performance matches original, N>1 shows expected scaling
Edited by Michael Tesch

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