Typed Linear Algebra - How to Not Crash on Mars
summary
An open source C++ library composes MPUnunits quantity types with existing backends (std::linalg/std::mdspan/Eigen/IGEN), using template metaprogramming, customization points and an element_cast to compute element types from two index type lists (n+m types suffice). Benchmarks show zero runtime cost with mdspan/Eigen but a big slowdown when storing elements in std::tuple; compilation time spikes (a 32×32 product compiles in ~16s vs <3s baseline) and larger sizes exhaust memory. Element-assignment via reinterpret_cast is undefined behavior and remains unsolved.
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chapters (12)
- 0:00Introduction
- 1:27Mars Climate Orbiter failure
- 8:58Buckingham Pi theorem
- 14:00Strongly typed linear algebra library
- 21:55Matrix class constructors
- 31:49Typed matrix algorithms
- 40:59Integration with Igen and BLAS
- 47:47Memory ownership in matrices
- 57:22Element access pitfalls
- 1:06:59Performance benchmarks
- 1:14:48Future work in typed linear algebra
- 1:22:12Q&A
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