Symbolic Calculus for High-performance Computing From Scratch Using C++23

on YouTube ↗01h 04m

" summary

Shows a working C++23 library that builds symbolic formulas from unevaluated lambdas as template parameters and unique symbol IDs (singleton addresses), implements stateless expression templates so data is injected later, and performs compile-time derivatives and integrals plus substitution and binding. Generated assembly is shown to validate the zero-cost abstraction claim. Implementation works across examples but partial substitution, rewrite rules and unit handling remain future work; source and examples live on GitHub.

AI-written summary · about

" chapters (11)

1. 0:00Symbolic calculus in C++23
2. 1:48Stateless expression templates
3. 3:39Lambda trick for symbol types
4. 8:41Symbols with unique IDs
5. 14:00Binding symbols with traits
6. 23:27Constraining symbol types
7. 31:40Building ASTs for formulas
8. 37:29Symbolic expressions and operators
9. 45:26Substitution and evaluation
10. 54:20Summary and future directions
11. 56:27Q&A: units, Unicode, hybrid

" related talks

• 37mSymbolic Numeric Programming in JuliaShashi Gowda · Strange Loop 2022
• 15mCoarsening Optimization for Differentiable ProgrammingErik Meijer, Guoqiang Zhang, Xipeng Shen, Olin Shivers, Irene Dea, Samantha Andow, Emilio Arroyo-Fang, Neal Gafter, Johann George, Melissa Grueter, Steffi Stumpos, Alanna Tempest, Christy Warden, Shannon Yang · OOPSLA 2021
• 01h 06mNumerical Integrators From Scratch in C++Vincent Reverdy · CppCon 2024
• 45mPractical Lambda CalculusEinar W. Høst, Jonas Winje · Lambda Days 2017
• 32mCompilation of Dynamic Sparse Tensor AlgebraSaman Amarasinghe, Stephen Chou · OOPSLA 2022
• 28mFunctional Sparse Tensor CompilationAmir Shaikhha, Shideh Hashemian · FProPer 2024
• 41mSYCL building blocks for C++ librariesGordon Brown · Meeting C++ 2016
• 01h 03mInside Every Calculus Is A Little Algebra Waiting To Get OutErik Meijer · SPLASH 2020 REBASE