Symbolic Numeric Programming in Julia

on YouTube ↗37m

" summary

Symbolics.jl traces numerical Julia code via multiple-dispatch to produce and regenerate code, claims removal of intermediate allocations and automatic multithreading, and demonstrates a 150x speedup on a 3D kernel by eliminating allocations and fusing loops. It computes sparse Jacobian/Hessian structure to reduce AD calls, provides O(1)-size representation for arrays and stencils, and exposes a unified interface with a e-graph based simplifier plus rule-based rewrites.

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" chapters (15)

1. 0:00Start
2. 5:12How Symbolics Works
3. 11:08Abstract Interpretation
4. 13:47Optimizations
5. 18:58Semi-Linear Form
6. 20:11Compiling this to Julia
7. 21:55Runtime Generated Functions
8. 23:49Symbolic Arrays
9. 25:45The Einstein Summation Notation
10. 27:01Vector Transpose
11. 27:32Rule System
12. 29:18Matrix Chain Multiplication Rule
13. 30:11Loop Vectorization
14. 32:22Periodic Boundary Conditions
15. 35:36Collaborators

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