# Message Handling # with Boolean Algebra  Ben Deane / CppCon / 2024-09-16 ## Alternative Title "The Unreasonable Unreasonable Effectiveness of Boolean Algebra in Software Design, Showing the Particular Application of a Message Handling Library, with an Excursion into the Roots of Programming" ## Frontmatter No AI/LLM was identifying (with matchers) a message coming off the wire. • The role of Boolean algebra in composing matchers. • Understanding Boolean implication and using it to simplify matchers. This talk is a series

Linear Algebra with The Eigen C++ Library ## +24 ## DANIEL HANSON ## Outline • A short history – linear algebra and C++ (1998 – Present) • The Eigen C++ Template Library for Linear Algebra • Linear Linear Algebra Interface in C++26 • Basics • Using with Eigen ## Disclaimers/Caveats • This presentation is on solving problems using • The Eigen linear algebra library • stdBLAS in C++26 • Not affiliated C++ growing in popularity • Wide adoption in financial programming • But, no support for linear algebra (pining for Fortran...) • Your options essentially were: • Write your own Matrix class and operations

## +23 ## std::Finalog: Linear Algebra Coming to Standard C++ ## MARK HOEMMEN ## 20 23 October 01 - 06 ## std::linalg: Linear Algebra Coming to Standard C++ Mark Hoemmen, NVIDIA | CppCon 2023 ![Im 8/p3_1.jpg) ## Agenda Motivating example: Matrix multiply Where std::linalg fits in linear algebra's layers std::linalg builds on the C++ Standard Library std::linalg builds on the long history scaled(alpha, A), transposed(B), scaled(beta, C), C); ## Does a “linear algebra library” do linear algebra? Aspirational linearity |We use math words|We mean a computer representation| |---|---|

differences between zero-dimensional arrays and scalars? Why are my Julia benchmarks for linear algebra operations different from other languages? 47.10 Julia Releases Do I want to use a release, beta 80 LibGit2 ..... 915 Functionality ..... 915 81 Dynamic Linker ..... 953 82 Linear Algebra ..... 955 82.1 Special matrices ..... 957 Elementary operations ..... 957 Matrix factorizations elementwise comparisons, which allows them to work on arrays. For example, 0. < A .< 1 gives a boolean array whose entries are true where the corresponding elements of A are between 0 and 1. Note the

differences between zero-dimensional arrays and scalars? 426 Why are my Julia benchmarks for linear algebra operations different from other languages? 426 46.10 Julia Releases 427 Do I want to use a release 79 LibGit2 ..... 913 Functionality ..... 913 80 Dynamic Linker ..... 951 81 Linear Algebra ..... 953 81.1 Special matrices ..... 955 Elementary operations ..... 955 Matrix factorizations elementwise comparisons, which allows them to work on arrays. For example, 0. < A .< 1 gives a boolean array whose entries are true where the corresponding elements of A are between 0 and 1. Note the

Arithmetic Operators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 6.2 Boolean Operators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 6.3 Bitwise Operators Lazy Artifacts 1447 CONTENTS xi 79 LibCURL 1448 80 LibGit2 1449 81 Dynamic Linker 1497 82 Linear Algebra 1501 82.1 Special matrices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . values in quantities that are known to be zero. See Knuth (1992) for motivation. 6.2 Boolean Operators The following Boolean operators are supported on Bool types: Expression Name !x negation x && y short-circuiting

zero-dimensional arrays and scalars? . . . . . . . . . . . . . . . 428 Why are my Julia benchmarks for linear algebra opera�ons different from other languages? . . . . . 429 47.11Julia Releases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 921 82 Dynamic Linker 959 83 Linear Algebra 961 83.1 Special matrices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . for elementwise comparisons, which allows them to work on arrays. For example, 0 .< A .< 1 gives a boolean array whose entries are true where the corresponding elements of A are between 0 and 1. Note the

SEI Graph/ML/AI algorithms for large- and small-scale parallel systems. Working on GBTL, a linear algebra-based C++ library for graph analytics. Copyright 2021 Carnegie Mellon University and Benjamin Brock Institute at permission@sei.cmu.edu. ## DM21-0916 ## This Talk Background: How and why to use matrix algebra for graphs? What are the important data structures and concepts? Prior work in the GraphBLAS community interoperate with standard C++, graph library proposal? ## This Talk Background: How and why to use matrix algebra for graphs? What are the important data structures and concepts? Prior work in the GraphBLAS community

modulo theories") combine domain-general search methods with domain-specific procedures. Computer algebra systems and specialized mathematical software packages provide means of carrying out mathematical #check b1 -- bool #check b1 && b2 -- "&&" is boolean and #check b1 || b2 -- boolean or #check tt -- boolean "true" -- Try some examples of your own. Any text between the #print "reducing pairs" #reduce (m, n).1 -- m #reduce (m, n).2 -- n #print "reducing boolean expressions" #reduce tt && ff -- ff #reduce ff && b -- ff #reduce b &&

29 ### 6 Mathematical Operations and Elementary Functions 30 6.1 Arithmetic Operators 30 6.2 Boolean Operators 31 6.3 Bitwise Operators 31 6.4 Updating operators 32 6.5 Vectorized "dot" operators 35.28 Performance of captured variable 474 35.29 Multithreading and linear algebra 475 35.30 Alternative linear algebra backends 476 35.31 Execution latency, package loading and package precompiling **1379** 76 **LibCURL** **1380** 77 **LibGit2** **1381** 78 **Dynamic Linker** **1429** 79 **Linear Algebra** **1433** 79.1 Special matrices 1436 79.2 Matrix factorizations 1438 79.3 Orthogonal matrices