Composing Ancient Mathematical Knowledge Into Powerful Bit-fiddling techniques Jamie Pond -- CppCon 2024TLDW; New insights from Ancient Egyptian Multiplication gives us the freedom of synthesising

lambda trick Comparison Binding Constraints Architecture Substitution Construction Conclusion Mathematical expressions Normal distribution PDF f = 1 √ 2πσ2 e− (x−µ)2 2σ2 2 + + 2 Normal distribution symbols Expression templates are stateful Stateless Expression Templates Formulas are stateless Data is injected in formulas Both live their lives in different world What changed since then? C++20 Conclusion Symbols with constraints It would be nice to be able to provide information on the mathematical entity it represents 1 symbol a; 2 symbol w; 3 symbol t; 4 symbol phi; 1 symbol a;

Theoretical foundations Outline of an implementation Conclusion Mathematical and software architecture Question How to abstract the problem? Mathematical abstractions Well-posed and abstracted in mathematics mathematics ⇒ ‘‘easy” to abstract in software Mathematical architecture ⇒ Software architecture Counter-example: units Intuitively understood in physics But very fuzzy foundations in mathematics ⇒ Incredibly DedicationIntroduction Firsts steps Context Theoretical foundations Outline of an implementation Conclusion The mathematical architecture of algorithms John C. Butcher Numerical Methods for Ordinary Differential Equations

Papers — GraphBLAS standards — SuiteSparse:GraphBLAS releases 0.9 1.0 1.2 1.3 1.0 3. 0 2.2 Mathematical foundations, HPEC Seven good reasons, ICCS Standards for graph algorithm primitives Monoids: Binary Operators with an Identity - Monoids are mathematical objects, consisting of: - A commutative binary operator - A type T - A mathematical identity 113[DISTRIBUTION STATEMENT A] This material Monoids: Binary Operators with an Identity - Monoids are mathematical objects, consisting of: - A commutative binary operator - A type T - A mathematical identity 114[DISTRIBUTION STATEMENT A] This material

characterized by the use of mathematical functions and the avoidance of side effects What is Functional Programming?● A programming paradigm characterized by the use of mathematical functions and the avoidance declarative syntax What is Functional Programming?● A programming paradigm characterized by the use of mathematical functions and the avoidance of side effects ● Functional programming is identified by the use and more What is Functional Programming?● A programming paradigm characterized by the use of mathematical functions and the avoidance of side effects ● Functional programming is identified by the use

Such solutions while working in most cases, are not without problems, both in terms of numerical/mathematical soundness (? any hash algorithm), but also in terms of flexibility/composition of the code using Such solutions while working in most cases, are not without problems, both in terms of numerical/mathematical soundness (? any hash algorithm), but also in terms of flexibility/composition of the code using Such solutions while working in most cases, are not without problems, both in terms of numerical/mathematical soundness (? any hash algorithm), but also in terms of flexibility/composition of the code using

on totally ordered sets Eric Hughes, Meadhbh Hamrick In brief stdx::interval implements the mathematical sense of an interval on a totally ordered set. The library reasons about intervals as sets, not set. Why you may care One level of abstraction higher than raw bounds. Intervals are a basic mathematical concept that appear in all kinds of algorithms, from recursive sorting to adaptive mesh refinement

term Functor ○ in mathematical terms it is a function which ■ takes one or more functions as its arguments ■ returns a function as the result ○ functor is also defined in mathematical category theory

Program Chair SG20Outline • Main Topic: use C++ to simulate the process of cancer initiation • The mathematical model and simulation study • Generate a single tumor (A single step of evolution) • Generate by changes in genes (DNA). • When cancer is found early, it may be easier to treat or cure • Mathematical models help understand the evolution quantitatively. (e.g. predict the window of opportunity

TA1L2pvYjcxMC0wNTMuanBn.jpg 9Functions A familiar term -- perhaps from your math class? 10Mathematical Functions (f(x)=x) (1/2) 11 ● Functions on graphs are one domain many begin to think of the ○ We have quite a lot of expressiveness in regards to how we express a functions operations!Mathematical Functions (f(x)=x) (2/2)a 12 ● Functions on graphs are one domain many begin to think of the