About me 2 6 ways for implementing math expressions calculator, Amir Kirsh Lecturer Academic College of Tel-Aviv-Yaffo and Tel-Aviv University Developer Advocate at Member of the Israeli ISO C++ NB NB Co-Organizer of the CoreCpp conference and meetup group3 6 ways for implementing math expressions calculator, Amir Kirsh Suffering from slow builds? It’s not just waste of time It affects your dev for implementing math expressions calculator, Amir KirshSuccess Stories 5 6 ways for implementing math expressions calculator, Amir KirshSuccess Stories 6 6 ways for implementing math expressions calculator

com/catchorg/Catch2 Frameworks Part 0: Basics 9auto abs(int x) -> int; math.hpp math.cpp test_math.cpp #include #include "math.hpp" TEST_CASE("Absolute value tests"){ CHECK( abs( 4 Frameworks Part 0: Basics 10auto abs(int x) -> int; math.hpp math.cpp test_math.cpp #include #include "math.hpp" TEST_CASE("Absolute value tests"){ CHECK( abs( │ └── math │ ├── math.cpp │ └── math.hpp └── test ├── stuff │ └── test_stuff.cpp ├── things │ └── test_things.cpp └── math └── test_math.cpp Where

shared-lib, static-lib, soft-float, and inline-asm Victor Istomin 🇺🇦 vi@6it.dev Templatizing math and geometry libs and tests Serhii Iliukhin 🇺🇦 sil@6it.dev Advising on C++ standard with Davidson 🇬🇧 gd@6it.dev Advising on math aspects, code organization and refactoring, reviews Dmytro Ivanchykhin 🇺🇦 di@6it.dev Implementing fixed- point math with floating-point fallback non-determinism_ CppCon 2024 sixit:: 13 CPU Compiler <math.h> 1 2 3Handling FP non-determinism_ CppCon 2024 sixit:: 14 CPU Compiler <math.h> 1 2 3 Modern CPUs and even MCUs do provide IEEE754-

to search faster. Usually done by wrapping objects in a bounding volume (sphere, AABB) and fancy math is done to determine if it intersects the frustum.Quadtrees & Octrees Used to partition space in exist, continue deeper into the tree else skip. ● When a node represents a game entity, do fancy math to determine frustum intersection.Once the tree is constructed, we search the tree for game entities exist, continue deeper into the tree else skip. ● When a node represents a game entity, do fancy math to determine frustum intersection.Once the tree is constructed, we search the tree for game entities

locations items into cells Store non-empty cells in a map - using array index as key Ideally to simplify math and logic - form from a big cube - centered on origin Speaker notesGRID CACHE MAP CHOICE HASHMAP HasNodesInBounds(const math::Box& bounds) const; bool HasNodesInBoundsOfType(const math::Box& bounds, const NodeTypes& types) const; std::vector GetNodesInBounds(const math::Box& bounds) const; std::vector GetNodesInBoundsOfType(const math::Box& bounds, const NodeTypes& types) const; const GridCellPtr& GetLargeGridCell() const; GridCellPtr GetGridCell(const math::Vector& point) const; std::vector

timestep); return (y0 + (k1 + 2 * k2 + 2 * k3 + k4) * timestep / 6); } double stateOut = common::math::runge_kutta4(derivFun, currTime, stateIn, dt); Usage Exampleatomosspace.com | 31 + (k1 + 2 * k2 + 2 * k3 + k4) * timestep / 6); } Eigen::Matrix stateOut = common::math::runge_kutta4>(derivFun, currTime, stateIn, dt); Usage Example stateOut = common::math::runge_kutta4>(derivFun, currTime, stateInOut, dt); Usage Example Continuedatomosspace.com | 33 double stateOut = common::math::runge_kutta4

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Aspirational linearity My impression of René Magritte’s “The Treachery of Images” (1929) We use math words We mean a computer representation Scalars 𝛼, 𝛽 in a field Fixed-length numbers Vectors Householder convention A standard notation, & a standard way of talking about computations We use math words We mean a computer representation Scalars 𝛼, 𝛽 in a field Fixed-length numbers Vectors Low-level math problems • Linear systems 𝐴𝑥 = 𝑏 (& determinants, etc.) • Least-squares problems min 𝑥 𝐴𝑥 − 𝑏 2 • Eigenvalue & singular value problems 𝐴𝑥 = 𝜆𝑥 • Layer 2: Higher-level math problems

https://aurora-opensource.github.io/au/main/reference/math/#inverse-functions 32Unit-aware inverses https://aurora-opensource.github.io/au/main/reference/math/#inverse-functions f = 400 Hz T = 1/f = 0.0025 io/au/main/reference/math/#inverse-functions f = 400 Hz T = 1/f = 0.0025 s = 2 500 μs f = 400 Hz T = 1/f = 0.0025 s = 2 500 μs 32.2Unit-aware inverses https://aurora-opensource.github.io/au/main/reference/math/#inverse-functions for (units of) 1... 32.3Unit-aware inverses https://aurora-opensource.github.io/au/main/reference/math/#inverse-functions f = 400 Hz T = 1/f = 0.0025 s = 2 500 μs f = 400 Hz T = 1/f = 0.0025 s = 2 500

Mvd2Vic2l0ZS8yMDIyLTA1L2pvYjcxMC0wNTMuanBn.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 We have quite a lot of expressiveness in regards to how we express a functions operations!Common Math Functions (1/2) ● As a start, as you may expect, languages like C++ provide in the standard library mmon Math Functions (2/2) ● As a start, as you may expect, languages like C++ provide in the standard library many common functions for us. 14 https://en.cppreference.com/w/cpp/numeric/math Functions

is essentially the same using System; class SuperMaths { public static double Square(int n) => Math.Pow(n,2); } class Program { static void Main() { Console.Write(SuperMaths.Square(2)); } } 111The is essentially the same using System; class SuperMaths { public static double Square(int n) => Math.Pow(n,2); } class Program { static void Main() { Console.Write(SuperMaths.Square(2)); } } 112 (free) functions using System; static class SuperMaths { public static double Square(int n) => Math.Pow(n,2); } class Program { static void Main() { Console.Write(SuperMaths.Square(2)); } } 114The