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

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 i ii CONTENTS 5 Mathematical Operations and Elementary Functions 27 5.1 Arithmetic Operators . . . . . . . . . . . . . . . . . . 588 45 Mathematics 589 45.1 Mathematical Operators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 589 45.2 Mathematical Functions . . . . . . . . . . . . . . . Python, but also supports general program- ming. To achieve this, Julia builds upon the lineage of mathematical programming languages, but also borrows much from popular dynamic languages, including Lisp,

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 i ii CONTENTS 5 Mathematical Operations and Elementary Functions 27 5.1 Arithmetic Operators . . . . . . . . . . . . . . . . . . 588 45 Mathematics 589 45.1 Mathematical Operators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 589 45.2 Mathematical Functions . . . . . . . . . . . . . . . Python, but also supports general program- ming. To achieve this, Julia builds upon the lineage of mathematical programming languages, but also borrows much from popular dynamic languages, including Lisp,

and one . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 12 Mathematical Operations and Elementary Functions 45 12.1 Arithmetic Operators . . . . . . . . . . . . . . . . . . 594 52 Mathematics 597 52.1 Mathematical Operators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 597 52.2 Mathematical Functions . . . . . . . . . . . . . . . Python, but also supports general program- ming. To achieve this, Julia builds upon the lineage of mathematical programming languages, but also borrows much from popular dynamic languages, including Lisp,

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 i ii CONTENTS 5 Mathematical Operations and Elementary Functions 25 5.1 Arithmetic Operators . . . . . . . . . . . . . . . . . . 605 43 Mathematics 607 43.1 Mathematical Operators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 607 43.2 Mathematical Functions . . . . . . . . . . . . . . . Python, but also supports general program- ming. To achieve this, Julia builds upon the lineage of mathematical programming languages, but also borrows much from popular dynamic languages, including Lisp,

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 i ii CONTENTS 5 Mathematical Operations and Elementary Functions 25 5.1 Arithmetic Operators . . . . . . . . . . . . . . . . . . 609 43 Mathematics 611 43.1 Mathematical Operators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 611 43.2 Mathematical Functions . . . . . . . . . . . . . . . Python, but also supports general program- ming. To achieve this, Julia builds upon the lineage of mathematical programming languages, but also borrows much from popular dynamic languages, including Lisp,

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 i ii CONTENTS 5 Mathematical Operations and Elementary Functions 27 5.1 Arithmetic Operators . . . . . . . . . . . . . . . . . . 588 45 Mathematics 589 45.1 Mathematical Operators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 589 45.2 Mathematical Functions . . . . . . . . . . . . . . . Python, but also supports general program- ming. To achieve this, Julia builds upon the lineage of mathematical programming languages, but also borrows much from popular dynamic languages, including Lisp,

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 i ii CONTENTS 5 Mathematical Operations and Elementary Functions 25 5.1 Arithmetic Operators . . . . . . . . . . . . . . . . . . 603 43 Mathematics 605 43.1 Mathematical Operators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 605 43.2 Mathematical Functions . . . . . . . . . . . . . . . Python, but also supports general program- ming. To achieve this, Julia builds upon the lineage of mathematical programming languages, but also borrows much from popular dynamic languages, including Lisp,

and one . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53 17 Mathematical Operations and Elementary Functions 55 17.1 Arithmetic Operators . . . . . . . . . . . . . . . . . . 612 57 Mathematics 615 57.1 Mathematical Operators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 615 57.2 Mathematical Functions . . . . . . . . . . . . . . . Python, but also supports general program- ming. To achieve this, Julia builds upon the lineage of mathematical programming languages, but also borrows much from popular dynamic languages, including Lisp,

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 i ii CONTENTS 5 Mathematical Operations and Elementary Functions 25 5.1 Arithmetic Operators . . . . . . . . . . . . . . . . . . 605 43 Mathematics 607 43.1 Mathematical Operators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 607 43.2 Mathematical Functions . . . . . . . . . . . . . . . Python, but also supports general program- ming. To achieve this, Julia builds upon the lineage of mathematical programming languages, but also borrows much from popular dynamic languages, including Lisp,