. . . . . . . . . . . . . . . 18 8 External dependencies 19 i ii CONTENTS III Manual 21 9 Ge�ng Started 23 9.1 Resources . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 11 Integers and Floa�ng-Point Numbers 31 11.1 Integers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 11.2 Floa�ng-Point Numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 Floa�ng-point zero . . . . . . . . . . . . . . . . .

. 18 8 External dependencies 19 i ii CONTENTS 9 Deprecated or removed 21 III Manual 23 10 Ge�ng Started 25 10.1 Resources . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 12 Integers and Floa�ng-Point Numbers 33 12.1 Integers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 12.2 Floa�ng-Point Numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 Floa�ng-point zero . . . . . . . . . . . . . . . . .

. 16 7 External dependencies 17 8 Deprecated or removed 19 i ii CONTENTS III Manual 21 9 Ge�ng Started 23 9.1 Resources . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 11 Integers and Floa�ng-Point Numbers 31 11.1 Integers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 11.2 Floa�ng-Point Numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 Floa�ng-point zero . . . . . . . . . . . . . . . . .

. 16 7 External dependencies 17 8 Deprecated or removed 19 i ii CONTENTS III Manual 21 9 Ge�ng Started 23 9.1 Resources . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 11 Integers and Floa�ng-Point Numbers 31 11.1 Integers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 11.2 Floa�ng-Point Numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 Floa�ng-point zero . . . . . . . . . . . . . . . . .

Deprecated or removed 19 9 External dependencies 21 10 Tooling Improvements 23 III Manual 25 11 Ge�ng Started 27 11.1 Resources . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 13 Integers and Floa�ng-Point Numbers 35 13.1 Integers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 13.2 Floa�ng-Point Numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 Floa�ng-point zero . . . . . . . . . . . . . . . . .

. 18 i ii CONTENTS 8 External dependencies 19 9 Tooling Improvements 21 III Manual 23 10 Ge�ng Started 25 10.1 Resources . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 12 Integers and Floa�ng-Point Numbers 33 12.1 Integers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 12.2 Floa�ng-Point Numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 Floa�ng-point zero . . . . . . . . . . . . . . . . .

is always converted to Float64. 18.2 Abstract Types Abstract types cannot be instantiated, and serve only as nodes in the type graph, thereby describing sets of related concrete types: those concrete Pointy{>:Int} true Much as plain old abstract types serve to create a useful hierarchy of types over concrete types, parametric abstract types serve the same purpose with respect to parametric composite Pointy{<:Real} true 138 CHAPTER 18. TYPES What purpose do parametric abstract types like Pointy serve? Consider if we create a point-like implementa- tion that only requires a single coordinate because

is always converted to Float64. 18.2 Abstract Types Abstract types cannot be instantiated, and serve only as nodes in the type graph, thereby describing sets of related concrete types: those concrete Pointy{>:Int} true Much as plain old abstract types serve to create a useful hierarchy of types over concrete types, parametric abstract types serve the same purpose with respect to parametric composite Pointy{<:Real} true 138 CHAPTER 18. TYPES What purpose do parametric abstract types like Pointy serve? Consider if we create a point-like implementa- tion that only requires a single coordinate because

is always converted to Float64. 18.2 Abstract Types Abstract types cannot be instantiated, and serve only as nodes in the type graph, thereby describing sets of related concrete types: those concrete Pointy{>:Int} true Much as plain old abstract types serve to create a useful hierarchy of types over concrete types, parametric abstract types serve the same purpose with respect to parametric composite Pointy{<:Real} true 138 CHAPTER 18. TYPES What purpose do parametric abstract types like Pointy serve? Consider if we create a point-like implementa- tion that only requires a single coordinate because

is always converted to Float64. 23.2 Abstract Types Abstract types cannot be instantiated, and serve only as nodes in the type graph, thereby describing sets of related concrete types: those concrete Pointy{>:Int} true Much as plain old abstract types serve to create a useful hierarchy of types over concrete types, parametric abstract types serve the same purpose with respect to parametric composite Pointy{<:Real} true 150 CHAPTER 23. TYPES What purpose do parametric abstract types like Pointy serve? Consider if we create a point-like implementa- tion that only requires a single coordinate because