(next slide) • Layout • Family of mappings, parameterized by extents • Layout mapping maps multi-D index (i, j) → 1-D offset k • Different layout example • Nondefault column major (layout_left) • Instead Upper triangle: 𝐴𝑖𝑗, 𝑖 ≤ 𝑗 Parts of a matrix Diagonal: 𝐴𝑖𝑗, 𝑖 = 𝑗 Row index 𝑖 Column index 𝑗28 Detailed example: Cholesky matrix factorization Solve a symmetric positive definite

redundant code • Minimize modifying existing code • Minimize preprocessor macrosThe Design • Implement a family of quaternion classes, an illustrative example from a larger project • Project build issues • ”simd.h" namespace plt::simd { struct Neon32 : Common {}; template concept Neon32Family = std::derived_from; }Quat_Neon32.h: Quat Class Declaration and Data may see a performance gain at this stageQuat Functions templateFamily SIMD> inline auto operator-(Quat q) -> Quat { float32x4_t value = q.NeonVal();

used outside of its target ● Flag compatibility ○ Sets belong to “families” ○ Each instance of a family’s set is a different flag compatibility view of the set (e.g., CMake configuration or importer-influenced importer-influenced flags) 19Build Databases: The Skeleton ● Top level ○ version, revision ○ sets ● Sets ○ family-name, name ○ visible-sets, translation-units ● Translation units ○ object, source, work-directory Modification times ○ Scanning performance metrics 21Build Databases: Sets ● Each set has: ○ Name ○ Family name ○ Translation units ○ Visible sets (names of sets that provide modules that may be imported

static constexpr bool is_named = true; static constexpr auto symbol = Symbol; using prefix_family = PF; }; CppCon 2020 | A Physical Units Library For the Next C++ Class Types as Non-Type Template = Symbol; using prefix_family = PF; }; template requires U::is_named && std::same_asfamily, typename U::prefix_family> struct prefixed_unit : constexpr bool is_named = true; static constexpr auto symbol = P::symbol + U::symbol; using prefix_family = no_prefix; }; CppCon 2020 | A Physical Units Library For the Next C++ Class Types as Non-Type

C++ supports generic programming with templates • A template is a parametrized description of a family of some facility • A template is not a thing – it is a recipe for making things • C++ provides More Detail – Function Templates • A function template is a recipe for generating a parametrized family of functions 28 template T const& min(T const& a, T const& b) //- Definition of function Bob Steagall Function Templates • A function template is a recipe for generating a parametrized family of functions 29 template T const& min(T const& a, T const& b) //- Definition of function

referred to generally as class types • Class template indicates a parametrized description of a family of classes • C++ also provides parametrized descriptions of • Functions • Member functions • template is the noun, indicating a parametrized description • thing is an adjective, specifying the family of things being parametrized So, we have: • Also, the associated verb is parametrize or parameterize parameterize – not templatize! 24 This kind of template... ... is a parametrized description of a family of… class template classes function template functions member function template member functions

completed_call_intensity modulation_rate, line_digit_rate\n(1 / duration)\n[Bd, 1/s] 84• Denotes a family of quantities belonging to the same kind – such quantity represents any quantity from a kind hierarchy 2024: Improving our safety with a quantities and units library kind_of modi�er 85• Denotes a family of quantities belonging to the same kind – such quantity represents any quantity from a kind hierarchy 2024: Improving our safety with a quantities and units library kind_of modi�er 85• Denotes a family of quantities belonging to the same kind – such quantity represents any quantity from a kind hierarchy

Two Forms of CRTP 47 CRTP for Static Interfaces … • … provides a base class for a related set/family of types; • … defines a common interface; • … is used via the base class interface; • … introduces 48 Guideline: Prefer to use the term “Static Interface” to express the intent to create a static family of types. Guideline: Prefer to use the term “Mixin” to express the intent to inherit implementation 53 Guideline: Prefer to use the term “Static Interface” to express the intent to create a static family of types. Guideline: Prefer to use the term “Mixin” to express the intent to inherit implementation

return { begin(v), p }; 36 The C++ version works for a family of containers: remove_if works for an array; the return statement works for a family of containersA word about beauty and elegance • There more precise, applying to a single class, a single function • …or, if that’s what is desired, to a family thereof • For example: class Popular { template friend struct Aficionado; int n = 0;

Genealogy • The process of finding where your family came from • Tracing stories with incomplete information • Answering the why and following the journey • Learning from the past 2 of 45 CppCon 2023 Solving mysteries given a known/semi-unknown macro history • Codebases are micro-histories much like family trees are to historical data • We can learn from how genealogists link together incomplete information