High Performance C++

Method

Every entry follows the same derivation. A subject is admitted only when it can be carried the whole way along it.

1. AbstractionThe mathematical object and the structure it carries.
2. SpecificationIts operations, laws and admissible domain, stated formally.
3. Type / conceptThe C++ encoding of that specification as a constrained interface.
4. ImplementationA generic algorithm written against the concept, not a type.
5. ComplexityOperation counts and working set under a stated cost model.
6. Hardware mappingLayout, locality, vector width, and the parallel decomposition.
7. MeasurementTimings against a declared machine, compiler and method.

Contents

1. Modern C++

   The language as a medium for stating abstractions exactly: templates, concepts, constraints, and computation performed during translation.

   Language · Templates · Generic programming · Concepts · Constraints · Metaprogramming · Compile-time programming · constexpr / consteval · Standard library

2. Mathematics

   The structures that generic components are written against (algebraic, analytic and probabilistic) stated in the form used later as concept requirements.

   Algebra · Linear algebra · Analysis · Numerical analysis · Optimization · Probability · Computational mathematics

3. High Performance

   Cost models above the asymptotic one: memory hierarchy, data layout, vector execution, and the machine models that concurrency is written against.

   Computational complexity · Memory · Cache locality · Data layout · SIMD · Vectorization · Parallelism · Concurrency · GPU computing

4. Scientific Computing

   Numerical kernels developed to the point of implementation: factorizations, sparse structure, quadrature, evolution equations and differentiation.

   Numerical linear algebra · Sparse computation · Numerical integration · Differential equations · Partial differential equations · Automatic differentiation · Optimization

5. Formal C++

   Types read as sets with operations, concepts as predicates over those types, and the semantic obligations that the type system does not check.

   Types as abstractions · Concepts as predicates · Constraints · Semantic requirements · Type-level programming · Compile-time reasoning · Correctness

Supporting material

• ExamplesComplete derivations, each carried from a mathematical statement to a measured implementation.
• BenchmarksMeasurement method, reported hardware, and results for the kernels developed in the reference.
• Essays and NotesLonger arguments about abstraction, cost and correctness that do not belong in a reference entry.