C++

Duality: The Hidden Structure of Opposites

Many structures come in pairs: forward/reverse AD, push/pull iteration, encode/decode. Recognizing duality lets you transfer theorems and insights between domains.

Seeing Structure First

A reflection on eleven explorations in generic programming, and how algorithms arise from algebraic structure.

Alexander Stepanov: Efficient Programming with Components (A9 Lectures)

Notes

18-part lecture series on efficient programming. Covers the intellectual foundations behind STL.

Elements of Programming

Notes

Rigorous foundations of generic programming. Connects algebra and algorithms. Stepanov’s magnum opus.

Sean Parent: C++ Seasoning (That's a Rotate)

Notes

Classic talk on recognizing algorithmic patterns. ‘No raw loops’ - shows how rotate solves many problems elegantly.

Alga: Algebraic Text Processing with Fuzzy Matching

A C++20 header-only library for algebraic text processing and compositional parsing with fuzzy matching.

CBT: Computational Basis Transforms

A C++17 header-only library that formalizes a pattern behind FFT, logarithmic arithmetic, and Bayesian inference: transform to a domain where your target operation is cheap.

libdis: Disjoint Interval Sets as a Complete Boolean Algebra

A C++ header-only library that treats disjoint interval sets as proper mathematical objects with Boolean algebra operations.

Alea: A Modern C++ Library for Algebraic Random Elements

Alga: Algebraic Parser Composition through Monadic Design A C++20 Template Library for Type-Safe Text Processing

ZeroIPC: Shared Memory as a Computational Substrate

ZeroIPC treats shared memory not as passive storage but as an active computational substrate, bringing futures, lazy evaluation, reactive streams, and CSP channels to IPC with zero-copy performance.

Algebraic Composition for Streaming Data Reduction: A Type-Safe Framework with Numerical Stability

Algebraic Hashing A Modern C++20 Library for Composable Hash Functions Version 2.0

Cryptographic perfect hash functions: A theoretical analysis on space efficiency, time complexity, and entropy

maph: Maps Based on Perfect Hashing for Sub-Microsecond Key-Value Storage

PFC: Zero-Copy Data Compression Through Prefix-Free Codecs and Generic Programming

Differentiation: Three Ways

Three approaches to computing derivatives, forward-mode AD, reverse-mode AD, and finite differences, each with different trade-offs for numerical computing and machine learning.

maph: Maps Based on Perfect Hashing for Sub-Microsecond Key-Value Storage

A key-value store built on memory-mapped I/O, approximate perfect hashing, and lock-free atomics. Sub-100ns median latency, 10M ops/sec single-threaded.

PFC: Zero-Copy Data Compression Through Prefix-Free Codecs

A header-only C++20 library that achieves 3-10x compression with zero marshaling overhead using prefix-free codes and Stepanov-style generic programming.

Accumux: Compositional Online Statistical Reductions in C++

A C++20 library for composing online statistical accumulators with numerically stable algorithms and algebraic composition.

Runtime Polymorphism Without Inheritance

Sean Parent's type erasure gives you value-semantic polymorphism without inheritance. Combined with Stepanov's algebraic thinking, you can type-erase entire algebraic structures.

Numerical Integration with Generic Concepts

Numerical integration meets generic programming. By requiring only ordered field operations, the quadrature routines work with dual numbers, giving you differentiation under the integral for free.

Reverse-Mode Automatic Differentiation

Reverse-mode automatic differentiation is just the chain rule applied systematically. I built one in C++20 to understand what PyTorch and JAX are actually doing.

Algebraic Hashing: Composable Hash Functions Through XOR

A C++ library for composable hash functions using algebraic structure over XOR, with template metaprogramming.

Numerical Differentiation

Choosing step size h for finite differences: small enough for a good approximation, not so small that floating-point errors eat your lunch.

Forward-Mode Automatic Differentiation

Dual numbers extend the reals with an infinitesimal epsilon where epsilon^2 = 0. Evaluate f(x + epsilon) and you get f(x) + f'(x)*epsilon. The derivative falls out of the algebra.

Teaching Linear Algebra with C++20 Concepts

elementa is a linear algebra library built to teach. Every design decision prioritizes clarity over cleverness. Code that reads like a textbook and compiles.

Polynomials as Euclidean Domains

The same GCD algorithm works for integers and polynomials because both are Euclidean domains. One structure, many types, same algorithms.

Exact Rational Arithmetic

Rational numbers give exact arithmetic where floating-point fails. The implementation connects GCD, the Stern-Brocot tree, and the algebraic structure of fields.

How Iterators Give You N+M Instead of NxM

Iterators reduce the NxM algorithm-container problem to N+M by interposing an abstraction layer, following Stepanov's generic programming approach.

Is It Prime?

The Miller-Rabin primality test demonstrates how probabilistic algorithms achieve arbitrary certainty, trading absolute truth for practical efficiency.

Modular Arithmetic as Rings

Integers modulo N form a ring, an algebraic structure that determines which algorithms apply. Understanding this structure unlocks algorithms from cryptography to competitive programming.

One Algorithm, Infinite Powers

The Russian peasant algorithm computes products, powers, Fibonacci numbers, and more, once you see the underlying algebraic structure.

Packed Containers: Zero-Waste Bit-Level Storage in C++

What if containers wasted zero bits? A C++ library for packing arbitrary value types at the bit level using pluggable codecs.