Accumux

Accumux is a modern C++20 library for compositional online data reductions with mathematical rigor. It provides a framework for combining statistical accumulators using algebraic composition, enabling single-pass computation of complex statistical measures with optimal numerical stability.

Key Features

• Numerically Stable: Kahan-Babuška-Neumaier and Welford algorithms for maximum accuracy
• Single-Pass Efficiency: Compute multiple statistics in O(1) space complexity
• Compositional: Natural algebraic syntax (a + b) for combining accumulators
• Type Safe: C++20 concepts prevent incorrect compositions at compile-time
• Header-Only: Zero dependencies, easy integration

Usage Example

#include "accumux/accumulators/kbn_sum.hpp"
#include "accumux/accumulators/welford.hpp"
#include "accumux/core/composition.hpp"

using namespace accumux;

// Create composed accumulator for sum + statistics
auto stats = kbn_sum<double>() + welford_accumulator<double>();

// Process data in single pass
for (const auto& value : data) {
    stats += value;
}

// Extract results
auto sum = stats.get_first().eval();
auto mean = stats.get_second().mean();
auto variance = stats.get_second().variance();
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Core Accumulators

• kbn_sum<T> - Numerically stable summation
• welford_accumulator<T> - Mean, variance, standard deviation
• minmax_accumulator<T> - Combined min/max tracking
• count_accumulator - Element counting
• product_accumulator<T> - Product with overflow protection

Built on solid algebraic foundations (monoids, homomorphisms) with performance benchmarks showing 476M values/sec for single accumulator operations.

View on GitHub | Conan Package