How do I summation algorithms like Kahan summation in C++?

The Kahan summation algorithm is an improved way to reduce numerical errors that can occur when adding a sequence of finite precision floating-point numbers. It helps to produce a more accurate sum by keeping track of small errors that are introduced during the addition process.

Example Implementation of Kahan Summation in C++

#include #include double kahanSummation(const std::vector& numbers) { double sum = 0.0; // Running sum double c = 0.0; // A running compensation for lost low-order bits for (double number : numbers) { double y = number - c; // So far, so good: c is zero. double t = sum + y; // Alas, sum is big, y small, so low-order digits of y are lost. c = (t - sum) - y; // (t - sum) recovers the high-order part of y; subtracting y recovers the lost low-order part. sum = t; // Algebraically, c should always be zero. } return sum; } int main() { std::vector numbers = { 1e10, 1.0, 1e-10 }; // Example numbers double result = kahanSummation(numbers); std::cout << "Kahan Summation Result: " << result << std::endl; return 0; }

Kahan summation numerical stability floating-point arithmetic C++ algorithms

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