Intuitive equals familiar
Summary
This blog post explores the subtle behavior of double-precision floating-point arithmetic when summing decimals (e.g., 0.1 + 0.2). It explains ulp, the hidden bit, and rounding quirks that cause surprising results, then generalizes to the sum of two numbers and introduces error-free transformations (2Sum, Veltkamp splitting, Dekker product) with practical code snippets to reason about and reduce floating-point errors.