Floating-Point Arithmetic Pitfalls¶

Floating-point operations are not associative; operation order affects results. Catastrophic cancellation, absorption, and accumulation patterns can amplify small errors into large ones.

Tension Addressed¶

Precision vs. Performance

Recognizable As¶

Kahan summation, numerically stable algorithms, condition number analysis, reordering operations for precision, different results on different hardware.

Canonical Sources¶

Goldberg, "What Every Computer Scientist Should Know About Floating-Point Arithmetic" (1991); Higham, Accuracy and Stability of Numerical Algorithms

Transfers To¶

Scientific computing, machine learning training, financial calculations, physics simulations

(a + b) + c may not equal a + (b + c) in floating-point. This seemingly minor detail has crashed financial systems, produced incorrect scientific results, and caused debugging nightmares. Numerical stability is a discipline.