Appendix D — Floating Point and Machine Precision

Warning

Appendix stub. Planned (author request, July 2026). See docs/backlog.md §1.

Every number in this book is a lie of finite precision. What a float actually is (sign, exponent, mantissa), machine epsilon, why \(0.1 + 0.2 \neq 0.3\), catastrophic cancellation, and the patterns deep learning uses to survive it: log-sum-exp (the trick inside every softmax), solving instead of inverting, and mixed-precision training (fp16/bf16) — the bridge to quantization in Chapter 17.