Further Reading: Floating-Point Arithmetic

Floating point has an unusually good literature — it is a small, deep subject with a few definitive sources. Everything below is Tier 1 (canonical, confidently recommended) or Tier 2 (real and worth seeking, but confirm the current edition or URL yourself). Read at least the Goldberg paper; it is the common ancestor of every treatment of the topic, including this chapter.

The one paper everyone cites

• David Goldberg, "What Every Computer Scientist Should Know About Floating-Point Arithmetic," ACM Computing Surveys, 1991. The classic, freely available online. It develops IEEE 754, rounding, machine epsilon, and cancellation from first principles, with the rigor this chapter compresses. If you read one thing beyond this chapter, read this. Tier 1.

Books on numerical accuracy

• Nicholas J. Higham, Accuracy and Stability of Numerical Algorithms (SIAM). The definitive treatment of rounding-error analysis, conditioning, and stability — the rigorous version of §20.5. Encyclopedic and authoritative; the reference you graduate to when "about $k$ digits" is not precise enough. Tier 1.
• Michael Overton, Numerical Computing with IEEE Floating Point Arithmetic (SIAM). A short, readable book devoted entirely to IEEE 754 — the bit layout, special values, and their consequences. An excellent next step from this chapter, at roughly this chapter's level. Tier 1.
• Jean-Michel Muller et al., Handbook of Floating-Point Arithmetic (Birkhäuser). The comprehensive reference on the standard and its algorithms (including compensated summation and correctly-rounded functions). A handbook to consult, not to read cover to cover. Tier 2.

The standard and the Fortran interface

• IEEE Std 754-2019, IEEE Standard for Floating-Point Arithmetic. The primary source: the exact encoding, rounding rules, and exception behavior every conforming processor implements. Dense, but authoritative when a detail is in dispute. Tier 1.
• Metcalf, Reid, and Cohen, Modern Fortran Explained (Oxford University Press). The chapters on the ieee_arithmetic, ieee_exceptions, and ieee_features intrinsic modules are the reference for what §20.4 introduced — including the full set of ieee_* inquiry and control routines beyond ieee_is_nan and ieee_is_finite. Tier 1.
• Stephen Chapman, Fortran for Scientists and Engineers (McGraw-Hill). Its treatment of kinds, precision, and the numeric inquiry intrinsics complements Chapter 3 and this chapter with more worked examples. Tier 1.

Free and online

• The GCC / gfortran documentation. The reference for how gfortran implements the real kinds, the ieee_arithmetic module, and the -ffpe-trap, -ffpe-summary, and -fno-underflow flags. Consult it for the exact spelling and behavior of the exception-trapping options from §20.4. Tier 1.
• float.exposed and similar IEEE-754 bit visualizers. Interactive pages that let you toggle the sign, exponent, and fraction bits of a single or double and watch the decimal value change. Ten minutes here makes §20.1 physical. (Any reputable "IEEE 754 visualizer" serves; confirm the current URL.) Tier 2.
• 0.30000000000000004.com. A one-page site that shows 0.1 + 0.2 in dozens of languages, all giving the same answer — vivid proof that this chapter is about the hardware, not about Fortran. Tier 2.

Suggested order

1. Read Goldberg now — it is the canonical companion to this chapter and freely available.
2. Play with an IEEE-754 bit visualizer to make the sign/exponent/fraction split from §20.1 concrete.
3. Keep Overton on the shelf as the friendly book-length treatment, and reach for Higham when you need to prove an error bound rather than estimate one.
4. When you use the ieee_arithmetic module in earnest, read its chapter in Metcalf, Reid, and Cohen for the routines beyond the two this chapter needed.