What Every Computer Scientist Should Know About Floating-Point Arithmetic.

Goldberg, D. (1991). What Every Computer Scientist Should Know About Floating-Point Arithmetic. ACM Computing Surveys, 23(1), 5-48.

Type

Journal article

Intellectual base

Primary research

Year

1991

DOI

10.1145/103162.103163

Link

https://docs.oracle.com/cd/E19957-01/806-3568/ncg_goldberg.html

Cited from

computer_science, mathematics

Cited by

5 citations across 5 artifacts.

Each citation links to the sentence it supports in the citing article.

Primes

• Algorithm
  • A common failure is reasoning about the abstract algorithm while the implementation silently violates its assumptions

    This sourceCanonical survey of how finite-precision floating-point implementation diverges from abstract real-number computation, producing rounding error, cancellation, and overflow not visible at the specification level

• Dense Set
  • The substitute-the-dense-subset move is what every floating-point computation relies on — finite-precision rationals standing in for the continuum up to machine tolerance.

    This sourceCanonical reference on finite-precision rationals standing in for the continuum up to machine tolerance.

• Monoid
  • IEEE-754 floating-point addition has a plausible unit in +0.0 and is not associative, so parallel summation of the same floats returns different totals under different partitionings — a defect that hides because it is invisible at small scale and on one core.

    This sourceShows that floating-point addition is not associative, so a summation's result depends on how the terms are grouped.

Domain-specific

• Extended-Precision Floating-Point Format
  • Extra intermediate capacity can reduce some roundoff and premature range failures, but it can also change branch outcomes, expose double-rounding cases, or undermine reproducibility when spills and optimization alter where narrowing occurs.

Mechanisms

• Cross-Representation Regression Suite
  • Set with the numerical realities in mind: floating-point arithmetic is not associative, so different summation orders legitimately differ in the last digits.

    This sourceExplains that floating-point addition is nonassociative and that reordered sums can legitimately produce different rounded results.

Verification

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Links previously used in the corpus

Before the registry existed this work was also linked 1 other way.

• https://doi.org/10.1145/103162.103163 ×4

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