Talk:Floating-point arithmetic

Digits of precision, a confusing early statement

I have removed the portion after the ellipses from the following text formerly found in the article: "12.345 is a floating-point number in a base-ten representation with five digits of precision...However, 12.345 is not a floating-point number with five base-ten digits of precision." I recognize the distinction made (a number with 5 base-ten digits of precision vs. a base-ten representation of a number with five digits of precision) and I suspect the author intended to observe that a binary representation of 12.345 would not have five base-ten digits of precision, but I can't divine what useful thing is intended to have been communicated there, so I've removed it. If I'm missing something obvious in the interpretation of this line, I suspect many others could, and encourage a more direct explanation if it's replaced. john factorial (talk) 18:44, 24 July 2023 (UTC)

The sentence was made nonsensical by this revision by someone who mistook 12.3456 for a typo rather than a counterexample: https://en.wikipedia.org/w/index.php?title=Floating-point_arithmetic&diff=prev&oldid=1166821013

I have reverted the changes, and added a little more verbiage to emphasize that 12.3456 is a counterexample. Taylor Riastradh Campbell (talk) 20:56, 24 July 2023 (UTC)

Counterexample of what?

I have no idea why we're trying to fit a number in 5 digits. ~2025-38812-55 (talk) 06:45, 3 January 2026 (UTC)

5 is the precision of the floating-point system in the example. But the presentation may not be very good. — Vincent Lefèvre (talk) 08:04, 3 January 2026 (UTC)

"Fast math" listed at Redirects for discussion

The redirect Fast math has been listed at redirects for discussion to determine whether its use and function meets the redirect guidelines. Readers of this page are welcome to comment on this redirect at Wikipedia:Redirects for discussion/Log/2026 January 5 § Fast math until a consensus is reached. consarn _{(talck) (contirbuton s)} 19:29, 5 January 2026 (UTC)

Mention 0 as a special case

It should be mentioned that 0 is a special case, just like ∞, because the underlying scheme (normalized mantissa + exponent) cannot represent it.

AFAIU 0 can be argued to be an edge case of Subnormal numbers, but 0 is supported even when subnormals aren't. Musaran (talk) 12:05, 3 February 2026 (UTC)

Whether 0 is regarded as a special case depends on the context. With the main definition of floating-point numbers, normalization is not used. In practice, IEEE 754 decimal formats do no use normalization (it is just required when a result is inexact). — Vincent Lefèvre (talk) 15:09, 3 February 2026 (UTC)

Proposed addition concerning accumulation stagnation in safety-critical system

Iam proposing a short addition to the section “Round-off error in iterative procedures”:

“In finite-precision arithmetic, repeated accumulation can eventually cease to change the running total when the magnitude of an increment falls below half the spacing between adjacent representable values at the magnitude of the accumulated result. In safety-critical embedded systems, this behaviour may require application-specific range analysis, error budgets, target-level verification, and defined handling of numerical failures.”

Possible supporting source:

• Bernhard Wagner, “Floating-Point Arithmetic in Safety-Critical Embedded Systems: A Practical Assurance Strategy for float32, Model-Based Development, and ISO 26262 and IEC 61508”, 2026, Zenodo, https://doi.org/10.5281/zenodo.22712770

Conflict-of-interest disclosure: I am the author of the proposed source. I have therefore not added the text or citation directly and request that an uninvolved editor assess whether the proposed content is relevant and whether the source satisfies Wikipedia’s requirements. The paper is a technical white paper deposited on Zenodo and has not been represented here as peer-reviewed.am proposing a short addition to the section “Round-off error in iterative procedures”: Ostersegler (talk) 05:25, 12 September 2026 (UTC)