Revision as of 01:12, 9 July 2025 edit Taylor Riastradh Campbell (talk \| contribs) 384 edits →Incidents: Clarify what happened with the Patriot missile battery, which was, despite popular wisdom, not caused by using floating-point, but rather by using two different unit conversions that disagreed, with a discrepancy that increased with uptime. ← Previous edit		Revision as of 11:30, 9 July 2025 edit undo Vincent Lefèvre (talk \| contribs) Extended confirmed users 5,208 edits →Incidents: The intent is that there is a single time unit: 0.1s. The issue is that the software assumed that its accuracy did not matter; Skeel says: "this time difference should be in error by only 0.0001%, a truly insignificant amount". Something that may remain true... until a cancellation occurs like here. Next edit →
Line 575: === Incidents === * On 25 February 1991, ana ~~error~~[[loss of significance]] in a [[MIM-104 Patriot]] missile battery [[MIM-104 Patriot#Failure at Dhahran\|prevented it from intercepting]] an incoming [[Al Hussein (missile)\|Scud]] missile in [[Dhahran]], [[Saudi Arabia]], contributing to the death of 28 soldiers from the U.S. Army's [[14th Quartermaster Detachment]].<ref name="GAO report IMTEC 92-26"/> The weapons control computer counted time in an integer number of tenths of a second since boot. For conversion to a floating-point number of seconds in velocity and position calculations, the software originally multiplied this number by a 24-bit [[Fixed-point arithmetic\|fixed-point]] binary approximation to 0.1, specifically <math display="block">0.00011001100110011001100_2 = 0.1 \times (1 - 2^{-20}).</math> Some parts of the software were later adapted to use a more accurate conversion to floating-point, but some parts were not updated and still used the 24-bit approximation.<ref name="Skeel"/> These parts of the software drifted from one another by about 3.43 milliseconds per hour. After 20 hours, the discrepancy of about 68.7 ms was enough for the radar tracking system to lose track of Scuds; the control system in the Dhahran missile battery had been running for about 100 hours when it failed to track and intercept an incoming Scud.<ref name="GAO report IMTEC 92-26"/> ~~The error arose not from the use of floating-point, but from the use of two different unit conversions when representing time in different parts of a calculation.~~ * {{Clarify\|date=November 2024\|reason=It is not clear how this is an incident (the section title may have to be modified to cover more than incidents) and how this is due to floating-point arithmetic (rather than number approximations in general). The term "invisible" may also be misleading without following explanations. \|text=[[Salami slicing tactics#Financial schemes\|Salami slicing]] is the practice of removing the 'invisible' part of a transaction into a separate account.}}

Floating-point arithmetic: Difference between revisions