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Comparison tolerance: Difference between revisions
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Rework to be CT instead of TC, following the style of IO and ML
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''' | {{Built-in|Comparison tolerance|⎕CT}} is the parameter governing '''tolerant comparison''', an inexact form of [[comparison]] used to mitigate the impact of floating-point rounding error on programs. Two [[number]]s are considered equal when their relative difference is smaller than the comparison tolerance, which is accessed with the [[system variable]] <syntaxhighlight lang=apl inline>⎕CT</syntaxhighlight>. In addition to the comparison functions, tolerance applies to [[Match]] and [[Not Match]], [[Floor]], [[Ceiling]], and [[Modulus]], and [[search function]]s defined in terms of Match (not [[Interval Index]]). | ||
{{quote|In an early talk Ken was explaining the advantages of tolerant comparison. A member of the audience asked incredulously, "Surely you don't mean that when <nowiki>A=B and B=C</nowiki>, A may not equal C?" Without skipping a beat, Ken replied, "Any carpenter knows that!" and went on to the next question.|—Paul Berry<ref>[[Roger Hui]]. [https://keiapl.org/anec/ Ken Iverson Quotations and Anecdotes]. 2005-09-30.</ref>}} | {{quote|In an early talk Ken was explaining the advantages of tolerant comparison. A member of the audience asked incredulously, "Surely you don't mean that when <nowiki>A=B and B=C</nowiki>, A may not equal C?" Without skipping a beat, Ken replied, "Any carpenter knows that!" and went on to the next question.|—Paul Berry<ref>[[Roger Hui]]. [https://keiapl.org/anec/ Ken Iverson Quotations and Anecdotes]. 2005-09-30.</ref>}} | ||
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Comparison tolerance was available in some form since [[APL\360]], where it was described as a "fuzz" (on the suggestion of [[Larry Breed]]<ref>[[Adin Falkoff]], and [[Ken Iverson]]. [https://dl.acm.org/doi/abs/10.1145/960118.808372 ''The Evolution of APL''] ([https://www.jsoftware.com/papers/APLEvol.htm web]). ACM SIGPLAN Notices, Volume 13, Number 8. 1978-08.</ref>) applied to some functions. The value <syntaxhighlight lang=apl inline>⎕CT</syntaxhighlight> to control it was defined with the introduction of [[system variable]]s in [[APL.SV]]. The formula now used for comparison tolerance was proposed by [[Dick Lathwell]] in 1976<ref>[[Dick Lathwell]]. [https://doi.org/10.1145/800114.803685 APL comparison tolerance] at [[APL76]] (also reproduced in [https://www.jsoftware.com/papers/satn23.htm SATN-23]).</ref> and later introduced in [[SHARP APL]] by [[Robert Bernecky]] and others<ref>[[Robert Bernecky]]. [https://www.jsoftware.com/papers/satn23.htm "Comparison Tolerance"]. SATN-23. 1977-06-10.</ref> and included in the APL standard [[ISO 8485:1989]].<ref>[[Adin Falkoff]] and D. L. Orth. [https://doi.org/10.1145/800137.804495 "Development of an APL standard"] at [[APL79]].</ref> However, comparison tolerance is not supported in many newer APLs such as [[ngn/apl]], [[dzaima/APL]], and [[Kap]]. | Comparison tolerance was available in some form since [[APL\360]], where it was described as a "fuzz" (on the suggestion of [[Larry Breed]]<ref>[[Adin Falkoff]], and [[Ken Iverson]]. [https://dl.acm.org/doi/abs/10.1145/960118.808372 ''The Evolution of APL''] ([https://www.jsoftware.com/papers/APLEvol.htm web]). ACM SIGPLAN Notices, Volume 13, Number 8. 1978-08.</ref>) applied to some functions. The value <syntaxhighlight lang=apl inline>⎕CT</syntaxhighlight> to control it was defined with the introduction of [[system variable]]s in [[APL.SV]]. The formula now used for comparison tolerance was proposed by [[Dick Lathwell]] in 1976<ref>[[Dick Lathwell]]. [https://doi.org/10.1145/800114.803685 APL comparison tolerance] at [[APL76]] (also reproduced in [https://www.jsoftware.com/papers/satn23.htm SATN-23]).</ref> and later introduced in [[SHARP APL]] by [[Robert Bernecky]] and others<ref>[[Robert Bernecky]]. [https://www.jsoftware.com/papers/satn23.htm "Comparison Tolerance"]. SATN-23. 1977-06-10.</ref> and included in the APL standard [[ISO 8485:1989]].<ref>[[Adin Falkoff]] and D. L. Orth. [https://doi.org/10.1145/800137.804495 "Development of an APL standard"] at [[APL79]].</ref> However, comparison tolerance is not supported in many newer APLs such as [[ngn/apl]], [[dzaima/APL]], and [[Kap]]. | ||
The application of comparison tolerance to [[search function]]s presents problems for standard hash-based search methods.<ref>[[Roger Hui]]. [https://www.jsoftware.com/papers/Hashing.htm "Hashing for Tolerant Index-Of"] at [[Dyalog '10]].</ref><ref>[[Roger Hui]]. "Tolerant Unique" ([https://www.dyalog.com/uploads/conference/dyalog17/presentations/D10_Tolerant_Unique.zip materials (1.5 MB)], [https://dyalog.tv/Dyalog17/?v=fPWky9IOG40 video (27 mins)]) at [[Dyalog '17]].</ref> | The application of comparison tolerance to [[search function]]s presents problems for standard hash-based search methods.<ref>[[Roger Hui]]. [https://www.jsoftware.com/papers/Hashing.htm "Hashing for Tolerant Index-Of"] at [[Dyalog '10]].</ref><ref>[[Roger Hui]]. "Tolerant Unique" ([https://www.dyalog.com/uploads/conference/dyalog17/presentations/D10_Tolerant_Unique.zip materials (1.5 MB)], [https://dyalog.tv/Dyalog17/?v=fPWky9IOG40 video (27 mins)]) at [[Dyalog '17]].</ref> Many algorithms can be sped up by setting <syntaxhighlight lang=apl>⎕CT←0</syntaxhighlight>, thus disabling tolerant comparison. | ||
== External links == | == External links == | ||