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Comparison function - Revision history
2024-03-28T20:17:50Z
Revision history for this page on the wiki
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Adám Brudzewsky: Text replacement - "<source" to "<syntaxhighlight"
2022-09-10T22:24:55Z
<p>Text replacement - "<source" to "<syntaxhighlight"</p>
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 22:24, 10 September 2022</td>
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<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>A '''comparison function''' is one of the six [[primitive function|primitive]] [[dyadic]] [[scalar function]]s whose result on scalars is a [[Boolean]] determined by the numerical ordering of the two [[argument]]s. Comparisons are subject to [[comparison tolerance]]. The comparison functions can be subdivided into two equalities <<del style="font-weight: bold; text-decoration: none;">source </del>lang=apl inline>=</syntaxhighlight> <<del style="font-weight: bold; text-decoration: none;">source </del>lang=apl inline>≠</syntaxhighlight>, which depend only on whether the arguments are equal and not on the ordering of the arguments, and may be applied to [[character]]s, and four inequalities <<del style="font-weight: bold; text-decoration: none;">source </del>lang=apl inline><</syntaxhighlight> <<del style="font-weight: bold; text-decoration: none;">source </del>lang=apl inline>≤</syntaxhighlight> <<del style="font-weight: bold; text-decoration: none;">source </del>lang=apl inline>≥</syntaxhighlight> <<del style="font-weight: bold; text-decoration: none;">source </del>lang=apl inline>></syntaxhighlight>, which depend on ordering and may not be applied to [[character]]s.</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>A '''comparison function''' is one of the six [[primitive function|primitive]] [[dyadic]] [[scalar function]]s whose result on scalars is a [[Boolean]] determined by the numerical ordering of the two [[argument]]s. Comparisons are subject to [[comparison tolerance]]. The comparison functions can be subdivided into two equalities <<ins style="font-weight: bold; text-decoration: none;">syntaxhighlight </ins>lang=apl inline>=</syntaxhighlight> <<ins style="font-weight: bold; text-decoration: none;">syntaxhighlight </ins>lang=apl inline>≠</syntaxhighlight>, which depend only on whether the arguments are equal and not on the ordering of the arguments, and may be applied to [[character]]s, and four inequalities <<ins style="font-weight: bold; text-decoration: none;">syntaxhighlight </ins>lang=apl inline><</syntaxhighlight> <<ins style="font-weight: bold; text-decoration: none;">syntaxhighlight </ins>lang=apl inline>≤</syntaxhighlight> <<ins style="font-weight: bold; text-decoration: none;">syntaxhighlight </ins>lang=apl inline>≥</syntaxhighlight> <<ins style="font-weight: bold; text-decoration: none;">syntaxhighlight </ins>lang=apl inline>></syntaxhighlight>, which depend on ordering and may not be applied to [[character]]s.</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>The six comparison functions are [[Less Than]] (<<del style="font-weight: bold; text-decoration: none;">source </del>lang=apl inline><</syntaxhighlight>), [[Less Than or Equal]] (<<del style="font-weight: bold; text-decoration: none;">source </del>lang=apl inline>≤</syntaxhighlight>), [[Equal to]] (<<del style="font-weight: bold; text-decoration: none;">source </del>lang=apl inline>=</syntaxhighlight>), [[Greater Than or Equal]] (<<del style="font-weight: bold; text-decoration: none;">source </del>lang=apl inline>≥</syntaxhighlight>), [[Greater Than]] (<<del style="font-weight: bold; text-decoration: none;">source </del>lang=apl inline>></syntaxhighlight>), and [[Not Equal to]] (<<del style="font-weight: bold; text-decoration: none;">source </del>lang=apl inline>≠</syntaxhighlight>). You can take a closer look at how these six comparison functions behave in [https://nbviewer.jupyter.org/github/Dyalog/dyalog-jupyter-notebooks/blob/master/Closer%20look%20at%20the%20comparison%20functions.ipynb this APL Jupyter notebook].</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>The six comparison functions are [[Less Than]] (<<ins style="font-weight: bold; text-decoration: none;">syntaxhighlight </ins>lang=apl inline><</syntaxhighlight>), [[Less Than or Equal]] (<<ins style="font-weight: bold; text-decoration: none;">syntaxhighlight </ins>lang=apl inline>≤</syntaxhighlight>), [[Equal to]] (<<ins style="font-weight: bold; text-decoration: none;">syntaxhighlight </ins>lang=apl inline>=</syntaxhighlight>), [[Greater Than or Equal]] (<<ins style="font-weight: bold; text-decoration: none;">syntaxhighlight </ins>lang=apl inline>≥</syntaxhighlight>), [[Greater Than]] (<<ins style="font-weight: bold; text-decoration: none;">syntaxhighlight </ins>lang=apl inline>></syntaxhighlight>), and [[Not Equal to]] (<<ins style="font-weight: bold; text-decoration: none;">syntaxhighlight </ins>lang=apl inline>≠</syntaxhighlight>). You can take a closer look at how these six comparison functions behave in [https://nbviewer.jupyter.org/github/Dyalog/dyalog-jupyter-notebooks/blob/master/Closer%20look%20at%20the%20comparison%20functions.ipynb this APL Jupyter notebook].</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Because comparison functions have Boolean results on Boolean arguments (they always have Boolean results), they are [[Boolean function]]s. In fact, the majority of nontrivial dyadic Boolean functions are comparison functions.</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Because comparison functions have Boolean results on Boolean arguments (they always have Boolean results), they are [[Boolean function]]s. In fact, the majority of nontrivial dyadic Boolean functions are comparison functions.</div></td></tr>
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<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>| <<del style="font-weight: bold; text-decoration: none;">source </del>lang=apl inline>≠</syntaxhighlight> || 1 || 0 || 1</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>| <<ins style="font-weight: bold; text-decoration: none;">syntaxhighlight </ins>lang=apl inline>≠</syntaxhighlight> || 1 || 0 || 1</div></td></tr>
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<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>The traditional APL ordering of the comparison functions used above, which was used at least as early as [[APL\360]], resembles a [[wikipedia:Gray code|Gray code]] ordering of the values which define the comparison functions. Adjacent values differ by only a change of one bit, but the list is not a true Gray code because it excludes the all-0 and all-1 combinations.</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>The traditional APL ordering of the comparison functions used above, which was used at least as early as [[APL\360]], resembles a [[wikipedia:Gray code|Gray code]] ordering of the values which define the comparison functions. Adjacent values differ by only a change of one bit, but the list is not a true Gray code because it excludes the all-0 and all-1 combinations.</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>{{APL built-ins}}[[Category:Comparison functions| ]][[Category:Lists]]</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>{{APL built-ins}}[[Category:Comparison functions| ]][[Category:Lists]]</div></td></tr>
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Adám Brudzewsky
https://aplwiki.com/index.php?title=Comparison_function&diff=9179&oldid=prev
Adám Brudzewsky: Text replacement - "</source>" to "</syntaxhighlight>"
2022-09-10T21:04:04Z
<p>Text replacement - "</source>" to "</syntaxhighlight>"</p>
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<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>|}</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>|}</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>A '''comparison function''' is one of the six [[primitive function|primitive]] [[dyadic]] [[scalar function]]s whose result on scalars is a [[Boolean]] determined by the numerical ordering of the two [[argument]]s. Comparisons are subject to [[comparison tolerance]]. The comparison functions can be subdivided into two equalities <source lang=apl inline>=</<del style="font-weight: bold; text-decoration: none;">source</del>> <source lang=apl inline>≠</<del style="font-weight: bold; text-decoration: none;">source</del>>, which depend only on whether the arguments are equal and not on the ordering of the arguments, and may be applied to [[character]]s, and four inequalities <source lang=apl inline><</<del style="font-weight: bold; text-decoration: none;">source</del>> <source lang=apl inline>≤</<del style="font-weight: bold; text-decoration: none;">source</del>> <source lang=apl inline>≥</<del style="font-weight: bold; text-decoration: none;">source</del>> <source lang=apl inline>></<del style="font-weight: bold; text-decoration: none;">source</del>>, which depend on ordering and may not be applied to [[character]]s.</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>A '''comparison function''' is one of the six [[primitive function|primitive]] [[dyadic]] [[scalar function]]s whose result on scalars is a [[Boolean]] determined by the numerical ordering of the two [[argument]]s. Comparisons are subject to [[comparison tolerance]]. The comparison functions can be subdivided into two equalities <source lang=apl inline>=</<ins style="font-weight: bold; text-decoration: none;">syntaxhighlight</ins>> <source lang=apl inline>≠</<ins style="font-weight: bold; text-decoration: none;">syntaxhighlight</ins>>, which depend only on whether the arguments are equal and not on the ordering of the arguments, and may be applied to [[character]]s, and four inequalities <source lang=apl inline><</<ins style="font-weight: bold; text-decoration: none;">syntaxhighlight</ins>> <source lang=apl inline>≤</<ins style="font-weight: bold; text-decoration: none;">syntaxhighlight</ins>> <source lang=apl inline>≥</<ins style="font-weight: bold; text-decoration: none;">syntaxhighlight</ins>> <source lang=apl inline>></<ins style="font-weight: bold; text-decoration: none;">syntaxhighlight</ins>>, which depend on ordering and may not be applied to [[character]]s.</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>The six comparison functions are [[Less Than]] (<source lang=apl inline><</<del style="font-weight: bold; text-decoration: none;">source</del>>), [[Less Than or Equal]] (<source lang=apl inline>≤</<del style="font-weight: bold; text-decoration: none;">source</del>>), [[Equal to]] (<source lang=apl inline>=</<del style="font-weight: bold; text-decoration: none;">source</del>>), [[Greater Than or Equal]] (<source lang=apl inline>≥</<del style="font-weight: bold; text-decoration: none;">source</del>>), [[Greater Than]] (<source lang=apl inline>></<del style="font-weight: bold; text-decoration: none;">source</del>>), and [[Not Equal to]] (<source lang=apl inline>≠</<del style="font-weight: bold; text-decoration: none;">source</del>>). You can take a closer look at how these six comparison functions behave in [https://nbviewer.jupyter.org/github/Dyalog/dyalog-jupyter-notebooks/blob/master/Closer%20look%20at%20the%20comparison%20functions.ipynb this APL Jupyter notebook].</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>The six comparison functions are [[Less Than]] (<source lang=apl inline><</<ins style="font-weight: bold; text-decoration: none;">syntaxhighlight</ins>>), [[Less Than or Equal]] (<source lang=apl inline>≤</<ins style="font-weight: bold; text-decoration: none;">syntaxhighlight</ins>>), [[Equal to]] (<source lang=apl inline>=</<ins style="font-weight: bold; text-decoration: none;">syntaxhighlight</ins>>), [[Greater Than or Equal]] (<source lang=apl inline>≥</<ins style="font-weight: bold; text-decoration: none;">syntaxhighlight</ins>>), [[Greater Than]] (<source lang=apl inline>></<ins style="font-weight: bold; text-decoration: none;">syntaxhighlight</ins>>), and [[Not Equal to]] (<source lang=apl inline>≠</<ins style="font-weight: bold; text-decoration: none;">syntaxhighlight</ins>>). You can take a closer look at how these six comparison functions behave in [https://nbviewer.jupyter.org/github/Dyalog/dyalog-jupyter-notebooks/blob/master/Closer%20look%20at%20the%20comparison%20functions.ipynb this APL Jupyter notebook].</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Because comparison functions have Boolean results on Boolean arguments (they always have Boolean results), they are [[Boolean function]]s. In fact, the majority of nontrivial dyadic Boolean functions are comparison functions.</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Because comparison functions have Boolean results on Boolean arguments (they always have Boolean results), they are [[Boolean function]]s. In fact, the majority of nontrivial dyadic Boolean functions are comparison functions.</div></td></tr>
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<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>! < !! = !! ></div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>! < !! = !! ></div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>|-</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>|-</div></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>| <source lang=apl inline><</<del style="font-weight: bold; text-decoration: none;">source</del>> || 1 || 0 || 0</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>| <source lang=apl inline><</<ins style="font-weight: bold; text-decoration: none;">syntaxhighlight</ins>> || 1 || 0 || 0</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>|-</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>|-</div></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>| <source lang=apl inline>≤</<del style="font-weight: bold; text-decoration: none;">source</del>> || 1 || 1 || 0</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>| <source lang=apl inline>≤</<ins style="font-weight: bold; text-decoration: none;">syntaxhighlight</ins>> || 1 || 1 || 0</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>|-</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>|-</div></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>| <source lang=apl inline>=</<del style="font-weight: bold; text-decoration: none;">source</del>> || 0 || 1 || 0</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>| <source lang=apl inline>=</<ins style="font-weight: bold; text-decoration: none;">syntaxhighlight</ins>> || 0 || 1 || 0</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>|-</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>|-</div></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>| <source lang=apl inline>≥</<del style="font-weight: bold; text-decoration: none;">source</del>> || 0 || 1 || 1</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>| <source lang=apl inline>≥</<ins style="font-weight: bold; text-decoration: none;">syntaxhighlight</ins>> || 0 || 1 || 1</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>|-</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>|-</div></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>| <source lang=apl inline>></<del style="font-weight: bold; text-decoration: none;">source</del>> || 0 || 0 || 1</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>| <source lang=apl inline>></<ins style="font-weight: bold; text-decoration: none;">syntaxhighlight</ins>> || 0 || 0 || 1</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>|-</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>|-</div></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>| <source lang=apl inline>≠</<del style="font-weight: bold; text-decoration: none;">source</del>> || 1 || 0 || 1</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>| <source lang=apl inline>≠</<ins style="font-weight: bold; text-decoration: none;">syntaxhighlight</ins>> || 1 || 0 || 1</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>|}</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>|}</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>The traditional APL ordering of the comparison functions used above, which was used at least as early as [[APL\360]], resembles a [[wikipedia:Gray code|Gray code]] ordering of the values which define the comparison functions. Adjacent values differ by only a change of one bit, but the list is not a true Gray code because it excludes the all-0 and all-1 combinations.</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>The traditional APL ordering of the comparison functions used above, which was used at least as early as [[APL\360]], resembles a [[wikipedia:Gray code|Gray code]] ordering of the values which define the comparison functions. Adjacent values differ by only a change of one bit, but the list is not a true Gray code because it excludes the all-0 and all-1 combinations.</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>{{APL built-ins}}[[Category:Comparison functions| ]][[Category:Lists]]</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>{{APL built-ins}}[[Category:Comparison functions| ]][[Category:Lists]]</div></td></tr>
</table>
Adám Brudzewsky
https://aplwiki.com/index.php?title=Comparison_function&diff=4566&oldid=prev
RGS: Fix two minor language issues and add link to jupyter notebook on the comparison functions.
2020-05-28T13:26:31Z
<p>Fix two minor language issues and add link to jupyter notebook on the comparison functions.</p>
<table style="background-color: #fff; color: #202122;" data-mw="interface">
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Older revision</td>
<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 13:26, 28 May 2020</td>
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<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>|}</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>|}</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>A '''comparison function''' is one of the six [[primitive function|primitive]] [[dyadic]] [[scalar function]]s whose result on scalars is a [[Boolean]] determined by the numerical ordering of the two [[argument]]s. Comparisons are subject to [[comparison tolerance]]. The comparison functions can be subdivided into two equalities <source lang=apl inline>=</source> <source lang=apl inline>≠</source>, which depend only on whether the arguments are equal and not the ordering of <del style="font-weight: bold; text-decoration: none;">unequal argument</del>, and may be applied to [[character]]s, and four inequalities <source lang=apl inline><</source> <source lang=apl inline>≤</source> <source lang=apl inline>≥</source> <source lang=apl inline>></source>, which depend on ordering and may not be applied to [[character]]s.</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>A '''comparison function''' is one of the six [[primitive function|primitive]] [[dyadic]] [[scalar function]]s whose result on scalars is a [[Boolean]] determined by the numerical ordering of the two [[argument]]s. Comparisons are subject to [[comparison tolerance]]. The comparison functions can be subdivided into two equalities <source lang=apl inline>=</source> <source lang=apl inline>≠</source>, which depend only on whether the arguments are equal and not <ins style="font-weight: bold; text-decoration: none;">on </ins>the ordering of <ins style="font-weight: bold; text-decoration: none;">the arguments</ins>, and may be applied to [[character]]s, and four inequalities <source lang=apl inline><</source> <source lang=apl inline>≤</source> <source lang=apl inline>≥</source> <source lang=apl inline>></source>, which depend on ordering and may not be applied to [[character]]s.</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>The six comparison functions are [[Less Than]] (<source lang=apl inline><</source>), [[Less Than or Equal]] (<source lang=apl inline>≤</source>), [[Equal to]] (<source lang=apl inline>=</source>), [[Greater Than or Equal]] (<source lang=apl inline>≥</source>), [[Greater Than]] (<source lang=apl inline>></source>), and [[Not Equal to]] (<source lang=apl inline>≠</source>).</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>The six comparison functions are [[Less Than]] (<source lang=apl inline><</source>), [[Less Than or Equal]] (<source lang=apl inline>≤</source>), [[Equal to]] (<source lang=apl inline>=</source>), [[Greater Than or Equal]] (<source lang=apl inline>≥</source>), [[Greater Than]] (<source lang=apl inline>></source>), and [[Not Equal to]] (<source lang=apl inline>≠</source>)<ins style="font-weight: bold; text-decoration: none;">. You can take a closer look at how these six comparison functions behave in [https://nbviewer.jupyter.org/github/Dyalog/dyalog-jupyter-notebooks/blob/master/Closer%20look%20at%20the%20comparison%20functions.ipynb this APL Jupyter notebook]</ins>.</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Because comparison functions have Boolean results on Boolean arguments (they always have Boolean results), they are [[Boolean function]]s. In fact, the majority of nontrivial dyadic Boolean functions are comparison functions.</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Because comparison functions have Boolean results on Boolean arguments (they always have Boolean results), they are [[Boolean function]]s. In fact, the majority of nontrivial dyadic Boolean functions are comparison functions.</div></td></tr>
</table>
RGS
https://aplwiki.com/index.php?title=Comparison_function&diff=4186&oldid=prev
Marshall at 10:26, 4 May 2020
2020-05-04T10:26:24Z
<p></p>
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 10:26, 4 May 2020</td>
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<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>The traditional APL ordering of the comparison functions used above, which was used at least as early as [[APL\360]], resembles a [[wikipedia:Gray code|Gray code]] ordering of the values which define the comparison functions. Adjacent values differ by only a change of one bit, but the list is not a true Gray code because it excludes the all-0 and all-1 combinations.</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>The traditional APL ordering of the comparison functions used above, which was used at least as early as [[APL\360]], resembles a [[wikipedia:Gray code|Gray code]] ordering of the values which define the comparison functions. Adjacent values differ by only a change of one bit, but the list is not a true Gray code because it excludes the all-0 and all-1 combinations.</div></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>{{APL built-ins}}[[Category:<del style="font-weight: bold; text-decoration: none;">Primitive </del>functions]]</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>{{APL built-ins}}[[Category:<ins style="font-weight: bold; text-decoration: none;">Comparison </ins>functions<ins style="font-weight: bold; text-decoration: none;">| ]][[Category:Lists</ins>]]</div></td></tr>
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Marshall
https://aplwiki.com/index.php?title=Comparison_function&diff=3660&oldid=prev
Marshall: Text replacement - "{{APL built-ins}}" to "{{APL built-ins}}Category:Primitive functions"
2020-04-30T13:43:54Z
<p>Text replacement - "{{APL built-ins}}" to "{{APL built-ins}}<a href="/wiki/Category:Primitive_functions" title="Category:Primitive functions">Category:Primitive functions</a>"</p>
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<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>The traditional APL ordering of the comparison functions used above, which was used at least as early as [[APL\360]], resembles a [[wikipedia:Gray code|Gray code]] ordering of the values which define the comparison functions. Adjacent values differ by only a change of one bit, but the list is not a true Gray code because it excludes the all-0 and all-1 combinations.</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>The traditional APL ordering of the comparison functions used above, which was used at least as early as [[APL\360]], resembles a [[wikipedia:Gray code|Gray code]] ordering of the values which define the comparison functions. Adjacent values differ by only a change of one bit, but the list is not a true Gray code because it excludes the all-0 and all-1 combinations.</div></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>{{APL built-ins}}</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>{{APL built-ins}}<ins style="font-weight: bold; text-decoration: none;">[[Category:Primitive functions]]</ins></div></td></tr>
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Marshall
https://aplwiki.com/index.php?title=Comparison_function&diff=3091&oldid=prev
Adám Brudzewsky at 20:48, 28 March 2020
2020-03-28T20:48:19Z
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 20:48, 28 March 2020</td>
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<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>The traditional APL ordering of the comparison functions used above, which was used at least as early as [[APL\360]], resembles a [[wikipedia:Gray code|Gray code]] ordering of the values which define the comparison functions. Adjacent values differ by only a change of one bit, but the list is not a true Gray code because it excludes the all-0 and all-1 combinations.</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>The traditional APL ordering of the comparison functions used above, which was used at least as early as [[APL\360]], resembles a [[wikipedia:Gray code|Gray code]] ordering of the values which define the comparison functions. Adjacent values differ by only a change of one bit, but the list is not a true Gray code because it excludes the all-0 and all-1 combinations.</div></td></tr>
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Adám Brudzewsky
https://aplwiki.com/index.php?title=Comparison_function&diff=1951&oldid=prev
RichPark: 1 revision imported
2019-11-21T09:38:39Z
<p>1 revision imported</p>
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RichPark
https://aplwiki.com/index.php?title=Comparison_function&diff=1950&oldid=prev
Miraheze>Marshall at 11:34, 12 November 2019
2019-11-12T11:34:03Z
<p></p>
<p><b>New page</b></p><div>{| class=vertical-navbox style="float:right; font-size:500%; margin:0 1ex;"<br />
|<code><</code> <code>≤</code> <code>=</code> <code>≥</code> <code>></code> <code>≠</code><br />
|}<br />
<br />
A '''comparison function''' is one of the six [[primitive function|primitive]] [[dyadic]] [[scalar function]]s whose result on scalars is a [[Boolean]] determined by the numerical ordering of the two [[argument]]s. Comparisons are subject to [[comparison tolerance]]. The comparison functions can be subdivided into two equalities <source lang=apl inline>=</source> <source lang=apl inline>≠</source>, which depend only on whether the arguments are equal and not the ordering of unequal argument, and may be applied to [[character]]s, and four inequalities <source lang=apl inline><</source> <source lang=apl inline>≤</source> <source lang=apl inline>≥</source> <source lang=apl inline>></source>, which depend on ordering and may not be applied to [[character]]s.<br />
<br />
The six comparison functions are [[Less Than]] (<source lang=apl inline><</source>), [[Less Than or Equal]] (<source lang=apl inline>≤</source>), [[Equal to]] (<source lang=apl inline>=</source>), [[Greater Than or Equal]] (<source lang=apl inline>≥</source>), [[Greater Than]] (<source lang=apl inline>></source>), and [[Not Equal to]] (<source lang=apl inline>≠</source>).<br />
<br />
Because comparison functions have Boolean results on Boolean arguments (they always have Boolean results), they are [[Boolean function]]s. In fact, the majority of nontrivial dyadic Boolean functions are comparison functions.<br />
<br />
== Classification ==<br />
<br />
The result of a comparison function on real numbers is determined by their ordering, which falls into one of three possible cases: the left argument is smaller (more negative), the arguments are [[Comparison tolerance|tolerantly]] equal, or the right argument is larger. A particular comparison function can thus be thought of as a choice of one [[Boolean]] value (0 or 1) for each of these three cases, which implies that there are eight total possibilities. Two of the possibilities—all 0 and all 1—are trivial and cannot be said to depend on the ordering of the arguments; they are not considered comparison functions. Every remaining possibility is one of the APL comparisons:<br />
<br />
{|class=wikitable style="text-align:center"<br />
!rowspan=2| Function !!colspan=3| Results<br />
|-<br />
! < !! = !! ><br />
|-<br />
| <source lang=apl inline><</source> || 1 || 0 || 0<br />
|-<br />
| <source lang=apl inline>≤</source> || 1 || 1 || 0<br />
|-<br />
| <source lang=apl inline>=</source> || 0 || 1 || 0<br />
|-<br />
| <source lang=apl inline>≥</source> || 0 || 1 || 1<br />
|-<br />
| <source lang=apl inline>></source> || 0 || 0 || 1<br />
|-<br />
| <source lang=apl inline>≠</source> || 1 || 0 || 1<br />
|}<br />
<br />
The traditional APL ordering of the comparison functions used above, which was used at least as early as [[APL\360]], resembles a [[wikipedia:Gray code|Gray code]] ordering of the values which define the comparison functions. Adjacent values differ by only a change of one bit, but the list is not a true Gray code because it excludes the all-0 and all-1 combinations.</div>
Miraheze>Marshall