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Template:Mod/doc - Revision history
2026-06-04T07:10:13Z
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imported>Stranger195: Add {{Sandbox other}} and remove the {{PAGENAME}} sort key
2018-02-22T11:39:04Z
<p>Add <a href="/mediawiki/index.php/Template:Sandbox_other" title="Template:Sandbox other">{{Sandbox other}}</a> and remove the {{PAGENAME}} sort key</p>
<p><b>New page</b></p><div>{{documentation subpage}}<br />
Implements the mathematical [[modular arithmetic|modulo]] operator. The returned result is always of the same sign as the ''modulus'' or nul, and its absolute value is lower than the absolute value of the ''modulus''. However, this template returns 0 if the ''modulus'' is nul (this template should never return a division by zero error). This template is '''not''' the same as the mod operator in the #expr [[m:Help:Calculation|parser function]], which first truncates both operands to an integer before calculating the remainder.<br />
<br />
This template can be substituted.<br />
<br />
; Usage<nowiki>:</nowiki><br />
: <code><nowiki>{{</nowiki>mod|</code>''dividend''<code>|</code>''modulus''<code>}}</code><br />
:: Computes the modulo dynamically.<br />
: <code><nowiki>{{</nowiki>subst:mod|</code>''dividend''<code>|</code>''modulus''<code>}}</code><br />
:: Substitute the template invokation by its computed value when saving an article wiki source.<br />
<br />
; Examples with positive integer modulus<nowiki>:</nowiki><br />
* <code><nowiki>{{mod|12|10}}</nowiki></code> = {{mod|12|10}}.<br />
* <code><nowiki>{{mod|10.1|10}}</nowiki></code> = {{mod|10.1|10}}.<br />
* <code><nowiki>{{mod|10|10}}</nowiki></code> = {{mod|10|10}}.<br />
* <code><nowiki>{{mod|2|10}}</nowiki></code> = {{mod|2|10}}.<br />
* <code><nowiki>{{mod|0|10}}</nowiki></code> = {{mod|0|10}}.<br />
* <code><nowiki>{{mod|-2|10}}</nowiki></code> = {{mod|-2|10}}.<br />
* <code><nowiki>{{mod|-10|10}}</nowiki></code> = {{mod|-10|10}}.<br />
* <code><nowiki>{{mod|-10.1|10}}</nowiki></code> = {{mod|-10.1|10}}.<br />
* <code><nowiki>{{mod|-12|10}}</nowiki></code> = {{mod|-12|10}}.<br />
<br />
; Examples with negative integer modulus<nowiki>:</nowiki><br />
* <code><nowiki>{{mod|12|-10}}</nowiki></code> = {{mod|12|-10}}.<br />
* <code><nowiki>{{mod|10.1|-10}}</nowiki></code> = {{mod|10.1|-10}}.<br />
* <code><nowiki>{{mod|10|-10}}</nowiki></code> = {{mod|10|-10}}.<br />
* <code><nowiki>{{mod|2|-10}}</nowiki></code> = {{mod|2|-10}}.<br />
* <code><nowiki>{{mod|0|-10}}</nowiki></code> = {{mod|0|-10}}.<br />
* <code><nowiki>{{mod|-2|-10}}</nowiki></code> = {{mod|-2|-10}}.<br />
* <code><nowiki>{{mod|-10|-10}}</nowiki></code> = {{mod|-10|-10}}.<br />
* <code><nowiki>{{mod|-10.1|-10}}</nowiki></code> = {{mod|-10.1|-10}}.<br />
* <code><nowiki>{{mod|-12|-10}}</nowiki></code> = {{mod|-12|-10}}.<br />
<br />
; Examples with positive non integer modulus<nowiki>:</nowiki><br />
* <code><nowiki>{{mod|21.5|10.5}}</nowiki></code> = {{mod|21.5|10.5}}.<br />
* <code><nowiki>{{mod|21.1|10.5}}</nowiki></code> = {{mod|21.1|10.5}}.<br />
* <code><nowiki>{{mod|21|10.5}}</nowiki></code> = {{mod|21|10.5}}.<br />
* <code><nowiki>{{mod|20.9|10.5}}</nowiki></code> = {{mod|20.9|10.5}}.<br />
* <code><nowiki>{{mod|11|10.5}}</nowiki></code> = {{mod|11|10.5}}.<br />
* <code><nowiki>{{mod|10.6|10.5}}</nowiki></code> = {{mod|10.6|10.5}}.<br />
* <code><nowiki>{{mod|10.5|10.5}}</nowiki></code> = {{mod|10.5|10.5}}.<br />
* <code><nowiki>{{mod|10.1|10.5}}</nowiki></code> = {{mod|10.1|10.5}}.<br />
* <code><nowiki>{{mod|10|10.5}}</nowiki></code> = {{mod|10|10.5}}.<br />
* <code><nowiki>{{mod|2|10.5}}</nowiki></code> = {{mod|2|10.5}}.<br />
* <code><nowiki>{{mod|0|10.5}}</nowiki></code> = {{mod|0|10.5}}.<br />
* <code><nowiki>{{mod|-2|10.5}}</nowiki></code> = {{mod|-2|10.5}}.<br />
* <code><nowiki>{{mod|-10|10.5}}</nowiki></code> = {{mod|-10|10.5}}.<br />
* <code><nowiki>{{mod|-10.1|10.5}}</nowiki></code> = {{mod|-10.1|10.5}}.<br />
* <code><nowiki>{{mod|-10.5|10.5}}</nowiki></code> = {{mod|-10.5|10.5}}.<br />
* <code><nowiki>{{mod|-10.6|10.5}}</nowiki></code> = {{mod|-10.6|10.5}}.<br />
* <code><nowiki>{{mod|-11|10.5}}</nowiki></code> = {{mod|-11|10.5}}.<br />
* <code><nowiki>{{mod|-20.9|10.5}}</nowiki></code> = {{mod|-20.9|10.5}}.<br />
* <code><nowiki>{{mod|-21|10.5}}</nowiki></code> = {{mod|-21|10.5}}.<br />
* <code><nowiki>{{mod|-21.1|10.5}}</nowiki></code> = {{mod|-21.1|10.5}}.<br />
* <code><nowiki>{{mod|-21.5|10.5}}</nowiki></code> = {{mod|-21.5|10.5}}.<br />
<br />
; Examples with nul modulus<nowiki>:</nowiki><br />
* <code><nowiki>{{mod|2|0}}</nowiki></code> = {{mod|2|0}}.<br />
* <code><nowiki>{{mod|0|0}}</nowiki></code> = {{mod|0|0}}.<br />
* <code><nowiki>{{mod|-2|0}}</nowiki></code> = {{mod|-2|0}}.<br />
<br />
== See also ==<br />
* [[m:Help:Mod, round, floor, ceil, trunc#Mod|mod operator for <code>#expr</code> parser function]]<br />
* {{tl|Module}}<br />
<br />
<includeonly>{{Sandbox other||<br />
[[Category:Mathematical function templates]]<br />
}}</includeonly></div>
imported>Stranger195