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; Description<nowiki>:</nowiki>

Implements the mathematical [[w:en:modulo|modulo]] operator. It should not be confused with the parser function [[ParserFunctions#.23expr:|mod]] (remainder of division after truncating both operands to an integer).

The returned result is always of the same sign as the divisor or zero, and its absolute value is lower than the absolute value of the divisor. This allows this template to be fully compatible with cyclic modular arithmetic (for exampel in calendar computations).

For example if the given ''modulus'' is 10, the result will always be positive or null and lower than 10 (all ''dividend'' values in that positive range will be returned without change). This is not true with the <span style="font-family: monospace;">mod</span> and <span style="font-family: monospace;">fmod</span> operators in expressions evaluated with the <span style="font-family: monospace;"><nowiki>#expr:</nowiki></span> ParserFunction extension of MediaWiki.

However, this template returns 0 if the divisor is null (this template should never return any division by zero error).

; Usage<nowiki>:</nowiki>
: <span style="font-family: monospace;"><nowiki>{{</nowiki>{{BASEPAGENAME}}|</span>''dividend''<span style="font-family: monospace;">|</span>''divisor''<span style="font-family: monospace;"><nowiki>}}</nowiki></span>

; Examples with subtitution of expressions when saving pages<nowiki>:</nowiki>
* <span style="font-family: monospace;"><nowiki>{{</nowiki>subst:{{BASEPAGENAME}}<nowiki>|</nowiki>12<nowiki>|</nowiki>7<nowiki>}}</nowiki></span> = 5.

; Examples with positive integer modulus (all results must be positive or zero)<nowiki>:</nowiki>
* <span style="font-family: monospace;"><nowiki>{{</nowiki>{{BASEPAGENAME}}<nowiki>|</nowiki>12<nowiki>|</nowiki>10<nowiki>}}</nowiki></span> = {{{{BASEPAGENAME}}|12|10}}.
* <span style="font-family: monospace;"><nowiki>{{</nowiki>{{BASEPAGENAME}}<nowiki>|</nowiki>10.1<nowiki>|</nowiki>10<nowiki>}}</nowiki></span> = {{{{BASEPAGENAME}}|10.1|10}}.
** compare: <span style="font-family: monospace;"><nowiki>{{#expr: 10.1 mod 10}}</nowiki></span><span style="font-family: monospace;"> = {{#expr: 10.1 mod 10}}.</span>
* <span style="font-family: monospace;"><nowiki>{{</nowiki>{{BASEPAGENAME}}<nowiki>|</nowiki>10<nowiki>|</nowiki>10<nowiki>}}</nowiki></span> = {{{{BASEPAGENAME}}|10|10}}.
* <span style="font-family: monospace;"><nowiki>{{</nowiki>{{BASEPAGENAME}}<nowiki>|</nowiki>2<nowiki>|</nowiki>10<nowiki>}}</nowiki></span> = {{{{BASEPAGENAME}}|2|10}}.
* <span style="font-family: monospace;"><nowiki>{{</nowiki>{{BASEPAGENAME}}<nowiki>|</nowiki>0<nowiki>|</nowiki>10<nowiki>}}</nowiki></span> = {{{{BASEPAGENAME}}|0|10}}.
* <span style="font-family: monospace;"><nowiki>{{</nowiki>{{BASEPAGENAME}}<nowiki>|</nowiki>-2<nowiki>|</nowiki>10<nowiki>}}</nowiki></span> = {{{{BASEPAGENAME}}|-2|10}}.
* <span style="font-family: monospace;"><nowiki>{{</nowiki>{{BASEPAGENAME}}<nowiki>|</nowiki>-10<nowiki>|</nowiki>10<nowiki>}}</nowiki></span> = {{{{BASEPAGENAME}}|-10|10}}.
* <span style="font-family: monospace;"><nowiki>{{</nowiki>{{BASEPAGENAME}}<nowiki>|</nowiki>-10.1<nowiki>|</nowiki>10<nowiki>}}</nowiki></span> = {{{{BASEPAGENAME}}|-10.1|10}}.
* <span style="font-family: monospace;"><nowiki>{{</nowiki>{{BASEPAGENAME}}<nowiki>|</nowiki>-12<nowiki>|</nowiki>10<nowiki>}}</nowiki></span> = {{{{BASEPAGENAME}}|-12|10}}.

; Examples with negative integer modulus (all results must be negative or zero)<nowiki>:</nowiki>
* <span style="font-family: monospace;"><nowiki>{{</nowiki>{{BASEPAGENAME}}<nowiki>|</nowiki>12<nowiki>|</nowiki>-10<nowiki>}}</nowiki></span> = {{{{BASEPAGENAME}}|12|-10}}.
** compare: <span style="font-family: monospace;"><nowiki>{{#expr: 12 mod -10}}</nowiki></span><span style="font-family: monospace;"> = {{#expr: 12 mod -10}}.</span>
** compare: <span style="font-family: monospace;"><nowiki>{{#expr: 12 fmod -10}}</nowiki></span><span style="font-family: monospace;"> = {{#expr: 12 fmod -10}}.</span>
* <span style="font-family: monospace;"><nowiki>{{</nowiki>{{BASEPAGENAME}}<nowiki>|</nowiki>10.1<nowiki>|</nowiki>-10<nowiki>}}</nowiki></span> = {{{{BASEPAGENAME}}|10.1|10}}.
* <span style="font-family: monospace;"><nowiki>{{</nowiki>{{BASEPAGENAME}}<nowiki>|</nowiki>10<nowiki>|</nowiki>-10<nowiki>}}</nowiki></span> = {{{{BASEPAGENAME}}|10|-10}}.
* <span style="font-family: monospace;"><nowiki>{{</nowiki>{{BASEPAGENAME}}<nowiki>|</nowiki>2<nowiki>|</nowiki>-10<nowiki>}}</nowiki></span> = {{{{BASEPAGENAME}}|2|-10}}.
* <span style="font-family: monospace;"><nowiki>{{</nowiki>{{BASEPAGENAME}}<nowiki>|</nowiki>0<nowiki>|</nowiki>-10<nowiki>}}</nowiki></span> = {{{{BASEPAGENAME}}|0|-10}}.
* <span style="font-family: monospace;"><nowiki>{{</nowiki>{{BASEPAGENAME}}<nowiki>|</nowiki>-2<nowiki>|</nowiki>-10<nowiki>}}</nowiki></span> = {{{{BASEPAGENAME}}|-2|-10}}.
* <span style="font-family: monospace;"><nowiki>{{</nowiki>{{BASEPAGENAME}}<nowiki>|</nowiki>-10<nowiki>|</nowiki>-10<nowiki>}}</nowiki></span> = {{{{BASEPAGENAME}}|-10|-10}}.
* <span style="font-family: monospace;"><nowiki>{{</nowiki>{{BASEPAGENAME}}<nowiki>|</nowiki>-10.1<nowiki>|</nowiki>-10<nowiki>}}</nowiki></span> = {{{{BASEPAGENAME}}|-10.1|-10}}.
* <span style="font-family: monospace;"><nowiki>{{</nowiki>{{BASEPAGENAME}}<nowiki>|</nowiki>-12<nowiki>|</nowiki>-10<nowiki>}}</nowiki></span> = {{{{BASEPAGENAME}}|-12|-10}}.

; Examples with positive non-integer modulus (all results must be positive or zero)<nowiki>:</nowiki>
* <span style="font-family: monospace;"><nowiki>{{</nowiki>{{BASEPAGENAME}}<nowiki>|</nowiki>21.5<nowiki>|</nowiki>10.5<nowiki>}}</nowiki></span> = {{{{BASEPAGENAME}}|21.5|10.5}}.
** compare: <span style="font-family: monospace;"><nowiki>{{#expr: 21.5 mod 10.5}}</nowiki></span><span style="font-family: monospace;"> = {{#expr: 21.5 mod 10.5}}.</span>
** compare: <span style="font-family: monospace;"><nowiki>{{#expr: 21.5 fmod 10.5}}</nowiki></span><span style="font-family: monospace;"> = {{#expr: 21.5 fmod 10.5}}.</span>
* <span style="font-family: monospace;"><nowiki>{{</nowiki>{{BASEPAGENAME}}<nowiki>|</nowiki>21.1<nowiki>|</nowiki>10.5<nowiki>}}</nowiki></span> = {{{{BASEPAGENAME}}|21.1|10.5}}.
* <span style="font-family: monospace;"><nowiki>{{</nowiki>{{BASEPAGENAME}}<nowiki>|</nowiki>21<nowiki>|</nowiki>10.5<nowiki>}}</nowiki></span> = {{{{BASEPAGENAME}}|21|10.5}}.
* <span style="font-family: monospace;"><nowiki>{{</nowiki>{{BASEPAGENAME}}<nowiki>|</nowiki>20.9<nowiki>|</nowiki>10.5<nowiki>}}</nowiki></span> = {{{{BASEPAGENAME}}|20.9|10.5}}.
* <span style="font-family: monospace;"><nowiki>{{</nowiki>{{BASEPAGENAME}}<nowiki>|</nowiki>11<nowiki>|</nowiki>10.5<nowiki>}}</nowiki></span> = {{{{BASEPAGENAME}}|11|10.5}}.
* <span style="font-family: monospace;"><nowiki>{{</nowiki>{{BASEPAGENAME}}<nowiki>|</nowiki>10.6<nowiki>|</nowiki>10.5<nowiki>}}</nowiki></span> = {{{{BASEPAGENAME}}|10.6|10.5}}.
* <span style="font-family: monospace;"><nowiki>{{</nowiki>{{BASEPAGENAME}}<nowiki>|</nowiki>10.5<nowiki>|</nowiki>10.5<nowiki>}}</nowiki></span> = {{{{BASEPAGENAME}}|10.5|10.5}}.
* <span style="font-family: monospace;"><nowiki>{{</nowiki>{{BASEPAGENAME}}<nowiki>|</nowiki>10.1<nowiki>|</nowiki>10.5<nowiki>}}</nowiki></span> = {{{{BASEPAGENAME}}|10.1|10.5}}.
* <span style="font-family: monospace;"><nowiki>{{</nowiki>{{BASEPAGENAME}}<nowiki>|</nowiki>10<nowiki>|</nowiki>10.5<nowiki>}}</nowiki></span> = {{{{BASEPAGENAME}}|10|10.5}}.
* <span style="font-family: monospace;"><nowiki>{{</nowiki>{{BASEPAGENAME}}<nowiki>|</nowiki>2<nowiki>|</nowiki>10.5<nowiki>}}</nowiki></span> = {{{{BASEPAGENAME}}|2|10.5}}.
* <span style="font-family: monospace;"><nowiki>{{</nowiki>{{BASEPAGENAME}}<nowiki>|</nowiki>0<nowiki>|</nowiki>10.5<nowiki>}}</nowiki></span> = {{{{BASEPAGENAME}}|0|10.5}}.
* <span style="font-family: monospace;"><nowiki>{{</nowiki>{{BASEPAGENAME}}<nowiki>|</nowiki>-2<nowiki>|</nowiki>10.5<nowiki>}}</nowiki></span> = {{{{BASEPAGENAME}}|-2|10.5}}.
* <span style="font-family: monospace;"><nowiki>{{</nowiki>{{BASEPAGENAME}}<nowiki>|</nowiki>-10<nowiki>|</nowiki>10.5<nowiki>}}</nowiki></span> = {{{{BASEPAGENAME}}|-10|10.5}}.
* <span style="font-family: monospace;"><nowiki>{{</nowiki>{{BASEPAGENAME}}<nowiki>|</nowiki>-10.1<nowiki>|</nowiki>10.5<nowiki>}}</nowiki></span> = {{{{BASEPAGENAME}}|-10.1|10.5}}.
* <span style="font-family: monospace;"><nowiki>{{</nowiki>{{BASEPAGENAME}}<nowiki>|</nowiki>-10.5<nowiki>|</nowiki>10.5<nowiki>}}</nowiki></span> = {{{{BASEPAGENAME}}|-10.5|10.5}}.
* <span style="font-family: monospace;"><nowiki>{{</nowiki>{{BASEPAGENAME}}<nowiki>|</nowiki>-10.6<nowiki>|</nowiki>10.5<nowiki>}}</nowiki></span> = {{{{BASEPAGENAME}}|-10.6|10.5}}.
* <span style="font-family: monospace;"><nowiki>{{</nowiki>{{BASEPAGENAME}}<nowiki>|</nowiki>-11<nowiki>|</nowiki>10.5<nowiki>}}</nowiki></span> = {{{{BASEPAGENAME}}|-11|10.5}}.
* <span style="font-family: monospace;"><nowiki>{{</nowiki>{{BASEPAGENAME}}<nowiki>|</nowiki>-20.9<nowiki>|</nowiki>10.5<nowiki>}}</nowiki></span> = {{{{BASEPAGENAME}}|-20.9|10.5}}.
* <span style="font-family: monospace;"><nowiki>{{</nowiki>{{BASEPAGENAME}}<nowiki>|</nowiki>-21<nowiki>|</nowiki>10.5<nowiki>}}</nowiki></span> = {{{{BASEPAGENAME}}|-21|10.5}}.
* <span style="font-family: monospace;"><nowiki>{{</nowiki>{{BASEPAGENAME}}<nowiki>|</nowiki>-21.1<nowiki>|</nowiki>10.5<nowiki>}}</nowiki></span> = {{{{BASEPAGENAME}}|-21.1|10.5}}.
* <span style="font-family: monospace;"><nowiki>{{</nowiki>{{BASEPAGENAME}}<nowiki>|</nowiki>-21.5<nowiki>|</nowiki>10.5<nowiki>}}</nowiki></span> = {{{{BASEPAGENAME}}|-21.5|10.5}}.

; Examples with negative non-integer modulus (all results must be positive or zero)<nowiki>:</nowiki>
* <span style="font-family: monospace;"><nowiki>{{</nowiki>{{BASEPAGENAME}}<nowiki>|</nowiki>21.5<nowiki>|</nowiki>-10.5<nowiki>}}</nowiki></span> = {{{{BASEPAGENAME}}|21.5|-10.5}}.
** compare: <span style="font-family: monospace;"><nowiki>{{#expr: 21.5 mod -10.5}}</nowiki></span><span style="font-family: monospace;"> = {{#expr: 21.5 mod -10.5}}.</span>
** compare: <span style="font-family: monospace;"><nowiki>{{#expr: 21.5 fmod -10.5}}</nowiki></span><span style="font-family: monospace;"> = {{#expr: 21.5 fmod -10.5}}.</span>

; Examples with null modulus (all results are zero by design in this template, without error)<nowiki>:</nowiki>
* <span style="font-family: monospace;"><nowiki>{{</nowiki>{{BASEPAGENAME}}<nowiki>|</nowiki>2<nowiki>|</nowiki>0<nowiki>}}</nowiki></span> = {{{{BASEPAGENAME}}|2|0}}.
** compare: <span style="font-family: monospace;"><nowiki>{{#expr: 2 mod 0}}</nowiki></span><span style="font-family: monospace;"> = {{#expr: 2 mod 0}}.</span>
** compare: <span style="font-family: monospace;"><nowiki>{{#expr: 2 fmod 0}}</nowiki></span><span style="font-family: monospace;"> = {{#expr: 2 mod 0}}.</span>
* <span style="font-family: monospace;"><nowiki>{{</nowiki>{{BASEPAGENAME}}<nowiki>|</nowiki>0<nowiki>|</nowiki>0<nowiki>}}</nowiki></span> = {{{{BASEPAGENAME}}|0|0}}.
** compare: <span style="font-family: monospace;"><nowiki>{{#expr: 0 mod 0}}</nowiki></span><span style="font-family: monospace;"> = {{#expr: 0 mod 0}}.</span>
** compare: <span style="font-family: monospace;"><nowiki>{{#expr: 0 fmod 0}}</nowiki></span><span style="font-family: monospace;"> = {{#expr: 0 mod 0}}.</span>
* <span style="font-family: monospace;"><nowiki>{{</nowiki>{{BASEPAGENAME}}<nowiki>|</nowiki>-2<nowiki>|</nowiki>0<nowiki>}}</nowiki></span> = {{{{BASEPAGENAME}}|-2|0}}.
** compare: <span style="font-family: monospace;"><nowiki>{{#expr: -2 mod 0}}</nowiki></span><span style="font-family: monospace;"> = {{#expr: 0 mod 0}}.</span>
** compare: <span style="font-family: monospace;"><nowiki>{{#expr: -2 fmod 0}}</nowiki></span><span style="font-family: monospace;"> = {{#expr: 0 mod 0}}.</span>

; Examples with possible overflows on servers using 32-bit integers<nowiki>:</nowiki>
* {{xpsoc|{{BASEPAGENAME}}|123|(2^32-1)}}
** compare:  {{xpsoc|#expr: 123 mod (2^32-1)}} (wrong on 32-bit servers)
** compare:  {{xpsoc|#expr: 123 fmod (2^32-1)}} (works on recent versions of MediaWiki)
* {{xpsoc|{{BASEPAGENAME}}|123|(2^64-1)}}
** compare:  {{xpsoc|#expr: 123 mod (2^64-1)}} (wrong on 32-bit and 64-bit serverw)
** compare:  {{xpsoc|#expr: 123 fmod (2^64-1)}} (works on recent versions of MediaWiki)

; Examples with non numeric parameters (all results are expression errors by design in this template)<nowiki>:</nowiki>
* <span style="font-family: monospace;"><nowiki>{{</nowiki>{{BASEPAGENAME}}<nowiki>|</nowiki>a<nowiki>|</nowiki>b<nowiki>}}</nowiki></span> = {{{{BASEPAGENAME}}|a|b}}.
** compare: <span style="font-family: monospace;"><nowiki>{{#expr: a mod b}}</nowiki></span><span style="font-family: monospace;"> = {{#expr: a mod b}}.</span>
** compare: <span style="font-family: monospace;"><nowiki>{{#expr: a fmod b}}</nowiki></span><span style="font-family: monospace;"> = {{#expr: a mod b}}.</span>

; See also<nowiki>:</nowiki>
* {{tl|Modint}}
* [[Help:Modulo and round]].
* Code and documentation initially imported from {{tiw|en|Mod}}.

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