Template:Mod

Implements the mathematical modulo operator. It should not be confused with the parser function 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. However, this template returns 0 if the divisor is nul (this template should never return a division by zero error).

Usage:

{{Mod|dividend|divisor}}

Examples with positive integer modulus:

• {{Mod|12|10}} = 2.
• {{Mod|10.1|10}} = 0.1.
  • compare: {{#expr:10.1 mod 10}} = 0.
• {{Mod|10|10}} = 0.
• {{Mod|2|10}} = 2.
• {{Mod|0|10}} = 0.
• {{Mod|-2|10}} = -2.
• {{Mod|-10|10}} = 0.
• {{Mod|-10.1|10}} = -0.1.
• {{Mod|-12|10}} = -2.

Examples with negative integer modulus:

• {{Mod|12|-10}} = 2.
• {{Mod|10.1|-10}} = 0.1.
• {{Mod|10|-10}} = 0.
• {{Mod|2|-10}} = 2.
• {{Mod|0|-10}} = 0.
• {{Mod|-2|-10}} = -2.
• {{Mod|-10|-10}} = 0.
• {{Mod|-10.1|-10}} = -0.1.
• {{Mod|-12|-10}} = -2.

Examples with positive non integer modulus:

• {{Mod|21.5|10.5}} = 0.5.
  • compare: {{#expr:21.5 mod 10.5}} = 1.
• {{Mod|21.1|10.5}} = 0.1.
• {{Mod|21|10.5}} = 0.
• {{Mod|20.9|10.5}} = 10.4.
• {{Mod|11|10.5}} = 0.5.
• {{Mod|10.6|10.5}} = 0.1.
• {{Mod|10.5|10.5}} = 0.
• {{Mod|10.1|10.5}} = 10.1.
• {{Mod|10|10.5}} = 10.
• {{Mod|2|10.5}} = 2.
• {{Mod|0|10.5}} = 0.
• {{Mod|-2|10.5}} = -2.
• {{Mod|-10|10.5}} = -10.
• {{Mod|-10.1|10.5}} = -10.1.
• {{Mod|-10.5|10.5}} = 0.
• {{Mod|-10.6|10.5}} = -0.1.
• {{Mod|-11|10.5}} = -0.5.
• {{Mod|-20.9|10.5}} = -10.4.
• {{Mod|-21|10.5}} = 0.
• {{Mod|-21.1|10.5}} = -0.1.
• {{Mod|-21.5|10.5}} = -0.5.

Examples with nul modulus:

• {{Mod|2|0}} = 0.
• {{Mod|0|0}} = 0.
• {{Mod|-2|0}} = 0.
• {{subst:Mod|12|7|subst=subst:}} = 5.

• {{mod|123|(2^32-1)}} → 123
• {{#expr:123mod(2^32-1)}} → 123 (wrong)

From w:en:Template:Mod.

See also:

• Template:Modint
• Help:Modulo and round.