Help:Modulo and round

{{h:h}}[[Category:Editor handbook]]

The MediaWiki extension [[m:ParserFunctions|ParserFunctions]] enables users to perform simple mathematical [[m:Help:Calculation|computations]].

<nowiki>#</nowiki>expr and #ifexpr allow mod and round.

{| cellpadding="6px" border=1 style="border:1px solid #C0C0C0; border-collapse:collapse;"
! ''Operator''
! ''Operation''
! ''Example''
|-
! [[w:en:Modulo operation|mod]]
|| "Modulo" (PHP operator [http://www.php.net/manual/en/language.operators.arithmetic.php %]): if a is nonnegative, a mod b is the remainder by division after truncating both operands to an integer, while (-a) mod b = - ( a mod b).<br /><br />Caveats:
*'''mod''' is different from all programming languages, see [[bugzilla:6068]] (marked as won't fix). For compatibility it seems wise to apply it only with integer arguments.
*It has been observed that on Windows a number, before mod is applied, is reduced to php data-type "signed INT", i.e. a signed 32-bits [http://en.wikipedia.org/wiki/Integer_(computer_science)#Common_integral_data_types integer]  [http://dev.mysql.com/doc/refman/5.0/en/numeric-types.html], i.e. mod gives wrong results for integers outside the range -2,147,483,648 through 2,147,483,647, see below.

||{{evaldemo|#expr: 30 mod 7}}<br />{{evaldemo|#expr: -8 mod -3}}<br />{{evaldemo|#expr: -8 mod +3}}<br />{{evaldemo|#expr: 8 mod 2.7}} (should be 2.6)<br />{{evaldemo|#expr: 8 mod 3.2}} (should be 1.6)<br />{{evaldemo|#expr: 8.9 mod 3}} (should be 2.9)
|-
| round ||(PHP function [http://nl3.php.net/manual/en/function.round.php round]): rounds the number on the left to the nearest multiple of 1/10 raised to the power given on the right; if two are equally near, rounding is away from zero.
||{{evaldemo|#expr: 30/7 round 3}}<br />{{evaldemo|#expr: 30/7 round 0}}<br />{{evaldemo|#expr: 3456 round -2}}
|}

Problem with mod in Windows:
*{{evd|#expr:-2147483650 mod 1000000000}} (should be -147483650; on Windows 147483646)
*{{evd|#expr:-2147483649 mod 1000000000}} (should be -147483649; on Windows 147483647)
*{{evd|#expr:-2147483648 mod 1000000000}} (should be -147483648; on Windows correct)
*{{evd|#expr:-2147483647 mod 1000000000}} (should be -147483647; on Windows correct)
*{{evd|#expr:2147483646 mod 1000000000}} (should be 147483646; on Windows correct)
*{{evd|#expr:2147483647 mod 1000000000}} (should be 147483647; on Windows correct)
*{{evd|#expr:2147483648 mod 1000000000}} (should be 147483648; on Windows -147483648)
*{{evd|#expr:2147483649 mod 1000000000}} (should be 147483649; on Windows -147483647)

See also '''{{tim|mod}}''', and operator '''fmod''' in [[mw:Extension:ParserFunctions (extended)]], which both do not have these problems. Also, in file expr.php (the standard one or the extended one) operation "$left % $right" can be replaced by "fmod($left,$right)". 

Spaces around mod and round are good for readability but not needed for working properly:
*{{evd|#expr:7mod3}}
*{{evd|#expr:7.5round0}}

Precedence:
*{{evaldemo|#expr:1.234 + 1.234 round 1 + 1 }}

(first additions, then round)

*{{evaldemo|#expr:3 * 4 mod 10 * 10 }}

(mod and multiplication have equal precedence, evaluation from left to right)

To remind the reader of the precedence, one might write:
*{{evaldemo|#expr:1.234+1.234 round 1+1 }}
*{{evaldemo|#expr:2 + 3*4mod10*10 + 5}}

;When using spaces where there is precedence, the layout of the expression may be confusing&#58;
:{{evaldemo|#expr:23+45 mod 10}}
;Instead one can write&#58;
:{{evaldemo|#expr:23 + 45 mod10}}
;or simply use parentheses&#58;
:{{evaldemo|#expr:23 + (45 mod 10)}}

==Mod==
To get a positive mod even for a negative number, use e.g. (700000 + x) mod7 instead of x mod7. The range of the result is now 0-6, provided that x > -700000.

Alternatively, use
*6 - ( 700006 - x ) mod7
or
*(x - 700006) mod7 + 6.
The range of the result is  0-6, provided that x < 700006.

Working for all x is:
*(x mod7 + 7) mod7

==Round==
*{{evd|#expr:2.5 round 0}}
*{{evd|#expr:1.5 round 0}}
*{{evd|#expr:.5 round 0}}
*{{evd|#expr:-.5 round 0}}
*{{evd|#expr:-1.5 round 0}}
*{{evd|#expr:-2.5 round 0}}

*{{evd|#expr:2.25 round 1}}
*{{evd|#expr:2.15 round 1}}
*{{evd|#expr:2.05 round 1}}
*{{evd|#expr:-2.05 round 1}}
*{{evd|#expr:-2.15 round 1}}
*{{evd|#expr:-2.25 round 1}}

To round an integer plus one half for x > -100000 toward plus infinity, use:
*(x + 100000 round 0) - 100000
and to round an integer plus one half for x < 100000 toward minus infinity, use:
*(x - 100000 round 0) + 100000

To round x toward minus infinity, use:
*x + ( x != x round 0 ) * ( ( ( x - .5 ) round 0 ) - x )
and toward plus infinity
*x + ( x != x round 0 ) * ( ( ( x + .5 ) round 0 ) - x )

If x is a long expression this multiplies the length by 5! Under conditions for x there are alternatives:

To round x > -100000 toward minus infinity, use:
*(x - 100000.5 round 0) + 100000
and to round x < 100000 toward plus infinity, use:
*(x + 100000.5 round 0) - 100000

If x is a multiple of 1/n with n<1000 we can round toward minus infinity with:
*x - .499 round 0

For arbitrary n > 1 we can choose instead of -.499 any number between -.5 and -.5 + 1/n.

To find the largest multiple of 7 not larger than x (i.e. to round toward minus infinity to a multiple of 7) we can do:
*((x-3)/7 round 0) * 7

==See also==
*{{tim|mod}}
*[[m:Category:Mathematical templates]]
*[[w:en:Category:Mathematical function templates]]
{{h:f|enname=Modulo and round}}