Help:Modulo and round

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The MediaWiki extension ParserFunctions enables users to perform simple mathematical computations.

#expr and #ifexpr allow mod and round.

Operator Operation Example
mod "Modulo" (PHP operator %): 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).

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 integer [1], i.e. mod gives wrong results for integers outside the range -2,147,483,648 through 2,147,483,647, see below.
{{ #expr: 30 mod 7}} {{#ifeq: =|=|=|gives}} {{#expr: 30 mod 7}}
{{ #expr: -8 mod -3}} {{#ifeq: =|=|=|gives}} {{#expr: -8 mod -3}}
{{ #expr: -8 mod +3}} {{#ifeq: =|=|=|gives}} {{#expr: -8 mod +3}}
{{ #expr: 8 mod 2.7}} {{#ifeq: =|=|=|gives}} {{#expr: 8 mod 2.7}} (should be 2.6)
{{ #expr: 8 mod 3.2}} {{#ifeq: =|=|=|gives}} {{#expr: 8 mod 3.2}} (should be 1.6)
{{ #expr: 8.9 mod 3}} {{#ifeq: =|=|=|gives}} {{#expr: 8.9 mod 3}} (should be 2.9)
round (PHP function 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. {{ #expr: 30/7 round 3}} {{#ifeq: =|=|=|gives}} {{#expr: 30/7 round 3}}
{{ #expr: 30/7 round 0}} {{#ifeq: =|=|=|gives}} {{#expr: 30/7 round 0}}
{{ #expr: 3456 round -2}} = {{#expr: 3456 round -2}}

Problem with mod in Windows:

  • {{ #expr:-2147483650 mod 1000000000{{#if:|{{{{{1n}}}}}}}{{#ifeq:+|-|||||{{#ifeq:-|+||||{{#ifeq:-|+|||}}}}}}}} gives {{#ifeq:-|+|{{#expr:-2147483650 mod 1000000000|||}}|{{#ifeq:-|+|{{#expr:-2147483650 mod 1000000000||}}|{{#ifeq:-|+|{{#expr:-2147483650 mod 1000000000|}}|{{#expr:-2147483650 mod 1000000000}}}}}}}} (should be -147483650; on Windows 147483646)
  • {{ #expr:-2147483649 mod 1000000000{{#if:|{{{{{1n}}}}}}}{{#ifeq:+|-|||||{{#ifeq:-|+||||{{#ifeq:-|+|||}}}}}}}} gives {{#ifeq:-|+|{{#expr:-2147483649 mod 1000000000|||}}|{{#ifeq:-|+|{{#expr:-2147483649 mod 1000000000||}}|{{#ifeq:-|+|{{#expr:-2147483649 mod 1000000000|}}|{{#expr:-2147483649 mod 1000000000}}}}}}}} (should be -147483649; on Windows 147483647)
  • {{ #expr:-2147483648 mod 1000000000{{#if:|{{{{{1n}}}}}}}{{#ifeq:+|-|||||{{#ifeq:-|+||||{{#ifeq:-|+|||}}}}}}}} gives {{#ifeq:-|+|{{#expr:-2147483648 mod 1000000000|||}}|{{#ifeq:-|+|{{#expr:-2147483648 mod 1000000000||}}|{{#ifeq:-|+|{{#expr:-2147483648 mod 1000000000|}}|{{#expr:-2147483648 mod 1000000000}}}}}}}} (should be -147483648; on Windows correct)
  • {{ #expr:-2147483647 mod 1000000000{{#if:|{{{{{1n}}}}}}}{{#ifeq:+|-|||||{{#ifeq:-|+||||{{#ifeq:-|+|||}}}}}}}} gives {{#ifeq:-|+|{{#expr:-2147483647 mod 1000000000|||}}|{{#ifeq:-|+|{{#expr:-2147483647 mod 1000000000||}}|{{#ifeq:-|+|{{#expr:-2147483647 mod 1000000000|}}|{{#expr:-2147483647 mod 1000000000}}}}}}}} (should be -147483647; on Windows correct)
  • {{ #expr:2147483646 mod 1000000000{{#if:|{{{{{1n}}}}}}}{{#ifeq:+|-|||||{{#ifeq:-|+||||{{#ifeq:-|+|||}}}}}}}} gives {{#ifeq:-|+|{{#expr:2147483646 mod 1000000000|||}}|{{#ifeq:-|+|{{#expr:2147483646 mod 1000000000||}}|{{#ifeq:-|+|{{#expr:2147483646 mod 1000000000|}}|{{#expr:2147483646 mod 1000000000}}}}}}}} (should be 147483646; on Windows correct)
  • {{ #expr:2147483647 mod 1000000000{{#if:|{{{{{1n}}}}}}}{{#ifeq:+|-|||||{{#ifeq:-|+||||{{#ifeq:-|+|||}}}}}}}} gives {{#ifeq:-|+|{{#expr:2147483647 mod 1000000000|||}}|{{#ifeq:-|+|{{#expr:2147483647 mod 1000000000||}}|{{#ifeq:-|+|{{#expr:2147483647 mod 1000000000|}}|{{#expr:2147483647 mod 1000000000}}}}}}}} (should be 147483647; on Windows correct)
  • {{ #expr:2147483648 mod 1000000000{{#if:|{{{{{1n}}}}}}}{{#ifeq:+|-|||||{{#ifeq:-|+||||{{#ifeq:-|+|||}}}}}}}} gives {{#ifeq:-|+|{{#expr:2147483648 mod 1000000000|||}}|{{#ifeq:-|+|{{#expr:2147483648 mod 1000000000||}}|{{#ifeq:-|+|{{#expr:2147483648 mod 1000000000|}}|{{#expr:2147483648 mod 1000000000}}}}}}}} (should be 147483648; on Windows -147483648)
  • {{ #expr:2147483649 mod 1000000000{{#if:|{{{{{1n}}}}}}}{{#ifeq:+|-|||||{{#ifeq:-|+||||{{#ifeq:-|+|||}}}}}}}} gives {{#ifeq:-|+|{{#expr:2147483649 mod 1000000000|||}}|{{#ifeq:-|+|{{#expr:2147483649 mod 1000000000||}}|{{#ifeq:-|+|{{#expr:2147483649 mod 1000000000|}}|{{#expr:2147483649 mod 1000000000}}}}}}}} (should be 147483649; on Windows -147483647)

See also Template:Links-core, 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:

  • {{ #expr:7mod3{{#if:|{{{{{1n}}}}}}}{{#ifeq:+|-|||||{{#ifeq:-|+||||{{#ifeq:-|+|||}}}}}}}} gives {{#ifeq:-|+|{{#expr:7mod3|||}}|{{#ifeq:-|+|{{#expr:7mod3||}}|{{#ifeq:-|+|{{#expr:7mod3|}}|{{#expr:7mod3}}}}}}}}
  • {{ #expr:7.5round0{{#if:|{{{{{1n}}}}}}}{{#ifeq:+|-|||||{{#ifeq:-|+||||{{#ifeq:-|+|||}}}}}}}} gives {{#ifeq:-|+|{{#expr:7.5round0|||}}|{{#ifeq:-|+|{{#expr:7.5round0||}}|{{#ifeq:-|+|{{#expr:7.5round0|}}|{{#expr:7.5round0}}}}}}}}

Precedence:

  • {{ #expr:1.234 + 1.234 round 1 + 1 }} {{#ifeq: +|-|{{{2}}}|gives}} {{#expr:1.234 + 1.234 round 1 + 1 }}

(first additions, then round)

  • {{ #expr:3 * 4 mod 10 * 10 }} {{#ifeq: +|-|{{{2}}}|gives}} {{#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:

  • {{ #expr:1.234+1.234 round 1+1 }} {{#ifeq: +|-|{{{2}}}|gives}} {{#expr:1.234+1.234 round 1+1 }}
  • {{ #expr:2 + 3*4mod10*10 + 5}} {{#ifeq: +|-|{{{2}}}|gives}} {{#expr:2 + 3*4mod10*10 + 5}}
When using spaces where there is precedence, the layout of the expression may be confusing:
{{ #expr:23+45 mod 10}} {{#ifeq: +|-|{{{2}}}|gives}} {{#expr:23+45 mod 10}}
Instead one can write:
{{ #expr:23 + 45 mod10}} {{#ifeq: +|-|{{{2}}}|gives}} {{#expr:23 + 45 mod10}}
or simply use parentheses:
{{ #expr:23 + (45 mod 10)}} {{#ifeq: +|-|{{{2}}}|gives}} {{#expr:23 + (45 mod 10)}}

Contents

[edit] 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

[edit] Round

  • {{ #expr:2.5 round 0{{#if:|{{{{{1n}}}}}}}{{#ifeq:+|-|||||{{#ifeq:-|+||||{{#ifeq:-|+|||}}}}}}}} gives {{#ifeq:-|+|{{#expr:2.5 round 0|||}}|{{#ifeq:-|+|{{#expr:2.5 round 0||}}|{{#ifeq:-|+|{{#expr:2.5 round 0|}}|{{#expr:2.5 round 0}}}}}}}}
  • {{ #expr:1.5 round 0{{#if:|{{{{{1n}}}}}}}{{#ifeq:+|-|||||{{#ifeq:-|+||||{{#ifeq:-|+|||}}}}}}}} gives {{#ifeq:-|+|{{#expr:1.5 round 0|||}}|{{#ifeq:-|+|{{#expr:1.5 round 0||}}|{{#ifeq:-|+|{{#expr:1.5 round 0|}}|{{#expr:1.5 round 0}}}}}}}}
  • {{ #expr:.5 round 0{{#if:|{{{{{1n}}}}}}}{{#ifeq:+|-|||||{{#ifeq:-|+||||{{#ifeq:-|+|||}}}}}}}} gives {{#ifeq:-|+|{{#expr:.5 round 0|||}}|{{#ifeq:-|+|{{#expr:.5 round 0||}}|{{#ifeq:-|+|{{#expr:.5 round 0|}}|{{#expr:.5 round 0}}}}}}}}
  • {{ #expr:-.5 round 0{{#if:|{{{{{1n}}}}}}}{{#ifeq:+|-|||||{{#ifeq:-|+||||{{#ifeq:-|+|||}}}}}}}} gives {{#ifeq:-|+|{{#expr:-.5 round 0|||}}|{{#ifeq:-|+|{{#expr:-.5 round 0||}}|{{#ifeq:-|+|{{#expr:-.5 round 0|}}|{{#expr:-.5 round 0}}}}}}}}
  • {{ #expr:-1.5 round 0{{#if:|{{{{{1n}}}}}}}{{#ifeq:+|-|||||{{#ifeq:-|+||||{{#ifeq:-|+|||}}}}}}}} gives {{#ifeq:-|+|{{#expr:-1.5 round 0|||}}|{{#ifeq:-|+|{{#expr:-1.5 round 0||}}|{{#ifeq:-|+|{{#expr:-1.5 round 0|}}|{{#expr:-1.5 round 0}}}}}}}}
  • {{ #expr:-2.5 round 0{{#if:|{{{{{1n}}}}}}}{{#ifeq:+|-|||||{{#ifeq:-|+||||{{#ifeq:-|+|||}}}}}}}} gives {{#ifeq:-|+|{{#expr:-2.5 round 0|||}}|{{#ifeq:-|+|{{#expr:-2.5 round 0||}}|{{#ifeq:-|+|{{#expr:-2.5 round 0|}}|{{#expr:-2.5 round 0}}}}}}}}
  • {{ #expr:2.25 round 1{{#if:|{{{{{1n}}}}}}}{{#ifeq:+|-|||||{{#ifeq:-|+||||{{#ifeq:-|+|||}}}}}}}} gives {{#ifeq:-|+|{{#expr:2.25 round 1|||}}|{{#ifeq:-|+|{{#expr:2.25 round 1||}}|{{#ifeq:-|+|{{#expr:2.25 round 1|}}|{{#expr:2.25 round 1}}}}}}}}
  • {{ #expr:2.15 round 1{{#if:|{{{{{1n}}}}}}}{{#ifeq:+|-|||||{{#ifeq:-|+||||{{#ifeq:-|+|||}}}}}}}} gives {{#ifeq:-|+|{{#expr:2.15 round 1|||}}|{{#ifeq:-|+|{{#expr:2.15 round 1||}}|{{#ifeq:-|+|{{#expr:2.15 round 1|}}|{{#expr:2.15 round 1}}}}}}}}
  • {{ #expr:2.05 round 1{{#if:|{{{{{1n}}}}}}}{{#ifeq:+|-|||||{{#ifeq:-|+||||{{#ifeq:-|+|||}}}}}}}} gives {{#ifeq:-|+|{{#expr:2.05 round 1|||}}|{{#ifeq:-|+|{{#expr:2.05 round 1||}}|{{#ifeq:-|+|{{#expr:2.05 round 1|}}|{{#expr:2.05 round 1}}}}}}}}
  • {{ #expr:-2.05 round 1{{#if:|{{{{{1n}}}}}}}{{#ifeq:+|-|||||{{#ifeq:-|+||||{{#ifeq:-|+|||}}}}}}}} gives {{#ifeq:-|+|{{#expr:-2.05 round 1|||}}|{{#ifeq:-|+|{{#expr:-2.05 round 1||}}|{{#ifeq:-|+|{{#expr:-2.05 round 1|}}|{{#expr:-2.05 round 1}}}}}}}}
  • {{ #expr:-2.15 round 1{{#if:|{{{{{1n}}}}}}}{{#ifeq:+|-|||||{{#ifeq:-|+||||{{#ifeq:-|+|||}}}}}}}} gives {{#ifeq:-|+|{{#expr:-2.15 round 1|||}}|{{#ifeq:-|+|{{#expr:-2.15 round 1||}}|{{#ifeq:-|+|{{#expr:-2.15 round 1|}}|{{#expr:-2.15 round 1}}}}}}}}
  • {{ #expr:-2.25 round 1{{#if:|{{{{{1n}}}}}}}{{#ifeq:+|-|||||{{#ifeq:-|+||||{{#ifeq:-|+|||}}}}}}}} gives {{#ifeq:-|+|{{#expr:-2.25 round 1|||}}|{{#ifeq:-|+|{{#expr:-2.25 round 1||}}|{{#ifeq:-|+|{{#expr:-2.25 round 1|}}|{{#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

[edit] See also

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