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}}" gives "2" [2]
"{{#expr: -8 mod -3}}" gives "-2" [3]
"{{#expr: -8 mod +3}}" gives "-2" [4]
"{{#expr: 8 mod 2.7}}" gives "0" [5] (should be 2.6)
"{{#expr: 8 mod 3.2}}" gives "2" [6] (should be 1.6)
"{{#expr: 8.9 mod 3}}" gives "2" [7] (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}}" gives "4.286" [8]
"{{#expr: 30/7 round 0}}" gives "4" [9]
"{{#expr: 3456 round -2}}" gives "3500" [10]

Problem with mod in Windows:

  • "{{#expr:-2147483650 mod 1000000000}}" gives "-147483648" [11] (should be -147483650; on Windows 147483646)
  • "{{#expr:-2147483649 mod 1000000000}}" gives "-147483648" [12] (should be -147483649; on Windows 147483647)
  • "{{#expr:-2147483648 mod 1000000000}}" gives "-147483648" [13] (should be -147483648; on Windows correct)
  • "{{#expr:-2147483647 mod 1000000000}}" gives "-147483647" [14] (should be -147483647; on Windows correct)
  • "{{#expr:2147483646 mod 1000000000}}" gives "147483646" [15] (should be 147483646; on Windows correct)
  • "{{#expr:2147483647 mod 1000000000}}" gives "147483647" [16] (should be 147483647; on Windows correct)
  • "{{#expr:2147483648 mod 1000000000}}" gives "-147483648" [17] (should be 147483648; on Windows -147483648)
  • "{{#expr:2147483649 mod 1000000000}}" gives "-147483647" [18] (should be 147483649; on Windows -147483647)

See also template:mod ( talk edit history links ), 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}}" gives "1" [19]
  • "{{#expr:7.5round0}}" gives "8" [20]

Precedence:

  • "{{#expr:1.234 + 1.234 round 1 + 1}}" gives "2.47" [21]

(first additions, then round)

  • "{{#expr:3 * 4 mod 10 * 10}}" gives "20" [22]

(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}}" gives "2.47" [23]
  • "{{#expr:2 + 3*4mod10*10 + 5}}" gives "27" [24]
When using spaces where there is precedence, the layout of the expression may be confusing:
"{{#expr:23+45 mod 10}}" gives "28" [25]
Instead one can write:
"{{#expr:23 + 45 mod10}}" gives "28" [26]
or simply use parentheses:
"{{#expr:23 + (45 mod 10)}}" gives "28" [27]

Contents

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

  • "{{#expr:2.5 round 0}}" gives "3" [28]
  • "{{#expr:1.5 round 0}}" gives "2" [29]
  • "{{#expr:.5 round 0}}" gives "1" [30]
  • "{{#expr:-.5 round 0}}" gives "-1" [31]
  • "{{#expr:-1.5 round 0}}" gives "-2" [32]
  • "{{#expr:-2.5 round 0}}" gives "-3" [33]
  • "{{#expr:2.25 round 1}}" gives "2.3" [34]
  • "{{#expr:2.15 round 1}}" gives "2.2" [35]
  • "{{#expr:2.05 round 1}}" gives "2.1" [36]
  • "{{#expr:-2.05 round 1}}" gives "-2.1" [37]
  • "{{#expr:-2.15 round 1}}" gives "-2.2" [38]
  • "{{#expr:-2.25 round 1}}" gives "-2.3" [39]

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


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