Help:Modulo and round
#expr and #ifexpr allow mod and round.
|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).
Template:Evaldemo (should be 2.6)
Template:Evaldemo (should be 1.6)
Template:Evaldemo (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.||Template:Evaldemo
Problem with mod in Windows:
- Template:Evd (should be -147483650; on Windows 147483646)
- Template:Evd (should be -147483649; on Windows 147483647)
- Template:Evd (should be -147483648; on Windows correct)
- Template:Evd (should be -147483647; on Windows correct)
- Template:Evd (should be 147483646; on Windows correct)
- Template:Evd (should be 147483647; on Windows correct)
- Template:Evd (should be 147483648; on Windows -147483648)
- Template:Evd (should be 147483649; on Windows -147483647)
See also Template:Tim, 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:
(first additions, then round)
(mod and multiplication have equal precedence, evaluation from left to right)
To remind the reader of the precedence, one might write:
- When using spaces where there is precedence, the layout of the expression may be confusing:
- Instead one can write:
- or simply use parentheses:
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.
- 6 - ( 700006 - x ) mod7
- (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
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