Module:Math

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For formatting mathematical expressions, LATEX-style, see Template:Math.

This module provides a number of mathematical functions. These functions can be used from #invoke or from other Lua modules.

Use from other Lua modules

To use the module from normal wiki pages, no special preparation is needed. If you are using the module from another Lua module, first you need to load it, like this:

localmm=require('Module:Math')

(The mm variable stands for Module Math; you can choose something more descriptive if you prefer.)

Most functions in the module have a version for Lua and a version for #invoke. It is possible to use the #invoke functions from other Lua modules, but using the Lua functions has the advantage that you do not need to access a Lua frame object. Lua functions are preceded by _, whereas #invoke functions are not.

random

See also: Module:Random

{{#invoke:math|random}} {{#invoke:math|random|max_value}} {{#invoke:math|random|min_value|max_value}} 

mm._random()mm._random(max_value)mm._random(min_value,max_value)

Generates a random number.

• If no arguments are specified, the number produced is greater than or equal to 0 and less than 1.
• If one argument is provided, the number produced is an integer between 1 and that argument. The argument must be a positive integer.
• If two arguments are provided, the number produced is an integer between the first and second arguments. Both arguments must be integers, but can be negative.

This function will not work properly for numbers less than −2³² and greater than 2³² − 1. If you need to use numbers outside of this range, it is recommended that you use Module:Random.

order

{{#invoke:math|order|n}} 

mm._order(n)

Determines the order of magnitude of a number.

precision

{{#invoke:math|precision|n}} {{#invoke:math|precision|x=n}} 

mm._precision(number_string)

Detemines the precision of a number. For example, for "4" it will return "0", for "4.567" it will return "3", and for "100" it will return "-2".

The function attempts to parse the string representation of the number, and detects whether the number uses E notation. For this reason, when called from Lua, very large numbers or very precise numbers should be directly input as strings to get accurate results. If they are input as numbers, the Lua interpreter will change them to E notation and this function will return the precision of the E notation rather than that of the original number. This is not a problem when the number is called from #invoke, as all input from #invoke is in string format.

max

{{#invoke:math|max|v1|v2|v3|...}} 

mm._max(v1,v2,v3,...)

Returns the maximum value from the values specified. Values that cannot be converted to numbers are ignored.

median

{{#invoke:math|median|v1|v2|v3|...}} 

mm._median(v1,v2,v3,...)

Returns the median value from the values specified. Values that cannot be converted to numbers are ignored.

min

{{#invoke:math|min|v1|v2|v3|...}} 

mm._min(v1,v2,v3,...)

Returns the minimum value from the values specified. Values that cannot be converted to numbers are ignored.

sum

{{#invoke:math|sum|v1|v2|v3|...}} 

mm._sum(v1,v2,v3,...)

Returns the sum of the values specified. Values that cannot be converted to numbers are ignored.

average

{{#invoke:math|average|v1|v2|v3|...}} 

mm._average(v1,v2,v3,...)

Returns the average of the values specified. (More precisely, the value returned is the arithmetic mean.) Values that cannot be converted to numbers are ignored.

round

{{#invoke:math|round|value|precision}} {{#invoke:math|round|value=value|precision=precision}} 

mm._round(value,precision)

Rounds a number to the specified precision as a power of ten (default is 0, meaning to the nearest whole number).

This is done with the following formula: ${\frac {\lfloor {\text{value}}\cdot 10^{\text{precision}}+0.5\rfloor }{10^{\text{precision}}}}$

Note: As of October 2019, there is a bug in the display of some rounded numbers. When trying to round a number that rounds to "n.0", like "1.02", to the nearest tenth of a digit (i.e. |r=1), this function should display "1.0", but it unexpectedly displays "1". Use the |precision_format= parameter instead.

log10

{{#invoke:math | log10 | x}} 

mm._log10(x)

Returns log10(x), the logarithm of x using base 10.

mod

{{#invoke:math|mod|x|y}} 

mm._mod(x,y)

Gets xmoduloy, or the remainder after x has been divided by y. This is accurate for integers up to 2⁵³; for larger integers Lua's modulo operator may return an erroneous value. This function deals with this problem by returning 0 if the modulo given by Lua's modulo operator is less than 0 or greater than y.

gcd

{{#invoke:math|gcd|v1|v2|...}} 

mm._gcd(v1,v2,...)

Finds the greatest common divisor of the values specified. Values that cannot be converted to numbers are ignored.

precision_format

{{#invoke:math|precision_format|value_string|precision}} 

mm._precision_format(value_string,precision)

Rounds a number to the specified precision and formats according to rules originally used for {{Rnd}}. Output is a string.

Parameter precision should be an integer number of digits after the decimal point. Negative values are permitted. Non-integers give unexpected results. Positive values greater than the input precision add zero-padding, negative values greater than the input order can consume all digits.

Formatting 8,765.567 with {{#invoke:Math|precision_format|8765.567|precision}} gives:

precision	Result
2	8,765.57
-2	8,800
6	8,765.567000
-6	0
2.5	8,765.5680426633
-2.5	8,854.3774484715

divide

{{#invoke:Math|divide|x|y|round=|precision=}} 

mm._divide(x,y,round,precision)

Divide x by y.

• If y if not a number, it is returned.
• Otherwise, if x is not a number, it is returned.
• If round is true ("yes" for #invoke), the result has no decimals
• Precision indicates how many digits of precision the result should have

If any of the arguments contain HTML tags, they are returned unchanged, allowing any errors in calculating the arguments to the division function to be propagated to the calling template.

cleanNumber

localnumber,number_string=mm._cleanNumber(number_string)

A helper function that can be called from other Lua modules, but not from #invoke. This takes a string or a number value as input, and if the value can be converted to a number, cleanNumber returns the number and the number string. If the value cannot be converted to a number, cleanNumber returns nil, nil.

See also

The above documentation is transcluded from Module:Math/doc. (edit | history)
Editors can experiment in this module's sandbox(edit | diff) and testcases(edit | run) pages.
Subpages of this module.

--[[This module provides a number of basic mathematical operations.]]localyesno,getArgs-- lazily initializedlocalp={}-- Holds functions to be returned from #invoke, and functions to make available to other Lua modules.localwrap={}-- Holds wrapper functions that process arguments from #invoke. These act as intemediary between functions meant for #invoke and functions meant for Lua.--[[Helper functions used to avoid redundant code.]]localfunctionerr(msg)-- Generates wikitext error messages.returnmw.ustring.format('<strong class="error">Formatting error: %s</strong>',msg)endlocalfunctionunpackNumberArgs(args)-- Returns an unpacked list of arguments specified with numerical keys.localret={}fork,vinpairs(args)doiftype(k)=='number'thentable.insert(ret,v)endendreturnunpack(ret)endlocalfunctionmakeArgArray(...)-- Makes an array of arguments from a list of arguments that might include nils.localargs={...}-- Table of arguments. It might contain nils or non-number values, so we can't use ipairs.localnums={}-- Stores the numbers of valid numerical arguments.localret={}fork,vinpairs(args)dov=p._cleanNumber(v)ifvthennums[#nums+1]=kargs[k]=vendendtable.sort(nums)fori,numinipairs(nums)doret[#ret+1]=args[num]endreturnretendlocalfunctionfold(func,...)-- Use a function on all supplied arguments, and return the result. The function must accept two numbers as parameters,-- and must return a number as an output. This number is then supplied as input to the next function call.localvals=makeArgArray(...)localcount=#vals-- The number of valid argumentsifcount==0thenreturn-- Exit if we have no valid args, otherwise removing the first arg would cause an error.nil,0endlocalret=table.remove(vals,1)for_,valinipairs(vals)doret=func(ret,val)endreturnret,countend--[[Fold arguments by selectively choosing values (func should return when to choose the current "dominant" value).]]localfunctionbinary_fold(func,...)localvalue=fold((function(a,b)iffunc(a,b)thenreturnaelsereturnbendend),...)returnvalueend--[[randomGenerate a random numberUsage:{{#invoke: Math | random }}{{#invoke: Math | random | maximum value }}{{#invoke: Math | random | minimum value | maximum value }}]]functionwrap.random(args)localfirst=p._cleanNumber(args[1])localsecond=p._cleanNumber(args[2])returnp._random(first,second)endfunctionp._random(first,second)math.randomseed(mw.site.stats.edits+mw.site.stats.pages+os.time()+math.floor(os.clock()*1000000000))-- math.random will throw an error if given an explicit nil parameter, so we need to use if statements to check the params.iffirstandsecondtheniffirst<=secondthen-- math.random doesn't allow the first number to be greater than the second.returnmath.random(first,second)endelseiffirstthenreturnmath.random(first)elsereturnmath.random()endend--[[orderDetermine order of magnitude of a numberUsage:{{#invoke: Math | order | value }}]]functionwrap.order(args)localinput_string=(args[1]orargs.xor'0');localinput_number=p._cleanNumber(input_string);ifinput_number==nilthenreturnerr('order of magnitude input appears non-numeric')elsereturnp._order(input_number)endendfunctionp._order(x)ifx==0thenreturn0endreturnmath.floor(math.log10(math.abs(x)))end--[[precisionDetemines the precision of a number using the string representationUsage:{{ #invoke: Math | precision | value }}]]functionwrap.precision(args)localinput_string=(args[1]orargs.xor'0');localtrap_fraction=args.check_fraction;localinput_number;ifnotyesnothenyesno=require('Module:Yesno')endifyesno(trap_fraction,true)then-- Returns true for all input except nil, false, "no", "n", "0" and a few others. See [[Module:Yesno]].localpos=string.find(input_string,'/',1,true);ifpos~=nilthenifstring.find(input_string,'/',pos+1,true)==nilthenlocaldenominator=string.sub(input_string,pos+1,-1);localdenom_value=tonumber(denominator);ifdenom_value~=nilthenreturnmath.log10(denom_value);endendendendinput_number,input_string=p._cleanNumber(input_string);ifinput_string==nilthenreturnerr('precision input appears non-numeric')elsereturnp._precision(input_string)endendfunctionp._precision(x)iftype(x)=='number'thenx=tostring(x)endx=string.upper(x)localdecimal=x:find('%.')localexponent_pos=x:find('E')localresult=0;ifexponent_pos~=nilthenlocalexponent=string.sub(x,exponent_pos+1)x=string.sub(x,1,exponent_pos-1)result=result-tonumber(exponent)endifdecimal~=nilthenresult=result+string.len(x)-decimalreturnresultendlocalpos=string.len(x);whilex:byte(pos)==string.byte('0')dopos=pos-1result=result-1ifpos<=0thenreturn0endendreturnresultend--[[maxFinds the maximum argumentUsage:{{#invoke:Math| max | value1 | value2 | ... }}Note, any values that do not evaluate to numbers are ignored.]]functionwrap.max(args)returnp._max(unpackNumberArgs(args))endfunctionp._max(...)localmax_value=binary_fold((function(a,b)returna>bend),...)ifmax_valuethenreturnmax_valueendend--[[medianFind the median of set of numbersUsage:{{#invoke:Math | median | number1 | number2 | ...}}OR{{#invoke:Math | median }}]]functionwrap.median(args)returnp._median(unpackNumberArgs(args))endfunctionp._median(...)localvals=makeArgArray(...)localcount=#valstable.sort(vals)ifcount==0thenreturn0endifp._mod(count,2)==0thenreturn(vals[count/2]+vals[count/2+1])/2elsereturnvals[math.ceil(count/2)]endend--[[minFinds the minimum argumentUsage:{{#invoke:Math| min | value1 | value2 | ... }}OR{{#invoke:Math| min }}When used with no arguments, it takes its input from the parentframe. Note, any values that do not evaluate to numbers are ignored.]]functionwrap.min(args)returnp._min(unpackNumberArgs(args))endfunctionp._min(...)localmin_value=binary_fold((function(a,b)returna<bend),...)ifmin_valuethenreturnmin_valueendend--[[sumFinds the sumUsage:{{#invoke:Math| sum | value1 | value2 | ... }}OR{{#invoke:Math| sum }}Note, any values that do not evaluate to numbers are ignored.]]functionwrap.sum(args)returnp._sum(unpackNumberArgs(args))endfunctionp._sum(...)localsums,count=fold((function(a,b)returna+bend),...)ifnotsumsthenreturn0elsereturnsumsendend--[[averageFinds the averageUsage:{{#invoke:Math| average | value1 | value2 | ... }}OR{{#invoke:Math| average }}Note, any values that do not evaluate to numbers are ignored.]]functionwrap.average(args)returnp._average(unpackNumberArgs(args))endfunctionp._average(...)localsum,count=fold((function(a,b)returna+bend),...)ifnotsumthenreturn0elsereturnsum/countendend--[[roundRounds a number to specified precisionUsage:{{#invoke:Math | round | value | precision }}--]]functionwrap.round(args)localvalue=p._cleanNumber(args[1]orargs.valueor0)localprecision=p._cleanNumber(args[2]orargs.precisionor0)ifvalue==nilorprecision==nilthenreturnerr('round input appears non-numeric')elsereturnp._round(value,precision)endendfunctionp._round(value,precision)localrescale=math.pow(10,precisionor0);returnmath.floor(value*rescale+0.5)/rescale;end--[[log10returns the log (base 10) of a numberUsage:{{#invoke:Math | log10 | x }}]]functionwrap.log10(args)returnmath.log10(args[1])end--[[modImplements the modulo operatorUsage:{{#invoke:Math | mod | x | y }}--]]functionwrap.mod(args)localx=p._cleanNumber(args[1])localy=p._cleanNumber(args[2])ifnotxthenreturnerr('first argument to mod appears non-numeric')elseifnotythenreturnerr('second argument to mod appears non-numeric')elsereturnp._mod(x,y)endendfunctionp._mod(x,y)localret=x%yifnot(0<=retandret<y)thenret=0endreturnretend--[[gcdCalculates the greatest common divisor of multiple numbersUsage:{{#invoke:Math | gcd | value 1 | value 2 | value 3 | ... }}--]]functionwrap.gcd(args)returnp._gcd(unpackNumberArgs(args))endfunctionp._gcd(...)localfunctionfindGcd(a,b)localr=blocaloldr=awhiler~=0dolocalquotient=math.floor(oldr/r)oldr,r=r,oldr-quotient*rendifoldr<0thenoldr=oldr*-1endreturnoldrendlocalresult,count=fold(findGcd,...)returnresultend--[[precision_formatRounds a number to the specified precision and formats according to rulesoriginally used for {{template:Rnd}}. Output is a string.Usage:{{#invoke: Math | precision_format | number | precision }}]]functionwrap.precision_format(args)localvalue_string=args[1]or0localprecision=args[2]or0returnp._precision_format(value_string,precision)endfunctionp._precision_format(value_string,precision)-- For access to Mediawiki built-in formatter.locallang=mw.getContentLanguage();localvaluevalue,value_string=p._cleanNumber(value_string)precision=p._cleanNumber(precision)-- Check for non-numeric inputifvalue==nilorprecision==nilthenreturnerr('invalid input when rounding')endlocalcurrent_precision=p._precision(value)localorder=p._order(value)-- Due to round-off effects it is neccesary to limit the returned precision under-- some circumstances because the terminal digits will be inaccurately reported.iforder+precision>=14theniforder+p._precision(value_string)>=14thenprecision=13-order;endend-- If rounding off, truncate extra digitsifprecision<current_precisionthenvalue=p._round(value,precision)current_precision=p._precision(value)endlocalformatted_num=lang:formatNum(math.abs(value))localsign-- Use proper unary minus sign rather than ASCII defaultifvalue<0thensign='−'elsesign=''end-- Handle cases requiring scientific notationifstring.find(formatted_num,'E',1,true)~=nilormath.abs(order)>=9thenvalue=value*math.pow(10,-order)current_precision=current_precision+orderprecision=precision+orderformatted_num=lang:formatNum(math.abs(value))elseorder=0;endformatted_num=sign..formatted_num-- Pad with zeros, if neededifcurrent_precision<precisionthenlocalpaddingifcurrent_precision<=0thenifprecision>0thenlocalzero_sep=lang:formatNum(1.1)formatted_num=formatted_num..zero_sep:sub(2,2)padding=precisionifpadding>20thenpadding=20endformatted_num=formatted_num..string.rep('0',padding)endelsepadding=precision-current_precisionifpadding>20thenpadding=20endformatted_num=formatted_num..string.rep('0',padding)endend-- Add exponential notation, if necessary.iforder~=0then-- Use proper unary minus sign rather than ASCII defaultiforder<0thenorder='−'..lang:formatNum(math.abs(order))elseorder=lang:formatNum(order)endformatted_num=formatted_num..'<span style="margin:0 .15em 0 .25em">×</span>10<sup>'..order..'</sup>'endreturnformatted_numend--[[divideImplements the division operatorUsage:{{#invoke:Math | divide | x | y | round= | precision= }}--]]functionwrap.divide(args)localx=args[1]localy=args[2]localround=args.roundlocalprecision=args.precisionifnotyesnothenyesno=require('Module:Yesno')endreturnp._divide(x,y,yesno(round),precision)endfunctionp._divide(x,y,round,precision)ify==nilory==""thenreturnerr("Empty divisor")elseifnottonumber(y)theniftype(y)=='string'andstring.sub(y,1,1)=='<'thenreturnyelsereturnerr("Not a number: "..y)endelseifx==nilorx==""thenreturnerr("Empty dividend")elseifnottonumber(x)theniftype(x)=='string'andstring.sub(x,1,1)=='<'thenreturnxelsereturnerr("Not a number: "..x)endelselocalz=x/yifroundthenreturnp._round(z,0)elseifprecisionthenreturnp._round(z,precision)elsereturnzendendend--[[Helper function that interprets the input numerically. If theinput does not appear to be a number, attempts evaluating it asa parser functions expression.]]functionp._cleanNumber(number_string)iftype(number_string)=='number'then-- We were passed a number, so we don't need to do any processing.returnnumber_string,tostring(number_string)elseiftype(number_string)~='string'ornotnumber_string:find('%S')then-- We were passed a non-string or a blank string, so exit.returnnil,nil;end-- Attempt basic conversionlocalnumber=tonumber(number_string)-- If failed, attempt to evaluate input as an expressionifnumber==nilthenlocalsuccess,result=pcall(mw.ext.ParserFunctions.expr,number_string)ifsuccessthennumber=tonumber(result)number_string=tostring(number)elsenumber=nilnumber_string=nilendelsenumber_string=number_string:match("^%s*(.-)%s*$")-- String is valid but may contain padding, clean it.number_string=number_string:match("^%+(.*)$")ornumber_string-- Trim any leading + signs.ifnumber_string:find('^%-?0[xX]')then-- Number is using 0xnnn notation to indicate base 16; use the number that Lua detected instead.number_string=tostring(number)endendreturnnumber,number_stringend--[[Wrapper function that does basic argument processing. This ensures that all functions from #invoke can use either the currentframe or the parent frame, and it also trims whitespace for all arguments and removes blank arguments.]]localmt={__index=function(t,k)returnfunction(frame)ifnotgetArgsthengetArgs=require('Module:Arguments').getArgsendreturnwrap[k](getArgs(frame))-- Argument processing is left to Module:Arguments. Whitespace is trimmed and blank arguments are removed.endend}returnsetmetatable(p,mt)