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:
local mm = 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
{{#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[clarification needed].
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 x
modulo y
, 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
local number, 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
--[[This module provides a number of basic mathematical operations.]]local yesno, getArgs -- lazily initializedlocal p = {} -- Holds functions to be returned from #invoke, and functions to make available to other Lua modules.local wrap = {} -- 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.]]local function err(msg)-- Generates wikitext error messages.return mw.ustring.format('<strong class="error">Formatting error: %s</strong>', msg)endlocal function unpackNumberArgs(args)-- Returns an unpacked list of arguments specified with numerical keys.local ret = {}for k, v in pairs(args) doif type(k) == 'number' thentable.insert(ret, v)endendreturn unpack(ret)endlocal function makeArgArray(...)-- Makes an array of arguments from a list of arguments that might include nils.local args = {...} -- Table of arguments. It might contain nils or non-number values, so we can't use ipairs.local nums = {} -- Stores the numbers of valid numerical arguments.local ret = {}for k, v in pairs(args) dov = p._cleanNumber(v)if v thennums[#nums + 1] = kargs[k] = vendendtable.sort(nums)for i, num in ipairs(nums) doret[#ret + 1] = args[num]endreturn retendlocal function fold(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.local vals = makeArgArray(...)local count = #vals -- The number of valid argumentsif count == 0 then return-- Exit if we have no valid args, otherwise removing the first arg would cause an error.nil, 0endlocal ret = table.remove(vals, 1)for _, val in ipairs(vals) doret = func(ret, val)endreturn ret, countend--[[Fold arguments by selectively choosing values (func should return when to choose the current "dominant" value).]]local function binary_fold(func, ...)local value = fold((function(a, b) if func(a, b) then return a else return b end end), ...)return valueend--[[randomGenerate a random numberUsage:{{#invoke: Math | random }}{{#invoke: Math | random | maximum value }}{{#invoke: Math | random | minimum value | maximum value }}]]function wrap.random(args)local first = p._cleanNumber(args[1])local second = p._cleanNumber(args[2])return p._random(first, second)endfunction p._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.if first and second thenif first <= second then -- math.random doesn't allow the first number to be greater than the second.return math.random(first, second)endelseif first thenreturn math.random(first)elsereturn math.random()endend--[[orderDetermine order of magnitude of a numberUsage:{{#invoke: Math | order | value }}]]function wrap.order(args)local input_string = (args[1] or args.x or '0');local input_number = p._cleanNumber(input_string);if input_number == nil thenreturn err('order of magnitude input appears non-numeric')elsereturn p._order(input_number)endendfunction p._order(x)if x == 0 then return 0 endreturn math.floor(math.log10(math.abs(x)))end--[[precisionDetemines the precision of a number using the string representationUsage:{{ #invoke: Math | precision | value }}]]function wrap.precision(args)local input_string = (args[1] or args.x or '0');local trap_fraction = args.check_fraction;local input_number;if not yesno thenyesno = require('Module:Yesno')endif yesno(trap_fraction, true) then -- Returns true for all input except nil, false, "no", "n", "0" and a few others. See [[Module:Yesno]].local pos = string.find(input_string, '/', 1, true);if pos ~= nil thenif string.find(input_string, '/', pos + 1, true) == nil thenlocal denominator = string.sub(input_string, pos+1, -1);local denom_value = tonumber(denominator);if denom_value ~= nil thenreturn math.log10(denom_value);endendendendinput_number, input_string = p._cleanNumber(input_string);if input_string == nil thenreturn err('precision input appears non-numeric')elsereturn p._precision(input_string)endendfunction p._precision(x)if type(x) == 'number' thenx = tostring(x)endx = string.upper(x)local decimal = x:find('%.')local exponent_pos = x:find('E')local result = 0;if exponent_pos ~= nil thenlocal exponent = string.sub(x, exponent_pos + 1)x = string.sub(x, 1, exponent_pos - 1)result = result - tonumber(exponent)endif decimal ~= nil thenresult = result + string.len(x) - decimalreturn resultendlocal pos = string.len(x);while x:byte(pos) == string.byte('0') dopos = pos - 1result = result - 1if pos <= 0 thenreturn 0endendreturn resultend--[[maxFinds the maximum argumentUsage:{{#invoke:Math| max | value1 | value2 | ... }}Note, any values that do not evaluate to numbers are ignored.]]function wrap.max(args)return p._max(unpackNumberArgs(args))endfunction p._max(...)local max_value = binary_fold((function(a, b) return a > b end), ...)if max_value thenreturn max_valueendend--[[medianFind the median of set of numbersUsage:{{#invoke:Math | median | number1 | number2 | ...}}OR{{#invoke:Math | median }}]]function wrap.median(args)return p._median(unpackNumberArgs(args))endfunction p._median(...)local vals = makeArgArray(...)local count = #valstable.sort(vals)if count == 0 thenreturn 0endif p._mod(count, 2) == 0 thenreturn (vals[count/2] + vals[count/2+1])/2elsereturn vals[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.]]function wrap.min(args)return p._min(unpackNumberArgs(args))endfunction p._min(...)local min_value = binary_fold((function(a, b) return a < b end), ...)if min_value thenreturn min_valueendend--[[sumFinds the sumUsage:{{#invoke:Math| sum | value1 | value2 | ... }}OR{{#invoke:Math| sum }}Note, any values that do not evaluate to numbers are ignored.]]function wrap.sum(args)return p._sum(unpackNumberArgs(args))endfunction p._sum(...)local sums, count = fold((function(a, b) return a + b end), ...)if not sums thenreturn 0elsereturn sumsendend--[[averageFinds the averageUsage:{{#invoke:Math| average | value1 | value2 | ... }}OR{{#invoke:Math| average }}Note, any values that do not evaluate to numbers are ignored.]]function wrap.average(args)return p._average(unpackNumberArgs(args))endfunction p._average(...)local sum, count = fold((function(a, b) return a + b end), ...)if not sum thenreturn 0elsereturn sum / countendend--[[roundRounds a number to specified precisionUsage:{{#invoke:Math | round | value | precision }}--]]function wrap.round(args)local value = p._cleanNumber(args[1] or args.value or 0)local precision = p._cleanNumber(args[2] or args.precision or 0)if value == nil or precision == nil thenreturn err('round input appears non-numeric')elsereturn p._round(value, precision)endendfunction p._round(value, precision)local rescale = math.pow(10, precision or 0);return math.floor(value * rescale + 0.5) / rescale;end--[[log10returns the log (base 10) of a numberUsage:{{#invoke:Math | log10 | x }}]]function wrap.log10(args)return math.log10(args[1])end--[[modImplements the modulo operatorUsage:{{#invoke:Math | mod | x | y }}--]]function wrap.mod(args)local x = p._cleanNumber(args[1])local y = p._cleanNumber(args[2])if not x thenreturn err('first argument to mod appears non-numeric')elseif not y thenreturn err('second argument to mod appears non-numeric')elsereturn p._mod(x, y)endendfunction p._mod(x, y)local ret = x % yif not (0 <= ret and ret < y) thenret = 0endreturn retend--[[gcdCalculates the greatest common divisor of multiple numbersUsage:{{#invoke:Math | gcd | value 1 | value 2 | value 3 | ... }}--]]function wrap.gcd(args)return p._gcd(unpackNumberArgs(args))endfunction p._gcd(...)local function findGcd(a, b)local r = blocal oldr = awhile r ~= 0 dolocal quotient = math.floor(oldr / r)oldr, r = r, oldr - quotient * rendif oldr < 0 thenoldr = oldr * -1endreturn oldrendlocal result, count = fold(findGcd, ...)return resultend--[[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 }}]]function wrap.precision_format(args)local value_string = args[1] or 0local precision = args[2] or 0return p._precision_format(value_string, precision)endfunction p._precision_format(value_string, precision)-- For access to Mediawiki built-in formatter.local lang = mw.getContentLanguage();local valuevalue, value_string = p._cleanNumber(value_string)precision = p._cleanNumber(precision)-- Check for non-numeric inputif value == nil or precision == nil thenreturn err('invalid input when rounding')endlocal current_precision = p._precision(value)local order = 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.if order + precision >= 14 thenif order + p._precision(value_string) >= 14 thenprecision = 13 - order;endend-- If rounding off, truncate extra digitsif precision < current_precision thenvalue = p._round(value, precision)current_precision = p._precision(value)endlocal formatted_num = lang:formatNum(math.abs(value))local sign-- Use proper unary minus sign rather than ASCII defaultif value < 0 thensign = '−'elsesign = ''end-- Handle cases requiring scientific notationif string.find(formatted_num, 'E', 1, true) ~= nil or math.abs(order) >= 9 thenvalue = 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 neededif current_precision < precision thenlocal paddingif current_precision <= 0 thenif precision > 0 thenlocal zero_sep = lang:formatNum(1.1)formatted_num = formatted_num .. zero_sep:sub(2,2)padding = precisionif padding > 20 thenpadding = 20endformatted_num = formatted_num .. string.rep('0', padding)endelsepadding = precision - current_precisionif padding > 20 thenpadding = 20endformatted_num = formatted_num .. string.rep('0', padding)endend-- Add exponential notation, if necessary.if order ~= 0 then-- Use proper unary minus sign rather than ASCII defaultif order < 0 thenorder = '−' .. 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>'endreturn formatted_numend--[[divideImplements the division operatorUsage:{{#invoke:Math | divide | x | y | round= | precision= }}--]]function wrap.divide(args)local x = args[1]local y = args[2]local round = args.roundlocal precision = args.precisionif not yesno thenyesno = require('Module:Yesno')endreturn p._divide(x, y, yesno(round), precision)endfunction p._divide(x, y, round, precision)if y == nil or y == "" thenreturn err("Empty divisor")elseif not tonumber(y) thenif type(y) == 'string' and string.sub(y, 1, 1) == '<' thenreturn yelsereturn err("Not a number: " .. y)endelseif x == nil or x == "" thenreturn err("Empty dividend")elseif not tonumber(x) thenif type(x) == 'string' and string.sub(x, 1, 1) == '<' thenreturn xelsereturn err("Not a number: " .. x)endelselocal z = x / yif round thenreturn p._round(z, 0)elseif precision thenreturn p._round(z, precision)elsereturn zendendend--[[Helper function that interprets the input numerically. If theinput does not appear to be a number, attempts evaluating it asa parser functions expression.]]function p._cleanNumber(number_string)if type(number_string) == 'number' then-- We were passed a number, so we don't need to do any processing.return number_string, tostring(number_string)elseif type(number_string) ~= 'string' or not number_string:find('%S') then-- We were passed a non-string or a blank string, so exit.return nil, nil;end-- Attempt basic conversionlocal number = tonumber(number_string)-- If failed, attempt to evaluate input as an expressionif number == nil thenlocal success, result = pcall(mw.ext.ParserFunctions.expr, number_string)if success thennumber = tonumber(result)number_string = tostring(number)elsenumber = nilnumber_string = nilendelsenumber_string = number_string:match("^%s*(.-)%s*$") -- String is valid but may contain padding, clean it.number_string = number_string:match("^%+(.*)$") or number_string -- Trim any leading + signs.if number_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)endendreturn number, 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.]]local mt = { __index = function(t, k)return function(frame)if not getArgs thengetArgs = require('Module:Arguments').getArgsendreturn wrap[k](getArgs(frame)) -- Argument processing is left to Module:Arguments. Whitespace is trimmed and blank arguments are removed.endend }return setmetatable(p, mt)