Module:Math

--

This module provides a number of basic mathematical operations.

local yesno, getArgs -- lazily initialized

local 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('Formatting error: %s', msg)

end

local function unpackNumberArgs(args)

	-- Returns an unpacked list of arguments specified with numerical keys.

	local ret =

	for k, v in pairs(args) do

		if type(k) == 'number' then

			table.insert(ret, v)

		end

	end

	return unpack(ret)

end

local 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) do

		v = p._cleanNumber(v)

		if v then

			nums#nums + 1 = k

			argsk = v

		end

	end

	table.sort(nums)

	for i, num in ipairs(nums) do

		ret#ret + 1 = argsnum

	end

	return ret

end

local 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 arguments

	if count == 0 then return

		-- Exit if we have no valid args, otherwise removing the first arg would cause an error.

		nil, 0

	end

	local ret = table.remove(vals, 1)

	for _, val in ipairs(vals) do

		ret = func(ret, val)

	end

	return ret, count

end

--

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 value

end

--

random

Generate a random number

Usage:

function wrap.random(args)

	local first = p._cleanNumber(args1)

	local second = p._cleanNumber(args2)

	return p._random(first, second)

end

function 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 then

		if first b end), ...)

	if max_value then

		return max_value

	end

end

--

median

Find the median of set of numbers

Usage:

OR

function wrap.median(args)

	return p._median(unpackNumberArgs(args))

end

function p._median(...)

	local vals = makeArgArray(...)

	local count = #vals

	table.sort(vals)

	if count == 0 then

		return 0

	end

	if p._mod(count, 2) == 0 then

		return (valscount/2 + valscount/2+1)/2

	else

		return valsmath.ceil(count/2)

	end

end

--

min

Finds the minimum argument

Usage:

OR

When used with no arguments, it takes its input from the parent

frame. Note, any values that do not evaluate to numbers are ignored.

function wrap.min(args)

	return p._min(unpackNumberArgs(args))

end

function p._min(...)

	local minvalue = binaryfold((function(a, b) return a = 14 then

		if order + p.precision(valuestring) >= 14 then

			precision = 13 - order;

		end

	end

	-- If rounding off, truncate extra digits

	if precision = 9 then

		value = value * math.pow(10, -order)

		currentprecision = currentprecision + order

		precision = precision + order

		formatted_num = lang:formatNum(math.abs(value))

	else

		order = 0;

	end

	formattednum = sign .. formattednum

	-- Pad with zeros, if needed

	if current_precision 0 then

				local zero_sep = lang:formatNum(1.1)

				formattednum = formattednum .. zero_sep:sub(2,2)

				padding = precision

				if padding > 20 then

					padding = 20

				end

				formattednum = formattednum .. string.rep('0', padding)

			end

		else

			padding = precision - current_precision

			if padding > 20 then

				padding = 20

			end

			formattednum = formattednum .. string.rep('0', padding)

		end

	end

	-- Add exponential notation, if necessary.

	if order ~= 0 then

		-- Use proper unary minus sign rather than ASCII default

		if order ×10' .. order ..

	end

	return formatted_num

end

--

divide

Implements the division operator

Usage:

--

function wrap.divide(args)

	local x = args1

	local y = args2

	local round = args.round

	local precision = args.precision

	if not yesno then

		yesno = require('Module:Yesno')

	end

	return p._divide(x, y, yesno(round), precision)

end

function p._divide(x, y, round, precision)

	if y == nil or y == "" then

		return err("Empty divisor")

	elseif not tonumber(y) then

		if type(y) == 'string' and string.sub(y, 1, 1) == '<' then

			return y

		else

			return err("Not a number: " .. y)

		end

	elseif x == nil or x == "" then

		return err("Empty dividend")

	elseif not tonumber(x) then

		if type(x) == 'string' and string.sub(x, 1, 1) == '<' then

			return x

		else

			return err("Not a number: " .. x)

		end

	else

		local z = x / y

		if round then

			return p._round(z, 0)

		elseif precision then

			return p._round(z, precision)

		else

			return z	

		end

	end

end

--

Helper function that interprets the input numerically. If the

input does not appear to be a number, attempts evaluating it as

a parser functions expression.

function p.cleanNumber(numberstring)

	if type(number_string) == 'number' then

		-- We were passed a number, so we don't need to do any processing.

		return numberstring, tostring(numberstring)

	elseif type(numberstring) ~= 'string' or not numberstring:find('%S') then

		-- We were passed a non-string or a blank string, so exit.

		return nil, nil;

	end

	-- Attempt basic conversion

	local number = tonumber(number_string)

	-- If failed, attempt to evaluate input as an expression

	if number == nil then

		local success, result = pcall(mw.ext.ParserFunctions.expr, number_string)

		if success then

			number = tonumber(result)

			number_string = tostring(number)

		else

			number = nil

			number_string = nil

		end

	else

		numberstring = numberstring:match("^%s(.-)%s$") -- String is valid but may contain padding, clean it.

		numberstring = numberstring:match("^%+(.*)$") or number_string -- Trim any leading + signs.

		if number_string:find('^%-?0xX') then

			-- Number is using 0xnnn notation to indicate base 16; use the number that Lua detected instead.

			number_string = tostring(number)

		end

	end

	return number, number_string

end

--

Wrapper function that does basic argument processing. This ensures that all functions from #invoke can use either the current

frame 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 then

			getArgs = require('Module:Arguments').getArgs

		end

		return wrapk(getArgs(frame)) -- Argument processing is left to Module:Arguments. Whitespace is trimmed and blank arguments are removed.

	end

end }

return setmetatable(p, mt)