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('&lt;strong class=&quot;error&quot;&gt;Formatting error: %s&lt;/strong&gt;', 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
 			args[k] = v
 		end
 	end
 	table.sort(nums)
 	for i, num in ipairs(nums) do
 		ret[#ret + 1] = args[num]
 	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 &quot;dominant&quot; 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:
 {{#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)
 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 &lt;= second then -- math.random doesn't allow the first number to be greater than the second.
 			return math.random(first, second)
 		end
 	elseif first then
 		return math.random(first)
 	else
 		return math.random()
 	end
 end
 
 --[[
 order
 
 Determine order of magnitude of a number
 
 Usage:
 {{#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 then
 		return err('order of magnitude input appears non-numeric')
 	else
 		return p._order(input_number)
 	end
 end
 
 function p._order(x)
 	if x == 0 then return 0 end
 	return math.floor(math.log10(math.abs(x)))
 end
 
 --[[
 precision
 
 Detemines the precision of a number using the string representation
 
 Usage:
 {{ #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 then
 		yesno = require('Module:Yesno')
 	end
 	if yesno(trap_fraction, true) then -- Returns true for all input except nil, false, &quot;no&quot;, &quot;n&quot;, &quot;0&quot; and a few others. See [[Module:Yesno]].
 		local pos = string.find(input_string, '/', 1, true);
 		if pos ~= nil then
 			if string.find(input_string, '/', pos + 1, true) == nil then
 				local denominator = string.sub(input_string, pos+1, -1);
 				local denom_value = tonumber(denominator);
 				if denom_value ~= nil then
 					return math.log10(denom_value);
 				end
 			end
 		end
 	end
 
 	input_number, input_string = p._cleanNumber(input_string);
 	if input_string == nil then
 		return err('precision input appears non-numeric')
 	else
 		return p._precision(input_string)
 	end
 end
 
 function p._precision(x)
 	if type(x) == 'number' then
 		x = tostring(x)
 	end
 	x = string.upper(x)
 
 	local decimal = x:find('%.')
 	local exponent_pos = x:find('E')
 	local result = 0;
 
 	if exponent_pos ~= nil then
 		local exponent = string.sub(x, exponent_pos + 1)
 		x = string.sub(x, 1, exponent_pos - 1)
 		result = result - tonumber(exponent)
 	end
 
 	if decimal ~= nil then
 		result = result + string.len(x) - decimal
 		return result
 	end
 
 	local pos = string.len(x);
 	while x:byte(pos) == string.byte('0') do
 		pos = pos - 1
 		result = result - 1
 		if pos &lt;= 0 then
 			return 0
 		end
 	end
 
 	return result
 end
 
 
 --[[
 max
 
 Finds the maximum argument
 
 Usage:
 {{#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))
 end
 
 function p._max(...)
 	local max_value = binary_fold((function(a, b) return a &gt; b end), ...)
 	if max_value then
 		return max_value
 	end
 end
 
 --[[
 median
 
 Find the median of set of numbers
 
 Usage:
 {{#invoke:Math | median | number1 | number2 | ...}}
 OR
 {{#invoke:Math | median }}
 ]]
 
 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 (vals[count/2] + vals[count/2+1])/2
 	else
 		return vals[math.ceil(count/2)]
 	end
 end
 
 --[[
 min
 
 Finds the minimum argument
 
 Usage:
 {{#invoke:Math| min | value1 | value2 | ... }}
 OR
 {{#invoke:Math| min }}
 
 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 min_value = binary_fold((function(a, b) return a &lt; b end), ...)
 	if min_value then
 		return min_value
 	end
 end
 
 --[[
 sum
 
 Finds the sum
 
 Usage:
 {{#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))
 end
 
 function p._sum(...)
 	local sums, count = fold((function(a, b) return a + b end), ...)
 	if not sums then
 		return 0
 	else
 		return sums
 	end
 end
 
 --[[
 average
 
 Finds the average
 
 Usage:
 {{#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))
 end
 
 function p._average(...)
 	local sum, count = fold((function(a, b) return a + b end), ...)
 	if not sum then
 		return 0
 	else
 		return sum / count
 	end
 end
 
 --[[
 round
 
 Rounds a number to specified precision
 
 Usage:
 {{#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 then
 		return err('round input appears non-numeric')
 	else
 		return p._round(value, precision)
 	end
 end
 
 function p._round(value, precision)
 	local rescale = math.pow(10, precision or 0);
 	return math.floor(value * rescale + 0.5) / rescale;
 end
 
 --[[
 log10
 
 returns the log (base 10) of a number
 
 Usage:
 {{#invoke:Math | log10 | x }}
 ]]
 
 function wrap.log10(args)
 	return math.log10(args[1])
 end
 
 --[[
 mod
 
 Implements the modulo operator
 
 Usage:
 {{#invoke:Math | mod | x | y }}
 
 --]]
 
 function wrap.mod(args)
 	local x = p._cleanNumber(args[1])
 	local y = p._cleanNumber(args[2])
 	if not x then
 		return err('first argument to mod appears non-numeric')
 	elseif not y then
 		return err('second argument to mod appears non-numeric')
 	else
 		return p._mod(x, y)
 	end
 end
 
 function p._mod(x, y)
 	local ret = x % y
 	if not (0 &lt;= ret and ret &lt; y) then
 		ret = 0
 	end
 	return ret
 end
 
 --[[
 gcd
 
 Calculates the greatest common divisor of multiple numbers
 
 Usage:
 {{#invoke:Math | gcd | value 1 | value 2 | value 3 | ... }}
 --]]
 
 function wrap.gcd(args)
 	return p._gcd(unpackNumberArgs(args))
 end
 
 function p._gcd(...)
 	local function findGcd(a, b)
 		local r = b
 		local oldr = a
 		while r ~= 0 do
 			local quotient = math.floor(oldr / r)
 			oldr, r = r, oldr - quotient * r
 		end
 		if oldr &lt; 0 then
 			oldr = oldr * -1
 		end
 		return oldr
 	end
 	local result, count = fold(findGcd, ...)
 	return result
 end
 
 --[[
 precision_format
 
 Rounds a number to the specified precision and formats according to rules
 originally 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 0
 	local precision = args[2] or 0
 	return p._precision_format(value_string, precision)
 end
 
 function p._precision_format(value_string, precision)
 	-- For access to Mediawiki built-in formatter.
 	local lang = mw.getContentLanguage();
 
 	local value
 	value, value_string = p._cleanNumber(value_string)
 	precision = p._cleanNumber(precision)
 
 	-- Check for non-numeric input
 	if value == nil or precision == nil then
 		return err('invalid input when rounding')
 	end
 
 	local 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 &gt;= 14 then
 		if order + p._precision(value_string) &gt;= 14 then
 			precision = 13 - order;
 		end
 	end
 
 	-- If rounding off, truncate extra digits
 	if precision &lt; current_precision then
 		value = p._round(value, precision)
 		current_precision = p._precision(value)
 	end
 
 	local formatted_num = lang:formatNum(math.abs(value))
 	local sign
 
 	-- Use proper unary minus sign rather than ASCII default
 	if value &lt; 0 then
 		sign = '−'
 	else
 		sign = ''
 	end
 
 	-- Handle cases requiring scientific notation
 	if string.find(formatted_num, 'E', 1, true) ~= nil or math.abs(order) &gt;= 9 then
 		value = value * math.pow(10, -order)
 		current_precision = current_precision + order
 		precision = precision + order
 		formatted_num = lang:formatNum(math.abs(value))
 	else
 		order = 0;
 	end
 	formatted_num = sign .. formatted_num
 
 	-- Pad with zeros, if needed
 	if current_precision &lt; precision then
 		local padding
 		if current_precision &lt;= 0 then
 			if precision &gt; 0 then
 				local zero_sep = lang:formatNum(1.1)
 				formatted_num = formatted_num .. zero_sep:sub(2,2)
 
 				padding = precision
 				if padding &gt; 20 then
 					padding = 20
 				end
 
 				formatted_num = formatted_num .. string.rep('0', padding)
 			end
 		else
 			padding = precision - current_precision
 			if padding &gt; 20 then
 				padding = 20
 			end
 			formatted_num = formatted_num .. 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 &lt; 0 then
 			order = '−' .. lang:formatNum(math.abs(order))
 		else
 			order = lang:formatNum(order)
 		end
 
 		formatted_num = formatted_num .. '&lt;span style=&quot;margin:0 .15em 0 .25em&quot;&gt;×&lt;/span&gt;10&lt;sup&gt;' .. order .. '&lt;/sup&gt;'
 	end
 
 	return formatted_num
 end
 
 --[[
 divide
 
 Implements the division operator
 
 Usage:
 {{#invoke:Math | divide | x | y | round= | precision= }}
 
 --]]
 function wrap.divide(args)
 	local x = args[1]
 	local y = args[2]
 	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 == &quot;&quot; then
 		return err(&quot;Empty divisor&quot;)
 	elseif not tonumber(y) then
 		if type(y) == 'string' and string.sub(y, 1, 1) == '&lt;' then
 			return y
 		else
 			return err(&quot;Not a number: &quot; .. y)
 		end
 	elseif x == nil or x == &quot;&quot; then
 		return err(&quot;Empty dividend&quot;)
 	elseif not tonumber(x) then
 		if type(x) == 'string' and string.sub(x, 1, 1) == '&lt;' then
 			return x
 		else
 			return err(&quot;Not a number: &quot; .. 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(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 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
 		number_string = number_string:match(&quot;^%s*(.-)%s*$&quot;) -- String is valid but may contain padding, clean it.
 		number_string = number_string:match(&quot;^%+(.*)$&quot;) 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)
 		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 wrap[k](getArgs(frame))  -- Argument processing is left to Module:Arguments. Whitespace is trimmed and blank arguments are removed.
 	end
 end }