--[[



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('<strong class="error">Formatting error: %s</strong>', 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:

{{#invoke: Math | random }}

{{#invoke: Math | random | maximum value }}

{{#invoke: Math | random | minimum value | maximum value }}

]]



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 <= 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 = (args1 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 = (args1 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, "no", "n", "0" 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 <= 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 > 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 (valscount/2 + valscount/2+1])/2

	else

		return valsmath.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 < 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(args1 or args.value or 0)

	local precision = p._cleanNumber(args2 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(args1])

end



--[[

mod



Implements the modulo operator



Usage:

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



--]]



function wrap.mod(args)

	local x = p._cleanNumber(args1])

	local y = p._cleanNumber(args2])

	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 <= ret and ret < 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 < 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 = args1 or 0

	local precision = args2 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 >= 14 then

		if order + p._precision(value_string) >= 14 then

			precision = 13 - order;

		end

	end



	-- If rounding off, truncate extra digits

	if precision < 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 < 0 then

		sign = '−'

	else

		sign = ''

	end



	-- Handle cases requiring scientific notation

	if string.find(formatted_num, 'E', 1, true) ~= nil or math.abs(order) >= 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 < precision then

		local padding

		if current_precision <= 0 then

			if precision > 0 then

				local zero_sep = lang:formatNum(1.1)

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



				padding = precision

				if padding > 20 then

					padding = 20

				end



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

			end

		else

			padding = precision - current_precision

			if padding > 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 < 0 then

			order = '−' .. lang:formatNum(math.abs(order))

		else

			order = lang:formatNum(order)

		end



		formatted_num = formatted_num .. '<span style="margin:0 .15em 0 .25em">×</span>10<sup>' .. order .. '</sup>'

	end



	return formatted_num

end



--[[

divide



Implements the division operator



Usage:

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



--]]

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(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("^%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)

		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)