Module:Math

--[[  Ce module fournit un certain nombre d'opérations mathématiques de base.  ]]  local yesno, getArgs -- lazily initialized  local p = {} -- Contient des fonctions à retourner de #Invoke et des fonctions pour mettre à la disposition des autres modules LUA. local wrap = {} -- Contient des fonctions en wrapper qui traitent les arguments de #Invoke. Ceux-ci agissent comme des fonctions entre les fonctions destinées à #Invoke et les fonctions destinées à Lua.  --[[ Fonctions d'assistance utilisées pour éviter le code redondant. ]]  local function err(msg) 	-- Génère des messages d'erreur Wikitext. 	return mw.ustring.format('<strong class="error">Formatting error: %s</strong>', msg) end  local function unpackNumberArgs(args) 	-- Renvoie une liste décompressée d'arguments spécifiés par des clés numériques. 	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(...) 	-- Crée un tableau d'arguments à partir d'une liste d'arguments pouvant inclure des valeurs nulles. 	local args = {...} -- Tableau des arguments. Il peut contenir des valeurs nulles ou non numériques, nous ne pouvons donc pas utiliser ipairs. 	local nums = {} --Stocke le nombre d'arguments numériques valides. 	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 applyFuncToArgs(func, ...) 		--Appliquez une fonction à tous les arguments fournis et renvoyez le résultat. La fonction doit accepter deux nombres comme paramètres. 		-- et doit renvoyer un nombre en sortie. Ce nombre est ensuite fourni en entrée à l'appel de fonction suivant. 	local vals = makeArgArray(...)	 	local count = #vals -- Le nombre d'arguments valides 	if count == 0 then return 		-- Quitter le programme si aucun argument valide n'est fourni ; sinon, la suppression du premier argument provoquerait une erreur. 		nil, 0 	end  	local ret = table.remove(vals, 1) 	for _, val in ipairs(vals) do 		ret = func(ret, val) 	end 	return ret, count end  --[[ random  Générer un nombre aléatoire  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)) 	-- La fonction math.random générera une erreur si elle reçoit un paramètre explicitement nul ; nous devons donc utiliser des instructions if pour vérifier les paramètres. 	if first and second then 		if first <= second then -- La fonction math.random n'autorise pas que le premier nombre soit supérieur au second. 			return math.random(first, second) 		end 	elseif first then 		return math.random(first) 	else 		return math.random() 	end end  --[[ order  Déterminer l'ordre de grandeur d'un nombre  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  Détermine la précision d'un nombre à l'aide de sa représentation sous forme de chaîne de caractères.  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, "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 function maxOfTwo(a, b) 		if a > b then 			return a 		else 			return b 		end 	end 	local max_value = applyFuncToArgs(maxOfTwo, ...) 	if max_value then 		return max_value 	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 function minOfTwo(a, b) 		if a < b then 			return a 		else 			return b 		end 	end 	local min_value = applyFuncToArgs(minOfTwo, ...) 	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 function getSum(a, b) 		return a + b 	end 	local sum, count = applyFuncToArgs(getSum, ...) 	if not sum then 		return 0 	else 		return sum 	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 function getSum(a, b) 		return a + b 	end 	local sum, count = applyFuncToArgs(getSum, ...) 	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  --[[ 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 <= 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 = applyFuncToArgs(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 >= 14 then 		orig_precision = p._precision(value_string) 		if order + orig_precision >= 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  --[[ 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 wrap[k](getArgs(frame))  -- Argument processing is left to Module:Arguments. Whitespace is trimmed and blank arguments are removed. 	end end }  return setmetatable(p, mt)