Changes

-- Generate random numberfunction z.random( frame ) first = tonumber(frame.args[1]) -- if it doesn't exist it's NaN, if not This module provides a number it's nil second = tonumber(frameof basic mathematical operations.args[2])

if first then ]] local yesno, getArgs -- lazily initialized local p = {} -- if NaN or nilHolds functions to be returned from #invoke, will skip down and functions to final returnmake available to other Lua modules. if first <local wrap = second then {} -- could match if both nil, but already checked Holds wrapper functions that first is a number in last lineprocess 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 mathmw.randomustring.format(first'<strong class="error">Formatting error: %s</strong>', secondmsg) end return mathlocal 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.randominsert(firstret, v) end end return math.randomunpack(ret)

local function makeArgArray(...) -- Determine order Makes an array of magnitudearguments from a list of arguments that might include nils.function z 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.order local ret = {} for k, v in pairs(frameargs)do return z v = p._order_cleanNumber(tonumber(frame.argsv) if v then nums[#nums + 1] or frame.= k args[k] = v end end table.x or 0sort(nums) for i, num in ipairs(nums)do ret[#ret + 1] = args[num] end return ret

 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 zcall._order local vals = makeArgArray(x...) local count = #vals -- The number of valid arguments if x count == 0 then return -- Exit if we have no valid args, otherwise removing the first arg would cause an error. nil, 0 end return math local ret = table.floorremove(math.log10vals, 1) for _, val in ipairs(math.absvals) do ret = func(x))ret, val) end return ret, count

-- Determines precision of a number using [[Fold arguments by selectively choosing values (func should return when to choose the string representationcurrent "dominant" value).]]local function zbinary_fold(func, ...precision) local value = fold( frame (function(a, b) if func(a, b) then return a else return z._precision( frameb end end), .args[1] or frame.args.x or '0' ) return value

-- Remove leading / trailing whitespace[[ x = x:match "^%s*(.-)%s*$";random

local decimal = string.find( x, '.', 1, true )Generate a random number Usage:{{#invoke: Math | random }} local exponent_pos = string.find( x, 'E', 1, true ){{#invoke: Math | random | maximum value }} local result = 0;{{#invoke: Math | random | minimum value | maximum value }} ]] if exponent_pos ~= nil then local exponent = stringfunction wrap.subrandom( x, exponent_pos + 1 args) x local first = stringp.sub_cleanNumber( x, 1, exponent_pos - args[1 ]) result = result - tonumber( exponent ) end if decimal ~ local second = nil then result = result + stringp.len_cleanNumber( x args[2]) - decimal return result end local pos = stringp.len_random( x ); while x:byte(pos) == string.byte('0'first, second) do pos = pos - 1 result = result - 1 if pos <= 0 then return 0 end end return result

-- Finds maximum argumentfunction zp.max_random( frame first, second) if frame math.args[1] == nil then return '' end local max_value = tonumberrandomseed( framemw.site.args[1] stats.edits + mw.site.stats.pages + os.time() local i = 2; while frame+ math.args[i] ~= nil do local val = tonumberfloor( frameos.args[i] clock() * 1000000000)); -- math.random will throw an error if val ~= given an explicit nil thenparameter, so we need to use if statements to check the params. if val > max_value first and second then max_value if first <= val;second then -- math.random doesn't allow the first number to be greater than the second. end return math.random(first, second) end i = i + 1; elseif first then end return math.random(first) else return max_valuemath.random() end

-- Finds minimum argument[[order Determine order of magnitude of a number Usage:{{#invoke: Math | order | value }}]] function zwrap.minorder( frame args) if frame.args[1] == nil then return '' end local min_value input_string = tonumber( frame.args[1] or args.x or '0'); local i input_number = 2; while framep.args[i] ~= nil do local val = tonumber_cleanNumber( frame.args[i] input_string); if val ~input_number == nil then if val < min_value then return err('order of magnitude input appears non-numeric') min_value = val; else end return p._order(input_number) end i = i + 1; end return min_value

function p._order(x) if x == 0 then return 0 end return math.floor(math.log10(math.abs(x)))end -- Rounds [[precision Detemines the precision of a number to specified using the string representation Usage:{{ #invoke: Math | precision| value }}]] function zwrap.roundprecision(frameargs) local value input_string = tonumber(frame.args[1] or frame.args.value x or '0'); local precision trap_fraction = args.check_fraction; local input_number;  if not yesno then yesno = tonumberrequire('Module:Yesno') end if yesno(frametrap_fraction, true) then -- Returns true for all input except nil, false, "no", "n", "0" and a few others.argsSee [[2Module:Yesno]] or frame.args 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.precision or 0sub(input_string, pos+1, -1); local denom_value = tonumber(denominator); if denom_value ~= nil then return zmath._roundlog10( valuedenom_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

 function zp._round_precision(x) if type(x) == 'number' then x = tostring( value, precision 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 rescale exponent = mathstring.powsub( 10x, precision exponent_pos + 1); return math x = string.floorsub(x, 1, exponent_pos - 1) result = result - tonumber( value * rescale exponent) end   if decimal ~= nil then result = result + 0string.len(x) - decimal return result end  local pos = string.5 len(x) / rescale; while x:byte(pos) == string.byte('0') do pos = pos - 1 result = result - 1 if pos <= 0 then return 0 end end  return result

local order = z._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 thenmax precision = 13 - order; endFinds the maximum argument

-- If rounding off, truncate extra digits if precision < current_precision then value = z._round( value, precision ); current_precision = z._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 = langUsage:formatNum( math.abs(value) ); else order = 0; end formatted_num = sign .. formatted_num; -- Pad with zeros, if needed if current_precision < precision then if current_precision <= 0 then if precision > 0 then local zero_sep = lang{{#invoke:formatNum( 1Math| max | value1 | value2 | .1 ); formatted_num = formatted_num .. zero_sep:sub(2,2); formatted_num = formatted_num .. string.rep( '0', precision ); end else formatted_num = formatted_num .. string.rep( '0', precision - current_precision ); end end}}

-- Add exponential notationNote, if necessaryany values that do not evaluate to numbers are ignored. if order ~= 0 then]] -- Use proper unary minus sign rather than ASCII default if order < 0 thenfunction wrap.max(args) order = '−' return p.. lang:formatNum_max( math.absunpackNumberArgs(orderargs) ); else order = lang:formatNum( order ); end formatted_num = formatted_num .. '<span style="margin:0 .15em 0 .25em">×</span>10^{' .. order .. '}' end return formatted_num;

function p._max(...) local max_value = binary_fold((function(a, b) return za > b end), ...) if max_value then return max_value endend --[[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)] endend --[[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 parentframe. 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 endend --[[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 endend --[[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 endend --[[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 <= ret and ret < y) then ret = 0 end return retend --[[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 resultend --[[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^{' .. order .. '}' end  return formatted_numend --[[Helper function that interprets the input numerically. If the input 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 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_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 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. endend } return setmetatable(p, mt)