Changes

local yesno, getArgs -- Generate random numberfunction z.random( frame ) first = tonumber(frame.args[1]) -- if it doesn't exist it's NaN, if not a number it's nil second = tonumber(frame.args[2])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 args[k] = v end end table.sort(nums) for i, num in ipairs(nums) do ret[#ret + 1] = args[num] end return retend 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, countend --[[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 valueend --[[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 NaN or given an explicit nilparameter, will skip down so we need to use if statements to final returncheck the params. if first and second then if first <= second then -- could match if both nil, but already checked that math.random doesn't allow the first is a number in last lineto be greater than the second. return math.random(first, second) end elseif first then return math.random(first) end else return math.random() end

{{#invoke: Math | order | value }}

 function zwrap.order(frameargs) local input_string = (frame.args[1] or frame.args.x or '0'); local input_number; input_number = zp._cleanNumber( frame, input_string ); if input_number == nil then return err('<strong class="error">Formatting error: Order order of magnitude input appears non-numeric</strong>') else return zp._order( input_number ) end

 function zp._order(x) if x == 0 then return 0 end return math.floor(math.log10(math.abs(x)))

{{ #invoke: Math | precision | value }}

 function zwrap.precision( frame args) local input_string = (frame.args[1] or frame.args.x or '0'); local trap_fraction = frame.args.check_fraction or false; local input_number; if type( trap_fraction ) == 'string' not yesno then trap_fraction yesno = trap_fraction:lowerrequire(); if trap_fraction == 'falseModule:Yesno' or trap_fraction == '0' or trap_fraction == 'no' or trap_fraction == '' then) trap_fraction = false; else trap_fraction = true; end 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 = zp._cleanNumber( frame, input_string ); if input_string == nil then return err('<strong class="error">Formatting error: Precision precision input appears non-numeric</strong>') else return zp._precision( input_string ) end

function p._precision(x) if type(x) == 'number' then x = tostring(x) end x = string.upper(x)  local decimal = string.x:find( x, '%.', 1, true ) local exponent_pos = string.x:find( x, 'E', 1, true ) 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

{{#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 endend --[[median Find the median of set of numbers Usage:{{#invoke:Math | median | number1 | number2 | ... }}

{{#invoke:Math| max median }}]] function wrap.median(args) return p._median(unpackNumberArgs(args))end

When used with no arguments, it takes its input from the parentfunction p._median(...)frame local vals = makeArgArray(. Note, any values that do not evaluate to numbers are ignored.]]function z.max( frame ) local args count = frame#vals table.args;sort(vals) if args[1] count == nil 0 then local parent = frame:getParent(); return 0 args = parent.args; end local max_value = nil; local i = 1; while args[i] ~= nil do local val = z if p._cleanNumber_mod( framecount, args[i] 2); if val ~= nil then if max_value == nil or val > max_value 0 then max_value = val; end end i = i return (vals[count/2] + vals[count/2+ 1;])/2 end else return vals[math.ceil(count/2)] return max_value end

{{#invoke:Math| min | value1 | value2 | ... }}

{{#invoke:Math| min }}

 function zwrap.min( frame args) local args = frame return p._min(unpackNumberArgs(args;)) end if args[1] == nil then function p._min(...) local parent min_value = frame:getParentbinary_fold((function(a, b); args = parentreturn a < b end), ...args;) end if min_value then local return min_value = nil; endend local i = 1; while args--[[isum  Finds the sum Usage:{{#invoke:Math| sum | value1 | value2 | ... }}OR{{#invoke:Math| sum }} Note, any values that do not evaluate to numbers are ignored.]] ~= nil do local val = zfunction wrap._cleanNumbersum( frame, args[i] ); if val ~= nil then return p._sum(unpackNumberArgs(args)) if min_value == nil or val < min_value thenend min_value = val; endfunction p._sum(...) local sums, count = fold((function(a, b) return a + b end ), ...) i = i + 1; if not sums then end return 0 else return min_valuesums end

{{#invoke:Math| average | value1 | value2 | ... }}

{{#invoke:Math| average }} When used with no arguments, it takes its input from the parentframe. Note, any values that do not evaluate to numbers are ignored.

 function zwrap.average( frame args) local args = frame return p._average(unpackNumberArgs(args;))end if args[1] == nil then local parent = frame:getParentfunction p._average(...); args = parent.args; end local sum = 0; local , count = 0; local i = 1; while args[i] ~= nil do local val = z._cleanNumberfold((function( framea, b) return a + b end), args[i] ...); if val ~= nil not sum then sum = sum + val count = count + 1 end i = i + 1; end return 0 else return (count == 0 and 0 or sum/count) end

{{#invoke:Math | round | value | precision }}

 function zwrap.round(frameargs) local value, precision; value = zp._cleanNumber( frame, frame.args[1] or frame.args.value or 0 ); local precision = zp._cleanNumber( frame, frame.args[2] or frame.args.precision or 0 ); if value == nil or precision == nil then return err('<strong class="error">Formatting error: Round round input appears non-numeric</strong>') else return zp._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;

 --[[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 zp._round_mod( valuex, precision y) local rescale ret = mathx % 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.pow_gcd( 10...) local function findGcd(a, precision b); return local r = b local oldr = a while r ~= 0 do local quotient = math.floor( value oldr / r) oldr, r = r, oldr - quotient * rescale + r end if oldr < 0then oldr = oldr * -1 end return oldr end local result, count = fold(findGcd, ...5 ) / rescale; return result

{{#invoke: Math | precision_format | number | precision }}

function wrap.precision_format(args) local order value_string = zargs[1] or 0 local precision = args[2] or 0 return p._order_precision_format( value value_string, precision); end  function p._precision_format(value_string, precision) -- Due For access to roundMediawiki built-off effects it is neccesary to limit the returned precision underin formatter. -- some circumstances because the terminal digits will be inaccurately reported local lang = mw.getContentLanguage(); if order + precision > local value value, value_string = 14 thenp._cleanNumber(value_string) orig_precision precision = zp._precision_cleanNumber( value_string precision); -- Check for non-numeric input if order + orig_precision >value == 14 then nil or precision = 13 - order; = nil then end return err('invalid input when rounding') end

-- If rounding off, truncate extra digits if precision < current_precision then value = z._round( value, precision ); local current_precision = zp._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 * mathp.pow( 10, -order ); current_precision = current_precision + order; precision = precision + order; formatted_num = lang:formatNum( math.abs_order(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 = -- 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 padding order + precision > 20 = 14 then padding = 20; end formatted_num orig_precision = formatted_num p.. string.rep_precision( '0', padding value_string); end else padding = precision - current_precision if padding order + orig_precision > 20 = 14 then padding precision = 20; end formatted_num = formatted_num .. string.rep( '0', padding )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_num;

function zp._cleanNumber( frame, number_string ) if type(number_string ) == nil '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:lenfind('%S') == 0 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 attempt success, result = frame:preprocesspcall( '{{#expr: ' mw.ext.ParserFunctions. expr, number_string .. '}}' ); attempt = tonumber( attempt ); if attempt ~= nil success then number = attempt;tonumber(result) number_string = tostring( number ); else number = nil; number_string = nil; end else number_string = number_string:match("^%s*(.-)%s*$") -- String is valid but may contain padding, clean it. number_string = number_string:match( "^%s*+(.-*)%s*$" )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;

--[[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 zfunction(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)