# 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('<strong>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 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:  

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 <= 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:  

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:  

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:  

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:  

OR  

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:  

OR  

When used with no arguments, it takes its input from the parent  
. 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:  

OR  

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:  

OR  

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:  

---

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:  

function wrap.log10(args)  
return math.log10(args[1])  
end  

---
mod  

Implements the modulo operator  

Usage:  

---

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:  

---

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 . Output is a string.  

Usage:  

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  
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>×</span>10<sup>' .. order .. '</sup>'  
end  

return formatted_num  
end  

---
divide  

Implements the division operator  

Usage:  

---
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 == "" 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  
or the parent , and it also trims whitespace for all arguments and removes blank arguments.  

local mt = { __index = function(t, k)  
return function  
if not getArgs then  
getArgs = require('Module:Arguments').getArgs  
end  
return wrap[k](getArgs) -- Argument processing is to Module:Arguments. Whitespace is trimmed and blank arguments are removed.  
end  
end }  

return setmetatable(p, mt)