Module:Roman

-- This module implements Template:Roman.

local p = {}

-- This function implements the {{{1}}} template. local function overline(s)

   return mw.ustring.format( '%s', s )

end

-- Gets the Roman numerals for a given numeral table. Returns both the string of -- numerals and the value of the number after it is finished being processed. local function getLetters(num, t)

   local ret = {}
   for _, v in ipairs(t) do
       local val, letter = unpack(v)
       while num >= val do
           num = num - val
           table.insert(ret, letter)
       end
   end

   return table.concat(ret), num

end

-- The main control flow of the module. local function _main(args)

   -- Get input and exit displaying nothing if the input is empty.
   if args[1] == nil then return end
   local num = tonumber(args[1])
   if not num or num < 0 or num == math.huge then
   	error('Invalid number ' .. args[1], 2)
   elseif num == 0 then
       return 'N'
   end

   -- Return a message for numbers too big to be expressed in Roman numerals.
   if num >= 5000000 then
       return args[2] or 'N/A'
   end

   local ret = 
   -- Find the Roman numerals for the large part of numbers.
   -- 23 April 2016 - tweaked to >= 4000 to accept big Roman 'IV'
   -- The if statement is not strictly necessary, but makes the algorithm 
   -- more efficient for smaller numbers.
   if num >= 4000 then
       local bigRomans = {
           { 1000000, 'M' },
           { 900000, 'CM' }, { 500000, 'D' }, { 400000, 'CD' }, { 100000, 'C' },
           {  90000, 'XC' }, {  50000, 'L' }, {  40000, 'XL' }, {  10000, 'X' },
           {   9000, 'IX' }, {   5000, 'V' }, {   4000, 'IV' },
       }
       local bigLetters
       bigLetters, num = getLetters(num, bigRomans)
       ret = overline(bigLetters)
   end

   -- Find the Roman numerals for numbers less than the big Roman threshold.
   local smallRomans = {
       { 1000, 'M' },
       { 900, 'CM' }, { 500, 'D' }, { 400, 'CD' }, { 100, 'C' },
       {  90, 'XC' }, {  50, 'L' }, {  40, 'XL' }, {  10, 'X' },
       {   9, 'IX' }, {   5, 'V' }, {   4, 'IV' }, {   1, 'I' }
   }
   local smallLetters = getLetters( num, smallRomans )
   ret = ret .. smallLetters

   if args.fraction == 'yes' then
       -- Find the Roman numerals for the fractional parts of numbers.
       -- If num is not a whole number, add half of 1/1728 (the smallest unit) to equate to rounding.
       -- Ensure we're not less than the smallest unit or larger than 1 - smallest unit
       -- to avoid getting two "half" symbols or no symbols at all
       num = num - math.floor(num)
       if num ~= 0 then
           num = math.max(1.1/1728, math.min(1727.1/1728, num + 1/3456))
       end
       local fractionalRomans = {
           { 1/2, 'S' }, { 5/12, ":•:" }, { 1/3, "::" },
           { 1/4, ":•" }, { 1/6, ":" }, { 1/12, '•' },
           { 1/24, 'Є' }, { 1/36, 'ƧƧ' }, { 1/48, 'Ɔ' }, { 1/72, 'Ƨ' }, { 1/144, 'Ƨ' },
           { 1/288, '℈' }, { 1/1728, '»' },
       }
       local fractionalLetters = getLetters(num, fractionalRomans)
       
       ret = ret .. fractionalLetters
   end

   return ret

end

function p.main(frame)

   -- If called via #invoke, use the args passed into the invoking
   -- template, or the args passed to #invoke if any exist. Otherwise
   -- assume args are being passed directly in from the debug console
   -- or from another Lua module.
   local origArgs
   if frame == mw.getCurrentFrame() then
       origArgs = frame:getParent().args
       for k, v in pairs(frame.args) do
           origArgs = frame.args
           break
       end
   else
       origArgs = frame
   end
   -- Trim whitespace and remove blank arguments.
   local args = {}
   for k, v in pairs(origArgs) do
       if type( v ) == 'string' then
           v = mw.text.trim(v)
       end
       if v ~=  then
           args[k] = v
       end
   end
   
   -- exit if not given anything
   if args == nil or args == {} then return end
   -- Given mathematical expression, simplify to a number
   if type(args[1]) == 'string' then
       args[1] = mw.ext.ParserFunctions.expr(args[1])
   end
   return _main(args)

end

return p