Module:Roman

This module implements the {{Roman}} template. For behavioral documentation, please see the template page. For test cases, please see Template:Roman/testcases.

• Module supports 0 as a Roman numeral, displays as 'N'.
• Prior to 25 April 2016, used to display 69105 as LXVMMMMCV. With the addition of IX and IV being 9000 and 4000 respectively, we now display 69105 as LXIXCV.
• Module handles decimal, fractional, and arithmetic expressions to a precision of 1/1728. Uses #expr: at line 118.

Handling tricky cases (like 0.00001 and 99.99999)

1. Find the Roman numerals for the integer part of the number.
2. If the number is not an integer:
   • Add half of the smallest unit (1/1728) to simulate rounding instead of truncation.
   • Ensure this new result is between 1/1728 and 1727/1728. (actually 1.1/1728 and 1727.1/1728 due to floating point rounding issues)
3. Hence, 0.00001 is guaranteed to have at least the smallest unit symbol (instead of being blank or 0), and 99.99999 does not display as 100 or 99 and 2 halves.

Validation

• Template:Roman/testcases
• Module:Roman/testcases - does not contain fractional/decimal tests
• The template supports subst: and safesubst:.

---

-- This module implements {{Roman}}.

local p = {}

-- This function implements the {{overline}} template.
local function overline(s)
    return mw.ustring.format( '<span style="text-decoration:overline;">%s</span>', 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, '<s>Ƨ</s>' },
            { 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