Roman numerals in Lua

roman_numerals.lua

--[[
    Rules:
    I = 1
    V = 5
    X = 10
    L = 50
    C = 100
    D = 500
    M = 1000

    The symbols "I", "X", "C", and "M" can be repeated 3 times in succession, but no more.
    They may appear more than three times if they appear non-sequentially, such as XXXIX.
    "D", "L", and "V" can never be repeated.
    "I" can be subtracted from "V" and "X" only.
    "X" can be subtracted from "L" and "C" only.
    "C" can be subtracted from "D" and "M" only.
    "V", "L", and "D" can never be subtracted.
    Only one small-value symbol may be subtracted from any large-value symbol.
]]--

--mapping of possible addition values
local addition_map = {
    I=1,
    X=10,
    C=100,
    M=1000
    }

--mapping of substraction offsets (what can be substracted from each number)
local substraction_map = {
    V = 1,
    X = 1,
    L = 10,
    C = 10,
    D = 100,
    M = 100
    }

--mapping of roman numerals to arabic values
local numerals_map = {
    I = 1,
    V = 5,
    X = 10,
    L = 50,
    C = 100,
    D = 500,
    M = 1000
    }

function roman2arabic(str)
    local result = {}
    if str and type(str) == 'string' then
        local strLen = string.len(str)
        local resultPos = 1

        for i=1,strLen do
            local letter = string.sub(str, i, i)
            if not result[resultPos] then
                table.insert( result, numerals_map[letter] )
                --no need to increment since it's first number
            else
                if result[resultPos] == substraction_map[letter] then --can substract prev value
                    result[resultPos] = numerals_map[letter] - result[resultPos]
                    resultPos = resultPos + 1 --go to next one
                elseif result[resultPos] == addition_map[letter] then --can add prev value
                    result[resultPos] = result[resultPos] + numerals_map[letter]
                    --no increment -> can still add
                else
                    --no addition/substraction -> add a new number
                    resultPos = resultPos + 1
                    table.insert( result, numerals_map[letter] )
                end
            end
        end
    else
        print("roman2arabic: invalid input")
    end
    local arabicNum = 0
    for i, v in ipairs(result) do
        arabicNum = arabicNum + v
    end

    return arabicNum
end

--roman numerals possible based on order (placement in number - units, tens, hundreds, thousands)
local roman_nums_order = { {"I", "V", "X"}, {"X", "L", "C"}, {"C", "D", "M"}, {"M", "M", "M"} }

function arabic2roman(str)
    result = ""
    if str and type(str) == 'string' and (string.len(str) <= 4) then
        local strLen = string.len(str)
        local revStr = string.reverse(str)

        for i=1,strLen do
            local letter = string.sub(revStr, i, i)
            --probably there's a better way to transform a letter to a digit, but i don't know now
            local digit = string.byte(letter,1) - string.byte('0',1)
            local orderRes = ""

            local symbolReps = 0 --num of times symbol has repeated (must not be > 3)
            local substSymbol = 1 --symbol to substitute with (from roman_nums_order table)
            local substSymbolIncrement = 1 --can be 1 or 2, depending if we are before 5 or after 5 (e.g. if we need to use V or X)
            local j=1
            while j <= digit do
            	orderRes = orderRes .. roman_nums_order[i][substSymbol]
            	symbolReps = symbolReps + 1
            	if symbolReps > 3 then
            	    if i >= 4 then --max number of order thousands supported is 3
            	        orderRes = "MMM"
            	        break
            	    end
            	    orderRes = roman_nums_order[i][substSymbol]
            	    substSymbol = substSymbol + substSymbolIncrement
                 	orderRes = orderRes .. roman_nums_order[i][substSymbol]
                 	symbolReps = 0
			--check if next digit exists in advance  -> to remove substraction possibility
			if j+1 <= digit then
			    orderRes = roman_nums_order[i][substSymbol]
                            j = j+1 --go to next numeral ( e.g. IV -> V )
			    substSymbol = substSymbol - substSymbolIncrement --go back to small units
			    substSymbolIncrement = substSymbolIncrement + 1
			end
            	end
            	j=j+1
            end
            substSymbolIncrement = 1 -- reset increment for next order digit
	    result = string.format("%s%s", orderRes, result)
        end
    end
    return result
end

local function main()
    local testRomanNums = { "MCXX", "III", "IVVII", "MCMXXXVIIIV", "MDCXXXIII", "MMMDVII", 1, "MMMDCCCLXXXVIII" }
    for i,v in ipairs(testRomanNums) do
        print( v .. " = " .. roman2arabic( v ) )
    end

    local testArabicNums = { "1", "5", "111", "567", "999", "955", "1975", "3368", "3888" }
    for i,v in ipairs(testArabicNums) do
        print( v .. " = " .. arabic2roman( v ) )
    end
end

main()