Base System + SciFi Notat

--Scifi notif in LuaU

-- functions
function splitChars(str)
    str = tostring(str)

    return str:split''
end

function flipTable(t)
    local t2 = {}

    for i, v in next, t do
        t2[v] = i
    end

    return t2
end

function arrayToCharDict(arr)
    local dict = {}

    for i, v in next, arr do
        dict[i - 1] = v
    end

    return dict
end

function stringToCharDict(str)
    return arrayToCharDict(splitChars(str))
end

--  base system
function factNumToStrFromBase(charsDict)
    local base = #charsDict + 1

    return function(num)
        local res = ''

        local iterations = 1 + math.max(0, math.floor( math.log(num, base)))

        for i = iterations, 1, -1  do -- going down number places
            local factor = base ^ (i - 1)

            local index = base - 1

            for largestDigit = base, 0, -1 do -- going down the base to 1
                local num2 = factor * largestDigit

                if num - num2 < 0 then continue end

                index = largestDigit
                num -= num2

                break
            end
            res ..= charsDict[index]
        end

        return res
    end
end

function factStrToNumFromBase(charsDict)
    local base = #charsDict + 1
    local flippedCharacters = flipTable(charsDict)

    return function(str)
        assert(type(str) == 'string')

        local res = 0

        for index = 1, #str do -- iterate each letter
            local letter = str:sub(index, index)

            local num = flippedCharacters[letter] * base ^ (#str - index)

            res += num
        end

        return res
    end
end

--  Scifi notif
function getScifiNotatSet(num, customBase)
    customBase = customBase or 10

    assert(
        type(num) == 'number' and
        type(customBase) == 'number'
    )

    local res = {
        exponent = 0;
        rational = num;
        sign = math.sign(num)
    }

    local absNum = math.abs(num)

    if absNum ~= 0 then
        -- check out function later
        -- get how many digits - 1 they have
        local logN = math.floor(math.log(absNum, customBase))

        res.exponent = logN

        local rational = absNum * customBase ^ (-logN)

        res.rational = rational
    else
        res.sign = 1
    end

    return res
end


function factNumToSciFiNotif(charsDict)
    local base = #charsDict + 1

    local numToStrConvert = factNumToStrFromBase(charsDict)

    return function(num)
        assert(type(num) == 'number')

        local res = {
            sign = charsDict[0];
            rational = '';
            exponent = charsDict[1]
        }

        -- get set
        local scifiNotifSet = getScifiNotatSet(num, base)

        -- set results
        res.sign = charsDict[scifiNotifSet.sign == -1 and 0 or 1]
        res.exponent = numToStrConvert(scifiNotifSet.exponent + 150)

        -- set rational
        local rationalStr = ''

        local rational = scifiNotifSet.rational

        local str = tostring(rational):gsub('%.','')

        local digit = 0


        --  repeat until we eventually reach near zero, note, we round instead of checking exactly because
        --    there is uncountably infinite amount of numbers between 0 and 1 and hitting 0 in a sea of
        --    numbers is touch. Also we offset the rational with 1e12 to try to preserve the decimals.
        while math.round(rational * 1e12) ~= 0 do

            -- go down the vase
            for index = 0, base do
                local num1 = index * (base ^ -digit)
                local num2 = rational - num1


                if math.sign(num2) == -1 then
                    rational -= ((index - 1) * (base ^ -digit))

                    rationalStr ..= charsDict[index - 1]

                    break
                end
            end

            digit += 1
        end

        res.rational = rationalStr

        -- return
        return res
    end
end

function factSciFiNotifToNum(charsDict)
    local base = #charsDict + 1

    local strToNumBaseConvert = factStrToNumFromBase(charsDict)
    local flippedDict = flipTable(charsDict)

    return function(scifiNotif)
        assert(
            type(scifiNotif) == 'table' and
                type(scifiNotif.exponent) == 'string' and
                type(scifiNotif.rational) == 'string' and
                type(scifiNotif.sign) == 'string'
        )

        local res = 0

        -- exponent and sign
        local exponent = strToNumBaseConvert(scifiNotif.exponent) - 150
        local sign = flippedDict[scifiNotif.sign] == 0 and -1 or 1

        -- give the int and mantissa their own section
        local rationalStr = scifiNotif.rational
        local intStr = rationalStr:sub(1,1)
        local mantissaStr = rationalStr:sub(2)

        local number = 0

        for exponentB = 0, #rationalStr - 1 do
            local charIndex = exponentB + 1

            local char = rationalStr:sub(charIndex, charIndex)

            number += flippedDict[char] * (base ^ -exponentB)
        end

        -- construct result
        res = sign * (number * (base ^ exponent))

        return res
    end
end


local dict = stringToCharDict'zxcvbnm,./asdfghjkl;qwertyuiop[]1234567890-=ZXCVBNM<>?ASDFGHJKL:"QWERTYUIOP{}|!@#$%^&*()_+'

local n = -1
local n2 = factNumToSciFiNotif(dict)(n)
print(n, n2, factSciFiNotifToNum(dict)(n2))