#! /usr/bin/env lua

local usage = [[
dvdaspect.lua [-pw] width height
returns the correct display aspect ratio of a dvd after cropping

options:
 -p  input is pal
 -w  input is widescreen
]]

local die = function(ret)
    print(usage)
    os.exit(ret or 0)
end

local rational = function(decimal, acc)
    acc = acc or 1E-3
    local sign, num, denum
    local sign = (decimal < 0) and -1 or 1
    decimal = math.abs(decimal)
    if decimal == math.floor(decimal) then
        num = decimal * sign
        denum = 1
        return num, denum
    end
    if decimal < 1E-19 then
        num = sign
        denum = 9999999999999999999
    elseif decimal > 1E+19 then
        num = 9999999999999999999 * sign
        denum = 1
    end
    local z = decimal
    local predenum = 0
    local sc
    denum = 1
    repeat
        z = 1 / (z - math.floor(z))
        sc = denum
        denum = denum * math.floor(z) + predenum
        predenum = sc
        num = math.floor(decimal * denum)
    until ((math.abs(decimal - (num / denum)) < acc) or (z == math.floor(z)))
    num = sign * num
    return num, denum
end

local flags, args = {}, {}
for i, v in ipairs(arg) do
    if v:match("^-") then
        for f in v:gmatch("%w") do
            flags[f] = true
        end
    else
        args[#args+1] = v
    end
end

local w, h = tonumber(args[1]), tonumber(args[2])
if not w or not h then
    die(1)
end

local region = flags.p and "pal" or "ntsc"
local screen = flags.w and "wide" or "full"

local pars = {
    ntsc = { wide = 40/33, full = 10/11 },
    pal  = { wide = 16/11, full = 12/11 }
}

local dar = (w / h) * pars[region][screen]
local num, den = rational(dar)
io.write(num, ":", den, "\n")