[LUA] Frac

local function to_frac(num)
  local int, fract = math.modf(num)
  if fract == 0 then
    return int, 1, 0
  end
  local W = math.floor(fract)
  local F = fract - W
  local pn, n, N = 0, 1
  local pd, d, D = 1, 0
  local x, err, q, Q
  repeat
    x = x and 1 / (x - q) or F
    q, Q = math.floor(x), math.floor(x + 0.5)
    pn, n, N = n, q*n + pn, Q*n + pn
    pd, d, D = d, q*d + pd, Q*d + pd
    err = F - N/D
  until math.abs(err) < 1e-15
  return N + D*W, D, int + err
end

if not _ARGS then return '!!fract [numb] (numb2)' end
local n, n2 = string:match(_ARGS, '(%S+)%s*(.*)')
n = tonumber(n)
if not n then return 'Send numb.' end
n2 = tonumber(n2)
if n2 then
    local numb, dec, int = to_frac(n / n2)
    return string.format('%g/%g = %d/%d + %g = %d/%d', n, n2, numb, dec, int, numb + int * dec, dec)
else
    local numb, dec, int = to_frac(n)
    return string.format('%g = %d/%d + %g = %d/%d', n, numb, dec, int, numb + int * dec, dec)
end