giantmath

--[[This API is solely built for performing with
numbers beyond normal levels (where floating-point
precision errors, the thing that so happens to be
the cause of the Far Lands begin to occur). It is
not advised to use this for small math problems.]]

--[[All math is done in tables, so it is
impossible to work with normal numbers.]]

--[[giantmath.convert() turns normal numbers to
table numbers.]]

function convert(n)

  ntable = {}
  d = math.floor(math.log10(n)) + 1
  for i = 1, d do
    set = d-(i-1)
    enzyme = (n % 10^(set) - n % 10^(set-1)) / 10^(set-1)
    ntable[i] = enzyme
  end
  return ntable

end


--[[giantmath.move() is essential for keeping the
table system stable.]]

function move(ntable)

  if ntable[0] ~= nil then
    table.insert(ntable, 0, "nil")
  end

  if ntable[1] == 0 then
    repeat
      table.remove(ntable, 1)
    until ntable[1] ~= 0
  end
  return ntable
end

--[[giantmath.tablen() is used to check the amount
of variables in a table.]]

function tablen(ntable)
  local i = 0
  while true do
    local i = i + 1
    if ntable[i] == nil then
      return i-1
    end
  end
end

--[[giantmath.check() is required for checking
carry-outs and borrows.]]

function check(ntable)

  --Carryout
  local i = 0
  repeat
    i = i + 1
    local itst = tablen(ntable) - (i - 1)
    if ntable[itst] >= 10 then

      local ndivide = math.floor(ntable[itst] / 10)
      local nmod = ntable[itst] % 10

      ntable[itst] = nmod
      ntable[itst-1] = ntable[itst-1] + ndivide
      move(ntable)

      --Can also be used for transforming whole
      --numbers into segmented table numbers
    end
  until i == tablen(ntable)

  --Borrow
  for i = 1, tablen(ntable) do
    itst = tablen(ntable) - (i - 1)
    if ntable[itst] < 0 then

      ntable[itst-1] = ntable[itst-1] - 1
      ntable[itst] = ntable[itst] + 10

    end
  end
  return ntable
end

--[[giantmath.align() is a base function used to
align two tables to be prepared for
manipulation.]]

function align(ntable1, ntable2)

  local x = tablen(ntable1)
  local y = tablen(ntable2)
  local state = 0

  if x == y then
    state = 0
  elseif x > y then
    state = 1
  elseif x < y then
    state = 2
  end

  local count = x - y
  if state == 1 then
    repeat
      table.insert(ntable2, 1, "0")
    until ntable2[x] ~= nil
  elseif state == 2 then
    repeat
      table.insert(ntable1, 1, "0")
    until ntable1[y] ~= nil
  elseif state == 0 then
    return ntable1, ntable2
  end
  return ntable1, ntable2
end


--[[giantmath.add() well... adds up two GiantMath
numbers.]]

function add(num, num2)

  local num, num2 = align(num, num2)
  local numb = tablen(num)

  for i = 1, numb do
    num3[i] = num1[i] + num2[i]
    print("2")
  end
  check(num3)
  return num3
end

num = {4, 3, 2, 1}
num2 = {2, 3, 9, 6}
num3 = add(num, num2)

for i = 1, 4 do
  write(num3[i])
end