#!/usr/bin/env lua

--

--

function debug(...)
--	print("DEBUG:", ...)
end

function write(...)
	io.write(...)
end

function writeln(...)
	io.write(...)
	io.write("\n")
end

function computePi(maxDigits)
    local SIZE = 1000
	
    local precision = (maxDigits-1) // 3 + 3
	debug(precision)
	
	-- initialize variables
	local remainder1, remainder2, remainder3, remainder4 = 0, 0, 0, 0
	local b, n, n2, carry = 0, 0, 0, 0
	local i, l = 0, 0
	local isZero = false

	-- arrays of numbers
    local p = {}
	local t = {}

    -- Initialize arrays.
    for i = 1, precision+1 do
        t[i] = 0
		p[i] = 0
    end
	
    -- Note, borrows and carries from the addition and subtraction
    -- are postponed till last.  See: http://www.boo.net/~jasonp/ord

    -- Compute arctan(1/5)

    -- t = t / 5, p = t
    t[1] = 1
    remainder1 = 0
    for i = 1, precision+1 do
        b = SIZE * remainder1 + t[i]
        t[i] = b // 5
        p[i] = t[i]
        remainder1 = b % 5
    end

    -- While t is not zero.
    n = -1
    n2 = 1
	isZero = false
    repeat
        -- t = t / 25, p = p - t / n, t = t / 25, p = p + t / (n+2)
        remainder1 = 0
        remainder2 = 0
        remainder3 = 0
        remainder4 = 0
        isZero = true
        n = n + 4
        n2 = n2 + 4
        for i = 1, precision+1 do
            b = SIZE * remainder1 + t[i]
            t[i] = b // 25
            remainder1 = b % 25

            b = SIZE * remainder2 + t[i]
            p[i] = p[i] - b // n
            remainder2 = b % n

            b = SIZE * remainder3 + t[i]
            t[i] = b // 25
            remainder3 = b % 25

            b = SIZE * remainder4 + t[i]
            p[i] = p[i] + b // n2
            remainder4 = b % n2 

            if isZero and t[i] ~= 0 then
                isZero = false
            end
        end
    until isZero

    -- p = p * 4
    carry = 0
    for i = precision+1, 1, -1 do
        b = p[i] * 4 + carry
        p[i] = b % SIZE
        carry = b // SIZE
    end

    -- Compute arctan(1/239)

    -- t = t / 239, p = p - t
    t[1] = 1
    remainder1 = 0
    for i = 1, precision+1 do
        b = SIZE * remainder1 + t[i]
        t[i] = b // 239
        p[i] = p[i] - t[i]
        remainder1 = b % 239
    end

    -- While t is not zero.
    n = -1
    n2 = 1
    repeat
        -- t = t / 57121, p = p + t / n, t = t / 57121, p = p - t / (n+2)
        remainder1 = 0
        remainder2 = 0
        remainder3 = 0
        remainder4 = 0
        isZero = true
        n = n + 4
        n2 = n2 + 4
        for i = 1, precision+1 do
            b = SIZE * remainder1 + t[i]
            t[i] = b // 57121
            remainder1 = b % 57121

            b = SIZE * remainder2 + t[i]
            p[i] = p[i] + b // n
            remainder2 = b % n

            b = SIZE * remainder3 + t[i]
            t[i] = b // 57121
            remainder3 = b % 57121

            b = SIZE * remainder4 + t[i]
            p[i] = p[i] - b // n2
            remainder4 = b % n2

            if isZero and t[i] ~= 0 then    -- is t zero?
                isZero = false
            end
        end
    until isZero

    -- p = p * 4
    carry = 0
    for i = precision+1, 1, -1 do
        b = p[i] * 4 + carry
        p[i] = b % SIZE
        carry = b // SIZE
    end

    -- Borrow and carry.
    for i = precision+1, 2, -1 do
        if p[i] < 0 then
            b = p[i] // SIZE
            p[i] = p[i] - (b - 1) * SIZE
            p[i-1] = p[i-1] + b - 1
        end
        if p[i] >= SIZE then
            b = p[i] // SIZE
            p[i] = p[i] - b * SIZE
            p[i-1] = p[i-1] + b
        end
    end

    ---
    return table.concat(text):sub(1, maxDigits+2)
end

do
	local digits = math.tointeger(arg[1]) or 10000
	writeln("Computing ", digits, " digits of Pi.")
	
	local pi = computePi(digits)
	
	-- Format and print the output
	local line = ""
	writeln("3.")
	for i = 3, pi:len() do
		local j = i - 2
		line = line .. pi:sub(i, i)
		if j % 1000 == 0 then
			writeln(line)
			writeln()
			line = ""
		elseif j % 50 == 0 then
			writeln(line)
			line = ""
		elseif j % 10 == 0 then
			line = line .. " "
		end
    end
	if line:len() > 0 then
		writeln(line)
	end
end