local floor = math.floor
local mod = math.mod
local char = string.char
local log = math.log
local log2 = log(2)

local inf = 1/0

function Serialize(num)
	local sign = num < 0 or num == 0 and tostring(num) == "-0"
	if sign then
			num = -num
	end
	local x, m
	if num ~= num or (num == inf and num == -inf) then
		-- NaN
		x = 2047
		m = 1
	elseif num == inf then
		x = 2047
		m = 0
	elseif num == 0 then
		x = 0
		m = 0
	else
		local exp = floor(log(num)/log2)
		m = num / 2^exp * 4503599627370496
		x = (exp + 1023)
	end
	if sign then
		x = x + 2048
	end
	return char(mod(x / 256, 256), mod(x, 256), mod(m / 281474976710656, 256), mod(m / 1099511627776, 256), mod(m / 4294967296, 256), mod(m / 16777216, 256), mod(m / 65536, 256), mod(m / 256, 256), mod(m, 256))
end
 
function Deserialize(code)
	local a = string.byte(code, 1)
	local b = string.byte(code, 2)
	local c = string.byte(code, 3)
	local d = string.byte(code, 4)
	local e = string.byte(code, 5)
	local f = string.byte(code, 6)
	local g = string.byte(code, 7)
	local h = string.byte(code, 8)
	local i = string.byte(code, 9)
	local x = a * 256 + b
	local m = c * 281474976710656 + d * 1099511627776 + e * 4294967296 + f * 16777216 + g * 65536 + h * 256 + i
	local mantissa = m / 4503599627370496
	local sign = x >= 2048
	local exp = x
	if sign then
		exp = exp - 2048
	end
	exp = exp - 1023
	local val = 2^exp * mantissa
	if sign then
		return -val
	end
	return val
end

function Test(num)
	local after = Deserialize(Serialize(num))
	if num ~= after then
		print(num .. " -> " .. after)
	end
end

for i = 1, 100000 do
	local num = math.random() / math.random()
	Test(num)
end
Test(1/0)
Test(-1/0)
Test(0/0)