-- Constants

local MAXIMUM_INT  = 2^53    -- The maximum double for where all integers can be represented exactly.
local MAXIMUM_ZERO = 10^-7   -- Used when attempting to determine fraction. Anything below is counted as 0.

--------------------------------------------------------------------------------
-- Util

local function is_integer (n)
	-- Predicate. Neither +inf, -inf nor nan are integer.
	return  n == math.floor(n)  and n ~= 1/0 and n ~= -1/0
end

local function factorial (n)
	-- Returns the factorial of n.
	-- That is n! = n * (n-1) * (n-2) * ... * 1
	local a = 1
	for i = 2, n do  a = a * i  end
	return a
end

local function calculate_fraction (n)
	-- Returns x and y such that x/y = n. If none could be found, returns nil.
	local a, b = 1, n % 1
	while MAXIMUM_ZERO < b and a <= MAXIMUM_INT do
		local r = math.pow(b, -1)
		a, b = a * r, r % 1
		-- Invariant:  n * a / a = n
	end
	-- Check the values make sense.
	local numerator, denumberator = math.floor(n * a), math.floor(a)
	if numerator / denumberator == n then
		return numerator, denumberator
	end
end

local MATH_SHORTHAND = {
	-- Only used if options.math_shorthand = true
	['0/0']          =  'nan',
	['1/0']          =   '∞',
	['-1/0']         =  '-∞',
	['math.pi']      =   'π',
	['math.exp(1)']  =   'e',
}

--------------------------------------------------------------------------------
-- Generate special number table

-- TODO: Restructure this.

local SPECIAL_NUMBER = {}
do
	SPECIAL_NUMBER[ 1/0]         =  '1/0'
	SPECIAL_NUMBER[math.pi]      =  'math.pi'
	SPECIAL_NUMBER[math.exp(1)]  =  'math.exp(1)'

	for i = -10, -6 do
		SPECIAL_NUMBER[math.pow(10, i)] = '10^'..i
	end
	for i = -15, -7 do
		SPECIAL_NUMBER[math.pow( 2, i)] =  '2^'..i
	end

	for i = 5, 308 do
		SPECIAL_NUMBER[math.pow(10, i)] = '10^'..i
	end

	for i = 17, 1023 do
		SPECIAL_NUMBER[math.pow( 2, i)    ] =  '2^'..i
		--SPECIAL_NUMBER[math.pow( 2, i) - 1] =  '2^'..i..'-1'
		--SPECIAL_NUMBER[math.pow( 2, i) + 1] =  '2^'..i..'+1'
	end

	for i = 9, 170 do
		SPECIAL_NUMBER[factorial(i)] = i..'!'
	end

	for i = 1, 100 do
		local sqrt = math.sqrt(i)
		if not is_integer(sqrt) then
			SPECIAL_NUMBER[1/sqrt] = '1/math.sqrt('..i..')'
			SPECIAL_NUMBER[sqrt] = 'math.sqrt('..i..')'
		end
	end

	for i = 1, 100 do
		local log = math.log(i)
		if not is_integer(log) then
			SPECIAL_NUMBER[log] = 'math.log('..i..')'
		end
	end
end

--------------------------------------------------------------------------------

local function format_number (n)
	-- Returns a string of n formatted as to allow easy back into a lua interpreter.
	if n ~= n then                 return '0/0'
	elseif n < 0 then              return '-' .. format_number(-n)
	elseif SPECIAL_NUMBER[n] then  return SPECIAL_NUMBER[n]
	end
	-- Maybe it's an integer?
	if is_integer(n) then  return tostring(n)  end
	-- Maybe it's a fraction?
	local numerator, denumberator = calculate_fraction(n)
	if numerator then
		return format_number(numerator)..'/'..format_number(denumberator)
	end
	return ( tostring(n):gsub('e%+?', '*10^') )  -- Parantheses to return first result.
end

return function (value, options, depth, l)
	l[#l+1] = format_number(value)
	if options.math_shorthand then
		l[#l] = MATH_SHORTHAND[ l[#l] ]
	end
end