Generates a function that maps an amount of integers to a single array index. Also generates a function that performs the inverse of the hash function.

GenerateHashFunc.lua

--[[GenerateHashFunc

Generates a function that maps an amount of integers to a single array index.
Also generates a function that performs the inverse of the hash function.

Input: The first two arguments indicate the base of the input and the output,
respectively. If not given, they default to 0 for the input, and 1 for the
output.

Each argument afterwards represents one argument to be passed to the generated
hash function. The value of each argument indicates the number of possible
states for the hash argument.

Output: The hash function, and the dehash function.

Example:

	-- 0-based input, 1-based output
	hash, dehash = GenerateHashFunc ( 0,1, 2,3 )

	hash ( 0, 0 ) --> 1
	hash ( 0, 1 ) --> 2
	hash ( 0, 2 ) --> 3
	hash ( 1, 0 ) --> 4
	hash ( 1, 1 ) --> 5
	hash ( 1, 2 ) --> 6

	dehash ( 1 ) --> 0, 0
	dehash ( 2 ) --> 0, 1
	dehash ( 3 ) --> 0, 2
	dehash ( 4 ) --> 1, 0
	dehash ( 5 ) --> 1, 1
	dehash ( 6 ) --> 1, 2

]]

function GenerateHashFunc(ib, ob, ...)
	ib = ib or 0
	ob = ob or 1

	local states = {...}
	local n = #states
	local err = 1
	local args, hash, dehash, dret = "", "return ", "", "return "

	for i = 1, n-1 do
		local mult = 1
		for s = i+1, n do
			mult = mult * states[s]
		end
		err = err + mult
		args = args .. "_" .. i .. ","
		hash = hash .. "_" .. i .. "*" .. mult .. "+"
		dehash = dehash .. "h/" .. mult .. "%" .. states[i] .. ","
		dret = dret .. "_" .. i .. "-_" .. i .. "%1"
		if ib < 0 then
			dret = dret .. "-" .. -ib
		elseif ib ~= 0 then
			dret = dret .. "+" .. ib
		end
		dret = dret .. ","
	end

	args = args .. "_" .. n
	hash = hash .. "_" .. n
	dehash = dehash .. "h%" .. states[n]
	dret = dret .. "_" .. n .. "-_" .. n .. "%1"
	if ib < 0 then
		dret = dret .. "-" .. -ib
	elseif ib ~= 0 then
		dret = dret .. "+" .. ib
	end

	local off = ob - err*ib
	if off < 0 then
		hash = hash .. "-" .. -off
	elseif off ~= 0 then
		hash = hash .. "+" .. off
	end
	dehash = "local " .. args .. "=" .. dehash .. " " .. dret
	if ob > 0 then
		dehash = "h=h-" .. ob .. " " .. dehash
	elseif ob ~= 0 then
		dehash = "h=h+" .. -ob .. " " .. dehash
	end

	return
		loadstring(string.format([[return function(%s)%s end]], args, hash))(),
		loadstring(string.format([[return function(h)%s end]], dehash))()
end