-- Vector math class with operators
local vector_meta
local vector_new
local function vector_check(v, n, name, argn)
	if not v.__is_vector then
		error('vector '..name..': argument #'..(argn or 1)
			..': expected vector, got '..type(v), n+1) end
end
local function vector_checksamelen(v1, v2, name)
	vector_check(v1, 3, name, 1)
	vector_check(v2, 3, name, 2)
	if #v1~=#v2 then
		error('vector '..name..': vector lengths do not match (lengths are '
			..#v1..' and '..#v2..')', 3) end
	return #v1
end
local function vector_checklen(v1, v2, name, len)
	vector_check(v1, 3, name, 1)
	vector_check(v2, 3, name, 2)
	if #v1~=len or #v2~=len then
		error('vector '..name..': vector lengths are not '..len..' (lengths are '
			..#v1..' and '..#v2..')', 3) end
end
local function vector_opnnn(name, op)
	return function(v1, v2)
		local len = vector_checksamelen(v1, v2, name)
		local v3 = {}
		for i = 1, len do
			v3[i] = op(v1[i], v2[i])
		end
		return vector_new(v3)
	end
end
local function vector_opnxn(name, op)
	return function(v1, v2)
		local v1v = type(v1)=='table' and v1.__is_vector
		local v2v = type(v2)=='table' and v2.__is_vector
		if v1v and v2v then
			local len = vector_checksamelen(v1, v2, name)
			local v3 = {}
			for i = 1, len do
				v3[i] = op(v1[i], v2[i])
			end
			return vector_new(v3)
		else
			if v2v then v1,v2 = v2,v1 end
			local len = #v1
			local v3 = {}
			for i = 1, len do
				v3[i] = op(v1[i], v2)
			end
			return vector_new(v3)
		end
	end
end
local function vector_opn0n(name, op)
	return function(v1)
		--vector_check(v1, 1, name)
		local len = #v1
		local v2 = {}
		for i = 1, len do
			v2[i] = op(v1[i])
		end
		return vector_new(v2)
	end
end
local vector_indices = {x = 1, y = 2, z = 3, w = 4, r = 1, g = 2, b = 3, a = 4}
local vector_meta = {
	__is_vector = true,
	__index = function(t, k)
		if tonumber(k) then return rawget(t, k)
		elseif vector_indices[k] then return rawget(t, vector_indices[k])
		else return getmetatable(t)[k]
		end
	end,
	__newindex = function(t, k, v)
		if tonumber(k) then rawset(t, k, v)
		elseif vector_indices[k] then rawset(t, vector_indices[k], v)
		else return
		end
	end,
	__add = vector_opnnn('add', function(x1, x2) return x1+x2 end),
	__sub = vector_opnnn('sub', function(x1, x2) return x1-x2 end),
	__mul = vector_opnxn('mul', function(x1, x2) return x1*x2 end),
	__div = vector_opnxn('div', function(x1, x2) return x1/x2 end),
	__pow = vector_opnxn('pow', function(x1, x2) return x1^x2 end),
	__unm = vector_opn0n('inv', function(x1) return -x1 end),
	__concat = nil,
	--__len = function(v1) return #v1 end,
	__len = nil,
	__eq = function(v1, v2)
		local len = vector_checksamelen(v1, v2, 'equals')
		for i = 1, len do
			if v1[i]~=v2[i] then return false end
		end
		return true
	end,
	__lt = nil,
	__le = nil,
	__call = nil,
	abs = vector_opn0n('abs', math.abs),
	length = function(v1)
		--vector_check(v1, 2, 'length')
		local len = #v1
		local l = 0
		for i = 1, len do
			l = l + v1[i]^2
		end
		return math.sqrt(l)
	end,
	normalize = function(v1)
		--vector_check(v1, 2, 'normal')
		local length = v1:length()
		local len = #v1
		local v3 = {}
		for i = 1, len do
			if length==0 then v3[i] = 0
			else v3[i] = v1[i]/length end
		end
		return vector_new(v3)
	end,
	__tostring = function(v1)
		--vector_check(v1, 2, 'tostring')
		local st = {}
		local len = #v1
		for i = 1, len do
			table.insert(st, tostring(v1[i]))
		end
		return 'vector{ '..table.concat(st, ', ')..' }'
	end,
	unpack = function(v1) return unpack(v1) end,
	floor = vector_opn0n('floor', function(x1) return math.floor(x1) end),
	ceil  = vector_opn0n('ceil' , function(x1) return math.ceil (x1) end),
	round = vector_opn0n('round', function(x1) return math.floor(x1+0.5) end),
	dot = function(v1, v2)
		local len = vector_checksamelen(v1, v2, 'dot')
		local x = 0
		for i = 1, len do
			x = x + v1[i]*v2[i]
		end
		return x
	end,
	cross = function(v1, v2)
		vector_checklen(v1, v2, 'cross', 3)
		return vector_new{
			v1[2]*v2[3] - v1[3]*v2[2],
			v1[3]*v2[1] - v1[1]*v2[3],
			v1[1]*v2[2] - v1[2]*v2[1],
		}
	end,
	rotateByAngleId = function(v1, r)
		--vector_check(v1, 2, 'rotate')
		if type(r)~='number' or r%1~=0 then
			error('vector rotateByAngleId: invalid rotation '..tostring(r), 2) end
		r = r%4
		local v2
		if     r==0 then v2 = vector_new{  v1[1],  v1[2], v1[3] }
		elseif r==1 then v2 = vector_new{  v1[2], -v1[1], v1[3] }
		elseif r==2 then v2 = vector_new{ -v1[1], -v1[2], v1[3] }
		elseif r==3 then v2 = vector_new{ -v1[2],  v1[1], v1[3] }
		else error('vector rotateByAngleId: invalid rotation '..r, 2) end
		return v2
	end,
	rotateZ = function(v, r)
		--vector_check(v, 2, 'rotate2d')
		if type(r)~='number' then
			error('vector rotateZ: invalid rotation '..tostring(r), 2) end
		local len = math.sqrt(v[1]^2 + v[2]^2)
		local ang = math.atan2(v[2], v[1]) + r
		local v2 = vector_new{ math.cos(ang)*len, math.sin(ang)*len }
		return v2
	end,
	tsString = function(v)
		--vector_check(v, 2, 'tsString')
		return table.concat(v, ' ')
	end,
	distance = function(v1, v2)
		local len = vector_checksamelen(v1, v2, 'distance')
		local sum = 0
		for i=1,len do
			sum = sum + (v1[i] - v2[i])^2
		end
		return math.sqrt(sum)
	end,
	copy = function(v)
		--vector_check(v, 2, 'copy')
		return vector_new(v)
	end,
}
vector_new = function(vi)
	if vi then
		if type(vi)=='string' then
			local vi2 = {}
			for val in vi:gmatch('[0-9%.%-e]+') do
				table.insert(vi2, tonumber(val))
			end
			vi = vi2
		elseif type(vi)~='table' then
			error('vector: argument #1: expected input table, got '..type(vi), 2)
		end
		local v = {}
		if #vi>0 then
			for i = 1, #vi do v[i] = vi[i] end
		else
			for n, i in pairs(vector_indices) do v[i] = vi[n] end
			if #v==0 then
				error('vector: argument #1: table contains no values', 2)
			end
		end
		setmetatable(v, vector_meta)
		return v
	else
		error('vector: argument #1: expected input table, got nil', 2)
	end
end

vector = vector_new
return vector_new