-- 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