Attempt to understand how #t works in Lua

tablen.lua

-- Execute with tarantool or luajit

assert(jit, "jit required")
local table_new = require 'table.new'

local function tablen(t, len)
	local j = len
	if j > 1 and t[j] == nil then
		-- Use i = 0 here because in Lua tables are 1-indexed:
		local i = 0
		-- Implements right binsearch.
		-- Finds first right non-nil value:
		while (j - i) > 1 do
			local m = math.floor((i+j)/2)
			if t[m] == nil then
				j = m
			else
				i = m
			end
		end
		return i
	end
	return j
end

local function testit(t, n)
	local len = tablen(t, n)
	assert(#t == len, "Failed: " .. len .. " != " .. #t)
	local m = {}
	for i = 1, n do
		if t[i] ~= nil then
			table.insert(m, ("[%d] = %s"):format(i, t[i]))
		end
	end
	print("Len=".. len, "{" .. table.concat(m, ", ") .. "}")
end

-- Returns table with less than 2*log(len) items with desired length
local function adopt_table(len)
	if len == 0 then
		return {}
	end
	local maxn = 2^math.floor(1+math.log(len, 2))
	local t = table_new(maxn, 0)

	local i = 0
	local j = maxn
	while (j - i) > 1 do
		local m = math.floor((i+j)/2)
		if m <= len then
			t[m] = i
			i = m
		else
			j = m
		end
	end

	return t, maxn
end


local t1 = {1, 2, nil, 4}
testit(t1, 4) --> 4

local t2 = {1, 2, nil, nil}
testit(t2, 4) --> 2

local t3 = {1, 2, 3, nil, 5, nil}
testit(t3, 6) --> 3

local t4 = {1, nil, 3, 4, 5, nil}
testit(t4, 6) --> 5

local t5 = table_new(129, 0)
testit(t5, 129) --> 0

local t6 = table_new(129, 0)
t6[64] = 64
testit(t6, 129) --> 64
t6[95] = 95
testit(t6, 129) --> 64
t6[80] = 80
testit(t6, 129) --> 80
t6[96] = 96
testit(t6, 129) --> 96

testit(adopt_table(100500)) --> 100500

for len = 1, 10000 do
	local t = adopt_table(len)
	assert(#t == len, len)

	local c = 0
	for _ in pairs(t) do c = c + 1 end
	if len > 16 then assert(c <= 2*math.log(len), len) end
end

--[[
Len=4	{[1] = 1, [2] = 2, [4] = 4}
Len=2	{[1] = 1, [2] = 2}
Len=3	{[1] = 1, [2] = 2, [3] = 3, [5] = 5}
Len=5	{[1] = 1, [3] = 3, [4] = 4, [5] = 5}
Len=0	{}
Len=64	{[64] = 64}
Len=64	{[64] = 64, [95] = 95}
Len=80	{[64] = 64, [80] = 80, [95] = 95}
Len=96	{[64] = 64, [80] = 80, [95] = 95, [96] = 96}
]]

Original code: https://github.com/tarantool/luajit/blob/tarantool/src/lj_tab.c#L697