Is nested function efficient?

Question

In programming languages like Scala or Lua, we can define nested functions such as

function factorial(n)
  function _fac(n, acc)
    if n == 0 then
      return          


        

Answer 1

Let's benchmark it in Lua with/without nested functions.

Variant 1 (inner function object is created on every call)

local function factorial1(n)
   local function _fac1(n, acc)
      if n == 0 then
         return acc
      else
         return _fac1(n-1, acc * n)
      end
   end

   return _fac1(n, 1)
end

Variant 2 (functions are not nested)

local function _fac2(n, acc)
   if n == 0 then
      return acc
   else
      return _fac2(n-1, acc * n)
   end
end

local function factorial2(n)
   return _fac2(n, 1)
end

Benchmarking code (calculate 12! 10 mln times and display used CPU time in seconds):

local N = 1e7

local start_time = os.clock()
for j = 1, N do
   factorial1(12)
end
print("CPU time of factorial1 = ", os.clock() - start_time)

local start_time = os.clock()
for j = 1, N do
   factorial2(12)
end
print("CPU time of factorial2 = ", os.clock() - start_time)

Output for Lua 5.3 (interpreter)

CPU time of factorial1 = 8.237
CPU time of factorial2 = 6.074

Output for LuaJIT (JIT-compiler)

CPU time of factorial1 = 1.493
CPU time of factorial2 = 0.141