apply function repeatedly in python without loops

I have a python function that I'd like to apply to a value many, many times. I know I can do it with a for loop:

for i in range(N_iter):
    val=f(val)

But is there a more efficient way, maybe using itertools or functools?

Solution

There's at least two things you can do: use local variables and unroll the loop.

Here's the baseline:

def f(x):
  return x+1

N_iter=16777216
val=0
for i in range(N_iter):
    val=f(val)
print(val)

On my system, this takes about 0m2.448s.

Here's the code when all references are local, meaning that Python won't have to load and store them each time:

def f(x):
  return x+1

def iterate(f, N_iter, val):
  for i in range(N_iter):
      val=f(val)
  print(val)

iterate(f, 16777216, 0)

This takes 0m1.648s.

You can also manually unroll the loop, doing more iterations per jump. Here's 8 (for simplicity it doesn't handle remainders):

def f(x):
  return x+1

def iterate(f, N_iter, val):
  for i in range(N_iter//8):
      val=f(val)
      val=f(val)
      val=f(val)
      val=f(val)
      val=f(val)
      val=f(val)
      val=f(val)
      val=f(val)
  print(val)

iterate(f, 16777216, 0)

This takes 0m1.327s.

Together, they've sped up this tight loop up by nearly 50%.

When you reach this level of microoptimization, it may be worth rethinking the whole approach or rewriting in a faster language.