While I generally like to reinvent the wheel, for hash functions I strongly recommend to use a proved good one. Djb2 by the venerable Daniel Bernstein satisfies all the requirements of TFA.

  h = 5381
  while still has data:
    h = h * 33 + next_byte()
  return h

PS of course if you think the multiplication is overkill, consider that it is nothing more than a shift and an addition.