case [0, 1, 2, 3, 4] / there is no cycle from index 0 we cant move to any direction

here is my solution

from math import fmod

class Solution:
  def loopExists(self, arr):
    # this method calculates the new index/direction after + or - shift
    # the new index will be in the range of array length
    def move(index, arr):
      val = arr[index]

      new_index = index + val

      # figure out the direction of the move
      direction = 'n' # no direction
      if new_index > index:
        direction = 'r' # right
      elif new_index < index:
        direction = 'l' # left

      # if index exceeds the boundary of the array
      if new_index < 0 or new_index >= len(arr):
        if new_index > 0:
          index = fmod(new_index, len(arr)) # positive or zero
        else:
          remain = fmod(new_index, len(arr))
          if remain < 0:
            index = len(arr) + remain # negative index. we need to get the positive index
          else:
            index = remain # zero case
      else:
        index += val
      return (int(index), direction)
    
    # initial slow pointer move
    slow = move(0, arr)

    # initial fast pointer move + record the direction
    fast = move(0, arr)
    prev_fast_dir = fast[1]
    prev_fast_node = fast[0]
    fast = move(fast[0], arr)
    
    while slow and fast:
      # pointers are not moving
      if fast[1] == 'n':
        return False
      # pointers meet in one direction and we have more that one node involved
      elif slow[0] == fast[0] and prev_fast_dir == fast[1] and prev_fast_node != fast[0]:
        return True
      # pointers meet in one direction and we have only one node 
      elif slow[0] == fast[0] and prev_fast_dir == fast[1] and prev_fast_node == fast[0]:
        return False
      # pointers meet in different directions
      elif slow[0] == fast[0] and prev_fast_dir != fast[1]:
        return False
      else:
        # move pointers store the last direction
        slow = move(slow[0], arr)
        fast = move(fast[0], arr)
        prev_fast_dir = fast[1]
        fast = move(fast[0], arr)

    return False