Binary search in Python

binary.py

def containsMatch(nums, lower, upper, match):
  """Returns `True` if `match` occurs within indices
    [`lower`, `upper`] of sorted list `nums`."""
  while True:
    i = (upper + lower) // 2
    cur = nums[i]
    
    if match == cur:
      return True
    elif lower >= upper:
      return False
    elif nums[i] < match:
      lower = i+1
    else:
      upper = i

# atLeastIndex and noMoreThanIndex are not guaranteed to find the
# highest index of a value if values are repeated.
      
def atLeastIndex(nums, lower, upper, atLeast):
  origLower = lower
  origUpper = upper
  while True:
    i = (upper + lower) // 2
    cur = nums[i]
    if cur == atLeast:
      return i
    elif lower >= upper:
      if cur < atLeast and i < origUpper:
        return i+1
      elif cur < atLeast:
        return None
      else:
        return i
    elif cur < atLeast:
      lower = i+1
    else:
      upper = i


def noMoreThanIndex(nums, lower, upper, noMoreThan):
  origLower = lower
  origUpper = upper
  while True:
    i = (upper + lower) // 2
    cur = nums[i]
    if noMoreThan == cur:
      return i
    elif lower >= upper:
      if cur > noMoreThan and i > origLower:
        return i-1
      elif cur > noMoreThan:
        return None
      else:
        return i
    elif cur < noMoreThan:
      lower = i+1
    else:
      upper = i