How to convert ‘start’, ‘stop’ and ‘step’ values in a for loop

Given the start, stop and step values, where start > stop and step < 0, how can I convert the values so that start < stop and step > 0 and use these values in a for loop that can yield the same index but in a reverse way. In other words, what should be the mathematical formula to use to set variables converted_start and converted_stop below?

start = 8
stop  = 0
step  = -2

for index in range(start, stop, step):
    print(index)   # prints 8, 6, 4 and 2


converted_start = ...     # convert `start`
converted_start = ...     # convert `stop`
converted_step  = -step   # convert `step`

for index in range(converted_start, converted_stop, converted_step):
    print(index)   # prints 2, 4, 6 and 8

Answer

Here come the formula:

def reverse_range(start, stop, step):
  new_start_offset = (stop - start) % step
  if new_start_offset == 0:
    new_start_offset = step
  new_start = stop - new_start_offset
  new_stop = start - step
  new_step = -step
  return new_start, new_stop, new_step

Here come the tests:

def print_range(start, stop, step):
  for i in range(start, stop, step):
    print(i, end=',')
  print()

print_range(0, 8, 2)
0,2,4,6,
print_range(*reverse_range(0,8,2))
6,4,2,0,

print_range(0, 9, 2)
0,2,4,6,8,
print_range(*reverse_range(0,9,2))
8,6,4,2,0,

print_range(8, 0, -2)
8,6,4,2,
print_range(*reverse_range(8, 0, -2))
2,4,6,8,

print_range(9, 0, -2)
9,7,5,3,1,
print_range(*reverse_range(9, 0, -2))
1,3,5,7,9,