project numbers in [a, b] as a cycle. (a-1 => b, b+1 => a)

cycle_transform.py

def transform(x, a, b):
    ''' projects x in [a, b] like a cycle. a-1=>b, b+1=>a '''
    n = b - a + 1
    return (x - a) % n + a


if __name__ == "__main__":
    a = 1
    b = 10

    assert all(map(lambda x: x == transform(x, a, b), range(a, b+1)))
    assert transform(a-1, a, b) == b
    assert transform(a-2, a, b) == b-1
    assert transform(b+1, a, b) == a
    assert transform(b+2, a, b) == a+1

    print('All tests passed')