Digital Extraction and Rotation

This will be a short one. In the Google Code Jam qualification round, Problem C involved rotating the digits of a number to the left, e.g., 12405 -> 24051 -> 40512 -> 5124.

Python lets us do this with easy string <-> int conversions, but these aren't particularly fast. Instead, we can do it mathematically by extracting digits with % and /. This requires us knowing the number of digits in the number beforehand, but this can be calculated with the log₁₀ function (which is relatively slow, because computers store numbers in binary). In the Code Jam problem the number of digits didn't vary, so I could just calculate the length once then pass it in to my shifting function.

>>> def rot(n, length):
     return n % (10**(length-1))*10 + n / (10**(length - 1))

 
>>> rot(12405, 5)
24051
>>> 
>>> rot(24051, 5)
40512
>>> rot(23829239, 8)
38292392

The % / trick is really great, especially in languages such as C where string <-> int conversions are less straight-forward. It works on two principles: integer division with / by a power of 10 allows us to strip off digits from the right. You can visualise this as moving the decimal point to the left, then deleting everything that follows it. For example, 14231 / 10² gives 142.31, which with int division is 142. Similarly, applying the modulo operator % with a power of 10 allows us to strip digits from the right. 14231 % 10² is the remainder when 14231 is divided by 100, which as we saw before is 31.

Can someone please confirm that mathematical shifting is faster than converting it to a string with str() and manipulating that? And also, that log₁₀ is relatively slow?