Question

What is a mathematical way of of saying 1 – 1 = 12 for a month calculation? Adding is easy, 12 + 1 % 12 = 1, but subtraction introduces 0, stuffing things up.

My actual requirement is x = x + d, where x must always be between 1 and 12 before and after the summing, and d any unsigned integer.

Answer 1

I’d work internally with a 0 based month (0-11), summing one for external consumption only (output, another calling method expecting 1-12, etc.), that way you can wrap around backwards just as easily as wrapping around forward.

>>> for i in range(15): ...  print '%d + 1 => %d' % (i, (i+1)%12) ... 0 + 1 => 1 1 + 1 => 2 2 + 1 => 3 3 + 1 => 4 4 + 1 => 5 5 + 1 => 6 6 + 1 => 7 7 + 1 => 8 8 + 1 => 9 9 + 1 => 10 10 + 1 => 11 11 + 1 => 0 12 + 1 => 1 13 + 1 => 2 14 + 1 => 3 >>> for i in range(15): ...  print '%d - 1 => %d' % (i, (i-1)%12) ... 0 - 1 => 11 1 - 1 => 0 2 - 1 => 1 3 - 1 => 2 4 - 1 => 3 5 - 1 => 4 6 - 1 => 5 7 - 1 => 6 8 - 1 => 7 9 - 1 => 8 10 - 1 => 9 11 - 1 => 10 12 - 1 => 11 13 - 1 => 0 14 - 1 => 1