Elementary mathematics | Computer arithmetic
Circular shift
In combinatorial mathematics, a circular shift is the operation of rearranging the entries in a tuple, either by moving the final entry to the first position, while shifting all other entries to the next position, or by performing the inverse operation. A circular shift is a special kind of cyclic permutation, which in turn is a special kind of permutation. Formally, a circular shift is a permutation Ο of the n entries in the tuple such that either modulo n, for all entries i = 1, ..., n or modulo n, for all entries i = 1, ..., n. The result of repeatedly applying circular shifts to a given tuple are also called the circular shifts of the tuple. For example, repeatedly applying circular shifts to the four-tuple (a, b, c, d) successively gives * (d, a, b, c), * (c, d, a, b), * (b, c, d, a), * (a, b, c, d) (the original four-tuple), and then the sequence repeats; this four-tuple therefore has four distinct circular shifts. However, not all n-tuples have n distinct circular shifts. For instance, the 4-tuple (a, b, a, b) only has 2 distinct circular shifts. In general the number of circular shifts of an n-tuple could be any divisor of n, depending on the entries of the tuple. In computer programming, a bitwise rotation, also known as a circular shift, is a bitwise operation that shifts all bits of its operand. Unlike an arithmetic shift, a circular shift does not preserve a number's sign bit or distinguish a floating-point number's exponent from its significand. Unlike a logical shift, the vacant bit positions are not filled in with zeros but are filled in with the bits that are shifted out of the sequence. (Wikipedia).
