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. Thus, a circular shift is given by the action of a particular permutation σ of the n positions in the tuple, for which modulo n for all i (or modulo n for the inverse operation). This permutation is a (very particular) instance of an n-cycle.
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, a, c) successively gives
- (c, a, b, a),
- (a, c, a, b),
- (b, a, c, a),
- (a, b, a, c) (the original four-tuple),
and then the sequence repeats; this four-tuple therefore has four circular shifts. However 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 circular shift (or bitwise rotation) is a shift operator 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 number's exponent from its mantissa. 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.
Read more about Circular Shift: Implementing Circular Shifts, Example, Applications
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