Bitrotationer

Bitrotationer, or bit rotations, are a class of bitwise operations performed on fixed-width binary words. In a rotation, each bit moves to a neighboring position and bits that would fall off one end re-enter at the opposite end. The operation is reversible and preserves the total number of set bits in the word.

The two basic forms are rotate left and rotate right. If x is a w-bit value and n is the rotation amount, then rotl(x, n) is defined as (x << n) | (x >> (w - n)), typically taken modulo 2^w to keep the result within w bits. Similarly, rotr(x, n) is (x >> n) | (x << (w - n)). In practice, n is considered modulo w, and results are masked to the word width. Rotations differ from ordinary shifts in that no bits are discarded or sign-extended; all bits are preserved by wrapping around.

Hardware and implementation: many modern processors provide dedicated rotate instructions (such as rol/ror on x86). In languages without explicit rotate operators, bit rotations can be implemented with shifts and ORs, plus masking to maintain the target width. Correct implementation must handle edge cases, such as rotating by zero or by a multiple of the word size, which yield the original value.

Applications: bitrotationer are widely used in cryptographic algorithms, hash functions, and pseudo-random number generators. They also appear in data packing, circular buffering, and various bit-manipulation techniques where a reversible, width-preserving permutation is advantageous.