Circular shifts: Mathematical concept and applications in software development
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Matrices of 8-element circular shifts to the left and right
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 σ 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. The number of distinct circular shifts of an n-tuple is , where k is a divisor of n, indicating the maximal number of repeats over all subpatterns.
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.
while the arithmetic right-shift is ideal for signed two's complement binary numbers. Another form of shift is the circularshift, bitwise rotation or bit...
connected to create a "circularshift register". A PIPO register (parallel in, parallel out) is simply a D-type register and is not a shift register, but is...
circuit implementing bit shifts Bit shift, an operation treating a value as a sequence of binary digits Arithmetic shiftCircularshift, often used in cryptography...
{\displaystyle e^{{\frac {i2\pi }{N}}nm}} for some integer m corresponds to a circularshift of the output X k {\displaystyle X_{k}} : X k {\displaystyle X_{k}}...
with a circularshift). A logical shift is often used when its operand is being treated as a sequence of bits instead of as a number. Logical shifts can...
exponents and using the barrel shifter to shift the smaller number to the right by the difference, in one cycle. Circularshift Abhilasha; Sudharshan; Anusha...
x_{n-1}} for some k , 0 ≤ k < n {\displaystyle k,0\leq k<n} , or a circularshift of such a sequence. Let p = ⌊ log 2 n ⌋ {\displaystyle p=\lfloor \log...
{\displaystyle m-n} X's. Each of these X's was the start of a dominating circularshift before anything was removed. For example, consider X X Y X Y {\displaystyle...
In coding theory, a cyclic code is a block code, where the circularshifts of each codeword gives another word that belongs to the code. They are error-correcting...
transportation), can be reduced. In a circular economy, business models play a crucial role in enabling the shift from linear to circular processes. Various business...
by segmenting the data and adding it to an accumulator that is circular right shifted between each summation. To keep the accumulator within return value...
three vectors given. The scalar triple product is unchanged under a circularshift of its three operands (a, b, c): a ⋅ ( b × c ) = c ⋅ ( a × b ) = b ⋅...
leading it. To convert circularly polarized light to the other handedness, one can use a half-waveplate. A half-waveplate shifts a given linear component...
32-bit words of the expanded key Also define RotWord as a one-byte left circularshift: RotWord ( [ b 0 b 1 b 2 b 3 ] ) = [ b 1 b 2 b 3 b 0 ] {\displaystyle...
group S4 using the generators (red) a right circularshift of all four set elements, and (blue) a left circularshift of the first three set elements....
were used then it would be necessary to shift all elements when one is consumed.) In other words, the circular buffer is well-suited as a FIFO (first in...
into two parts and then to invert the order of the parts (similar to circularshift). This puts all endings and beginnings (presumably the location of most...
Let the function s {\displaystyle s} be a cyclic binary rotation (or circularshift): it rotates the bits by 1 to the left, pushing the latest bit in the...
Rotation (which in the FFT is multiplication by a complex phasor) is a circularshift of the component waveform. Various groups have also published "FFT"...
complex conjugate and [ m + n ] N {\displaystyle [m+n]_{N}} represents a circularshift. The linear autocorrelation of an MLS approximates a Kronecker delta...
number. In other words, the decimal representation undergoes a right circularshift by one place. For example: 4 × 128205 = 512820, so 128205 is 4-parasitic...
dividing the octave as a sequence of steps T t s T t T s (or some circularshift or "rotation" of it). To be called a regular diatonic tuning, each of...
reality television dating game show ROtate bits Left, also known as left circularshift Reorder level for replacing used or sold inventory Republic of Lakotah...
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