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This table specifies the input permutation on a 64-bit block. The meaning is as follows: the first bit of the output is taken from the 58th bit of the input; the second bit from the 50th bit, and so on, with the last bit of the output taken from the 7th bit of the input.
If creating a new permutation table, care should be taken to ensure uniform distribution of the values. [11] To get a gradient vector using the permutation table the coordinates of a grid point are looked up sequentially in the permutation table adding the value of each coordinate to the permutation of the previous coordinate.
A main problem in permutation codes is to determine the value of (,), where (,) is defined to be the maximum number of codewords in a permutation code of length and minimum distance . There has been little progress made for 4 ≤ d ≤ n − 1 {\displaystyle 4\leq d\leq n-1} , except for small lengths.
An input-consuming logic gate L is reversible if it meets the following conditions: (1) L(x) = y is a gate where for any output y, there is a unique input x; (2) The gate L is reversible if there is a gate L´(y) = x which maps y to x, for all y. An example of a reversible logic gate is a NOT, which can be described from its truth table below:
In a 1977 review of permutation-generating algorithms, Robert Sedgewick concluded that it was at that time the most effective algorithm for generating permutations by computer. [2] The sequence of permutations of n objects generated by Heap's algorithm is the beginning of the sequence of permutations of n+1 objects.
In general, an S-box takes some number of input bits, m, and transforms them into some number of output bits, n, where n is not necessarily equal to m. [3] An m × n S-box can be implemented as a lookup table with 2 m words of n bits each.
Permute instructions occur in both scalar processors as well as vector processing engines as well as GPUs.In vector instruction sets they are typically named "Register Gather/Scatter" operations such as in RISC-V vectors, [2] and take Vectors as input for both source elements and source array, and output another Vector.
On the other hand, some data structures like hash tables have very poor worst-case behaviors, but a well written hash table of sufficient size will statistically never give the worst case; the average number of operations performed follows an exponential decay curve, and so the run time of an operation is statistically bounded.