Since any computer data can be represented as one or more machine words, one generally needs hash functions for three types of domains : machine words ( " integers " ); fixed-length vectors of machine words; and variable-length vectors ( " strings " ).
32.
In other words, it will always be found either in its original hashed array entry, or in one of the next " H-1 " neighboring entries . " H " could, for example, be 32, a common machine word size.
33.
On typical modern computers, additions and multiplications take constant time independent of the values of the operands ( so long as the operands fit in single machine words ), so there are large gains in packing as much of a bignumber as possible into each element of the digit array.
34.
It's very rare to see characters described in octal ( partially because octal is pretty rare in general, but mostly because we're not using some weird architecture like a PDP-1 where the number of bits in a machine word is a multiple of 3 ).
35.
Load-link / store-conditional ( LL / SC ) offered by many RISC processors can be viewed as the most basic transactional memory support; however, LL / SC usually operates on data that is the size of a native machine word, so only single-word transactions are supported.
36.
The natural implementation of sparse matrix arithmetic on a computer makes it easy to compute the sequence " S " in parallel for a number of vectors equal to the width of a machine word indeed, it will normally take no longer to compute for that many vectors than for one.
37.
In the uniform cost model ( suitable for analyzing the complexity of gcd calculation on numbers that fit into a single machine word ), each step of the algorithm takes constant time, and Lam?s analysis implies that the total running time is also " O " ( " h " ).
38.
:I guess it made sense to Ken Thompson and Dennis Richie and those guys back in the day, to have a type that was the size of the machine word, although in practice it's pretty hard to think of a programming case that having that adaptive int makes for easier programming of a given task than using a fixed-size.
39.
Applying above " exp-by-squaring " algorithm, with " * " interpreted as " x " * " y " = " xy " mod 2345 ( that is a multiplication followed by a division with remainder ) leads to only 27 multiplications and divisions of integers which may all be stored in a single machine word.
40.
This gives the most compact representation of arbitrary permutations, and in computing is particularly attractive when " n " is small enough that " N " can be held in a machine word; for 32-bit words this means " n " d " 12, and for 64-bit words this means " n " d " 20.
