By R. Sedgewick
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Extra info for Algorithms
This leads us to a random number generator suitable for easy implementation on a general-purpose computer. Using a feedblack register with bits b and c tapped corresponds to using the recursion: a[k]==(a[k-b]+a[k-c]) mod m. ” However, it has been shown that good random numbers are likely to be produced even if normal integer addition is used. This is termed the additive congwential method. bers. The computation proceeds by replacing one of the numbers in the table by the sum of two of the other numbers in the table.
Another interesting fact is that the calculation can be done a word at a time, rather than a bit at a time, according to the same recursion formula. In our example, if we take the bitwise “exclusive or” of two successive words, we get the word which appears three places later in the list. This leads us to a random number generator suitable for easy implementation on a general-purpose computer. Using a feedblack register with bits b and c tapped corresponds to using the recursion: a[k]==(a[k-b]+a[k-c]) mod m.
For example, x55 can be computed from the above values with four more multiphcations: In general, the binary representation of N can be used to choose which computed values to use. ) The successive squares can be computed and the bits of N tested within the same loop. Two methods are available to implement this using only PoLYNoMlALs 47 one “accumulator,” like Horner’s method. One algorithm involves scanning the binary representation of N from left to right, starting with 1 in the accumulator. At each step, square the accumulator and also multiply by z when there is a 1 in the binary representation of N.