Boots – shoes – and leggings
Patent
1992-08-24
1994-06-21
Malzahn, David M.
Boots, shoes, and leggings
G06F 758
Patent
active
053233387
DESCRIPTION:
BRIEF SUMMARY
FIELD OF THE INVENTION
This invention relates to pseudo-random sequence generators.
BACKGROUND TO THE INVENTION
Pseudo-random sequences of integers find many applications, for example in the sampling and simulation technologies. Sampling is an important factor for example in the pharmaceutical, biotechnological, medical and social sciences, and simulation of random events is used in many methods of destruction testing and prototype development in mechanical and civil engineering. Pseudo-random sequence generators also find applications in electronics, computer and communication technologies.
A random sequence is one in which, for all integral values of n, however large, the (n+1)th term in the sequence cannot be determined from knowledge of all the previous terms from the first to the (n)th. For example, data collected from 1,000,000 throws of a conventional six-faced die is of no assistance in determining the result of the 1,000,001th throw.
A pseudo-random sequence is a sequence for which it is perceived to be impossible to determine the (n+1)th term solely from knowledge of all the n previous terms unless n exceeds a very large number. In the state of the art, such a number is of the order of 1.times.10.sup.190 and there are statistical techniques available, such as the Berlekamp-Massey and the Sloane-Reeds tests which permit a formal judgement of the perception of impossibility. In this context the period of a sequence is the value of C such that, for all values of n, the (n+C) the term is identical to the (n)th term.
An object of the present invention is to make it possible to provide a pseudo-random generator wherein the period can be arranged to be very high while still retaining practical levels of speed and cost.
SUMMARY OF THE INVENTION
According to the present invention there is provided a pseudo-random sequence generator characterised by comprising a plurality of substantially similar elements adapted to operate in parallel, each said element including: element, and intermediate numbers of higher value than either of said first and second numbers and modulating means having a modulating number for subsequently reducing those intermediate numbers to values below the modulating number, whereby said processing means is adapted to generate a first sequence that has a period not less than half the number range of said first sequence; and parallel elements to permit generation of a pseudo-random sequence of higher period.
In preferred embodiments of the present invention the use of the combination of multiplying and pipelined modulating algorithms permits each parallel element to generate a pseudo-random sequence with a significantly high period, e.g. of the order of 30,000 in one embodiment when the modulus used for modulating is a prime number of the order of 60,000. This is a convenient level for 16 bit computer operation because 2.sup.16 -1=65,535. The use of a number V of such similar elements operating in parallel permits the combined output pseudo-random sequence to have a period of the order of 30,000 to the power V. Thus the relationship between period and number of parallel elements is as follows:
______________________________________ V approximate period
______________________________________
5 30,000.sup.5 = 2.4 .times. 10.sup.22
6 30,000.sup.6 = 7.3 .times. 10.sup.26
7 30,000.sup.7 = 2.2 .times. 10.sup.31
20 30,000.sup.20 = 3.5 .times. 10.sup.89
43 30,000.sup.43 = 3.3 .times. 10.sup.192
______________________________________
The highest period currently required in the technological use of randomness is 5.times.10.sup.189, and thus 43 parallel elements can fulfil this requirement.
Advantageously there is provided a pseudo-random sequence generator of the type described above characterised by each said element including: provide a remainder number, number successively by powers of the second number, subjecting each product of this multiplication to said modulation, and storing the results of those successive modulations, and second means for multiplying each said
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L'Ecuyer, Pierre, "Efficient and Portable 32-Bit Random Variate Generators," Proceedings of the 1986 Winter Simulation Conference, Dec. 10, 1986, pp. 275-277.
Westlake, W. J., "A Uniform Random Number Generator Based on the Combination of Two Congruential Generators," Journal of the Association for Computing Machinery, Apr. 1967, vol. 14, No. 2, pp. 337-340.
Enfranchise Sixty Limited
Malzahn David M.
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