Sum-discrepancy test on pseudorandom number generators

We introduce a non-empirical test on pseudorandom number generators (prng), named sum-discrepancy test. We compute the distribution of the sum of consecutive m outputs of a prng to be tested, under the assumption that the initial state is uniformly randomly chosen. We measure its discrepancy from the ideal distribution, and then estimate the sample size which is necessary to reject the generator. These tests are effective to detect the structure of the outputs of multiple recursive generators with small coefficients, in particular that of lagged Fibonacci generators such as random() in BSD-C library, as well as add-with-carry and subtract-with-borrow generators like RCARRY. The tests show that these generators will be rejected if the sample size is of order 106. We tailor the test to generators with a discarding procedure, such as ran_array and RANLUX, and exhibit empirical results. It is shown that ran_array with half of the output discarded is rejected if the sample size is of the order of 4×1010. RANLUX with luxury level 1 (i.e. half of the output discarded) is rejected if the sample size is of the order of 2×108, and RANLUX with luxury level 2 (i.e. roughly 3/4 is discarded) will be rejected for the sample size of the order of 2.4×1018. In our previous work, we have dealt with the distribution of the Hamming weight function using discrete Fourier analysis. In this work, we replace the Hamming weight with the continuous sum, using a classical Fourier analysis, i.e. Poisson's summation formula and Levy's inversion formula

Review of High-Quality Random Number Generators

This is a review of pseudorandom number generators (RNG's) of the highest quality, suitable for use in the most demanding Monte Carlo calculations. All the RNG's we recommend here are based on the Kolmogorov-Anosov theory of mixing in classical mechanical systems, which guarantees under certain conditions and in certain asymptotic limits, that points on the trajectories of these systems can be used to produce random number sequences of exceptional quality. We outline this theory of mixing and establish criteria for deciding which RNG's are sufficiently good approximations to the ideal mathematical systems that guarantee highest quality. The well-known RANLUX (at highest luxury level) and its recent variant RANLUX++ are seen to meet our criteria, and some of the proposed versions of MIXMAX can be modified easily to meet the same criteria.Comment: 21 pages, 4 figure

Rules and principles in cognitive diagnoses

Cognitive simulation is concerned with constructing process models of human cognitive behavior. Our work on the ACM system (Automated Cognitive Modeler) is an attempt to automate this process. The basic assumption is that all goal-oriented cognitive behavior involves search through some problem space. Within this framework, the task of cognitive diagnosis is to identify the problem space in which the subject is operating, identify solution paths used by the subject, and find conditions on the operators that explain those solution paths and that predict the subject's behavior on new problems. The work presented in this paper uses techniques from machine learning to automate the tasks of finding solution paths and operator conditions. We apply this method to the domain of multi-column subtraction and present results that demonstrate ACM's ability to model incorrect subtraction strategies. Finally, we discuss the difference between procedural bugs and misconceptions, proposing that errors due to misconceptions can be viewed as violations of principles for the task domain

A Portable High-Quality Random Number Generator for Lattice Field Theory Simulations

The theory underlying a proposed random number generator for numerical simulations in elementary particle physics and statistical mechanics is discussed. The generator is based on an algorithm introduced by Marsaglia and Zaman, with an important added feature leading to demonstrably good statistical properties. It can be implemented exactly on any computer complying with the IEEE--754 standard for single precision floating point arithmetic.Comment: pages 0-19, ps-file 174404 bytes, preprint DESY 93-13

Pseudo-random number generators for Monte Carlo simulations on Graphics Processing Units

Basic uniform pseudo-random number generators are implemented on ATI Graphics Processing Units (GPU). The performance results of the realized generators (multiplicative linear congruential (GGL), XOR-shift (XOR128), RANECU, RANMAR, RANLUX and Mersenne Twister (MT19937)) on CPU and GPU are discussed. The obtained speed-up factor is hundreds of times in comparison with CPU. RANLUX generator is found to be the most appropriate for using on GPU in Monte Carlo simulations. The brief review of the pseudo-random number generators used in modern software packages for Monte Carlo simulations in high-energy physics is present.Comment: 31 pages, 9 figures, 3 table

A digital controller using multirate sampling for gain control

Digital controller using multirate sampling for gain contro

Hurst's Rescaled Range Statistical Analysis for Pseudorandom Number Generators used in Physical Simulations

The rescaled range statistical analysis (R/S) is proposed as a new method to detect correlations in pseudorandom number generators used in Monte Carlo simulations. In an extensive test it is demonstrated that the RS analysis provides a very sensitive method to reveal hidden long run and short run correlations. Several widely used and also some recently proposed pseudorandom number generators are subjected to this test. In many generators correlations are detected and quantified.Comment: 12 pages, 12 figures, 6 tables. Replaces previous version to correct citation [19

Hardware verification at Computational Logic, Inc.

The following topics are covered in viewgraph form: (1) hardware verification; (2) Boyer-Moore logic; (3) core RISC; (4) the FM8502 fabrication, implementation specification, and pinout; (5) hardware description language; (6) arithmetic logic generator; (7) near term expected results; (8) present trends; (9) future directions; (10) collaborations and technology transfer; and (11) technology enablers