Model selection
On the lattice structure of the add-with-carry and subtract-with-borrow random number generators
ACM Transactions on Modeling and Computer Simulation (TOMACS)
On the lattice structure of certain linear congruential sequences related to AWC/SWB generators
Mathematics of Computation
The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
Mersenne twister: a 623-dimensionally equidistributed uniform pseudo-random number generator
ACM Transactions on Modeling and Computer Simulation (TOMACS) - Special issue on uniform random number generation
Sparse Serial Tests of Uniformity for Random Number Generators
SIAM Journal on Scientific Computing
Common defects in initialization of pseudorandom number generators
ACM Transactions on Modeling and Computer Simulation (TOMACS)
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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.