### Contents C189

, 2006

"... Marsaglia recently introduced a class of ‘xorshift ’ random number generators with periods 2n−1 for n = 32, 64,.... Here Marsaglia’s xor-shift generators are generalised to obtain fast and high quality random number generators with extremely long periods. Whereas random number generators based on pr ..."

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Marsaglia recently introduced a class of ‘xorshift ’ random number generators with periods 2n−1 for n = 32, 64,.... Here Marsaglia’s xor-shift generators are generalised to obtain fast and high quality random number generators with extremely long periods. Whereas random number generators based on primitive trinomials may be unsatisfac-tory, because a trinomial has very small weight, these new generators can be chosen so that their minimal polynomials have a large number of non-zero terms and, hence, a large weight. A computer search using Magma found good random number generators for n a power of two up to 4096. These random number generators are implemented in a

### High Dimensional Approximation

, 2007

"... A pseudo-random number generator (RNG) might be used to generate w-bit random samples in d dimensions if the number of state bits is at least dw. Some RNGs perform better than others and the concept of equidistribution has been introduced in the literature in order to rank different RNGs. In this ta ..."

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A pseudo-random number generator (RNG) might be used to generate w-bit random samples in d dimensions if the number of state bits is at least dw. Some RNGs perform better than others and the concept of equidistribution has been introduced in the literature in order to rank different RNGs. In this talk I shall define what it means for a RNG to be (d, w)-equidistributed, and then argue that (d, w)-equidistribution is not necessarily a desirable property. Presented at a Workshop on

### GPU-Accelerated Monte Carlo Simulations of Dense Stellar Systems

"... Computing the interactions between the stars within dense stellar clusters is a problem of fundamental importance in theoretical astrophysics. However, simulating realistic sized clusters of about 10 6 stars is computationally intensive and often takes a long time to complete. This paper presents th ..."

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Computing the interactions between the stars within dense stellar clusters is a problem of fundamental importance in theoretical astrophysics. However, simulating realistic sized clusters of about 10 6 stars is computationally intensive and often takes a long time to complete. This paper presents the parallelization of a Monte Carlo method-based algorithm for simulating stellar cluster evolution on programmable Graphics Processing Units (GPUs). The kernels of this algorithm involve numerical methods of root-bisection and von Neumann rejection. Our experiments show that although these kernels exhibit data dependent decision making and unavoidable non-contiguous memory accesses, the GPU can still deliver substantial near-linear speed-ups which is unlikely to be achieved on a CPU-based system. For problem sizes ranging from 10 6 to 7 × 10 6 stars, we obtain up to 28 × speedups for these kernels, and a 2 × overall application speedup on an NVIDIA GTX280 GPU over the sequential version run on an AMD c ○ Phenom TM Quad-Core Processor.

### Presented at a Workshop on High Dimensional Approximation Australian National University

, 2007

"... There is no such thing as a random number – there are only methods to produce random numbers, and a strict arithmetic procedure of course is not such a method. John von Neumann Suppose we are performing a simulation in d dimensions. For simplicity let the region of interest be the unit hypercube H = ..."

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There is no such thing as a random number – there are only methods to produce random numbers, and a strict arithmetic procedure of course is not such a method. John von Neumann Suppose we are performing a simulation in d dimensions. For simplicity let the region of interest be the unit hypercube H = [0, 1) d. For the simulation we may need a sequence y0, y1,... of points uniformly and independently distributed in H. A pseudo-random number generator gives us a sequence x0, x1,... of points in [0, 1). Thus, it is natural to group these points in blocks of d, that is

### unknown title

"... A PRNG specialized in double precision floating point numbers using an affine transition Mutsuo Saito and Makoto Matsumoto Abstract We propose a pseudorandom number generator specialized to generate double precision floating point numbers. It generates 52-bit pseudo-random patterns supplemented by a ..."

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A PRNG specialized in double precision floating point numbers using an affine transition Mutsuo Saito and Makoto Matsumoto Abstract We propose a pseudorandom number generator specialized to generate double precision floating point numbers. It generates 52-bit pseudo-random patterns supplemented by a constant most significant 12 bits (sign and exponent), so that the concatenated 64 bits represents a floating point number obeying the IEEE 754 format. To keep the constant part, we adopt an affine transition function instead of the usual F2-linear transition, and ex-tend algorithms computing the period and the dimensions of equidistribution to the affine case. The resulted generator generates double precision floating point numbers faster than the Mersenne Twister, whose output numbers only have 32-bit precision. 1

### Random Numbers for Parallel Computers: Requirements and Methods, With Emphasis on GPUs

"... We examine the requirements and the available methods and software to provide (or imitate) uniform random numbers in parallel computing environ-ments. In this context, for the great majority of applications, independent streams of random numbers are required, each being computed on a single processi ..."

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We examine the requirements and the available methods and software to provide (or imitate) uniform random numbers in parallel computing environ-ments. In this context, for the great majority of applications, independent streams of random numbers are required, each being computed on a single processing element at a time. Sometimes, thousands or even millions of such streams are needed. We explain how they can be produced and managed. We devote particular attention to multiple streams for GPU devices.

### Secure Online Scientific Visualization of Atmospheric Nucleation Processes

"... Abstract—With the fast increases in the size of the scientific data, the visualization technique has been widely adopted to transform the information into an easy-to-understand repre-sentation. Since the security clearance and access rights of the end users may vary greatly in a scientific visualiza ..."

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Abstract—With the fast increases in the size of the scientific data, the visualization technique has been widely adopted to transform the information into an easy-to-understand repre-sentation. Since the security clearance and access rights of the end users may vary greatly in a scientific visualization system, the security mechanisms must be properly designed and deployed. In this paper, we present a key management and update approach for online visualization of atmospheric nucleation. The users are divided into multiple groups and the personal secrets are determined by combining the user identities and polynomials. The personal secrets support both user authentication and visualization result encryption. We also describe the stateless key update mechanism. The proposed approach has been integrated with our visualization system and tested with real scientific data.