Results 1  10
of
16
SIMDoriented fast Mersenne twister: A 128bit pseudorandom number generator
 and QuasiMonte Carlo Methods 2006
, 2007
"... Summary. Mersenne Twister (MT) is a widelyused fast pseudorandom number generator (PRNG) with a long period of 2 19937 − 1, designed 10 years ago based on 32bit operations. In this decade, CPUs for personal computers have acquired new features, such as Single Instruction Multiple Data (SIMD) opera ..."
Abstract

Cited by 46 (4 self)
 Add to MetaCart
(Show Context)
Summary. Mersenne Twister (MT) is a widelyused fast pseudorandom number generator (PRNG) with a long period of 2 19937 − 1, designed 10 years ago based on 32bit operations. In this decade, CPUs for personal computers have acquired new features, such as Single Instruction Multiple Data (SIMD) operations (i.e., 128bit operations) and multistage pipelines. Here we propose a 128bit based PRNG, named SIMDoriented Fast Mersenne Twister (SFMT), which is analogous to MT but making full use of these features. Its recursion fits pipeline processing better than MT, and it is roughly twice as fast as optimised MT using SIMD operations. Moreover, the dimension of equidistribution of SFMT is better than MT. We also introduce a blockgeneration function, which fills an array of 32bit integers in one call. It speeds up the generation by a factor of two. A speed comparison with other modern generators, such as multiplicative recursive generators, shows an advantage of SFMT. The implemented Ccodes are downloadable from
Algorithms for Finding Almost Irreducible and Almost Primitive Trinomials
 in Primes and Misdemeanours: Lectures in Honour of the Sixtieth Birthday of Hugh Cowie Williams, Fields Institute
, 2003
"... Consider polynomials over GF(2). We describe ecient algorithms for nding trinomials with large irreducible (and possibly primitive) factors, and give examples of trinomials having a primitive factor of degree r for all Mersenne exponents r = 3 mod 8 in the range 5 < r < 10 , although t ..."
Abstract

Cited by 21 (6 self)
 Add to MetaCart
(Show Context)
Consider polynomials over GF(2). We describe ecient algorithms for nding trinomials with large irreducible (and possibly primitive) factors, and give examples of trinomials having a primitive factor of degree r for all Mersenne exponents r = 3 mod 8 in the range 5 < r < 10 , although there is no irreducible trinomial of degree r.
A Primitive Trinomial of Degree 6972593
 Mathematics of Computation
, 2003
"... We describe a search for primitive trinomials of degree 6972593 over GF(2). The only primitive trinomials found were x + 1 and its reciprocal. This completes the search for primitive trinomials whose degree is a Mersenne exponent less than ten million. ..."
Abstract

Cited by 16 (10 self)
 Add to MetaCart
(Show Context)
We describe a search for primitive trinomials of degree 6972593 over GF(2). The only primitive trinomials found were x + 1 and its reciprocal. This completes the search for primitive trinomials whose degree is a Mersenne exponent less than ten million.
An application of finite field: Design and implementation of 128bit instructionbased fast pseudorandom number generator
, 2007
"... (1) SIMDoriented Mersenne Twister (SFMT) is a new pseudorandom number generator (PRNG) which uses 128bit Single Instruction Multiple Data (SIMD) operations. SFMT is designed and implemented on C language with SIMD extensions and also implemented on standard C without SIMD. (2) Properties of SFMT a ..."
Abstract

Cited by 8 (0 self)
 Add to MetaCart
(Show Context)
(1) SIMDoriented Mersenne Twister (SFMT) is a new pseudorandom number generator (PRNG) which uses 128bit Single Instruction Multiple Data (SIMD) operations. SFMT is designed and implemented on C language with SIMD extensions and also implemented on standard C without SIMD. (2) Properties of SFMT are studied by using finite field theories, and they are shown to be equal or better than Mersenne Twister (MT), which is a widely used PRNG. (3) Generation speed of SFMT is measured on Intel Pentium M, Pentium IV, AMD Athlon 64 and PowerPC G4. It is shown to be about two times faster than MT implemented using SIMD. 1
Redundant trinomials for finite fields of characteristic 2
 Proceedings of ACISP 05, LNCS 3574
, 2005
"... Abstract. In this paper we introduce socalled redundant trinomials to represent elements of nite elds of characteristic 2. The concept is in fact similar to almost irreducible trinomials introduced by Brent and Zimmermann in the context of random numbers generators in [BZ 2003]. See also [BZ]. In f ..."
Abstract

Cited by 8 (0 self)
 Add to MetaCart
(Show Context)
Abstract. In this paper we introduce socalled redundant trinomials to represent elements of nite elds of characteristic 2. The concept is in fact similar to almost irreducible trinomials introduced by Brent and Zimmermann in the context of random numbers generators in [BZ 2003]. See also [BZ]. In fact, Blake et al. [BGL 1994, BGL 1996] and Tromp et al. [TZZ 1997] explored also similar ideas some years ago. However redundant trinomials have been discovered independently and this paper develops applications to cryptography, especially based on elliptic curves. After recalling well known techniques to perform e cient arithmetic in extensions of F2, we describe redundant trinomial bases and discuss how to implement them e ciently. They are well suited to build F2n when no irreducible trinomial of degree n exists. Depending on n ∈ [2, 10, 000] tests with NTL show that improvements for squaring and exponentiation are respectively up to 45 % and 25%. More attention is given to relevant extension degrees for doing elliptic and hyperelliptic curve cryptography. For this range, a scalar multiplication can be speeded up by a factor up to 15%. 1.
Fast and reliable random number generators for scientific computing
 PROC. PARA'04 WORKSHOP ON THE STATEOFTHEART INSCIENTIFIC COMPUTING
, 2004
"... Fast and reliable pseudorandom number generators are required for simulation and other applications in Scientific Computing. We outline the requirements for good uniform random number generators, and describe a class of generators having very fast vector/parallel implementations with excellent sta ..."
Abstract

Cited by 6 (2 self)
 Add to MetaCart
(Show Context)
Fast and reliable pseudorandom number generators are required for simulation and other applications in Scientific Computing. We outline the requirements for good uniform random number generators, and describe a class of generators having very fast vector/parallel implementations with excellent statistical properties. We also discuss the problem of initialising random number generators, and consider how to combine two or more generators to give a better (though usually slower) generator.
Almost Irreducible and Almost Primitive Trinomials
 in Primes and Misdemeanours: Lectures in Honour of the Sixtieth Birthday of Hugh Cowie Williams, Fields Institute
, 2003
"... Consider polynomials over GF(2). We de ne almost irreducible and almost primitive polynomials, explain why they are useful, and give some examples and conjectures relating to them. 2 ..."
Abstract

Cited by 4 (2 self)
 Add to MetaCart
Consider polynomials over GF(2). We de ne almost irreducible and almost primitive polynomials, explain why they are useful, and give some examples and conjectures relating to them. 2
Fuzzy and Tile Coding Approximation Techniques for Coevolution in Reinforcement Learning
, 2005
"... This thesis investigates reinforcement learning algorithms suitable for learning in large state space problems and coevolution. In order to learn in large state spaces, the state space must be collapsed to a computationally feasible size and then generalised about. This thesis presents two new imple ..."
Abstract

Cited by 2 (0 self)
 Add to MetaCart
This thesis investigates reinforcement learning algorithms suitable for learning in large state space problems and coevolution. In order to learn in large state spaces, the state space must be collapsed to a computationally feasible size and then generalised about. This thesis presents two new implementations of the classic temporal difference (TD) reinforcement learning algorithm Sarsa that utilise fuzzy logic principles for approximation, FQ Sarsa and Fuzzy Sarsa. The effectiveness of these two fuzzy reinforcement learning algorithms is investigated in the context of an agent marketplace. It presents a practical investigation into the design of fuzzy membership functions and tile coding schemas. A critical analysis of the fuzzy algorithms to a related technique in function approximation, a coarse coding approach called tile coding is given in the context of three different simulation environments; the mountaincar problem, a predator/prey gridworld and an agent marketplace. A further comparison between Fuzzy Sarsa and tile coding in the context of the nonstationary environments of the agent marketplace and predator/prey gridworld is presented. This thesis shows that the Fuzzy Sarsa algorithm achieves a significant reduction of state space over traditional Sarsa, without loss of the finer detail that the FQ Sarsa algorithm experiences. It also shows that Fuzzy Sarsa and gradient descent Sarsa(λ) with tile coding learn similar levels of distinction against a stationary strategy. Finally, this thesis demonstrates that Fuzzy Sarsa performs better in a competitive multiagent domain than the tile coding solution.
From Mersenne Primes to Random Number Generators ∗
, 2006
"... ∗ Advanced Computation seminar, ANU. Copyright c○2006, the author. AdvCom1t Fast and reliable pseudorandom number generators are required for simulation and other applications in Scientific Computing. Because of Moore’s law, random number generators that were satisfactory in the past may be inadequ ..."
Abstract
 Add to MetaCart
∗ Advanced Computation seminar, ANU. Copyright c○2006, the author. AdvCom1t Fast and reliable pseudorandom number generators are required for simulation and other applications in Scientific Computing. Because of Moore’s law, random number generators that were satisfactory in the past may be inadequate today. We outline some requirements for good uniform random number generators, and describe a class of generators having very fast vector/parallel implementations. These generators are based on primitive or almost primitive polynomials, and the degrees of the polynomials correspond to the exponents of certain Mersenne primes. We consider how to combine two generators to give a generator with better statistical and/or cryptographic properties, and also discuss the problem of initialization. We also mention some new “xorshift ” generators. 2