NHSE Review^TM 1996 Volume Second Issue

Random Number Generators for Parallel Computers

| <- HREF="node21.html" Prev | Index | Next -> |
NHSE Review^TM: Comments · Archive · Search

References

1

D.E. Knuth, The Art of Computer Programming Vol. 2: Seminumerical Methods (second edition), Addison-Wesley, Reading, Mass., 1981.

2

G.A. Marsaglia, A current view of random number generators, in Computational Science and Statistics: The Interface, ed. L. Balliard, Elsevier, Amsterdam, 1985.

3

S.K. Park and K.W. Miller, Random number generators: Good ones are hard to find, Comm. ACM 31:10, 1192 (1988).

4

S.L. Anderson, Random number generators on vector supercomputers and other advanced architectures, SIAM Rev. 32, 221 (1990).

5

F. James, A review of pseudorandom number generators, Comp. Phys. Comm. 60, 329 (1990).

6

P. L'Ecuyer, Random numbers for simulation, Comm. ACM 33:10, 85 (1990).

7

R.P. Brent, Uniform random number generators for supercomputers, Proc. Fifth Australian Supercomputer Conference, Melbourne, December 1992, p. 95.

8

C. Kalle and S. Wansleben, Problems with the random number generator RANF implemented on the CDC CYBER 205, Comp. Phys. Comm. 33, 343 (1984).

9

G. Parisi and F. Rapuano, Effects of the random number generator on computer simulations, Phys. Lett. 157B, 301 (1985).

10

A. Hoogland, A. Compagner and H.W.J. Blöte, Smooth finite-size behavior of the three-dimensional Ising model, Physica 132A, 593 (1985).

11

T. Filk, M. Marcu and K. Fredenhagen, Long range correlations in random number generators and their influence on Monte Carlo simulations, Phys. Lett. B165, 125 (1985).

12

A. Milchev, K. Binder, D.W. Heermann, Fluctuations and lack of self-averaging in the kinetics of domain growth, Z. Phys. B 63, 521 (1986).

13

A.M. Ferrenberg, D.P. Landau and Y.J. Wong, Monte Carlo simulations: Hidden errors from ``good'' random number generators, Phys. Rev. Lett. 69, 3382 (1992).

14

P. Grassberger, On correlations in ``good'' random number generators, Phys. Lett. A 181, 43 (1993).

15

P.D. Coddington, Analysis of random number generators using Monte Carlo simulation, Int. J. Mod. Phys. C 5, 547 (1994).

16

I. Vattulainen, T. Ala-Nissila and K. Kankaala, Physical tests for random numbers in simulations, Phys. Rev. Lett. 73, 2513 (1994).

17

I. Vattulainen, T. Ala-Nissila and K. Kankaala, Physical models as tests of randomness, Phys. Rev. E 52, 3205 (1995).

18

E.T. Dudewicz and T.G. Ralley, The Handbook of Random Number Generation and Testing with TESTRAND Computer Code, American Science Press, Columbus, Ohio, 1981.

19

K. Binder ed., Monte Carlo Methods in Statistical Physics, Springer-Verlag, Berlin, 1986; K. Binder and D.W. Heermann, Monte Carlo Simulation in Statistical Physics, Springer-Verlag, Berlin, 1988.

20

H. Gould and J. Tobochnik, An Introduction to Computer Simulation Methods, Vol. 2, Addison-Wesley, Reading, Mass., 1988.

21

S. Kirkpatrick and E. Stoll, A very fast shift-register sequence random number generator, J. Comput. Phys. 40, 517 (1981).

22

R.M. Ziff, Reduction of correlations in shift-register sequence random number generators using multiple feedback taps, unpublished.

23

P.D. Coddington, Tests of random number generators using Ising model simulations, in Proc. of the 1995 US-Japan Bilateral Seminar on New Trends in Computer Simulations of Spin Systems, Int. J. Mod. Phys. C 7, 295 (1996).

24

P.D. Coddington, S.-H. Ko, W.E. Mahoney and J.M. del Rosario, Monte Carlo tests of parallel random number generators, in preparation.

25

S.A. Cuccaro, M. Mascagni and D.V. Pryor, Techniques for testing the quality of parallel pseudo-random number generators, in Proc. of the 7th SIAM Conf. on Parallel Processing for Scientific Computing, SIAM, Philadelphia, 1995, p. 279.

26

A. De Matteis, S. Pagnutti, Controlling correlations in parallel Monte Carlo, Parallel Computing 21, 73 (1995).

27

G.A. Marsaglia, Random numbers fall mainly in the planes, Proc. Nat. Acad. Sci. 61, 25 (1968).

28

R.P. Brent, On the periods of generalized Fibonacci recurrences, Math. Comp. 63, 389 (1994).

29

N. Zierler and J. Brillhart, On primitive trinomials (mod 2), Information and Control 13, 541 (1968).

30

J.R. Heringa, H.W.J. Blöte and A. Compagner, Mersenne-exponent degrees for random-number generation, Int. J. Mod. Phys. C 3, 561 (1992).

31

G.A. Marsaglia and L.H. Tsay, Matrices and the structure of random number sequences, Linear Algebra Appl. 67, 147 (1985).

32

P. L'Ecuyer, Efficient and portable combined random number generators, Comm. ACM 31:6, 742 (1988).

33

H. Neiderreiter, Quasi-Monte Carlo methods and pseudo-random numbers, Bull. Amer. Math. Soc. 84, 957 (1978).

34

O.E. Percus and J.K. Percus, Long range correlations in linear congruential generators, J. Comput. Phys. 77, 267 (1988).

35

J. Eichenauer-Herrmann and H. Grothe, A remark on long-range correlations in multiplicative congruential pseudo-random number generators, Numer. Math. 56, 609 (1989).

36

A. De Matteis and S. Pagnutti, Parallelization of random number generators and long range-correlations, Numer. Math. 53, 595 (1988).

37

D.H. Lehmer, Mathematical methods in large-scale computing units, Ann. Comput. Lab. Harvard U. 26, 141 (1951).

38

R.C. Tausworthe, Random numbers generated by linear recurrence modulo two, Math. Comp. 19, 201 (1965).

39

S.W. Golomb, Shift Register Sequences, Holden-Day, San Francisco, 1967.

40

G.S. Fishman, Multiplicative congruential random number generators with modulus : an exhaustive analysis for and a partial analysis for , Math. Comp. 54, 331 (1990).

41

P. L'Ecuyer, F. Blouin, and R. Couture, A search for good multiple recursive generators, ACM Trans. on Modeling and Computer Simulation 3, 87 (1993).

42

L.-H. Deng, E.O. George and Y.-C. Chiu, On improving pseudo-random number generators, in Proc. of the 1991 Winter Simulation Conference, ed. B.L. Nelson et al, p. 1035.

43

B.A. Wichmann and I.D. Hill, An efficient and portable pseudorandom number generator, Appl. Statist. 31, 188 (1982).

44

P. L'Ecuyer and S. Tezuka, Structural properties for two classes of combined random number generators, Math. Comp. 57, 735 (1991).

45

G.A. Marsaglia, Toward a universal random number generator, Stat. Prob. Lett. 8, 35 (1990).

46

W.F. Eddy, Random number generators for parallel processors, J. Comp. Appl. Math. 31, 63 (1990).

47

W. Celmaster and K.J.M. Moriarty, A method for vectorized random number generators, J. Comput. Phys. 64, 271 (1986).

48

K.O. Bowman and M.T. Robinson, Studies of random number generators for parallel processing, in Proc. 2nd Conference on Hypercube Multiprocessors, ed. M.T. Heath, SIAM, Philadelphia, 1987, p. 445.

49

G. Fox et al., Solving Problems on Concurrent Processors, Vol. 1, Prentice-Hall, Englewood Cliffs, 1988.

50

W. Evans and B. Sugla, Parallel random number generation, in Proc. of the 4th Conference on Hypercube Concurrent Computers and Applications, ed. J. Gustafson, Golden Gate Enterprises, Los Altos, CA, 1989, p. 415.

51

P. L'Ecuyer and S. Côté, Implementing a random number package with splitting facilities, ACM Trans. Math. Soft. 17, 98 (1991).

52

S. Aluru, G.M. Prabhu and J. Gustafson, A random number generator for parallel computers, Parallel Computing 18, 839 (1992).

53

C. Koelbel et al., The High Performance Fortran Handbook, MIT Press, Cambridge, Mass., 1994.

54

P.D. Coddington, S.H. Ko, O. Odeyemi and C. Stoner, A random number generator for High Performance Fortran, in preparation.

55

T.-W. Chiu, Shift-register sequence random number generators on the hypercube concurrent computers, in Proc. of the 3rd Conference on Hypercube Concurrent Computers and Applications, ed. G. Fox, (ACM Press, New York, 1988), p. 1421.

56

W.P. Peterson, Some vectorized random number generators for uniform, normal, and Poisson distributions for the CRAY X-MP, J. Supercomput. 1, 327 (1988).

57

CM Scientific Software Library, Thinking Machines Corporation, Reading, Mass., 1993.

58

S. Wolfram, Random sequence generation by cellular automata, Adv. Appl. Math. 7, 123 (1986).

59

CM Fortran User's Guide, Thinking Machines Corporation, Reading, Mass., 1994.

60

See the online manual pages for the Maspar.

61

XL High Performance Fortran for AIX Language Reference V1.1, IBM Corporation, 1996.

62

pghpf User's Guide V2.0, The Portland Group, Inc., Wilsonville, Oregon, October 1995.

63

D.V. Pryor, S.A. Cuccaro, M. Mascagni and M.L. Robinson, Implementation and usage of a portable and reproducible parallel pseudorandom number generator, in Proc. of Supercomputing '94, IEEE, 1994, p. 311.

64

M. Mascagni and D.H. Bailey, Requirements for a parallel pseudorandom number generator, Supercomputing Research Center technical report, unpublished.

65

Cherri Pancake et al., Specification of Baseline Development Environment, Section 3, Component BDE-3i, in Guidelines for Writing System Software and Tools Requirements for Parallel and Clustered Computers.
Available at http://www.nero.net/pancake/SSTguidelines/baseline.html

66

P. Rodgers, Physics World (Feb. 1991) p. 13;
S. Aoki et al., Int. J. Mod. Phys. C 2, 829 (1991);
K. Binder, Large-scale simulations in condensed matter physics - the need for a teraflop computer, Int. J. Mod. Phys. C 3, 565 (1992).

| <- HREF="node21.html" Prev | Index | Next -> |
NHSE Review^TM: Comments · Archive · Search