From: krishna.myneni@ccreweb.org   
      
   On 9/9/24 03:55, Anton Ertl wrote:   
   > mhx@iae.nl (mhx) writes:   
   >> On Mon, 9 Sep 2024 6:55:49 +0000, Lars Brinkhoff wrote:   
   >>   
   >> [..]   
   >>> I would like to recommend Marsaglia's newer and better xorshift family   
   >>> of PRNGs, and preferably the further development by Sebastiano Vigna   
   >>> called xoroshiro.  The output (with suitable parameters) is very good*,   
   >>> yet the implementation is very simple.   
   ...   
   > Having better randomness at the same speed or better speed with   
   > similar randomness is also relevant outside cryptographic   
   > applications.   
   >   
      
   Supposedly "good" PRNGs give large errors compared to theoretical values   
   for some physics simulations. These errors have been studied for a 2D   
   Ising model of ferromagnetism at the phase transition temperature, T =   
   T_c (transition from ordered spins to disordered spins).   
      
   Ref. [1] shows that a simple 32-bit congruential generator (CONG) gave   
   more accurate answers for the average energy  and specific heat    
   of the model lattice in Monte-Carlo simulations than the supposedly   
   superior R250 XOR based shift register generator or a subtract with   
   carry generator (SWC) -- incidentally, the R250 generator is included in   
   the FSL. All other things being the same for the simulations, the   
   following errors (in std deviations) were observed with the different PRNGs:   
      
   PRNG   error in    error in    
   CONG   -0.31             0.82   
   R250   42.09          -107.16   
   SWC   -16.95            32.81   
      
   Ref. [2] compares the performance of the following "high quality" PRNGs   
   (Xorshift, Xorwow, Mersenne Twister, and additive lagged Fibonnaci   
   generator (ALFG)) on simulation of other theoretical properties of large   
   2D Ising models (32768 x 32768). They found the Xorshift PRNG to give   
   much larger errors than the other PRNGs. "The other three tested PRNGs,   
   Mersenne Twister, Xorwow, and ALFG, perform well ... staying mostly   
   within a few standard errors of their theoretical values."   
      
   Note: I don't know what the difference is between Xorshift and R250 PRNGs.   
      
   --   
   Krishna   
      
   References   
      
   1. A. M. Ferrenberg, D. P. Landau, and Y. J. Wang, "Monte Carlo   
   Simulations: Hidden Errors from 'Good' Random Number Generators,"   
   Physical Review Letters, vol. 69, p. 3382 (1992).   
      
   2. D. Zhu, Y. Lin, G. Sun, and F. Wang, "Critical exponents testing of a   
   random number generator with the Wolff cluster algorithm," Journal of   
   Statistical Mechanics: Theory and Experiment, 063202 (2024).   
      
   --- SoupGate-Win32 v1.05   
    * Origin: you cannot sedate... all the things you hate (1:229/2)