Re: KISS 64-bit pseudo-random number generator

On 9/10/24 19:30, Krishna Myneni wrote:

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 <E> and specific heat <C> 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 <E>   error in <C>
CONG   -0.31             0.82
R250   42.09          -107.16
SWC   -16.95            32.81
 

...
I ran a simple Monte-Carlo integration of the area in a unit circle using the 64-bit LCG PRNG (from random.4th in kForth dist) and Marsaglia's 64-bit KISS PRNG. Hard to say which is better for this problem.
--
Krishna
=== Comparison of 64-bit LCG and KISS PRNGs ===
PRNG: RANDOM  (random.4th)
Ntrials   Area      log(error)
-------------------------------
10^2     3.28        -0.86
10^3     3.18        -1.42
10^4     3.1724      -1.51
10^5     3.14048     -2.95
10^6     3.14350     -2.72
10^7     3.14225     -3.18
10^8     3.14152     -4.14
PRNG: RAN-KISS (kiss.4th)
Ntrials   Area      log(error)
-------------------------------
10^2     3.24       -1.01
10^3     3.10       -1.38
10^4     3.1252     -1.79
10^5     3.14084    -3.12
10^6     3.14073    -3.06
10^7     3.14184    -3.61
10^8     3.14167    -4.11