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From: Krishna Myneni <krishna.myneni@ccreweb.org>
Newsgroups: comp.lang.forth
Subject: Re: KISS 64-bit pseudo-random number generator
Date: Wed, 25 Sep 2024 18:15:31 -0500
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On 9/19/24 06:45, Krishna Myneni wrote:
> On 9/19/24 03:57, albert@spenarnc.xs4all.nl wrote:
>> In article <vcgok8$gol7$1@dont-email.me>,
>> Krishna Myneni  <krishna.myneni@ccreweb.org> wrote:
>> <SNIP>
>>> Moments of speed
>>>   N       <v> (m/s)    <v^2> (m/s)^2    <v^3> (m/s)^3
>>> 10^2     1181.0956     1656472.7       2604709063.
>>> 10^3     1293.3130     1952149.7       3300955817.
>>> 10^4     1259.3279     1862988.3       3108515117.
>>> 10^5     1260.5577     1872157.8       3147664636.
>>> 10^6     1259.4425     1868918.9       3139487337.
>>> 10^7     1259.6136     1869145.0       3139092438.
>>
>> I think for a Monte Carlo simulation at least three tests
>> must be done with different seeds.
> 
> Good point. For a meaningful comparison of errors between PRNGs at a 
> specific N, the statistical variation of the <v^n> need to be measured 
> for different seed values.
> 
> I can add some code to measure this sigma at each N, with 32 seeds 
> uniformly spaced between 0 and UMAX.
> 

I've calculated the statistical variation in the moments for each set of 
N, using 16 different seeds (spaced apart over the interval for UMAX). 
The standard dev. for the 16 <v^i>, computed for N trials is comparable 
to the relative error between the moment and its theoretical value. 
Thus, the relative errors are indeed a meaningful comparison between the 
two prngs tested here, and I think this implies that for N > 10^5 the 
LCG PRNG  (RANDOM) gives more accurate answers than the KISS 64 bit PRNG 
(RAN-KISS), for this problem. The LCG PRNG is faster than the KISS 
64-bit PRNG.

minforth stated earlier that he would prefer to use diehard tests to 
decide between which of these two PRNGs to use for computing these 
results from random trials. It will be interesting to see if diehard 
tests are consistent with what I find from actually using the PRNGs and 
comparing the results to the expected results (for large N and ideal PRNG).

--
Krishna