[issue9816] random.jumpahead and PRNG sequence independence

[Joseph Schaeffer]

New submission from Joseph Schaeffer :

Reading the Python 2.6 docs, it appeared that using random.jumpahead would 
allow the initialization of several generators with the same seed but having 
much different internal states. While the resulting PRNG appear to have 
different internal states, the produced random numbers [via .random()] are 
exactly the same after a small initial segment.

Attached is some example code which shows the first point at which they all 
agree - in my testing (Mac OS X, Python versions 2.5, 2.6, 2.7) the generated 
numbers all agreed on the 12th number generated. For smaller differences in 
jumpahead it was noticeable a lot earlier - n=1,2 differ only in the first 
sample from each.

The internal state of the PRNGs is indeed different even after the successive 
sampling, so it may be that this is intended - however if so the docs may cause 
confusion: my particular case was where I need random numbers for a stochastic 
markov process and in addition needed many such generators [one for each 
trajectory] and was hoping to use random.jumpahead to have indepedent PRNG's 
without having to generate [and prove] my own independent set of seeds. Thus 
having a long sequence of non-independent random numbers near the initial start 
condition causes random.jumpahead to be unusable for my situation.

It appears that Python 3.1 removed random.jumpahead - if so, it may be useful 
to note in the 2.6 docs why this was / the issues with random.jumpahead: 
reading how it changed after 2.3 made it sound like it was exactly what I 
wanted. 

Possible cause: I suspect the issue may be related to how a Mersenne Twister 
algorithm can take a while to recover from poor seeding (excessive 0's), but do 
not know enough to explore that idea.

--
components: Library (Lib)
files: random_test.py
messages: 115985
nosy: Joseph.Schaeffer
priority: normal
severity: normal
status: open
title: random.jumpahead and PRNG sequence independence
type: behavior
versions: Python 2.5, Python 2.6, Python 2.7
Added file: http://bugs.python.org/file18816/random_test.py

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[issue9816] random.jumpahead and PRNG sequence independence

[Joseph Schaeffer]

Joseph Schaeffer  added the comment:

Thanks for looking into it! I'm glad that issue will be fixed, as at least one 
website was actually recommending using .jumpahead(i) for i in 1..100 for 
independent seed. 

I suspect in my use case I'll want to continue my previous methods; I work with 
stochastic Markov processes and I need to seed a large number (10k+) of 
generators - one per trajectory - and also have the requirement of needing a 
deterministic PRNG. So having a single Mersenne Twister seed plus salting 
values that worked with .jumpahead would be a simpler representation; my 
previous code in C did basically that with a LCG to create those seeding values 
for the Mersenne Twister. So that's roughly equivalent [I think?] to the fixed 
random.jumpahead. 

Thanks again!

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