What are good PRNG for calculators?

08212014, 03:25 PM
(This post was last modified: 08212014 03:27 PM by Namir.)
Post: #1




What are good PRNG for calculators?
In your opinion, what are very good algorithms for pseudorandom number generators (uniformly distributed) for programmable calculators? I am talking about algorithms that you and I can program ourselves to generate uniform random numbers between 0 and 1. So saying that the Rand# in the HP15C is very good does not count, because it is already hardwired in the firmware.
Balancing between simplicity and efficiency (i.e good numeric distribution and long cycles) is very good! Namir 

08212014, 04:19 PM
Post: #2




RE: What are good PRNG for calculators?
See Knuth for algorithms and Pickover for testing (not with my specific sources right now).
TomC 

08212014, 04:28 PM
(This post was last modified: 08212014 04:58 PM by Thomas Klemm.)
Post: #3




RE: What are good PRNG for calculators?
This is from the Games Pac:
LBL "RNDM" RCL 00 9821 * .211327 + FRC STO 00 END Quote:Another interesting portion of this program is the random number generator: ARITHMETIC TEACHER / HP41C STANDARD APPLICATIONS Cheers Thomas 

08212014, 06:35 PM
(This post was last modified: 08212014 06:38 PM by Dieter.)
Post: #4




RE: What are good PRNG for calculators?
(08212014 03:25 PM)Namir Wrote: Balancing between simplicity and efficiency (i.e good numeric distribution and long cycles) is very good! In terms of simplicity it will not get much simpler than a good old linear congruential RNG, i.e. something like r_{n+1} = (a · r_{n} + b) mod c. However, the cycle length obviously is limited. So a good idea might be the combination of several RNGs of this kind. A wellknown method using this approach is the WichmannHill generator that was introduced in Applied Statistics, vol. 31 (1982). But caveat lector: the original paper included an error that was corrected in 1984. ;) The cycle length of this RNG is approx. 7 · 10^{12}. Dieter 

08212014, 07:05 PM
Post: #5




RE: What are good PRNG for calculators?
(08212014 03:25 PM)Namir Wrote: So saying that the Rand# in the HP15C is very good does not count, because it is already hardwired in the firmware. This Python program simulates the RAN# function of the HP15C: Code: seed = 7365289446 # or any other number Of course in the HP15C the value will be e.g. 0.7365289446 instead. Cheers Thomas PS: It's similar in the HP48. How RAND Works 

08212014, 07:21 PM
Post: #6




RE: What are good PRNG for calculators?
(08212014 06:35 PM)Dieter Wrote: In terms of simplicity it will not get much simpler than a good old linear congruential RNG, You might be interested in this paper: Xorshift RNGs. But they aren't suited well for programmable calculators. 

08212014, 09:22 PM
Post: #7




RE: What are good PRNG for calculators?
(08212014 04:28 PM)Thomas Klemm Wrote: This is from the Games Pac: Thomas, This algorithm is used in the RN label of the PPC ROM. The book "Enter" by JeanDaniel Dodin does mention it too! Namir 

08212014, 09:23 PM
Post: #8




RE: What are good PRNG for calculators?
(08212014 07:21 PM)Thomas Klemm Wrote:(08212014 06:35 PM)Dieter Wrote: In terms of simplicity it will not get much simpler than a good old linear congruential RNG, How do you do bit shifting in the HP25, HP67, HP41C? Namir 

08212014, 09:56 PM
(This post was last modified: 08212014 09:56 PM by Paul Dale.)
Post: #9




RE: What are good PRNG for calculators?  
08212014, 10:55 PM
Post: #10




RE: What are good PRNG for calculators?
(08212014 09:56 PM)Paul Dale Wrote:It would be quite slow, but you can do XOR a bit at a time with addition and modulus. If X and Y contain a single bit then(08212014 09:23 PM)Namir Wrote: How do you do bit shifting in the HP25, HP67, HP41C? Code: + 2 MOD  John 

08212014, 11:54 PM
Post: #11




RE: What are good PRNG for calculators?
I have been comparing several simple PRNGs for calculators. I conducted a series of long runs and found the following algorithms to do well:
1) u = frac(997 * u) 2) u = frac(GoldenRatio + u)^5) (it does better than frac(pi+u)^5). 3) u = Frac(u * 99821 + 0.211327) Namir 

08222014, 02:52 AM
Post: #12




RE: What are good PRNG for calculators?
I always use the 997 * RNG because it is shorter than the others.
Of course, if you're using the 41CL, then I use the ones Angel wrote into his ROMs. :) 

08222014, 05:32 AM
Post: #13




RE: What are good PRNG for calculators?
(08222014 02:52 AM)Gene Wrote: Of course, if you're using the 41CL, then I use the ones Angel wrote into his ROMs. :) Which (to demystify it) is just the same one referred above (used in the Games Pac and the PPC), plus a timemodule based seed  that's the nice part  all conveniently stored in a buffer for repeat usage. 

08222014, 06:01 AM
Post: #14




RE: What are good PRNG for calculators?  
08222014, 06:20 AM
Post: #15




RE: What are good PRNG for calculators?
Hello,
On the ZX Spectrum was used this formula: x = ( x * 75 ) mod 65537 See also x = ( x * 279470273 ) mod 4294967291 http://en.wikipedia.org/wiki/Lehmer_rand..._generator 

08222014, 01:45 PM
Post: #16




RE: What are good PRNG for calculators?
(08222014 02:52 AM)Gene Wrote: I always use the 997 * RNG because it is shorter than the others.I don't know where this originally came from, but it was described by HP at least as far back as the HP67 user's guide. On the "less than short" side, just for fun I implemented the Mersenne Twister on my HP 50g.  John 

08222014, 02:16 PM
Post: #17




RE: What are good PRNG for calculators?
(08222014 01:45 PM)John R. Graham Wrote:(08222014 02:52 AM)Gene Wrote: I always use the 997 * RNG because it is shorter than the others.I don't know where this originally came from, but it was described by HP at least as far back as the HP67 user's guide. Listing for the HP50G implementation? Namir 

08222014, 02:43 PM
Post: #18




RE: What are good PRNG for calculators?
I'll post this weekend. No connectivity kit at work.
 John 

08242014, 01:06 AM
Post: #19




RE: What are good PRNG for calculators?
(08212014 09:56 PM)Paul Dale Wrote: The problem here is the exclusive or operations. Exactly. I think Namir needs to define "good" in this context, as different PRNG algorithms tend to have different properties. The linear congruential RNG's commonly used are fine for small simulations, Monte Carlo techniques, seeding games, etc. because they are a) simple and b) provide reasonable uniformity. But they're highly predictable. Linear Feedback Shift Registers, which depend upon lots of XOR'ing, have the additional property of being much less predictable, which makes them ideal for cryptographic applications. Fortunately, performing crypto on a scientific calculator is rarely required, and when it is done, it's rather like a singing dog  not remarkable because it's bad (slow), more remarkable that it's done at all.  Les [http://www.lesbell.com.au] 

08252014, 05:15 PM
Post: #20




RE: What are good PRNG for calculators?
The TI SR51(A) has a RAN# function that returns a two digit random number. I couldn't find more info about it but I have the feeling that it's not a pseudo random number generator but a real random number function. Can someone confirm this? To support my assumption, there is no seed function.
Marcus von Cube Wehrheim, Germany http://www.mvcsys.de http://wp34s.sf.net http://mvcsys.de/doc/basiccompare.html 

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