More pseudo random number generators for calculators

07082020, 02:19 PM
Post: #1




More pseudo random number generators for calculators
Hi All,
I posted a new study about "more random number generators for calculators." The study takes the efficient algorithm used by HP in the HP67 Stat Pac and attempts to tweak it to find better variants. The study looks at 55 algorithms and ranks them using Matlab code. I use Matlab because it can handle very large arrays which I needed to get better results. To download the pdf article click here. To download the Matlab code click here. Enjoy! Namir 

07082020, 07:51 PM
Post: #2




RE: More pseudo random number generators for calculators
Hello Namir,
For me this is a completely different way to look at PRNG's. I am active in telecom and know the shift register based maximum length generators using a polynome. Thanks a lot for this study, I have something to read and play with this weekend. Erik 

07092020, 03:45 AM
Post: #3




RE: More pseudo random number generators for calculators
A short search on the HP50g gives the following parameters that should work there.
X(j+1)=X(j)*227716313950 mod 549755813507 X(0) not 0 This should generate all integers less than the modulus except zero. The numbers should be small enough not to screw up the division on the HP50g. (All this assumes that I copied the numbers from the display into the computer correctly.) 

07092020, 11:19 AM
Post: #4




RE: More pseudo random number generators for calculators
Hi, Namir
Some algorithms you tested might get stuck, even with nonzero fractional part guess Example, say with 12 digits calculator: r = 0.999 999 999 r = frac(997/r) → r = frac(997.000000 997000000 997000000 ...) = .000 000 997 r = frac(997/r) → r = 0 r = frac(997/r) → r = NaN To avoid rounding errrors like above, multiply based versions is safer. With 15 digits internal precision, and 3 digits factor k, r = frac(k*r) is guaranteed exact. This may be why baseline use r = frac(997*r) 

07092020, 01:42 PM
Post: #5




RE: More pseudo random number generators for calculators
Good points about getting stuck. The theory may show cyclic (or at least unending wandering) but rounding can cause fixed points to appear, usually 0.0.
For my big integer version above. I set the modulus with MODSTO just use MULTMOD. Then I can divide by the modulus to scale (I kept the modulus so it should be representable.) No problem with low order bits. (All assuming I copied things correctly.) 

07092020, 07:35 PM
Post: #6




RE: More pseudo random number generators for calculators
(07092020 11:19 AM)Albert Chan Wrote: Hi, Namir You certainly have a point. However, in each "run" I would generate a billion random numbers and I never had a runtime error. So the likelihood of getting a random number very close to 1 is small. Of course dealing with floating point number depends on many aspects of the software being used. 

07092020, 09:15 PM
Post: #7




RE: More pseudo random number generators for calculators
(07092020 07:35 PM)Namir Wrote: You certainly have a point. However, in each "run" I would generate a billion random numbers and I never had a runtime error. So the likelihood of getting a random number very close to 1 is small. Of course dealing with floating point number depends on many aspects of the software being used. Gene: Which is CERTAINLY more than any HP model other than the PRIME would ever need. :) 

07092020, 09:45 PM
Post: #8




RE: More pseudo random number generators for calculators
(07092020 09:15 PM)Gene Wrote:(07092020 07:35 PM)Namir Wrote: You certainly have a point. However, in each "run" I would generate a billion random numbers and I never had a runtime error. So the likelihood of getting a random number very close to 1 is small. Of course dealing with floating point number depends on many aspects of the software being used. Absolutely right! 

07102020, 11:25 PM
(This post was last modified: 07112020 12:23 PM by Namir.)
Post: #9




RE: More pseudo random number generators for calculators
(07092020 03:45 AM)ttw Wrote: A short search on the HP50g gives the following parameters that should work there. I ran your algorithm in my extended calculations. It came out 9th among 56 algorithm (counting the algorithm itself). So it's an OK algorithm and works with calculators that can store the two big numbers and handle well the multiplication of large integers. Cheers, Namir 

07132020, 03:00 PM
Post: #10




RE: More pseudo random number generators for calculators
The generator I posted was the result of a 5minute search. I'm going to find one for some computations but getting "better" (however measured) takes more time.
I use long LCGs for Monte Carlo (whenever my quasiMonte Carlo stuff doesn't apply) as the precision does matter. I have a short generator on the calculator (or I did, it's easy to redesign) with three shift registers lengths 15,16,17, combined with a 16bit GCD. The total cycle is (2^151)*(2^161)*(2^171)*2^16 (the cycle lengths are prime) giving just under 2^64 as a cycle. However, the precision is only 15 bits. A true 64bit RNG would have a precision of 64 bits. A problem arises in simulating exponential or Gaussian distributions by the BoxMuller method. With fifteen bits, the greatest exponential number is ln(2^16) or about 11 whereas with 64 bits one gets ln(2^64) or 44. With the Gaussian, the largest number generated is about Sqrt(2*Ln(2^16)) or a sigma of 4.7. Not even 6sigma quality. With 64 bits one gets Sqrt(2*Ln(2^64)) or 9.4. The smaller precision does not explore rare events. In real life, one should use a rareevent generator. 

07152020, 06:12 AM
Post: #11




RE: More pseudo random number generators for calculators
(07102020 11:25 PM)Namir Wrote:(07092020 03:45 AM)ttw Wrote: A short search on the HP50g gives the following parameters that should work there. I also tested: X(j+1)=(X(j)*227716313950 + 22771631395) mod 549755813507 which gave satifactory (better than r = frac997*r) results. The above algorithm handles zero values for X(j). 

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