Quick HP42S question

05242020, 11:31 PM
Post: #1




Quick HP42S question
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Hi, all: Just a quick HP42S question, as I don't have the manual at hand now and can't remember if it's even possible: How can you change the Polar/Rectangular mode programmatically ? Manually from the keyboard is just a matter of setting the correct mode in the MODES menu, and programmatically you can test the current mode by checking whether Flag 73 is set or not. But Flag 73 is a system flag and so it can't be set/cleared by the user. Are there some keywords that will change the mode from a running program (as part of an initialization procedure, for instance) ? Sorry if this is a trivial question. Thanks. V. . All My Articles & other Materials here: Valentin Albillo's HP Collection 

05242020, 11:36 PM
(This post was last modified: 05242020 11:37 PM by ijabbott.)
Post: #2




RE: Quick HP42S question
The quickest way is to select RECT or POLAR from the MODES menu in a program. But you can also select them from the CATALOG menu.
— Ian Abbott 

05242020, 11:37 PM
Post: #3




RE: Quick HP42S question
The RECT and POLAR commands from the MODES menu are programmable.


05252020, 12:17 AM
Post: #4




RE: Quick HP42S question
(05242020 11:37 PM)Thomas Okken Wrote: The RECT and POLAR commands from the MODES menu are programmable. Thank you very much, ijabbot and Thomas. I had located both functions in the catalog but mistook them for rectangular/polar conversions By the way, Thomas, a question regarding Free42/BCD for Android (though I think it will be the same for other operating systems). I've programmed the exact same algorithm for both Free42 and the HP71B. The algorithm generates and uses many thousand random numbers, initialized with 1, SEED in Free42 and RANDOMIZE 1 in the HP71B. As I thought Free42 includes the exact same RNG that a physical HP42S uses (which was taken from the HP71B), I expected both programs to give the same results, but upon running them I discovered that in fact they don't. Both sequences of random numbers stay the same for a while but after some time they begin to not be exactly alike and when the programs use them they give slightly different results, perhaps 2147 and 2148, respectively. The question is: is the RNG in Free42 guaranteed to produce the exact same sequence of random numbers as a physical HP42S would, no matter how long, or will they eventually part ways ? If the RNG in Free42 is actually different, how many random numbers will it provide before repeating ? I know the one in the HP71B and so the HP42S will produce 1,000,000,000,000 random values before repeating, and the sequence passes the Spectral Test. Is this also the case for the one in Free42 or does it have a longer period ? Thanks and best regards. V. All My Articles & other Materials here: Valentin Albillo's HP Collection 

05252020, 12:29 AM
Post: #5




RE: Quick HP42S question
(05252020 12:17 AM)Valentin Albillo Wrote: The question is: is the RNG in Free42 guaranteed to produce the exact same sequence of random numbers as a physical HP42S would, no matter how long, or will they eventually part ways ? I won't go so far as to guarantee that the RNG in Free42 will produce the exact same sequence as the real HP42S, but I believe the algorithms are the same (see https://www.hpmuseum.org/forum/thread9556.html for an earlier discussion, including a link to the article where I found the algorithm). I tried comparing the Free42 RNG to Emu42, both starting from Memory Clear, and they returned identical sequences as far as I could tell... I don't remember how long I let the test run, whether it was hundreds or thousands of iterations or more. At what point do you see a divergence? 

05252020, 02:41 AM
(This post was last modified: 05252020 02:47 AM by Joe Horn.)
Post: #6




RE: Quick HP42S question
(05252020 12:17 AM)Valentin Albillo Wrote: If the RNG in Free42 is actually different, how many random numbers will it provide before repeating ? I know the one in the HP71B and so the HP42S will produce 1,000,000,000,000 random values before repeating... According to Richard Nelson's article "HP’s Pseudorandom Number Generator" on page 58 of HP Solve #31 (April 2013), the PRNG used in most HP 12digitmantissa models from the '71 onward has a cycle length of 5E13, not 1E12. Also, it produces the same cycle from the same seed on all models EXCEPT the 33s and 35s, which occasionally differ by one digit in the last place due to a bug they introduced in those models, namely, they round the output instead of truncating it like all the other models do. Example: Seed the random number generator with the square root of 5. Then generate two random numbers. All the nonbuggy models output this as the second one: 0.0593946804209 The 33s and 35s alone output this instead: 0.0593946804210 Richard's footnote about this discrepancy follows: Quote:(7) Bug Hunter Joseph K. Horn explains: “Bottom Line: HP 33s and 35s programs that use random numbers cannot be relied upon to obtain precisely the same results as the other HP models that use the same RNG engine. This is critically important if the RNG is reseeded with one of these different random numbers; in that case, the random number sequence in the 33s and 35s will diverge from the other models.” The DM42 agrees with the nonbuggy outputs above. I do not have an HP42S to check whether it is buggy, but the divergence that you are seeing MIGHT be caused by that. Please perform the square root of 5 seed test mentioned above and let us know what you get. Thanks! <0ɸ0> Joe 

05252020, 05:30 AM
Post: #7




RE: Quick HP42S question
Root 5 seed test on real 42S returned
........209 for ROM C (SNr 3144S) & for ROM A (SNr 2914S). 

05252020, 06:40 AM
Post: #8




RE: Quick HP42S question
1 SEED
then produced 10 million random numbers, on Free2 and Emu42. They're still the same. Werner 

05252020, 07:22 AM
Post: #9




RE: Quick HP42S question
The following comment section in HP's original source code for the HP 48 series gives further support to the random number generator's period being 5E13 long if the seed ends in 1, 3, 7, or 9, which the RDZ code automatically does.
Code: STITLE %RANDOMIZE <0ɸ0> Joe 

05252020, 08:57 AM
(This post was last modified: 05252020 09:15 AM by ijabbott.)
Post: #10




RE: Quick HP42S question
(05252020 05:30 AM)Gerald H Wrote: Root 5 seed test on real 42S returned Additionally, the 11 SEED RAN SEED RAN RAN RAN test produces the same sequence as the RPL models: 0.975035362027, 0.529463266203, 0.783522353434 (for ROM 42SE). The equivalent keystrokes on HP27S (11 STO RAN# STO RAN# RAN# RAN#) produces the same sequence (for ROM 27SE). — Ian Abbott 

05252020, 09:06 AM
(This post was last modified: 05252020 09:08 AM by JF Garnier.)
Post: #11




RE: Quick HP42S question
(05252020 06:40 AM)Werner Wrote: 1 SEED Same for the HP71B (emu71). But... the 100,000th number is .935105198 (with 3 tailing 0s) the 1,000,000th number is .83105198 (with 4 tailing 0s) the 10,000,000th number is .4105198 (with 5 tailing 0s) Even if the period is in the range of 1E121E13, it seems there are correlations between numbers long before. Has this been already noticed? Probably not before the use of emulators/simulators and fast CPUs. JF 

05252020, 09:33 AM
Post: #12




RE: Quick HP42S question
(05252020 12:17 AM)Valentin Albillo Wrote: I've programmed the exact same algorithm for both Free42 and the HP71B. The algorithm generates and uses many thousand random numbers, initialized with 1, SEED in Free42 and RANDOMIZE 1 in the HP71B. I think we've established it's the same sequence now. The different results you see in your program must be due to arithmetical rounding differences elsewhere in the code, which is not surprising since Free42 BCD uses higher precision arithmetic than the 42S or 71B. — Ian Abbott 

05252020, 02:35 PM
Post: #13




RE: Quick HP42S question
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Hi, all: (05252020 09:06 AM)JF Garnier Wrote: Same for the HP71B (emu71). Thanks to all of you for your replies, I've checked right now and the sequence of random numbers generated from a seed of 1 is exactly the same for at least the first 100,000,000 random numbers in both Free42 and Emu71 and I see this as quite convincing evidence that they'll remain the same to the bitter end, the differences in my programs lie elsewhere. As for the correlations, yes, I did notice it in August last year while vacationing. They're clearly exposed by running the following HP71B program (the equivalent Free42 program does produce the exact same results): 10 DESTROY ALL @ INPUT "K=";K 20 FOR J=0 TO K @ N=10^J @ RANDOMIZE 1 30 FOR I=1 TO N @ X=RND @ NEXT I 40 DISP USING "10D,2X,Z.12D";N,X @ NEXT J >RUN K= 8 [END LINE] N N^{th} random number  1 0.731362440213 10 0.723555832003 100 0.056136887198 1 000 0.411709251980 10 000 0.823130519800 100 000 0.935105198000 1 000 000 0.831051980000 10 000 000 0.410519800000 100 000 000 0.205198000000 Not very randomlooking, methinks, and that many trailing zeros ... Regards. V. All My Articles & other Materials here: Valentin Albillo's HP Collection 

05252020, 05:09 PM
Post: #14




RE: Quick HP42S question
(05252020 02:35 PM)Valentin Albillo Wrote: N N^{th} random number This apply to any LCG RNG: seed * a mod m kth random number = seed * a^k mod m If k = order(a,m), we have a^k mod m = 1 If k  order(a,m), we expect a nonrandom pattern for s = a^k mod m Example, to reproduce above numbers: >>> a, m = 2851130928467, 10**15 >>> seed = 10**14 + 11 # seed for RANDOMIZE 1 >>> for i in xrange(9): # note: order(a,m) = 5E13 ... n = 10 ** i # note: n  order(a,m) ... s = pow(a,n,m) ... print '%9d %015d %015d' % (n, s, s*seed % m) ... 1 002851130928467 731362440213137 10 165777802909449 723555832003939 100 268739717018001 056136887198011 1000 573791750180001 411709251980011 10000 429375501800001 823130519800011 100000 439555018000001 935105198000011 1000000 975550180000001 831051980000011 10000000 755501800000001 410519800000011 100000000 555018000000001 205198000000011 Most significant digits are more random than least siginificant digits. Thus, last 3 digits were chopped off, to produce RND() 

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