What comes next?
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10-15-2024, 01:53 PM
(This post was last modified: 10-15-2024 01:54 PM by Gil.)
Post: #21
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RE: What comes next?
Gilles, hi.
I want to try your code but I don't use libraries (LstX library). In your code « DUPDUP RHEAD SWAP 2 OVER SIZE START ΔLIST DUP RHEAD ROT + SWAP NEXT + ADD how are defined RHEAD & ΔLIST, please? Thanks for your help. Regards, Gil |
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10-15-2024, 02:53 PM
(This post was last modified: 10-15-2024 05:37 PM by Thomas Klemm.)
Post: #22
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RE: What comes next?
(10-15-2024 01:34 PM)Gil Wrote: My next question is if I may ask: what is the code algorithm you used in your first post to get the binomial coefficient? Let me again add some comments: Code: 00 { 24-Byte Prgm } ; a_n We keep the increasing number of elements \(n\) in register 00. Let's assume we're at the situation of post #4 and we want to add 35. The difference is calculated in register X while the sum for the next value is calculated in register Y: \( \begin{array}{|l|l|l|} \hline X & Y & Z \\ \hline 35 & 35 & 6 \\ 15=35-20 & 50=35+15 & 5 \\ 5=15-10 & 55=50+5 & 4 \\ 1=5-4 & 56=55+1 & 3 \\ 0=1-1 & 56=56+0 & 2 \\ 0=0-0 & 56=56+0 & 1 \\ \hline \end{array} \) Meanwhile the counter in register Z is decremented until it is 0. I suggest to give Free42 a try. You can copy and paste the program when the simulator is in program mode: PRGM. Switch back and clear the registers with CLEAR ▼ CLRG. And then just follow the example. Press ▼ to single step through the program. |
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10-15-2024, 03:08 PM
Post: #23
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RE: What comes next?
(10-15-2024 01:34 PM)Gil Wrote: Last question, what will you get in your calculator or l'émulation for the next number of the following list? Using Free42: -313'323'742'215'540 This is the contents of the registers: 00: 47 01: 5'958'939'610'275 02: -78'383'926'242'917 03: -81'440'397'593'595 04: -61'857'014'876'959 05: -41'068'588'193'054 06: -25'166'184'482'905 07: -14'575'039'183'813 08: -8'077'783'405'239 09: -4'315'910'331'471 10: -2'233'812'545'366 11: -1'123'843'700'063 12: -551'048'120'900 13: -263'882'576'032 14: -123'622'702'625 15: -56'724'531'441 16: -25'506'257'595 17: -11'232'717'406 18: -4'834'604'086 19: -2'024'788'492 20: -819'077'008 21: -316'401'610 22: -114'802'997 23: -38'274'698 24: -11'472'693 25: -3'158'214 26: -1'009'379 27: -554'630 28: -400'969 29: -243'086 30: -83'702 31: 34'596 32: 95'896 33: 109'634 34: 95'153 35: 70'112 36: 45'767 37: 27'055 38: 14'703 39: 7'456 40: 3'600 41: 1'701 42: 805 43: 376 44: 158 45: 48 46: 7 47: 63 |
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10-15-2024, 04:08 PM
(This post was last modified: 10-15-2024 04:12 PM by Gilles.)
Post: #24
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RE: What comes next?
(10-15-2024 01:53 PM)Gil Wrote: how are definedIn NewRPL ? RHEAD : << DUP SIZE GET >> ΔLIST is the the same than in stock RPL In NewRPL with lists, the commands + and ADD are switched. With stock HP50, the program could be (not tested) : Code: « |
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10-15-2024, 05:39 PM
Post: #25
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RE: What comes next?
(10-14-2024 08:35 PM)Gilles Wrote: newRPL with LstX library. Enter the first numbers as a list and you get a list with a new guess number. etc. For "Old RPL" with the ListExt Library, RHEAD can be replaced by LPOPR NIP. |
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10-15-2024, 09:09 PM
Post: #26
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RE: What comes next? | |||
10-15-2024, 10:59 PM
Post: #27
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RE: What comes next?
(10-15-2024 05:39 PM)John Keith Wrote:(10-14-2024 08:35 PM)Gilles Wrote: newRPL with LstX library. Enter the first numbers as a list and you get a list with a new guess number. etc. … and with the GoferLists (1.0) Library (another jewel), RHEAD can be replaced by Last (with a capital L). Bruno Sanyo CZ-0124 ⋅ TI-57 ⋅ HP-15C ⋅ Canon X-07 + XP-140 Monitor Card ⋅ HP-41CX ⋅ HP-28S ⋅ HP-50G ⋅ HP-50G |
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10-16-2024, 12:56 AM
Post: #28
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RE: What comes next?
(10-15-2024 04:08 PM)Gilles Wrote: With stock HP50, the program could be (not tested) : This works mostly with an HP-48: Code: DIR For a list with a single element I get: ΔLIST Error: Invalid Dimension |
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10-16-2024, 04:51 AM
Post: #29
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RE: What comes next?
I wondered why I used this in my T program but now NXT also works with a single element list:
Code: \<< DUP LST OVER Also the usage is similar to my initial program since the last + command was removed. If the prediction of what comes next matches, add it to the list. Otherwise DROP it and add the proper one. |
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10-16-2024, 10:14 AM
(This post was last modified: 10-16-2024 10:30 AM by Gil.)
Post: #30
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RE: What comes next?
Question to Gilles relative to his post #24
Changing last line + + into ADD + Code:
and building Code:
we get { 5 10 19 32 }. Deleting the number 32 from the above list, we get { 5 10 19 } and with that latter list as argument with your program we get 36 instead of "my" 32. Question: How is it possible? If the 4th number were indeed 36, as given by your program, then the underlying polynomial should be f(x): '2/3*x^3+13/3*x+5' and the next number after 36 would be (with the above given new polynomial) 65. But, with the sequence list {5 10 19 36}, your output is then 69, and not 65. Regards, Gil |
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10-16-2024, 11:41 AM
Post: #31
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RE: What comes next? | |||
10-16-2024, 01:17 PM
Post: #32
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RE: What comes next?
Thanks again to all contributers.
Just test Gilles' astonishing compact and extremely fast program : less than 0.05 second vs several minutes with my program to get the next number after { 17 72 97 8 32 15 63 97 57 60 83 48 26 12 62 3 49 55 77 97 98 0 89 57 34 92 29 75 13 40 3 2 3 83 69 1 48 87 27 54 92 3 67 28 97 56 63 }, which is -313323742215540. Congratulations! |
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10-16-2024, 04:54 PM
Post: #33
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RE: What comes next?
(10-16-2024 01:17 PM)Gil Wrote: Thanks again to all contributers. You must have a very fast computer. That takes about 0.18 seconds on my old laptop which means about 7 seconds on a physical calc (I didn't bother to type the whole list into my 50g.) Note also that the result will be meaningless unless the initial sequence is defined by a polynomial. |
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10-16-2024, 07:45 PM
(This post was last modified: 10-16-2024 07:59 PM by Gilles.)
Post: #34
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RE: What comes next?
(10-16-2024 04:54 PM)John Keith Wrote: You must have a very fast computer. That takes about 0.18 seconds on my old laptop which means about 7 seconds on a physical calc (I didn't bother to type the whole list into my 50g.) In newRPL I confirm that it takes 0.048 sec with the physical 50g and 0 sec on my laptop with the Windows version. A 140x faster ratio between newRPL and RPL does not surprise me for this kind of calculation. |
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10-16-2024, 08:38 PM
Post: #35
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RE: What comes next?
This program might be faster:
Code: \<< DUP ROT + SWAP DUP { } + SWAP ROT It is of order \(\mathcal{O}(n)\) instead of \(\mathcal{O}(n^2)\) and works similarly to my initial program for the HP-42S. Example { 1 } 2 NXT { 2 1 } 3 DROP 4 NXT { 4 2 1 } 7 DROP 8 NXT { 8 4 2 1 } 15 DROP 16 NXT { 16 8 4 2 1 } 31 NXT { 31 15 7 3 1 0 } 57 NXT { 57 26 11 4 1 0 0 } 99 NXT { 99 42 16 5 1 0 0 0 } 163 NXT { 163 64 22 6 1 0 0 0 0 } 256 |
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10-17-2024, 05:15 AM
Post: #36
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RE: What comes next?
The same program with stack comments:
Code: \<< @ A a |
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10-17-2024, 10:16 AM
(This post was last modified: 10-18-2024 10:47 PM by Gil.)
Post: #37
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RE: What comes next?
Precisions regarding the execution (time) for finding the next number of the polynomial that creates the initial string
{ 17 72 97 8 32 15 63 97 57 60 83 48 26 12 62 3 49 55 77 97 98 0 89 57 34 92 29 75 13 40 3 2 3 83 69 1 48 87 27 54 92 3 67 28 97 56 63}: 1) time to find out f(47), the 48th number = -313323742215540: about 0.05 s (most of the time about 0.049s, but maximum time 0.058s); 2) Code used (\GS is —>capital delta) Code:
3) No NewRPL, but original user RPL; 4) No computer, but EMU48 on Samsung phone A53; 5) Like 4, but with setting "Authentication Calculator Speed": about 5.3s —> here then more than 100 times slower. |
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10-18-2024, 07:53 PM
(This post was last modified: 10-18-2024 07:57 PM by Gilles.)
Post: #38
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RE: What comes next?
A recursive version en newRPL :
Next? Code: « DUP RHEAD SWAP ΔLIST DUP SIZE 1 > « Next? » IFT + » ex : { 0 0 0 0 1 5 15 35 70 126 } Next? -> { 210 } |
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10-18-2024, 10:49 PM
Post: #39
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RE: What comes next?
Is really the above code complete as lastly written by Gilles?
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10-18-2024, 11:57 PM
(This post was last modified: 10-18-2024 11:59 PM by John Keith.)
Post: #40
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RE: What comes next? | |||
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