[VA] Short & Sweet Math Challenge #22: April 1st, 2018 Spring Special

04012018, 09:08 PM
Post: #1




[VA] Short & Sweet Math Challenge #22: April 1st, 2018 Spring Special
Hi all, After a mere 10year hiatus here's again my superduper S&SMC April 1st, 2018 Spring Special to welcome the new season and give you all a chance to put to good use both your favourite HP calculator and your programming ingenuity. The thing is, I've always been very interested in primes and algorithms for factorization and primality tests of big numbers and recently computed the factorization of 555555555555554444444444444443333333333333332222222222222222211111111111111 and proceeded to check it out with my trusty HP71B (it checked OK!), so I got the idea of making some kind of primality testing the main subject of this S&SMC#22, plus assorted goodies. Read on !: Notes : Any HP model of your choice may be used but I'll suggest a Minimum Recommended Model (MRM) for each problem, which is the minimum model I deem capable of solving it more or less comfortably. Obviously, using a more powerful model might make life easier and, conversely, using a less powerful model might succeed or not. If you use an HP41C/CX/CV you can also use any of these ROM: Math, Advantage, Card Reader, Printer. No other ROM or extra routines allowed. If you use an HP71B, you can also use any of these ROM: Math, HPIL, JPC, STRNGLEX Lex file. No other ROMs or LEX files allowed. Using a PC or any computing device other than a physical or emulated HP calculator is strictly disallowed. You can write your code in any language supported in any HP calc and it must run in that calc (i.e.: RPN, RPL, 71B BASIC, 71B FORTH, etc). Googling for the solutions is lame beyond belief, frankly. The Challenge  Main Course: [MRM: HP42S and up] Write code that takes as input any of the following six test numbers and simply outputs whether it's a prime or not (no need to compute or output its factorization if not prime). Your code might or might not work for some other arbitrary numbers of arbitrary length but it should definitely output the correct result for each of the following six test numbers: 8082737769637879 89698373657765787367698082737769 677977807983738469788577666982 7365778082737769847979 677977807983738469658387697676 7378686969688082737769 Your code must be as short and fast as possible, in that order. Within a few days I'll give a 72byte solution for the HP71B (an UserDefined Function) and a 39byte solution for the HP42S (a program) but meanwhile let's see what you can do. The Challenge  4 Desserts: 1) [MRM: HP10C and up] Starting from no assumptions (angular mode, stack contents, memory contents, etc) write a program to output the constant 9.99999999999 (for 12digit machines, 12 nines) or 9.999999999 (for 10digit machines, 10 nines). Your code must be as short as possible. For instance, in the HP71B you could use: 1 DISP 9.99999999999 but this is 14 bytes long and as "1 DISP" itself takes 5 bytes you're using 9 additional bytes to generate the constant, which are way too many. I'll give an 85 = 3byte solution for the plain vanilla HP71B, see what you can do with your favourite HP calc. 2) [HP71B specific; perhaps RPL models too, not sure] Everyone has seen math expressions which give the machine value of Pi as a result so let's try for a slightly different thing here. Starting from no assumptions (angular mode, stack contents, memory contents, etc) find the shortest, simplest commandline math expression which upon evaluation in your calc produces the machine value of Pi (i.e.: 3.14159265359 for 12digit calcs, 3.141592654 for 10digit ones). Your expression can't use PI (of course!), strings/string functions, trigonometric/logarithmic/exponential/gamma/complex functions, and also last but not least, neither any digits (in any base) nor "" should appear in it. I'll give a 6byte, 16character solution for the HP71B, let's see yours. Also, if you succeed, try to get Pi/100 or even Pi/10000 under the same conditions. I'll also give a 6byte solution for those as well. 3) [MRM: HP11C and up] Informally, for realvalued functions of realvalued arguments we may say that G(X) is the inverse function of F(X) if theoretically G(F(X)) = X. For instance, with F(X)=EXP(X) we have that G(X)=LN(X) and G(F(X)) = LN(EXP(X)) = X. This said, produce some realvalued F(X) of a realvalued argument X and its theoretical inverse G(X) for your favourite HP calc such that the actual evaluation of G(F(X)) differs from X by at least 2% of X for some relatively small argument X, say X less than 20 in absolue value. No code required, just the F(X) and G(X). If you succeed in finding such an F(X), try to find the smallest value of X which results in said 2% difference. I'll give my solution for the HP11C, HP42S and HP71B (the exact details differ slightly from calc to calc). 4) [HP71B specific; perhaps RPL models too, not sure] Produce the shortest singlestatement commandline expression which when executed outputs this line: 0 1 2 3 4 5 6 7 8 9 10 Your expression can´t use either strings/string functions or any digits in any base and must fit in a single 1statement line (i.e., no statement concatenation via @ in the HP71B) less than 80 characters in length, and also can't call any program code, it must generate the ouput by itself. I'll give my 74character solution for the HP71B in a few days but meanwhile give it a try ! Finally, a caveat: PLEASE do NOT include "CODE:" panels in your replies to this thread, as it makes it difficult for me to generate the final PDF document which will include the full thread in order to make it available online for free and for everyone in the future. I sincerely expect you'll kindly comply with this reasonable requirement but in any case I'll remove from the final PDF document any replies featuring CODE: panels. Thank you. That's all. Hope you'll enjoy it ! Best regards. V. Find All My HPrelated Materials here: Valentin Albillo's HP Collection 

04012018, 10:45 PM
Post: #2




RE: [VA] Short & Sweet Math Challenge #22: April 1st, 2018 Spring Special
Hi Valentin, thanks for this nicely crafted challenge !
Let me start with the easy part, the first dessert:  for the HP71B, 8 bytes : 1 DISP MAXREAL*EPS  for the HP25, 7 bytes : 01 FIX 9 02 . 03 3 04 1/x 05 3 06 x 07 GTO 00 

04022018, 12:24 AM
(This post was last modified: 04022018 06:00 PM by rprosperi.)
Post: #3




RE: [VA] Short & Sweet Math Challenge #22: April 1st, 2018 Spring Special
For Desert #2:
SGN(EXPONENT(EPS))*RAD(ANGLE(SGN(EXPONENT(EPS)),EPS)) 53 chars and 23 bytes with line number. It works and meets the criteria, but it's still waaay too long. Will keep looking for shorter ways to generate 1... Edit 1: Shorter, but still long: SGN(DVZ)*RAD(ANGLE(SGN(DVZ),EPS)) Bob Prosperi 

04022018, 01:38 AM
Post: #4




RE: [VA] Short & Sweet Math Challenge #22: April 1st, 2018 Spring Special
Desert 3.
F(X) = X + 10^{90}. G(X) = X  10^{90}. G(F(X)) is zero for x < 20. It's correct only at X=0. The smallest X where the difference is > 2% will be the largest negative number allowed in the small range around zero i.e. 19.999...999. The smallest in absolute will be the smallest positive X such that X  X/50 doesn't underflow. 

04022018, 10:18 AM
Post: #5




RE: [VA] Short & Sweet Math Challenge #22: April 1st, 2018 Spring Special
(04012018 09:08 PM)Valentin Albillo Wrote: Finally, a caveat: PLEASE do NOT include "CODE:" panels in your replies to this thread, as it makes it difficult for me to generate the final PDF document which will include the full thread in order to make it available online for free and for everyone in the future. I sincerely expect you'll kindly comply with this reasonable requirement but in any case I'll remove from the final PDF document any replies featuring CODE: panels. Thank you. Just an observation. Why do you say "code" shouldn't be included? If you see the thread with the printable version (at the end of the thread there is a link) listing in code are not bad when properly formatted. See for example http://www.hpmuseum.org/forum/printthread.php?tid=8555 search for "listHeadIterate". It is pretty nice. Wikis are great, Contribute :) 

04022018, 04:37 PM
(This post was last modified: 04022018 06:29 PM by JF Garnier.)
Post: #6




RE: [VA] Short & Sweet Math Challenge #22: April 1st, 2018 Spring Special
Desserts #1 and #3 (related solutions), on HP71 w/ Math ROM or Pioneer machines.
#1: 1 DISP TANH(14)*10 [edited: not an efficient solution of the challenge, of course] #3 F(X)=TANH G(X)=ATANH X=14.5 JF 

04022018, 07:53 PM
Post: #7




RE: [VA] Short & Sweet Math Challenge #22: April 1st, 2018 Spring Special
Dessert #4 [HP71 specific]
One 74char. solution: INXINX;INX=INX;INXOVF;INXDVZ;INX;UNF;OVF;DVZ;IVL;INXUNF;INXOVF JF 

04022018, 08:17 PM
(This post was last modified: 04022018 08:19 PM by Dieter.)
Post: #8




RE: [VA] Short & Sweet Math Challenge #22: April 1st, 2018 Spring Special
(04012018 11:44 PM)Mike (Stgt) Wrote: [9,999999999] Yes, this does it on a 10digit calculator – I had the same idea. ;) But it doesn't work with 12 digits. (04012018 11:44 PM)Mike (Stgt) Wrote: (Sorry, not using code: multiple blanks get lost.) You may use hard blanks (Alt+0160): 01 1 1 02 0 0 03 11 SQRT 04 42 11 x^2 But, as already mentioned, "view a printable version" at the page bottom expands all code boxes, so such tricks should not be required. Dieter 

04022018, 08:53 PM
Post: #9




RE: [VA] Short & Sweet Math Challenge #22: April 1st, 2018 Spring Special
After the desserts, back to the main course!
I have a nice little HP71 program that is able to output the (assumed) correct result for each of the six test numbers. However, I will not publish my very clever program here, just the results as NO or YES: 8082737769637879 NO 89698373657765787367698082737769 YES 677977807983738469788577666982 NO 7365778082737769847979 YES 677977807983738469658387697676 NO 7378686969688082737769 YES :) JF 

04022018, 09:06 PM
Post: #10




RE: [VA] Short & Sweet Math Challenge #22: April 1st, 2018 Spring Special
(04022018 07:53 PM)JF Garnier Wrote: Dessert #4 [HP71 specific] Brilliant! This must be the same result as Valentin's. You have me digging into parts of the 71 manual that are not familiar... Bob Prosperi 

04022018, 09:53 PM
Post: #11




RE: [VA] Short & Sweet Math Challenge #22: April 1st, 2018 Spring Special  
04022018, 10:06 PM
Post: #12




RE: [VA] Short & Sweet Math Challenge #22: April 1st, 2018 Spring Special
(04022018 09:53 PM)Gerson W. Barbosa Wrote: Slightly shorter and still too long: You beat me Gerson, I was just exploring INX (JFG's post was an excellent hint!). I suspect by 'no trig functions' Valentin was implying SIN/COS/etc. but you could be right. We have to wait for a judge's ruling on that, but I'll keep digging.) Bob Prosperi 

04022018, 10:13 PM
Post: #13




RE: [VA] Short & Sweet Math Challenge #22: April 1st, 2018 Spring Special
(04022018 09:53 PM)Gerson W. Barbosa Wrote:(04022018 12:24 AM)rprosperi Wrote: Shorter, but still long: Nice solutions, and I'm learning new HP71 tricks with this challenge. Unfortunately they work in Degrees but not in Radians angular mode. 

04022018, 10:19 PM
Post: #14




RE: [VA] Short & Sweet Math Challenge #22: April 1st, 2018 Spring Special
(04022018 10:13 PM)Didier Lachieze Wrote:(04022018 09:53 PM)Gerson W. Barbosa Wrote: Slightly shorter and still too long: Indeed, the 71 has lots of these kinds of tricks buried deep inside. 6 bytes means Valentin found a solution with only 3 XROM (function) calls... so there are clearly still some tricks hidden Bob Prosperi 

04032018, 02:17 PM
Post: #15




RE: [VA] Short & Sweet Math Challenge #22: April 1st, 2018 Spring Special
(04022018 10:06 PM)rprosperi Wrote: I suspect by 'no trig functions' Valentin was implying SIN/COS/etc. but you could be right. We have to wait for a judge's ruling on that, but I'll keep digging.) If RAD is allowed then RAD(UNF*OVF*OVF) does the trick, regardless the angle mode. (Using other people’s ideas only, yours included) 

04032018, 08:47 PM
Post: #16




RE: [VA] Short & Sweet Math Challenge #22: April 1st, 2018 Spring Special
(04032018 02:17 PM)Gerson W. Barbosa Wrote: If RAD is allowed then RAD(UNF*OVF*OVF) does the trick, regardless the angle mode. Cool! String length is right, though byte count is higher (11 bytes with line number, I think 8 for just the expression). Valentin is laughing now... can you hear it? Bob Prosperi 

04032018, 09:05 PM
(This post was last modified: 04032018 09:06 PM by Gerson W. Barbosa.)
Post: #17




RE: [VA] Short & Sweet Math Challenge #22: April 1st, 2018 Spring Special
(04032018 08:47 PM)rprosperi Wrote: [quote='Gerson W. Barbosa' pid='94428' dateline='1522765035'] On the other hand, Valentin said “1 DISP itself takes 5 bytes”, so I assume the expression takes 6 bytes, unless I’m wrong, of course. Six byte and 16 characters for pi is indeed awesome. I would need much more just for pi :) LN(SQRT(SQRT((305^3+25^3+5^3+5)/(4^3+3^3+2^3)))) 16*3 characters and 6*6 bytes 

04032018, 09:31 PM
Post: #18




RE: [VA] Short & Sweet Math Challenge #22: April 1st, 2018 Spring Special
(04032018 09:05 PM)Gerson W. Barbosa Wrote: On the other hand, Valentin said “1 DISP itself takes 5 bytes”, so I assume the expression takes 6 bytes, unless I’m wrong, of course. Sorry, I missed that note inside Desert #1 when I skipped straight to Desert #2. I was not sure how many bytes a line number takes, but it looks like it's 3. So then yes, of course this is the answer. Good job team! I wonder if Valentin awards partial credit? Bob Prosperi 

04042018, 12:08 AM
Post: #19




RE: [VA] Short & Sweet Math Challenge #22: April 1st, 2018 Spring Special
.
Hi all, First of all thanks for the overwhelming interest in my humble SSMC#22, I'm very grateful for it. I'll post my original solutions to Main Course and 4 Desserts within two days (next April, 5) so you've still got time to solve them all, but meanwhile I'll address here some of the things you either commented or asked. Read on: Didier Lachieze Wrote:Hi Valentin, thanks for this nicely crafted challenge ! You're welcome, thanks for your appreciation. pier4r Wrote:Just an observation. Why do you say "code" shouldn't be included? If you see the thread with the printable version (at the end of the thread there is a link) listing in code are not bad when properly formatted. You may be right but for this challenge I'll stick to my plea not to use it. I make change my mind though after I do some tests. Thanks for pointing this out to me. Mike (Stgt) Wrote:"At one's ease"? So the following determinations are not too serious? Please explain. Please, Mike (Stgt), English is not my native language and I'm doing what I can with it so please cut me some slack, will you ? Gerson W. Barbosa Wrote:Both ANGLE and RAD are listed under Trigonometric Operations in the Keyword Index, though. They're not trigonometric *functions* so they're perfectly legal. rprosperi Wrote:Valentin is laughing now... can you hear it? Indeed I was, you all are quite funny and it's a pleasure to read your attempts (and eventual success!). And yes, I award credit to all involved. That's all, see you next April 5. Best regards and keep on trying till you get all solved, Main Course & 4 Desserts. V. . Find All My HPrelated Materials here: Valentin Albillo's HP Collection 

04042018, 02:38 AM
(This post was last modified: 04042018 02:39 AM by Gerson W. Barbosa.)
Post: #20




RE: [VA] Short & Sweet Math Challenge #22: April 1st, 2018 Spring Special
(04032018 09:31 PM)rprosperi Wrote: So then yes, of course this is the answer. OVF*OVF*RAD(UNF) is another variation. But Dessert #2 won’t be over until Pie/100 and Pie/10000 are served. RAD(INX+UNF)/UNF returns Pie/100, but we need Pie/100. It looks like Pie and wine don’t match :) 

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