Windows better than Linux research

[Qfwfq]

That's a good one, the IOCCC. I don't do it for job security though, and I don't go to the extent of using #define solely for illegibility.

 

The only time I delighted in making code as tricky as could be done in Coffee in a job for a customer, was when I had been put under a young project leader that was treating me like an idiot and there wasn't much chance of otherwise changing her attitude. Boss thought the world of her but imv she was little more than a student and certainly not enough of a genius to justify being so haughty. It was a non-trivial thing anyway but I was packing as much as I could into single expressions and so on. One evening she tried looking at it because of new specs, when I had left for home, she had hoped to make a little change or two herself and she had a fit. It caused a great row but eventually she realized she had no grounds to treat me that way.

thats so easy to do though. I am trying to learn to take it easy with him, if he posts something that enrages you, ignore it, just post your thoughts in peace.

Yeah, I'm tring to ignore his outright insolence while showing that my execution times are good.

 

but i've also been writing a large number class that would easily allow me to do math with large inegers, so far adding 2 10000 digit positive numbers with their generation takes less than 1/2 a second, but my multiplication process is crapping out, some logic flaw that's bothered me for a while, so i've been avoiding it hoping to get a revealing idea about how to do it all better...

I developed a class Rational, which uses a class Looong, but there is still room for improvement. Looong can add and subtact integers of over a thousand bytes, it would be straightforward to change the max length, it builds them up by multiplying unsigned longs each with an exponent and it is used by Rational to factorize the results. Instead of giving Looong full arithmetic, Rational has it but this implies the sometimes heavy factoring after algebric sums with the limit on prime factors.

 

For your query about the count of a number's factors, prime and not prime, I thought it would be a good idea for Rational to also give users a way of iterating over the prime factors, without making the class fragile. This could be done easy enough, when I get round to it.

[alexander]

Looong can add and subtact integers of over a thousand bytes, it would be straightforward to change the max length, it builds them up by multiplying unsigned longs each with an exponent and it is used by Rational to factorize the results. Instead of giving Looong full arithmetic, Rational has it but this implies the sometimes heavy factoring after algebric sums with the limit on prime factors.

what i'm writing can add over 3 billion digit long numbers, but again, so far its only capable of adding 2 positive integers with no floatpoints, cant do much else, but when i get time to start working on it again i hope to get it to multiply (not by adding the values over and over and over again), subtract and divide as well as finding the modulus (pain, if you have some kind of an algorithm, please i'll be looking for it eventually) and do exponentiation (not via multiplication (also need a mathemagical solution, maybe some base shifting math exponentiation craziness))... eventually hoping to come up with something that will do RSA encryption the way that it was intended to be done (with really really large numbers), really stinks that bc does not accept input from the command line, bc is so awesome...)

[alexander]

my execution times are good.

build in the timing function, store the system time before start in one var... you know the drill, then you'd have exact time of execution of your function, then run TM's program, compare the results on the same system, then you'd have the necessary data to back up your point :eek:

In any case his algorithm is not that great either take some 50-60 digit long number and it will take him years to get the results, if you are talking about factoring here is a few thoughts:

here's wikis on most commonly used factoring algorithms (I personally prefer gnfs although some curve factoring is needed in large numbers):

http://en.wikipedia.org/wiki/Category:Integer_factorization_algorithms

RSA's favorite algorithms:

http://www.rsasecurity.com/rsalabs/node.asp?id=2190

and little something in the quantum world and Shor's algorithms:

http://ece.gmu.edu/crypto/student_projects/physics.htm

[Qfwfq]

I did timing tests on my code and there's no comparison with times TM has posted for the same things. I'll have a look at those links, though I haven't been dedicating much time to cryptography.

 

My Rational class raises to exponents easily. It is trivial, in prime factor representation. Raising rational values to non-integer exponents may give irrational values but I was thinking of an idea about that. For the moment my class only does integer exponents, positive and negative.

[alexander]

i just wish that bc could accept input from standard in, so you could use it, it can within 5 seconds calculate what 12345*12345^12345 is...

[Qfwfq]

The calculator on W2K can do it in a few seconds, giving the result:

 

8,2246509487853475599542489438859e+101018

 

12345 = 823 * 5 * 3, so that would be:

 

(((12345^2)^3)^5)^823

 

but the calculator only handles it if the exponents are done in decreasing order. Of course, you probably want the exact value, an integer of around 50kbytes. The only way to do this is by repeated multiplication.

[alexander]

no no, i'm talking about the exact number, in standard aterm its about 9 pages worth of numbers.

the thing is i would have computed 1234567890^1234567890 but i have little time to actually do this, but if you are interested i can do it and print out the results ;)

[Buffy]

Save the trees! Use e-mail!

 

Environmentally,

Buffy

[alexander]

buffy, i'll post it here tomorrow...

[Qfwfq]

no no, i'm talking about the exact number, in standard aterm its about 9 pages worth of numbers.

That's what I figured:

 

Of course, you probably want the exact value, an integer of around 50kbytes. The only way to do this is by repeated multiplication.

About 50 kbyte for 12345. Uhm, let's see, for 1234567890... 3^2 * 13717421 which isn't prime but I gave up trying to factor it by hand, I can't jot down a quick program either. In the gigabytes anyway.

 

How many million pages? Better keep it on disk!

[C1ay]

That's what I figured:

 

About 50 kbyte for 12345. Uhm, let's see, for 1234567890... 3^2 * 13717421 which isn't prime but I gave up trying to factor it by hand....

Try 2*3*3*5*3607*3803

[Qfwfq]

Thanx.

 

For the record, I had divded by 2 * 5 in my head, but that immane effort blew my brain a bit so I forgot to include those two factors. Just in case anyone checked my numbers up, back there.

[alexander]

oh yeah i promised to post what bc says 12345^12345 is, here it comes:

12345^12345

2867865225003669442826455604983179963965839852965721255676827662815696261243172347789319941760086956841965972700488642307045998675445189849609967378621179958073791426749071929893397188800652848434847092204652299777212519222211211855775790000672091949348154957381093342803689165122900820157088604214710502544876982691049541677186794836992989079740817470605462087183753892043144454972158817946948946846873753596268760733357119146627102186168829460473430237573969632881043182702791429564012052045914119507177013466017683361896410615937679211596486179865647392870635436678987536715133198284973093222583966794178115970438760485533505646234130050245188848572209672049045875030270825541569291261774669278244106484828994632562101627549885941841239456897046254146146753094478034086813219933215422175735000653202662472156102866134886087009703639642096226577723775317689111392189874003378194890920193852284575948889936107770362650428857291232870576275298576598547537064712932903036903959252994976552148022399172352350540836780723068926265599430911839657677557622985839797342281852749452094422457510612646139387975714094893457608648370452911166293025732673098563711917350608799043711114596917413088573518842105072077291635994948244282848929551583843146542858830924646837561091577615306412825930019751895356249723968659386320571413954180682126480826934558995094745140923185080150305914142566631321515964797235381322579264609397170933425248511820769298757817538175883456769241770268391574850318357185927701851379439604231217379898775230591002605892467013739904633668695753609626491937049172768000677034310548400845583026662141260668337029608140712541413032574640374266803209889769669657329257230191380168377374259659709783837636047059101730334292478246111073565105294973384523707786032452448340167890292244313345347370404462083139036509318045222023989938255845241837330172145516765920655016069883702212753989145539947033108063481474285686348570645162072862861624249448943577045380466719996250693879633873774745643418481237613355737348391967117336019335590032374339934710772460377361255107264919083061950473803225121688723553924370265448433268904799607285835097258954763495613423971231691404200561466639135531565670401262273873303874928556793490722740814325065140633473990574329929180940887355915555528341520381824811864964806989793259622419798380018188348968598861956700554403395580473055947946028171692117610444375250686532269657216932451458583291414278069762224007837918758822678563839011980527485926370136963793180184536359401966813639646085351278121903035969684857607519918402864950459066720163880069218205239977237614967438636832898767016828228038063021522246582231202305575167888149043817722265491913732748522580146762311958874636140039589265992550925417023826375368630790904732829118892660794002491100965602617814334201120957100433131519892302615816399517516708688323515429589963680229337861430389712426743161516643838171371933712602780018744918584046197467074320597692107666800183289246115208568479946132832311131569789178195752595201302186009990877627622319252766398163745291099040970419210304870737289380891244490047241686594624583732488927361829333366702226736603453801890418728529348078155412960044881761866799206006803600363726062680419712302499372595474635441522853117681790229458503356235859014114037467506695579714816567577063901307345491267448741908477220033205842357034707468452867895422642976756602251205584532792899075301764472641561079730376314486075212548440725405314947913315845746415080665907097986000163644205155225454662060222320741403412301478741833386537641271694873414300533987905504425124635781852095681122604197901740156064277009304428804168257191656241411187402556390497793596388049356621206490534305895198276189976121480248556994745980524970168714790810833848256648526535772464785732755224104335748836070109436524525604190069363908098312516925205828939047290185103052977857606863337807859883895426817746688835369439736651133051390302105253502066225282791331768768744502969968337956141053012409750447862528529522614954187659088000707928093830877300740770686766531929796856152512303447923517748388095154552095651875287546996418628001590549664542429129838965708258514088769787904908791176712741471815960802818216360203484462744801896694763652020194770291050179056721747172497647066353876109233421777433524710297804122824520152943874181407078051676139560499094240837666168613712122677178662455877270574617372719807833665332100135568840077354015390279734170062911121453915754810686515434639376994877843365579227245118261242852217261717779843836795547084752535463429891576567322767193923851647259114195125433769

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total time to start bc, type in equation and excute is under 10 seconds (while comiling gnomr base).

pretty amazing huh?

(i can be missing numbers, i had to edit out the endline slashes and newlines)

[Qfwfq]

what bc says 12345^12345 is

I thought it was supposed to be 12345*12345^12345. Equivalent to 12345^(2*12345), it'll have about twice the number of digits.

[C1ay]

oh yeah i promised to post what bc says 12345^12345 is, here it comes:

total time to start bc, type in equation and excute is under 10 seconds (while comiling gnomr base).

pretty amazing huh?

(i can be missing numbers, i had to edit out the endline slashes and newlines)

Could you check 12345^12345 +- 2 for primality while you're at it? Robust asked for some prime numbers in another thread. :)

[Qfwfq]

Oh, Alex, if you post more such results, please use CODE tags, they give a scrollable frame!

[alexander]

but it was supposed to be impressive, and i actually considered it, but decided against it...

oh, yeah i'll post 12345*12345^12345 if you want to with propper timing and everything, but thats tomorrow, but for now i go and code...