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Talk:Pseudorandom number generator

Corrected K1 criterion
Criterion K1 doesn't state that consecutive number repeats should have low probability, i.e. probability any lower than any other number, rather, if one generates random vectors of numbers, these should be different from one another with high probability. Here's the original text: "There should be a high probability that random vectors (r1,…,rc),(rc+1,…,r2c),…,(rMc+1,…,rM) formed from random numbers r1,r2,… are mutually different." I've tried to correct the K1 summarization to be truer to the source text, yet maintaining the simplicity of the writing. Todd (talk) 16:53, 6 January 2017 (UTC)

removed bad Math
Whoever added: (Assuming one bit is produced every picosecond, a state of 64 bits would suffice as (1 picosecond)*264= over 142 million years.) This is mistake. 1 picosecond)*264 = 18,446,744 seconds = 213 days. Well over the lifetime of a fruit fly.  This is not a good example either, since generating a random number takes well over 1 picosecond, and supercomputer can generate hundreds of them or even thousands in parallel.  I'd vote for removing this paragraph entirely, but I left it to be polite and discuss.  I removed error, since it is so extremely misleading to anyone wanting to learn this material, I could not in good conscience leave it.

about Mersenne twister; good article is started
About Matsumoto's and Nishimura's Mersenne Twister I can say that it really works almost as Nature's randomness - believe it or not. This algorithm is already fully implemented on VOG a Russian server for board games. I've played there quite vast period of time on Backgammon arena and on Reversi one. The C function int rand (int) is not as good as PRNG based on Mersenne twister - that is for sure. Try it and feel it. Nice you've started a PRNG at last. We really needed this one. I was already thinking to do your job. Can you put some Knuth's work on this field too. About the simpliest PRNG and such. XJam [2002.03.23] 6 Saturday (0)
 * It's not clear one's feelings about using a PRNG are a reliable quality metric. In any case there is some serious dispute about whether the Mersenne twister is as good a PRNG as is sometimes thought.

ww (talk) 03:35, 5 August 2009 (UTC)

 * Mersenne Twister is merely the newest member of a family of generators with very well understood properties, meaning both good and bad. Among the bad is the very long correlation length, or as the authors euphemistically call it "recovery" time. If you initialize the vector with mostly zeros, you will continue to get mostly zeros for the next ten thousand iterations. This is because, there is only one new bit out of 19937 on every iteration. The other 19936 are just shifted and reused.

Kotika98 (talk) 13:33, 26 December 2012 (UTC)

dimensions?
> It has a colossal period of 219937-1 iterations, is proven to be equidistributed in 623 dimensions. Ostrich can you please explain a liitle bit more what herein dimensions means exactly? Otherwise everything else is explained as clear as can be. XJam [2002.03.23] 6 Saturday (1st ed)

Statistical patterns in a sequence may appear in many ways. The dimensions noted are ways of examining the sequence for patterns. See Knuth Semi-numerical algorithms for more detail. Please note that this article needs serious revision, particularly with regard to CSPRNGs. It is not easy to build these and statements that 'one could' have one if one does this or that are dangerous. Someone might rely on them and get into considerable (insecure) trouble as a result. Indeed, many PRNGs are built with block cypher encryption algorithms operating in CTR mode. However, the description of CTR mode here is inadequate. Note that CSPRNGs not only must satisfy certain statistical properties, but also must not be predictable which is another kettle of bits altogether.

The spectral test article and the RANDU article have an example of what "dimensions" means in this context. --DavidCary (talk) 02:11, 31 December 2014 (UTC)

poor code formatting
For some reason my Delphi/Pascal code is not formated correctly with the <pre> tag. Suggestions? - Jim

Move Cryptography Material
I see that most of the material in Cryptographically secure pseudorandom number generators is repeated on its own page. Can we remove or summarize it here?

Sander123 13:13, 21 Jul 2004 (UTC)
 * Sander, The biggest use of RNGs is in crypto by now and so some (all?) of this coverage belongs here. Some RNGs suitable for other uses are not suitable for crypto use, so some attempt to bring out the different requirements is apposite.
 * As for duplication, much the same can be said for coverage of the material from a crypto perspective, so a redirect of one title to the other will probably cause difficulties. I too feel an urge to minimize duplicated content, but in this case have managed to restrain myself. I suspect we all should. ww 14:53, 21 Jul 2004 (UTC)

 * ww: "The biggest use of RNGs is in crypto" — are you sure? — Matt 23:16, 21 Jul 2004 (UTC)
 * It would help, I suppose, if I were regularly patrolling talk pages for comments directed at me. As I'm not, this one has escaped my notice for an extended time.
 * Well, let's say that I read mostly crypto related material, not the modeling or statistical literature, so there may be a bias. Would you be happier with 'most PRNG use'? Actually, the most critical use of such things in crypto (not news to you, of course, but perhaps to some readers) is a subset of RNGs, and of PRNGs, namely CSPRNGs. Randomness is a very central problem in crypto applications, and crypto theory as well (eg, the random oracle model used for analysis). But nevertheless, still PRNGs (and RNGs). ww (talk) 16:45, 23 September 2008 (UTC)

 * I read mostly non-crypto-related material, so I may be biased in the other direction.
 * I suspect that the top two applications of PRNGs are in mobile phones and GPS receivers. My understanding is that most mobile phones have both kinds of PRNG -- a non-crypto high-speed "linear" PRNG for CDMA, and a separate lower speed CSPRNG to support encryption such as A5/1. My understanding is that the vast majority of GPS receivers are civilian GPS receivers, which include only non-crypto "linear" PRNGs.
 * From that I conclude that there are slightly more non-crypto PRNGs (cell phones + GPS receivers + a few other non-crypto PRNGs) than CSPRNGs (cell phones + a few other CSPRNGs).

 * I support the move of text from this pseudorandom number generator article to cryptographically secure pseudorandom number generator, leaving a WP:SUMMARY in this article. --DavidCary (talk) 16:13, 10 April 2012 (UTC)

rule of thumb

 * A general rule of thumb is to have only a summary paragraph about a subtopic, and include a prominent link to the subtopic article; I think we do this here, although the subtopic article (CSPRNG) is not as complete as it probably should be, and arguably the summary paragraph in PRNG is slightly too long as well. — Matt 23:16, 21 Jul 2004 (UTC)

 * I agree with Matt. The problem that I see is that repeating the material makes maintanace difficult. In fact I came across this because I wanted to add some material. And there is a lot of material that I want to add here--Make the requirements more explicit, say some more about the standards availlable, list designs that were broken and the problems they caused, etc, etc.

 * Eventually this could be quite a large topic. Should I add all that to the main page? I propose that I make sure that everthing on the main page is included in crypto page, and then summarize the main page. Everybody agree? Sander123 08:50, 23 Jul 2004 (UTC)

 * Seems like a sound refactoring to me, thanks. — Matt 17:00, 23 Jul 2004 (UTC)

author, author -- but no title...
In the citation to the von Neumann paper, several authors are given, but there is no title. Perhaps an editing glitch ate it? Can anyone suggest what it was before this supposed whale of an editor swallowed up our Jonah of a title? ww 08:52, 26 March 2006 (UTC)

Linked term: "random", the rap artist
The "random" link in the first paragraph goes to an article about some rap artist, named "Random." Can someone fix?

poor writing
This page hasn't been written by the world's most gifted writer. E.g.:

"Because any PRNG run on a deterministic computer (contrast quantum computer) is necessarily a deterministic algorithm" "The outputs of pseudorandom number generators only approximate some of the properties of random numbers" "Careful mathematical analysis is required to have any confidence the algorithm generates numbers that are sufficiently "random" to suit the intended use"

The whole article reads like a mathematical text book, not an article from an encyclopedia.

 * anon poster, It's a tricky topic and more than many, preciosn of language -- at the expense of kludgey phrasing -- is hard to avoid. Please, suggest improvements which do not do damage to the meaning (including this precision, at least where we've amanaged it). It is not easy to do. And if it is for you, have I got some articles for you to look at... ww 06:40, 19 July 2006 (UTC)

 * Absolutely correct: encyclopedias are meant to be informative, not a reference book for mathematical computer science geniuses. It should be informative to the uninformed and it should do so without phrases like: "computer (contrast quantum computer) is necessarily a deterministic algorithm"" which is absolutely meaningless for someone like me. The trick is to be informative without being sloppy in your language. THe problem is, is that I am too ignorant on the topic to make the required changes, which is why SOMEONE who knows better should take that initiative.--ToyotaPanasonic 02:40, 21 February 2007 (UTC)

 * I made pass at cleaning the article up. It is still not as clear as it could be, but I hope it is less convoluted. I also took out the 1/q generator which does not seem terribly practical and I am not aware of it's being widely used. --agr 04:16, 21 February 2007 (UTC)

Mersenne Twister Linearity
The article claims that, "However, it is possible to efficiently analyze the output of the Mersenne Twister algorithm and to detect that it is non-random (as with the Berlekamp-Massey algorithm or an extension of it, such as the Reed-Sloane algorithm)."

I've actually done the experiment with the Berlkamp-Massey algorithm and the Mersenne Twister. The Mersenne Twister is not linear.

At the risk of being pedantic, let me discuss Berlkamp-Massey. This agorithm will determine the shortest linear feedback shift register that can produce a given bit sequence. This length is the sequence's linear complexity. The algorithm is used to verify that a PRNG isn't linear (in the strict sense of being equivalent to a linear feedback shift register) and to examine its linear complexity profile.

The Mersenne Twister is not equivalent to any linear feedback shift register. The Berlkmap-Massey algorithm doesn't reveal any bias or predicatability in the output of the Mersenne Twister. That does not imply that no bias or predictablity exists. Predictability always exists if the PRNG algorithm and the internal state of the PRNG is known or can be inferred.

I'm very curious about the author's source for the claim quoted above.

More about the Mersenne Twister
I have recently experimented with the Mersenne Twister, in particular by analyzing its output with the Berlkamp-Massey algorithm. My recent changes to this page are motivated by what I discovered. For details, search the sci.crypt.random-numbers newsgroup for Mersenne Twister Linearity. I am still very interested in any actual numerical analysis of the output of this (and other!) generator's output.

Dude, sign your postings, and also read WP policy regarding original research, OR is not allowed in any article on WP. Kotika98 (talk) 13:41, 26 December 2012 (UTC)

Microsoft RAND function

 * The RAND function included in current Microsoft operating systems has only 15 bits of state and thus repeats after generating 32768 bytes.

That's a little hard to believe... do we have a source for that? --Tgr 15:35, 26 October 2006 (UTC)

In Visual Studio 2005, the default rand produces values in 0..0x7fff. This C program: :int main { int i,j,k; j=(rand<<15)|rand; for (i=0; i<0xffffffff; ++i) { k=((k<<15)|rand)&0x3fffffff; if (j==k) printf("%.8x\n", i); }} reports repeats at 0x18932e78, 0x37c97143, 0x7fffffff, 0x98932e78, 0xb7c97143. So it has a cycle length of 2^^31 values, not 2^^15 values. That implies an internal state of at least 31 bits. (The 0x1e932e78 alone doesn't indicate a cycle, it just happened those two values appeared sequentially again. PRNGs are allowed ... are SUPPOSED ... to do that occasionally.)  Though, the original comment might have been referring to some other rand shipped by Microsoft.

I've removed that line for the time being. A generator with a cycle length of 2^^31 values is still awfully bad in my book, but unfortunately not exceptionally bad. 2^^15 would be exceptionally bad. (I also rearranged the quotes at the top of the page: Jon Von Neumann's "state of sin" quote is about the distinction between random and pseudorandom numbers, not the difficulty of generating adequate pseudorandom numbers.)

 * Actually the Microsoft C/C++ random number generator is not all that good. It's not hard to come up with a test of randomness that this generator will fail. Correlations between a one number and the fourth one after can be detected. If you're doing something where the results of your program depend on having a high quality PRNG, don't use the one in the C standard library. --71.38.172.8 (talk) 23:49, 29 January 2010 (UTC)

R P Brent's algorithm?

 * R P Brent's algorithm can be used to determine the period length of deterministic PRNGs; (...)

This intriguing statement is a little isolated within the article. Could someone elaborate or provide a source or link? GdB 15:29, 3 January 2007 (UTC)

Non-uniform generators
A lot of practical uses of random numbers involves non-uniform distributions; which are often produced via a non-linear function upon a uniform random number generator: e.g. tan(x) for Gaussian pseudo-random. I've started a section.

 * Good luck with this subject, where can we see your efforts? This page says: A simple approximation is to use the tan(x) as the inverse cumulative gaussian and a uniform distribution from -pi to pi non-inclusive. but I don't see how that works. Ziggurat algorithm is workable and fast. Please sign your posts. Cuddlyable3 08:15, 20 July 2007 (UTC)

The section is presumably correct, except that it only indicates one method, which needs determination of a cumulative distribution function. There is at least one other method, usable practically when the range of possible values is finite and the distribution function is (in the range) everywhere finite and not grossly uneven (or when the required distribution can be mapped to that).

Choose a random X in the range, and a random Y within a range from 0 to at least the peak probability. If Y is less than the desired probability of X, then return X; otherwise, try again.

Advantage : works with any distribution in a range, without additional algebra. Disadvantage : needs two randoms per go, and on average more than one go per result.

The above description may contain errors in detail; but it should be good enough to identify the method.

82.163.24.100 (talk) 12:09, 5 May 2010 (UTC)

Knuth and Marsaglia
How can you have an article about RNG's without discussing Knuth's work on statistical testing and Marsaglia's extensive work on inventing and testing random number generators. It is naive to focus so much attention on the Twister algorithm, which in fact is far too slow and complicated for many numerical applications. There should be some discussion of the extremely efficient multiply-with-carry generators, which pass statistical testing and only emply a few machine instructions. The article needs work. DonPMitchell 04:53, 31 October 2007 (UTC)

Inner State
Under the BSI evaluation criteria the article mentions "inner state". This should probably be defined somewhere. —Preceding unsigned comment added by ColinGillespie (talk • contribs) 17:49, 31 January 2009 (UTC)

 * Could we move the entire pseudo-random number generator section to the cryptographically secure pseudorandom number generator article? Is there anything in that section relevant to non-crypto PRNG? --DavidCary (talk) 16:13, 10 April 2012 (UTC)

 * Did I comment on that somewhere else already? I don't recall. Anyway, evaluation criteria K1 and K2 are not of interest to the latter article, but all of the criteria are relevant to this article. So it should definitely stay here, though the BSI evaluation criteria could possibly be shortly mentioned in the other article. Nageh (talk) 11:49, 4 May 2012 (UTC)

block removed from article
Tis para was removed from the end of the article because 1) it is out of place in the language interwiki list 2) extensive text in other languages is out of place on enWP 2a) not clear it isn't vandalism of an obscure type. Anyone who clarify any of this should lend a hand.

 * Vietnamese: “Một máy phát tín hiệu giả - ngẫu nhiên là một thuật toán dùng để tạo ra chuỗi  số có tính chất gần giống với số ngẫu nhiên, chuỗi số đó thực sự không phải ngẫu nhiên khi nó hoàn toàn được xác định bởi một tập hợp các giá tị nhỏ tương đối ban đầu, gọi là trạng thái PRNG.”

ww (talk) 18:22, 4 August 2009 (UTC)

New Approach to Generating Truly Random Numbers
Should we mention somehow results of recent research (research paper: )? Maxal (talk) 21:00, 25 March 2010 (UTC)

 * The underlying problem is difficult. This journalistic report is insufficient in several respects. There are several claims here about twenty times more random and similar. It's not clear such a phrase can mean anything.
 * Whatever the virtues of the method these folks have developed, more information and consideration is needed before it should be added here, other than speculatively. ww (talk) 05:27, 26 March 2010 (UTC)

(CS)PRG, (CS)PRNG, (CS)PRBG, etc.
This article really confuses the definitions. In general, I'd say it should discuss pseudo-random generators (PRGs). Pseudo-random bit generators (PRBGs) and pseudo-random number generators (PRNGs) should be introduced as sub-classes of PRGs. Don't say a PRNG is a deterministic RBG (or PRBG). Anyway, I would love to see the distinction addressed in a proper reference. Anyone has a good ref?

Next, it may be desirable to point out that in computational complexity theory the definition of PRG equals that of a CSPRG.

Nageh (talk) 21:50, 20 May 2010 (UTC)

 * I think of bit generators as a sub-class of number generators, rather than a separate class -- although I agree that a good reference either way would be an improvement. --DavidCary (talk) 16:13, 10 April 2012 (UTC)

Cryptographically secure PRNGS: integer factorization is not a "known hard problem"
I've removed the example of integer factorization as a "known hard problem". It isn't proven that integer factorization is NP-complete and is currently believed not to be in this class (but rather, in the class of NP-indeterminate problems). See the article on integer factorization.

If anyone can propose a better example, please insert it in the text. Ross Fraser (talk) 08:35, 4 October 2011 (UTC)

 * The concept of a hard problem in cryptography is not related to that of a hard problem in complexity theory as in NP-hard. The definition is as follows:
 * A problem is called hard or infeasible if no algorithm exists that given some random input (from the input domain of the problem) solves the problem in PPT (of some security parameter k) with non-negligible probability.
 * Nageh (talk) 09:39, 4 October 2011 (UTC)
 * Actually, it's not quite correct to say that the concept of a hard problem in cryptography is unrelated to that of a hard problem in complexity theory as in NP-hard. PP contains NP (see the WP article on PP). To prove this, we show that the NP-complete satisfiability problem (SAT) belongs to PP. Consider a probabilistic algorithm that, given a formula F(x1, x2, ..., xn) chooses an assignment x1, x2, ..., xn uniformly at random. Then, the algorithm checks if the assignment makes the formula F true. If yes, it outputs YES. Otherwise, it outputs YES with probability 1/2 and NO with probability 1/2. If the formula is unsatisfiable, the algorithm will always output YES with probability 1/2. If there exists a satisfying assignment, it will output YES with probability more than 1/2 (exactly 1/2 if it picked an unsatisfying assignment and 1 if it picked a satisfying assignment, averaging to some number greater than 1/2). Thus, this algorithm puts satisfiability in PP. As SAT is NP-complete, and we can prefix any deterministic polynomial-time many-one reduction onto the PP algorithm, NP is contained in PP. Because it is closed under complement, PP also contains co-NP.
 * As I mentioned above, integer factorization is believed by some to be in the class of NP-indeterminate problems. Ross Fraser (talk) 09:17, 16 October 2011 (UTC)
 * Sigh, wrong wording on my part. Of course there is a relation, I just tried to explain that the concepts of hard are different. Nageh (talk) 09:19, 16 October 2011 (UTC)
 * Btw, just noticing this now, PPT refers to algorithms in BPP not PP, because otherwise it would be hard to get a negligible error bound. Nageh (talk) 11:42, 17 October 2011 (UTC)
 * Oh, and I have replaced "known hard problem" with "problem thought to be hard". It's all assumptions nonetheless. Nageh (talk) 10:12, 4 October 2011 (UTC)
 * As above, there is no citation to support this assumption and currently no established mathematical intuition for the utility of the integer factorization problem for this purpose.   Ross Fraser (talk) 06:12, 15 October 2011 (UTC)
 * What? It is not an established assumption that integer factorization is hard??? Are you kidding me? (I am not talking about NP-hard!) Nageh (talk) 09:19, 16 October 2011 (UTC)
 * How does an assumption become "established" other than by mathematical proof?--agr (talk) 10:37, 17 October 2011 (UTC)
 * Established in practice??? Wrong wording on my part? I dunno, I'm not a native English speaker, but I think it's pretty fair to say that the integer factorization problem is an established hardness assumption in cryptography. Hell, why do I even link computational hardness assumption in the article if you guys pretend it's all not true? Nageh (talk) 11:00, 17 October 2011 (UTC)
 * You can say "widely assumed" or "As of 2011, the best factorization methods are only capable of xxx" or "Zorch Corp claims numbers longer than YYYY bits cannot be factored in the foreseeable future" (the latter two with refs, of course), but established and assumption don't go together without a proof. Mathematics isn't based on opinion polls.--agr (talk) 15:34, 17 October 2011 (UTC)
 * When I said "established" I meant "widely used/relied on in practice". I'm not sure I understand where the ambiguity comes from; is it because it may be understood as "settled" or "solved"? Nageh (talk) 16:22, 17 October 2011 (UTC)

 * Ross, I just read again what you have written above. There are multiple issues with what you say:
 * IF is in NP-indeterminate. Would you care to explain what NP-indeterminate is? I suppose you meant NP-intermediate.
 * As I mentioned above, a cryptographically hard problem does not require that it be NP-complete (or even NP-hard). All that matters is that no PPT algorithm exists for breaking it.
 * Ad "there is no citation to support this assumption and currently no established mathematical intuition for the utility of the integer factorization problem for this purpose": All I can say is that this statement is incredibly naive!
 * Ok, let's go for a few facts. Yes, IF is widely believed to be in NP-intermediate. The argument still holds that no PPT algorithm exists for solving it (otherwise it would be in BPP). Because IF is widely assumed to be not tractable in PPT it is the basis for many cryptographic primitives, notably including the RSA algorithm. The concept of reducing the security of cryptographic primitives to a widely accepted computational hardness assumptions (note the word hard in there) is the basis of what is known as provable security.
 * So, now that I have hopefully clarified a few things would you please explain exactly for which claim you would like to see a reference? Thank you. Nageh (talk) 16:44, 17 October 2011 (UTC)
 * Well, for starters, your statement that for a problem to be cryptographically hard "All that matters is that no PPT algorithm exists for breaking it." Assuming by nonexistance you mean "not know to exist" as opposed to "proven not to exist," that's ludicrous on its face. I can pose a problem today and it will be considered cryptographically hard if there's no PPT algorithm (yet)? Problems become "widely accepted computational hardness assumptions" after they have attracted the efforts of many highly competent researchers over decades (centuries for IF) and have lower bounds on solutions that have been relatively stable. Even so they are still assumptions, not proven facts.  --agr (talk) 15:14, 18 October 2011 (UTC)
 * Sigh. I have said days ago that "it's all assumptions", didn't I??? And yes indeed, from a theoretical POV, a problem is suitable for cryptographic purposes if it is easy to solve for legitimate parties and hard to solve by any adversary bound to PPT (at least that is true for the complexity-theoretic POV in cryptography). As formulated, it is true for the trapdoor concept. One-way functions are more basic concepts, and the quintessential primitives in modern cryptography, but here again it must be hard to invert a one-way function given some random input in PPT (dependent on some security parameter k). And yes, for a problem to become an accepted hardness assumption it takes years of efforts by researchers to build confidence in their hardness. Ludicrous what I am saying, right? Well, just tell me the references you would like to see, I'm not willing to get put words into my mouth I didn't say and never intended so. Nageh (talk) 15:55, 18 October 2011 (UTC)
 * Exact choice of words are important here. The question raised in this section was whether this article should say that integer factorization is a "known hard problem." If we can all agree on saying "integer factorization is problem widely assumed to be hard" then I am satisfied.--agr (talk) 18:53, 18 October 2011 (UTC)
 * Oh shoot, it just occurred to me that you guys were interpreting the phrase "[integer factorization is] thought to be hard" as "it is thought that no efficient (i.e., PPT) algorithm exists for factoring", while the intended meaning was "it is thought that no efficient algorithm for factoring exists within the near future", making it practical for cryptographic purposes. My bad, sorry. I will just replace "thought" by "assumed" in the article, hopefully addressing the problem at hand. Thanks for your input after all. Nageh (talk) 22:36, 18 October 2011 (UTC)
 * Thank you. Now that the wording has been changed, I've inserted a goo reference citation to integer factorization being assumed hard.  Ross Fraser (talk) 07:36, 26 October 2011 (UTC)
 * May I attempt a summary? Integer factorization is hard in practice, but some people think it may eventually be done in amount of time which is polynomial in the number of digits. This is relevant to cryptography because some crypto algorithms rely on integer factorization being hard. Kotika98 (talk) 13:50, 26 December 2012 (UTC)

State of Sin?
I enjoy the witty quote about the generation of random numbers being too important to be left to chance and think it is one that a very broad spectrum of readers would appreciate. But the von Neumann quote about being in a state of sin will puzzle many (most?) and adds little to the article. It is excruciatingly specific to Catholicism (von Neumann received the last rites and may or may not have converted to Roman Catholicism on his marriage) and many readers simply won't know what he means by state of sin, at least not in relation to mathematics, which is usually thought of as utterly divorced from Christian theology. In any event, it certainly doesn't tell the reader anything about PRNGs. Donald Knuth's "Random numbers should not be generated with a method chosen at random." is at least as good and at least informative to the reader. (Donald Knuth, The Art of Computer Programming, Vol. II, 1969, section 3.1). But really, it's best to just drop it and leave the one good quote from Coveyou. Ross Fraser (talk) 12:22, 14 November 2011 (UTC)

 * You enjoy the quote, you find it witty, but you want to delete it because you fear others might be unable to understand it? Perhaps you underestimate the intercultural competence of others. Whoever is reading this encyclopedia (ever thought about the catholic connotations of that word?) has at least some basic knowledege of English, a language that is impregnated by millenia of Christian history anyway. As an atheist, brought up as a protestant, I have not the least difficulty in understanding what von Neumann meant. -- Nsda (talk) 17:00, 14 November 2011 (UTC)

 * There are TWO quotes. I enjoy the witty quote by Robert R. Coveyou and of course I don't want to delete it. I see no value in the smug insider remark by von Neumann, as it says nothing about PRNGs.  Ross Fraser (talk) 12:20, 30 November 2011 (UTC)

 * I am puzzled as well, in two ways. I do not consider myself religious and I'm not a native English speaker, yet it is perfectly obvious to me what "in a state of sin" would mean. In fact, if someone would directly translate it into my language it would be perfectly clear as well. The second statement that puzzles me is that you want Neumann's quote deleted but Coveyou's, for which there is no context given (though I suspect he was referring to the importance of PRGs in practice), kept. I could be convinced that the quotes are not suitable for the lead section, and should probably go somewhere towards the end of the article, but deleting any of them? No. Nageh (talk) 20:18, 14 November 2011 (UTC)

 * The Coveyou quote doesn't need context: it is a direct comment on random number generation. Ross Fraser (talk) 12:20, 30 November 2011 (UTC)

 * No, it does need context. Did Coveyou state his quote as a consequence of the problem of designing good PRNGs, or as a general statement that reproducible seemingly random numbers are important in practice? Or is it because the output of real random generators can only be probabilistically described whereas PRNGs may be required to have specific output guarantees, such as no more than x consecutive zeros, as seems to imply? Nageh (talk) 15:04, 30 November 2011 (UTC)

strfry(3) example
I don't think the flaw described in strfry(3) has anything to do with its PRNG (it does also suffer from the standard "remainder problem", but that's another usage error). Unless I'm mistaken, the sentence/reference should just be removed. --Tardis (talk) 13:14, 9 April 2012 (UTC)

 * You are right. I have removed it. Nageh (talk) 13:39, 9 April 2012 (UTC)

A mathematical definition
Maybe it's just me, but it seems there are so many symbols to explain so little. Angry bee (talk) 21:03, 14 June 2013 (UTC)

Mersenne twister can't be equidistributed
78.229.106.132 (talk) 20:01, 11 March 2014 (UTC)"Mersenne twister [...] is proven to be equidistributed ".

Wrong. What is proved in the 1998 Matsumoto's paper, is that it is equidistributed "to v-bits accuracy", not completely equidistributed. It could not be, anyway. The algorithm generates a finite list of numbers (huge, but finite), say in [a,b]. Therefore there are a lot of (very small) intervals that contain no generated numbers at all. Let [c,d] be such an interval. If you generate n numbers in [a,b], the number k(n) of generated numbers in [c,d] is zero. So the ratio k(n)/n is also zero, and can not tend to (d-c)/(b-a) when n increases.

Of course, in practice, on a computer it does not make any difference, but it may be worth noting that some algorithms (and simpler to code, in fact) generate infinite lists that are equidistributed.

Definition of pseudo-random
The article currently has this: The PRNG-generated sequence is not truly random, because it is completely determined by a relatively small set of initial values, called the PRNG's seed (which may include truly random values).

Is that correct? For example, a 63-bit LFSR has 263-1 possible seeds. Since that LFSR produces a sequence of 263-1 numbers, the set of initial values is not relatively small. As I understand it, it is not truly random because the sequence is generated algorithmically and is therefore predictable to anyone knowing the algorithm. See http://en.wiktionary.org/wiki/pseudorandom --158.158.240.230 (talk) 16:26, 23 April 2015 (UTC) Aric.

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Potential problems with deterministic generators : untrue statement to be revised
The statement "The first PRNG to avoid major problems and still run fairly quickly was the Mersenne Twister (discussed below), which was published in 1998. Other high-quality PRNGs have since been developed." is untrue and should be corrected. High-quality PRNGs existed prior to 1998, including the ACORN family of generators developed in 1984 and published in 1989 (and sans doute others), and although ignored or possbly misunderstood by the 'mainstream', they are still valid, passing all current test suites as of August 2019, while MT fails on or two in TestU01. I propose to replace this incorrect statement but other opinions would probably be a very good thing. Options include Dear fellow-wikipedians, what are your reactions to my suggestions? jw (talk) 16:10, 12 August 2019 (UTC)
 * -1- delete the incriminated statement completely
 * -2.1- replace it with a mention of ACORN and/or -2.2- other(s) as appropriate
 * -3- a more nuanced discussion of computational performance, statistical quality
 * -4- as option-3- above, extended to a discussion of the history and arguments around PRNG quality and performance

I have moderated the statement about MT being 'the first' but I'm not yet happy with this ... any reactions ? jw (talk) 15:40, 27 September 2019 (UTC)

Irrelevant material on this page
I propose to delete two separate bits of irrelevant material from this page:

1. the 'implementation' paragraph introduced here 6 month ago, giving unreferenced source-code as an example, together with a statement which may or may not be true.

2. an 'external link' to wsphynx which was introduced here two years ago (and on a few other pages from which it was removed without ceremony) - this link brings no added value to the article.

Please react before I make the changes. jw (talk) 07:33, 11 February 2023 (UTC)

title: Talk:Pseudorandom number generator


text:
Aldo Rossi

Aldo Rossi (3 May 1931 – 4 September 1997) was an Italian architect and designer who achieved international recognition in four distinct areas: architectural theory, drawing and design and also product design. He was one of the leading proponents of the postmodern movement.

He was the first Italian to receive the Pritzker Prize for architecture.

Early life
He was born in Milan, Italy. After early education by the Somascan Religious Order and then at Alessandro Volta College in Lecco in 1949, he went to the school of architecture at the Polytechnic University of Milan. His thesis advisor was Piero Portaluppi and he graduated in 1958.

In 1955, he had started writing for, and from 1959 was one of the editors of, the architectural magazine Casabella-Continuità, with the editor in chief Ernesto Nathan Rogers. Rossi left in 1964 when the chief editorship went to Gian Antonio Bernasconi. Rossi went on to work for Società magazine and Il_contemporaneo, making him one of the most active participants in the fervent cultural debate of the time.

His early articles cover architects such as Alessandro Antonelli, Mario Ridolfi, Auguste Perret and Emil Kaufmann and much of this material became part of his second book, Scritti scelti sull'architettura e la città 1956-1972 (Selected writings on architecture and the city from 1956 to 1972). He married the Swiss actress Sonia Gessner, who introduced him to the world of film and theatre. Culture and his family became central to his life. His son Fausto was active in movie-making both in front of and behind the camera. His daughter Vera was involved with theatre.

Career
He began his professional career at the studio of Ignazio Gardella in 1956, moving on to the studio of Marco Zanuso. In 1963 also he began teaching, firstly as an assistant to Ludovico Quaroni (1963) at the school of urban planning in Arezzo, then to Carlo Aymonino at the Institute of Architecture in Venice. In 1965, he was appointed lecturer at the Polytechnic University of Milan, and the following year he published The Architecture of the City, which soon became a classic of architectural literature. His professional career, initially dedicated to architectural theory and small building work took a huge leap forward when Aymonino allowed Rossi to design part of the Monte Amiata complex in the Gallaratese quarter of Milan. In 1971, he won the design competition for the extension of the San Cataldo Cemetery in Modena, which made him internationally famous.

After suspension from teaching in Italy in those politically troubled times, he moved to ETH Zurich, occupying the chair in architectural design from 1971 to 1975.

In 1973, he was director of the International Architecture Section at the XV Milan Triennial Exhibition of Decorative Arts and Modern Architecture, where he presented, among others, his student Arduino Cantafora. Rossi's design ideas for the exhibition are explained in the International Architecture Catalogue and in a 16mm documentary Ornament and crime directed by Luigi Durissi and produced along with Gianni Braghieri and Franco Raggi. In 1975, Rossi returned to the teaching profession in Italy, teaching architectural composition in Venice.

In 1979, he was made a member of the prestigious Academy of Saint Luke. Meanwhile, there was international interest in his skills. He taught at several universities in the United States, including Cooper Union in New York City and Cornell University in Ithaca (New York State). At Cornell, he participated in the Institute for Architecture and Urban Studies joint venture with New York's Museum of Modern Art, travelling to China and Hong Kong and attending conferences in South America.

In 1981, he published his autobiography, A scientific autobiography. In this work the author, "in discrete disorder", brings back memories, objects, places, forms, literature notes, quotes, and insights and tries to "... go over things or impressions, describe, or look for ways to describe." In the same year, he won first prize at the international competition for the design of an apartment block on the corner of Kochstraße and Wilhelmstraße in central Berlin.

In 1984, together with Ignazio Gardella and Fabio Reinhart, he won the competition for the renovation of the Teatro Carlo Felice in Genoa, which was not fully completed until 1991. In 1985 and 1986, Rossi was director of the 3rd (respectively 4th) International Architecture Exhibition at the Venice Biennale including further away display spaces such as Villa Farsetti in Santa Maria di Sala.

In 1987, he won two international competitions: one for a site at the Parc de la Villette in Paris, the other for the Deutsches Historisches Museum in Berlin, which was never brought to fruition. In 1989, he continued product design work for Unifor (now part of Molteni Furniture) and Alessi. His espresso maker La Cupola, designed for Alessi came out in 1988.

In 1990, he was awarded the Pritzker Prize. The city of Fukuoka in Japan honoured him for his work on the hotel complex The Palace and he won the 1991 Thomas Jefferson Medal in Public Architecture from the American Institute of Architects. These prestigious awards were followed by exhibitions at the Centre Georges Pompidou in Paris, the Beurs van Berlage in Amsterdam, the Berlinische Galerie in Berlin and the Museum of Contemporary Art in Ghent, Belgium.

In 1996, he became an honorary member of the American Academy of Arts and Letters and the following year he received their special cultural award in architecture and design. He died in Milan on 4 September 1997, following a car accident. Posthumously he received the Torre Guinigi prize for his contribution to urban studies and the Seaside Prize of the Seaside Institute, Florida, where he had built a detached family home in 1995.

On appeal, his proposals won the 1999 competition for the restoration of the Teatro La Fenice, Venice and it reopened in 2004. In 1999, the Faculty of Architecture of the University of Bologna, based in Cesena, was named after him.

Work
His earliest works of the 1960s were mostly theoretical and displayed a simultaneous influence of 1920s Italian modernism (see Giuseppe Terragni), classicist influences of Viennese architect Adolf Loos, and the reflections of the painter Giorgio de Chirico. A trip to the Soviet Union to study Stalinist architecture also left a marked impression.

In his writings, Rossi criticized the lack of understanding of the city in current architectural practice. He argued that a city must be studied and valued as something constructed over time; of particular interest are urban artifacts that withstand the passage of time. Rossi held that the city remembers its past (our "collective memory"), and that we use that memory through monuments; that is, monuments give structure to the city. Inspired by the persistence of Europe's ancient cities, Rossi strove to create similar structures immune to obsolescence.

He became extremely influential in the late 1970s and 1980s, as his body of built work expanded and his theories were promoted in his books The Architecture of the City (L'architettura della città, 1966) and A Scientific Autobiography (Autobiografia scientifica, 1981). The largest of Rossi's projects in terms of scale was the San Cataldo Cemetery, in Modena, Italy, which began in 1971, but is yet to be completed. Rossi referred to it as a "city of the dead".

The distinctive independence of his buildings is reflected in the micro-architectures of the products designed by Rossi. In the 1980s, Rossi designed stainless steel cafetières and other products for Alessi, Pirelli, and others.

Exhibits
For the Venice Biennale in 1979, Rossi designed a floating Teatro del Mondo that seated 250 people. For the Venice Biennale in 1984, he designed a triumphal arch at the entrance to the exhibition site. In 2006 two pylons based on an original 1989 design by Aldo Rossi were erected in front of the Bonnefanten Museum in Maastricht by the Delft architectural firm Ufo Architecten. The MAXXI museum in Rome staged a retrospective titled Aldo Rossi, The Architect and the Cities in 2021.

Awards
Aldo Rossi won the prestigious Pritzker Prize for architecture in 1990. Ada Louise Huxtable, architectural critic and Pritzker juror, has described Rossi as "a poet who happens to be an architect."

Architecture

 * 1960 Villa ai Ronchi in Versilia
 * 1962 Competition for the Monument to the Resistance in Cuneo
 * 1964 Competition for the new Paganini theatre and Piazza della Pilotta in Parma
 * 1964 Bridge for the Triennale in Milan
 * 1965 Monumental fountain at Segrate
 * 1966 Competition for the district of San Rocco in Monza
 * 1967-74 Monte Amiata complex, Gallaratese Quarter, Milan, with Carlo Aymonino
 * 1968 Design for the town hall in Scandicci
 * 1971-84 Ossuary and the Cemetery of San Cataldo in Modena
 * 1972 Design for City Hall Muggiò
 * 1972 Primary school in Fagnano Olona
 * 1973 Documentary movie "Ornament and crime" for the Triennale in Milan
 * 1974 Design for the regional council headquarters and for a student residence in Trieste
 * 1976 Design for a student residence in Chieti
 * 1977 Design for a business centre in Florence
 * 1977 Single-family homes in Mozzo
 * 1978 Teatrino scientifico
 * 1979 The floating 250 seat Teatro del Mondo and triumphal arch, both built for the Venice Biennale
 * 1979 Apartments in Südliche Friedrichstadt for the exhibition IBA 84 in West Berlin, Germany
 * 1979 Torri shopping centre in Parma
 * 1979 Middle school in Broni, with Arduino Cantafora
 * 1979 Monumental tower, Melbourne, Australia
 * 1981-1988 Berlin Block on Kochstraße at its junction with Wilhelmstraße in Berlin, Germany
 * 1982 Head Office of Fontivegge in Perugia
 * 1982 House Pocono Pines, Mount Pocono in Pennsylvania, USA
 * 1982 Isle of Elba cabins for Bruno Longoni
 * 1983 Design for the town hall of Borgoricco
 * 1984-1987 Casa Aurora, home of GFT Financial Textile Group, Turin
 * 1984 Preparation for the Pitti-Uomo men's fashion event in Florence
 * 1984-1991 Renovation of Teatro Carlo Felice, Genoa
 * 1985 Preparation of a trade exhibition stand for GFT Financial Textile Group, Turin
 * 1985 Residential building in the Vialba quarter of Milan
 * 1986-1989 Palace Hotel in Fukuoka, Japan
 * 1986 South Villette in Paris, France
 * 1987 Lighthouse Theatre, Toronto
 * 1988-91 Hotel Duca di Milano, Milan
 * 1988-90 Monument to Sandro Pertini, Milan
 * 1989 de Lamel appartements, the Hague, Netherlands
 * 1989 Urban plan for the greater urban area Pisorno, Tirrenia (Pisa)
 * 1990-1992 Residential building and former industrial area, Città di Castello
 * 1990-1993 Club House of the Cosmopolitan Golf Club in Tirrenia (Pisa)
 * 1990 Social health complex in via Canova in Florence
 * 1991 Administrative building for The Walt Disney Company in Orlando, Florida
 * 1991 Contemporary arts centre on the island of Vassivière in Beaumont-du-Lac, France
 * 1991 Redevelopment of former industrial cotton mill Cantoni in Castellanza as the main campus of the University Carlo Cattaneo
 * 1991 Post office and apartments near the City of Music in Paris (19th arrondissement), France
 * 1992 Reconstruction of the Teatro Carlo Felice in Genoa with Ignazio Gardella
 * 1993 Personal Florentine wardrobe for Bruno Longoni
 * 1994-1998 Schützenstraße quarter, Berlin (photographs)
 * 1995 Bonnefantenmuseum in Maastricht, Netherlands
 * 1995 Regeneration of the former Kursaal area in Montecatini
 * 1996 Complex for a magazine in Berlin, Germany
 * 1996 Ca' di Cozzi central district in Verona
 * 1996-1998 Mojiko Hotel, Kitakyushu, Japan
 * 1997 Design for the Arts Factory district in Bologna
 * 1997 Terranova shopping centre, Olbia, Sardinia
 * 1999-2004 Refurbishment of Teatro La Fenice, Venice
 * 2000 Riverside Building at the Walt Disney Studios, Burbank, California
 * 2001 Scholastic Corporation Headquarters, New York City, USA

Product design
In addition to architecture, Rossi created product designs, including:

 * 1982 The Conical coffee maker and kettle for Alessi
 * 1983 Teatro chair for Molteni Group with the collaboration of Luca Meda;
 * 1987 Milan chair for Molteni Group;
 * 1988 La Cupola coffee maker for Alessi;
 * 1988 Il Conico tea kettle for Alessi;
 * 1989 Paris chair for Unifor now part of Molteni Group;
 * 1989 Decartes bookshelf for Unifor now part of Molteni Group;
 * 1989 Consiglio table for Unifor now part of Molteni Group;
 * 1989 Moment clock for Alessi.

Publications

 * L'architettura della città (The Architecture of the City), Padua: Marsilio 1966.
 * Scritti scelti sull'architettura e la città: 1956-1972 (Selected Writings on architecture and the city: 1956-1972), edited by R. Bonicalzi, Milan: ULC, 1975.
 * Autobiografia scientifica (A scientific autobiography), Parma: Practices, 1990.

license: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/4.0/

title: Aldo Rossi


text:
Alessi (Italian company)

Alessi is a housewares and kitchen utensil company in Italy, manufacturing and marketing everyday items authored by a wide range of designers, architects, and industrial designers — including Achille Castiglioni, Richard Sapper, Marco Zanuso, Alessandro Mendini, Ettore Sottsass, Wiel Arets, Zaha Hadid, Toyo Ito, Hani Rashid, Tom Kovac, Greg Lynn, MVRDV, Jean Nouvel, UN Studio, Michael Graves, and Philippe Starck. The Alessi company in the UK is worth around £2.4 million.

History
Alessi was founded in 1921 by Giovanni Alessi who was born in Italy and raised in Switzerland. A few years after World War I, Alessi started with producing a wide range of tableware items in nickel, chromium and silver-plated brass. The company began when Carlo Alessi (born 1916), the son of Giovanni, was named chief designer. Between 1935 and 1945 he developed most of the products Alessi released.

1950s and 1960s
In 1969 the company was under the leadership of Carlo Alessi. It was his brother Luigi who introduced the collaboration with external designers in 1955. With some architects, he designed several items that were created for the hotel needs. He helped introduce many best-sellers, such as the historical series of wire baskets. From 1957 by Luigi Massaroni and Carlo Mazzeri. This was designed in a series with an Ice bucket and Ice tongs as part of the Program 4 for the 11 Triennale in Milan. This was the first time that the Alessi products got shown with manufactured goods. The 1950s were a difficult time as it was only a few years after World War II and many people could not afford to buy designer objects.

1970s and 1980s
In 1970, Alberto Alessi was responsible for the third transformation of the company. Alessi was considered one of the "Italian Design Factories". In this decade under the leadership of Alberto Alessi the company collaborated with some design maestros like Achille Castiglioni, Richard Sapper, Alessandro Mendini, and Ettore Sottsass. In the 1970s, Alessi produced the Condiment set (salt, pepper and toothpicks) by Ettore Sottsass, the Espressomaker by Sapper.

The 1980s marked a period in which Italian design factories had to compete with mass production. These movements had a different view on design, for the Italian design factories the design and therefore the designer was the most important part of the process while for the mass production the design had to be functional and easy to be reproduced. Also in the 1980s, they changed their marketing image from factory to industrial research lab, a place for research and production. For Alessi the 1980s are marked with some designs like the Two tone kettle by Sapper, their first cutlery set Dry by Castiglioni. Alessi collaborated with new designers, including Aldo Rossi, Michael Graves, and Philippe Starck, who have been responsible for the some of Alessi's all-time bestsellers like the kettle with a bird whistle by Graves.

Alessi faced increasing competition from other international manufacturers, especially in lower-cost products mass-produced for retailers such as Target Corporation and J. C. Penney.

1990s
In the 1990s, Alessi started to work more with plastics, at the request of designers who found it an easier material to work with than metal, offering more design freedom and innovative possibilities. The 1990s were marked by the theme "Family Follows Fiction", with playful and imaginative objects. Artists designing for this theme included Stefano Giovannoni and Alessandro Mendini, who designed Fruit Mama and the bestseller Anna G. Metal still remained a popular material, for example the Girotondo family by King Kong.

2000s
During the 2000s, Alessi collaborated with several architects for its "coffee and tea towers", with a new generation of architects, including Wiel Arets, Zaha Hadid, Toyo Ito, Tom Kovac, Greg Lynn, MVRDV, Jean Nouvel, and UN Studio. These sets had a limited production of 99 copies. Another design in the 2000s was the Blow Up series by Fratelli Campana. The brothers played with form and shape to create baskets and other objects that look like they would fall apart when touched.

In 2006, the company reclassified its products under three lines: "A di Alessi", "Alessi", and "Officina Alessi". A di Alessi is more "democratic" and more "pop", the lower price range of Alessi. Officina Alessi is more exclusive, innovative, and experimental, marked by small-batch production series and limited series.

in 2007, Hani Rashid and Lise Anne Couture Asymptote Architecture (New York) designed the New York city flagship store for Alessi in the SoHo neighborhood on Greene Street. The space featured an Alessi gallery, espresso bar and retail in a renovated historic loft building. Asymptote was responsible for not only the interior design of the space but also branding and the graphic identity, updating Alessi's image from its 1980s Postmodern style to a contemporary architectural ethos.

Alessi products are on display in museums worldwide, including the Museum of Modern Art (New York), the Metropolitan Museum of Art, the Victoria and Albert Museum, the Pompidou Centre, the Design Museum Holon, and the Stedelijk Museum Italy. A collaboration with the National Palace Museum of Taiwan produced a collection of various kitchenware products with Asian themes.

Designers and their designs
From 1945 until today, Alessi has collaborated with designers and even other brands or companies for their products. Some key designs and their designers:
 * 1945 Bombé tea and coffee service by Carlo Alessi Anghini
 * 1978 Condiment set (salt, pepper and toothpicks) by Ettore Sottsass
 * 1979 Programma 5 barware by Ettore Sottsass
 * 1979 9090 espresso maker by Richard Sapper. This design won the first Compasso d'Oro award for Alessi.
 * 1982 Dry flatware/cutlery by Achille Castiglioni the first cutlery produced by Alessi
 * 1983 Bollitore whistling water kettle by Richard Sapper. Alessi's first "designer kettle", with a whistle whose pipe sings two tones, mi and si, in harmony
 * 1984 La Conica by Aldo Rossi. This was Rossi's first mass-production design and its image earned immediate success for the then-new Officina Alessi brand, as well as becoming a 1980s design symbol. Therefore, it was soon to be followed by more Rossi designs in this theme.
 * 1985 Kettle by Michael Graves. The Graves' kettle is known for its singing bird when the water boils. Followed by matching products like a sugar bowl and a creamer, also designed by Graves. This product has sold the greatest number of units in the history of the company.
 * 1987 Nuovo Milano cutlery set designed by Ettore Sottsass with assistance of Alberto Gozzi. Won XVIth Compasso d'oro award in 1991.
 * 1988 Pito kettle by Frank Gehry
 * 1989 Girotondo family by King-Kong
 * 1989 Hot Bertaa kettle by Philippe Starck
 * 1990 Juicy Salif by Philippe Starck
 * 1993 Fruit Mama by Stefano Giovannoni. The first design for the Family Follows Fiction series; noteworthy for its aesthetic juxtaposition of plastic and stainless steel.
 * 1994 Anna G corkscrew by Alessandro Mendini. A best seller since it was first produced, with its smiling face, it engendered the Anna family of related objects for the table and kitchen.
 * 1995 Mary Biscuit by Stefano Giovannoni. Biscuit or cookie container.
 * 1997 Nono di Antonio garlic crusher by Guido Venturini
 * 2004 Blow Up range of baskets and citrus holders by Fratelli Campana
 * 2006 Kaj watch by Karim Rashid
 * 2013 Dressed dinnerware and flatware by Marcel Wanders
 * 2015 Collo Alto cutlery set by Inga Sempé
 * 2017 Forma cheese grater by Zaha Hadid

Critical reception
Although Alessi is credited with introducing many iconic design objects, critics have also complained about items designed for everyday household use, which do not perform their basic functions well.

title: Alessi (Italian company)