On May 1, 9:54=A0am, VK <schools_r...@yahoo.com> wrote: > Assuming one needs to have a function returning false or true on each > call in pseudo-random order.and using JavaScript native Math.random() > method as the basis of the pseudo-randomness. Say the variants of such > function are: > > getAnswer1() { > =A0var n =3D Math.round(Math.random()); > =A0return n ? true : false; > > } > > getAnswer2() { > =A0var n =3D Math.floor(Math.random()*2); > =A0return (n=3D=3D2) ? true : false; > > } > > Leaving obvious practical testing by platforms aside: > > Is there are theoretical considerations that pseudo-randomness > (predictability) of either of above will be better or worse than the > other one? JavaScript Kit site claims that the second bits first: > =A0http://www.javascriptkit.com/javatutors/randomnum.shtml > but they don't disclose the underlaying reasoning. Why not { return Math.random() >=3D 0.5; } ? -- Jorge.

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5/1/2010 9:30:58 AM

On May 1, 1:30=A0pm, Ry Nohryb <jo...@jorgechamorro.com> wrote: > On May 1, 9:54=A0am, VK <schools_r...@yahoo.com> wrote: > > > > > Assuming one needs to have a function returning false or true on each > > call in pseudo-random order.and using JavaScript native Math.random() > > method as the basis of the pseudo-randomness. Say the variants of such > > function are: > > > getAnswer1() { > > =A0var n =3D Math.round(Math.random()); > > =A0return n ? true : false; > > > } > > > getAnswer2() { > > =A0var n =3D Math.floor(Math.random()*2); > > =A0return (n=3D=3D2) ? true : false; > > > } > > > Leaving obvious practical testing by platforms aside: > > > Is there are theoretical considerations that pseudo-randomness > > (predictability) of either of above will be better or worse than the > > other one? JavaScript Kit site claims that the second bits first: > > =A0http://www.javascriptkit.com/javatutors/randomnum.shtml > > but they don't disclose the underlaying reasoning. > > Why not { return Math.random() >=3D 0.5; } ? I have no idea. The linked source at http://www.javascriptkit.com/javatutors/randomnum.shtml claims this: "Some of you may be curious as to why Math.floor(), instead of Math.round(), is used in the above code. While both successfully round off its containing parameter to an integer within the designated range, Math.floor does so more "evenly", so the resulting integer isn't lopsided towards either end of the number spectrum. In other words, a more random number is returned using Math.floor()." It may be some actual behavior or an author's fantasy - no arguments are given on the page. From the Math.round and Math.floor methods descriptions: https://developer.mozilla.org/En/Core_JavaScript_1.5_Reference/Objects/Mat= h/Round Returns the value of a number rounded to the nearest integer. https://developer.mozilla.org/En/Core_JavaScript_1.5_Reference/Objects/Mat= h/Floor Returns the largest integer less than or equal to a number. I am failing to grasp the exact difference between of them. I only assume that the only place of rounding inequality results could be in "border cases" like 0.5xxxxxx etc. so with .5 being the first fractional digit. Respectively if such inequality really exists then there must be something with pseudo-random generation in whole or in how it is implemented in Math.random() that would suggest 0.5xxxxx or 0.5 generation being lesser random than other results. Or it is just another urban legend.

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5/1/2010 9:49:07 AM

On May 1, 1:49=A0pm, VK <schools_r...@yahoo.com> wrote: > =A0https://developer.mozilla.org/En/Core_JavaScript_1.5_Reference/Object.= ... > =A0Returns the value of a number rounded to the nearest integer. > > =A0https://developer.mozilla.org/En/Core_JavaScript_1.5_Reference/Object.= ... > =A0Returns the largest integer less than or equal to a number. > > I am failing to grasp the exact difference between of them. I only > assume that the only place of rounding inequality results could be in > "border cases" like 0.5xxxxxx etc. so with .5 being the first > fractional digit. Respectively if such inequality really exists then > there must be something with pseudo-random generation in whole or in > how it is implemented in Math.random() that would suggest 0.5xxxxx or > 0.5 generation being lesser random than other results. Or it is just > another urban legend. Another direction to look for is that the computer pseudo-random generation operates in non-closed properly set [0,1[ with the upper border not included so the result can be 0 but never 1. That shifts the predictability pattern down toward 0. This is why actually why Shannon's Clairvoyant can quickly tell for any sequence is it's truly random or pseudo-random. btw Wiki's http://en.wikipedia.org/wiki/Pseudorand= om_function_family claim that "No efficient algorithm can distinguish (with significant advantage) between a function chosen randomly from the PRF family" is a complete b.s. but I am too lazy to argue with the entire ACM. Let them believe what they want to believe. So it might be that Math.floor somehow "re-balance" the outcome making it lesser predictable. I just don't see how could it be. I am really puzzled... Maybe I should get all JavaScript stuff out and post it as a purely math question to sci.math

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5/1/2010 10:20:04 AM

On May 1, 2:20=A0pm, VK <schools_r...@yahoo.com> wrote: > So it might be that Math.floor somehow "re-balance" the outcome making > it lesser predictable. I just don't see how could it be. I am really > puzzled... Maybe I should get all JavaScript stuff out and post it as > a purely math question to sci.math Posted at sci.math as a mathematical problem: http://groups.google.com/group/sci.math/browse_frm/thread/5846c8a74170acfd

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5/1/2010 10:50:55 AM

VK" wrote: > Assuming one needs to have a function returning false or true > on each call in pseudo-random order. ... <snip> > function are: > > getAnswer1() { > var n = Math.round(Math.random()); > return n ? true : false; > } > > getAnswer2() { > var n = Math.floor(Math.random()*2); > return (n==2) ? true : false; > } > > Leaving obvious practical testing by platforms aside: <snip> You leave practical testing aside far to often in your posted code. Any reasonable testing (or your just understanding the methods/operations employed) would observe that your proposed - getAnswer2 - function only ever returns false. Thus, it fails to satisfy your "returning false or true on each call in pseudo-random order". > Is there are theoretical considerations that pseudo-randomness > (predictability) of either of above will be better or worse than > the other one? Yes, but mostly because the obvious bugs in the second prevent it from doing anything useful at all. > JavaScript Kit site claims that the second bits first: > http://www.javascriptkit.com/javatutors/randomnum.shtml > but they don't disclose the underlaying reasoning. The subject of the comments on that page is the choice of the use of Math.floor over Math.round (where Math.round is commonly used in example javascript random number generators found on the Internet). Math.random returns a (pseudo-random) number that is in the range zero to less than one (i.e. anything non-negative that is smaller than one). If you multiply that number by an integer you will get a result that is in the range from zero to less than that number. If two were taken as an example of such a number (i.e. - (Math.random * 2) - the result would be a number in the range zero to less than two. If you apply - Math.round - to all the numbers in the range zero to less than two the range zero to <0.5 (a quarter of the total range) would result in zero, between 0.5 and <1.5 (half the total range) would result in one, and 1.5 to <2 would result in two. So, using Math.round, a random number in the 0 to <2 range has a 25% chance of coming our zero, a 50% chance of coming out one and a 25% chance of coming out 2. This is not an even distribution. (Extending this to multiplying by any positive integer; it is the values at the two extremes of output that end up being half as likely in the output as any numbers in between, however if that integer were one then there would be no numbers in between the extremes of the range and so then the distribution between zero and one would be equal.) If you apply - Math.floor - to numbers in the range 0 to <2 then the range 0 to <1 (half the original range) result in 0 and the range 1 to <2 (the other half of the original range) result in 1; a 50/50 distribution. Richard.

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5/1/2010 11:16:35 AM

VK wrote: >On May 1, 1:30 pm, Ry Nohryb wrote: >> On May 1, 9:54 am, VK wrote: >>> Assuming one needs to have a function returning false or true >>> on each call in pseudo-random order.and using JavaScript native >>> Math.random() method as the basis of the pseudo-randomness. Say >>> the variants of such function are: >> >>> getAnswer1() { >>> var n = Math.round(Math.random()); >>> return n ? true : false; ><snip> >> Why not { return Math.random() >= 0.5; } ? > > I have no idea. The linked source at > http://www.javascriptkit.com/javatutors/randomnum.shtml > claims this: "Some of you may be curious as to why Math.floor(), > instead of Math.round(), Given that there has been a prevalence of examples of javascript (so- called) random number generators posted to the web that did use Math.round and did then produce a non-even distribution of numbers in their output, a fair number of readers of that article may well be curious about its author's choice. > is used in the above code. While both successfully round off > its containing parameter to an integer within the designated > range, This bit isn't actually true as if you did a direct substitute of - Math.round - for - Math.floor - then the range of the output would increase by one. > Math.floor does so more "evenly", so the resulting integer > isn't lopsided towards either end of the number spectrum. "Lopsided" is probably inappropriate as well, as the output distribution following a substitution of - Math.random - for - Math.floor - is still symmetrical. > In other words, a more random number is returned using > Math.floor()." > > It may be some actual behavior or an author's fantasy Most likely an overlay hurried explanation of a common fault in javascript authoring, with a couple of mistakes getting in the way of making the point. > - no arguments are given on the page. From the Math.round > and Math.floor methods descriptions: > > https://developer.mozilla.org/En/Core_JavaScript_1.5_Reference/Objects/Math/Round > Returns the value of a number rounded to the nearest integer. > > https://developer.mozilla.org/En/Core_JavaScript_1.5_Reference/Objects/Math/Floor > Returns the largest integer less than or equal to a number. > > I am failing to grasp the exact difference between of them. Then you are the author of:- <URL: http://groups.google.com/group/comp.lang.javascript/browse_frm/thread/b495b4898808fde0/63c2ad2bdbdf0b40 > - so we know the subtleties of rounding in javascript don't have to get that subtle before you cannot comprehend them. > I only assume ... <snip> Don't waste you time in assuming. The best you will do is invent an elaborate fantasy explanation. Just wait for someone to tell you the answer, and then avoid ever trying to put it into your own words. Richard.

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5/1/2010 11:37:37 AM

On May 1, 3:16=A0pm, "Richard Cornford" <Rich...@litotes.demon.co.uk> wrote: > You leave practical testing aside far to often in your posted code. Any > reasonable testing (or your just understanding the methods/operations > employed) would observe that your proposed - getAnswer2 - function only > ever returns false. Thus, it fails to satisfy your "returning false or > true on each call in pseudo-random order". Yeah... My mind was distracted a lot by the binary trees observations, sorry. > > Is there are theoretical considerations that pseudo-randomness > > (predictability) of either of above will be better or worse than > > the other one? > > Yes, but mostly because the obvious bugs in the second prevent it from > doing anything useful at all. > > > JavaScript Kit site claims that the second bits first: > >http://www.javascriptkit.com/javatutors/randomnum.shtml > > but they don't disclose the underlaying reasoning. > > The subject of the comments on that page is the choice of the use of > Math.floor over Math.round (where Math.round is commonly used in example > javascript random number generators found on the Internet). > > Math.random returns a (pseudo-random) number that is in the range zero > to less than one (i.e. anything non-negative that is smaller than one). > If you multiply that number by an integer you will get a result that is > in the range from zero to less than that number. If two were taken as an > example of such a number (i.e. - (Math.random * 2) - the result would be > a number in the range zero to less than two. > > If you apply - Math.round - to all the numbers in the range zero to less > than two the range zero to <0.5 (a quarter of the total range) would > result in zero, between 0.5 and <1.5 (half the total range) would result > in one, and 1.5 to <2 would result in two. So, using Math.round, a > random number in the 0 to <2 range has a 25% chance of coming our zero, > a 50% chance of coming out one and a 25% chance of coming out 2. This is > not an even distribution. (Extending this to multiplying by any positive > integer; it is the values at the two extremes of output that end up > being half as likely in the output as any numbers in between, however if > that integer were one then there would be no numbers in between the > extremes of the range and so then the distribution between zero and one > would be equal.) > > If you apply - Math.floor - to numbers in the range 0 to <2 then the > range 0 to <1 (half the original range) result in 0 and the range 1 to > <2 (the other half of the original range) result in 1; a 50/50 > distribution. Right. Similar answer from sci.math : http://groups.google.com/group/sci.math/msg/5a878f7a0aea0b90 <quote> Reply concerning this page, and not your description. Let X be uniformly distributed in [0,1). Then floor(X*11) takes values 0,1,...,10 each with probability 1/11 ... that is what the page means by "even". However round(X*10) takes value 0 with probability 1/20, values 1,...,9 each with probability 1/10 and value 10 with probability 1/20. Not "even" according to the page. </quote> So the question is then a) if it is possible to use Math.floor for a pseudo-random input to get binary output (1/0, true/false) b) if so than will it be more even probability for output than for Math.round(Math.random()) or (Math.random >=3D 0.5) .... or Math.floor(Math.random()*N) benefits appear only for ternary and wider ranges "0 or 1 or 2", "0 or 1 or 2 or 3" etc. ?

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5/1/2010 11:38:01 AM

On May 1, 3:37=A0pm, Henry <rcornf...@raindrop.co.uk> wrote: > > It may be some actual behavior or an author's fantasy > > Most likely an overlay hurried explanation of a common fault in > javascript authoring, with a couple of mistakes getting in the way of > making the point. Not so. A probability theory outcome: see my answer to Richard Cornford > >https://developer.mozilla.org/En/Core_JavaScript_1.5_Reference/Object... > > Returns the value of a number rounded to the nearest integer. > > >https://developer.mozilla.org/En/Core_JavaScript_1.5_Reference/Object... > > Returns the largest integer less than or equal to a number. > > > I am failing to grasp the exact difference between of them. > > Then you are the author of:- > > <URL:http://groups.google.com/group/comp.lang.javascript/browse_frm/threa= d... > > > > - so we know the subtleties of rounding in javascript don't have to > get that subtle before you cannot comprehend them. First of all that was about IEEE-754 FP-DP rounding and calculation vs. top level methods - not about the probability theory and how does it apply to JavaScript Math methods. And yes, I couldn't grasp how Math.floor would be more "even probability-friendly" than Math.round until I got explanations of that. I don't see you grasping it on the spot as your answer is silent about it. At least your first guess quoted at the top was wrong.

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5/1/2010 11:54:55 AM

VK wrote: >On May 1, 3:16 pm, Richard Cornford wrote: >> You leave practical testing aside far to often in your posted code. >> Any reasonable testing (or your just understanding the >> methods/operations employed) would observe that your proposed - >> getAnswer2 - function only ever returns false. Thus, it fails to >> satisfy your "returning false or true on each call in pseudo-random >>order". > > Yeah... My mind was distracted a lot by the binary trees > observations, sorry. The thousandth excuse for making the same mistake isn't any more convincing than the second. <snip> >> ... , however if that integer were one then there would be no numbers >> in between the extremes of the range and so then the distribution >> between zero and one would be equal.) <snip> >Right. Similar answer from sci.math : > http://groups.google.com/group/sci.math/msg/5a878f7a0aea0b90 <snip> Unsurprisingly. > So the question is then > a) if it is possible to use Math.floor for a pseudo-random input to > get binary output (1/0, true/false) Strange question; of course it is possible. > b) if so than will it be more even probability for output than for > Math.round(Math.random()) or (Math.random >= 0.5) Properly implemented, there should be no difference. A bias towards the numbers that are not at the ends of the range of output does not apply when all of the possible outputs are at the ends of their range. >... or Math.floor(Math.random()*N) benefits appear only for ternary >and wider ranges "0 or 1 or 2", "0 or 1 or 2 or 3" etc. ? The issue only applies to rages with more than two values in them. But still, Jorge's remains the better implementation for javascript (FPU handled math operation over a method call), and it uses neither Math.round nor Math.floor. Richard.

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5/1/2010 12:02:12 PM

On May 1, 4:02=A0pm, "Richard Cornford" <Rich...@litotes.demon.co.uk> wrote: > >... or Math.floor(Math.random()*N) benefits appear only for ternary > >and wider ranges "0 or 1 or 2", "0 or 1 or 2 or 3" etc. ? > > The issue only applies to rages with more than two values in them. But > still, Jorge's remains the better implementation for javascript (FPU > handled math operation over a method call), and it uses neither > Math.round nor Math.floor. Then would it be properly to state that in order to have the least compromised pseudo-random sequence of integers from a set of two elements one should use return (Math.random() >=3D 0.5) ? _this : _that; and for all sets with more than two elements one should use return Math.floor( n * Math.random() ); where the range is [0, n-1] Would it be appropriate to correct this in the FAQ http://www.jibbering.com/faq/#randomNumber and maybe add a short math explanation note based on the sci.math post so not leaving reader to wonder why the hey floor() and what's wrong with round() ?

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5/1/2010 12:17:38 PM

On Sat, 1 May 2010 at 02:49:07, in comp.lang.javascript, VK wrote: >On May 1, 1:30�pm, Ry Nohryb <jo...@jorgechamorro.com> wrote: <snip> >From the Math.round and Math.floor methods >descriptions: > > https://developer.mozilla.org/En/Core_JavaScript_1.5_Reference/Objects >/Math/Round > Returns the value of a number rounded to the nearest integer. > > https://developer.mozilla.org/En/Core_JavaScript_1.5_Reference/Objects >/Math/Floor > Returns the largest integer less than or equal to a number. > >I am failing to grasp the exact difference between of them. <snip> In case anyone has been confused by VK here are some facts. round 0.9 is 1.0 floor 0.9 is 0.0 John -- John Harris

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5/1/2010 5:21:23 PM

On Sat, 1 May 2010 at 05:17:38, in comp.lang.javascript, VK wrote: <snip> > return (Math.random() >= 0.5) ? _this : _that; <snip> >Would it be appropriate to correct this in the FAQ <snip> The FAQ is correct already. Would beginners benefit from seeing a slightly faster routine for a special case ? John -- John Harris

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5/1/2010 5:25:10 PM

VK <schools_ring@yahoo.com> writes: > Assuming one needs to have a function returning false or true on each > call in pseudo-random order.and using JavaScript native Math.random() > method as the basis of the pseudo-randomness. Say the variants of such > function are: > > getAnswer1() { > var n = Math.round(Math.random()); > return n ? true : false; > } > > getAnswer2() { > var n = Math.floor(Math.random()*2); > return (n==2) ? true : false; As stated elsewhere, this should read return (n == 1) ? true : false; or, preferably, return n == 1; > } > > Leaving obvious practical testing by platforms aside: > > Is there are theoretical considerations that pseudo-randomness > (predictability) of either of above will be better or worse than the > other one? No, they are (obviously?) exactly identical. They map exactly the same results of Math.random() to true and false respectively. In both cases, a value in the range [0..0.5[ is mapped to false and a value in the range [0.5..1[ is mapped to true. > JavaScript Kit site claims that the second bits first: > http://www.javascriptkit.com/javatutors/randomnum.shtml > but they don't disclose the underlaying reasoning. I guess their point is that to generate an integer in the range [0..n[, Math.floor(Math.random() * n) is better, in general, than Math.round(Math.random() * (n - 1)) .... which is pretty old news (not that people still don't bungle it regularly, but it's embarrasing every time it happens). The funny thing is that for n = 2, the unevenness of using the Math.round doesn't matter, which is the case you are asking about. -- Lasse Reichstein Holst Nielsen 'Javascript frameworks is a disruptive technology'

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5/1/2010 7:30:44 PM

Lasse Reichstein Nielsen wrote on 01 mei 2010 in comp.lang.javascript: > As stated elsewhere, this should read > return (n == 1) ? true : false; > or, preferably, > return n == 1; > or: return !n-1; -- Evertjan. The Netherlands. (Please change the x'es to dots in my emailaddress)

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5/1/2010 9:20:52 PM

On May 1, 11:20=A0pm, "Evertjan." <exjxw.hannivo...@interxnl.net> wrote: > Lasse Reichstein Nielsen wrote on 01 mei 2010 in comp.lang.javascript: > > > As stated elsewhere, this should read > > =A0 =A0return (n =3D=3D 1) ? true : false; > > or, preferably, > > =A0 =A0return n =3D=3D 1; > > or: > > return !n-1; return !n; -- Jorge.

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5/2/2010 10:32:32 AM

VK : > Shannon's Clairvoyant can quickly tell for any sequence is it's > truly random or pseudo-random. Of course not. It is quite difficult to define "random" and "pseudo- random" in a precise and satisfactory way, but an essential part of any reasonable definition is that there is no quick way to tell the difference given the sequences. What you call "Shannon's Clairvoyant" (I don't know it by that name from any other source than you) is a rather clever illustration of the shortcomings of *humans* as sources of random or pseudo-random sequences, nothing more. Computers are much better, and easily defeat your "clairvoyant". > btw Wiki's http://en.wikipedia.org/wiki/Pseudorandom_function_family > claim that "No efficient algorithm can distinguish (with significant > advantage) between a function chosen randomly from the PRF family" > is a complete b.s. No, it is a sensible definition. > but I am too lazy to argue with the entire ACM. Perhaps some lingering remains of sanity, as well, like when you chickened out of a bet you proposed yourself on the subject. Some part of you may dimly realise that some people actually know more about the subject than you. Still, I am curious to see your implementation of "Shannon's Clairvoyant" when you finish it, even if does not allow me to win $10,000 against the loss of $10 according to the flip of a coin. -- Johannes

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5/2/2010 11:48:37 AM

In comp.lang.javascript message <1b5852ed-217d-4b0a-8952-1212f96c5107@i9 g2000yqi.googlegroups.com>, Sat, 1 May 2010 00:54:03, VK <schools_ring@yahoo.com> posted: >Assuming one needs to have a function returning false or true on each >call in pseudo-random order.and using JavaScript native Math.random() >method as the basis of the pseudo-randomness. Say the variants of such >function are: > >getAnswer1() { > var n = Math.round(Math.random()); > return n ? true : false; >} > >getAnswer2() { > var n = Math.floor(Math.random()*2); > return (n==2) ? true : false; >} That one always returns false. >Leaving obvious practical testing by platforms aside: > >Is there are theoretical considerations that pseudo-randomness >(predictability) of either of above will be better or worse than the >other one? JavaScript Kit site claims that the second bits first: > http://www.javascriptkit.com/javatutors/randomnum.shtml >but they don't disclose the underlaying reasoning. The cited page is basically incorrect; the author is probably rephrasing something that he does not understand. Only the incompetent, or those writing for them, feel a need to write ? true : false or ? false : true. The proper answer is not to use Math.random >= 0.5 , but to use Math.random < 0.5 - the result should be equally good, but the latter takes fewer characters and out to be equally quick. Implementations of Math.random should be pretty good at returning the same number of results < 0.5 as not < 0.5 - but if there are any based on N-bit shift registers with XOR feedback, then there should be with those on average in every 2^N-1 results one more in one "half" than in the other. That can, in practice, only be tested in JavaScript by incipient struldbrugs. One could use !Math.round(Math.random()) , but in principle one should first check (in all browsers) that Math.round does not do Bankers' Rounding. Anti-Bankers would be OK. -- (c) John Stockton, nr London UK. ???@merlyn.demon.co.uk Turnpike v6.05 MIME. Web <URL:http://www.merlyn.demon.co.uk/> - FAQish topics, acronyms, & links. Check boilerplate spelling -- error is a public sign of incompetence. Never fully trust an article from a poster who gives no full real name.

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5/2/2010 3:43:49 PM

In comp.lang.javascript message <ocgz5sij.fsf@gmail.com>, Sat, 1 May 2010 21:30:44, Lasse Reichstein Nielsen <lrn.unread@gmail.com> posted: >As stated elsewhere, this should read > return (n == 1) ? true : false; >or, preferably, > return n == 1; Or return ! Math.floor(Math.random()*2); That gives the opposite answer, but who cares? return Math.random()<0.5 should be quicker. >I guess their point is that to generate an integer in the range [0..n[, > Math.floor(Math.random() * n) >is better, in general, than > Math.round(Math.random() * (n - 1)) >... which is pretty old news (not that people still don't bungle it >regularly, but it's embarrasing every time it happens). > >The funny thing is that for n = 2, the unevenness of using the Math.round >doesn't matter, which is the case you are asking about. Since using Math.round makes the two end bins each half as probable as the rest, n = 1 and n = 1 are the only cases where it gives equi- probability. However, there is a class of problems where Math.round is good : "a metre stick is repeatedly put at random positions within a ten-metre tube marked out in one-metre sections - what is the probability distribution of which section its centre is in?" (for the metrically-challenged : use .replace(/re\b/g, "er") on that) -- (c) John Stockton, nr London, UK. ?@merlyn.demon.co.uk Turnpike v6.05 IE 7. Web <URL:http://www.merlyn.demon.co.uk/> - FAQish topics, acronyms, & links. MiniTrue is good for viewing/searching/altering files, at a DOS / CMD prompt; free, DOS/Win/UNIX, new via <URL:http://www.merlyn.demon.co.uk/pc-links.htm>.

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5/2/2010 3:43:59 PM