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-   -   Math.random() and Math.round(Math.random()) and Math.floor(Math.random()*2) (http://www.velocityreviews.com/forums/t941093-math-random-and-math-round-math-random-and-math-floor-math-random-2-a.html)

VK 05-01-2010 07:54 AM

Math.random() and Math.round(Math.random()) and Math.floor(Math.random()*2)
 
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;
}

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.

Ry Nohryb 05-01-2010 09:30 AM

Re: Math.random() and Math.round(Math.random()) andMath.floor(Math.random()*2)
 
On May 1, 9:54*am, 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() {
> *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:
>
> 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.


Why not { return Math.random() >= 0.5; } ?
--
Jorge.

VK 05-01-2010 09:49 AM

Re: Math.random() and Math.round(Math.random()) andMath.floor(Math.random()*2)
 
On May 1, 1:30*pm, Ry Nohryb <jo...@jorgechamorro.com> wrote:
> On May 1, 9:54*am, 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() {
> > *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:

>
> > 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.

>
> 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(), 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/Cor...cts/Math/Round
Returns the value of a number rounded to the nearest integer.

https://developer.mozilla.org/En/Cor...cts/Math/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.


VK 05-01-2010 10:20 AM

Re: Math.random() and Math.round(Math.random()) andMath.floor(Math.random()*2)
 
On May 1, 1:49*pm, VK <schools_r...@yahoo.com> wrote:
> *https://developer.mozilla.org/En/Cor...ference/Object....
> *Returns the value of a number rounded to the nearest integer.
>
> *https://developer.mozilla.org/En/Cor...ference/Object....
> *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.


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/Pseudor...unction_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


VK 05-01-2010 10:50 AM

Re: Math.random() and Math.round(Math.random()) andMath.floor(Math.random()*2)
 
On May 1, 2:20*pm, 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.m...46c8a74170acfd

Henry 05-01-2010 11:37 AM

Re: Math.random() and Math.round(Math.random()) andMath.floor(Math.random()*2)
 
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/Cor...cts/Math/Round
> Returns the value of a number rounded to the nearest integer.
>
> https://developer.mozilla.org/En/Cor...cts/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....c2ad2bdbdf0b40
>


- 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.

VK 05-01-2010 11:38 AM

Re: Math.random() and Math.round(Math.random()) andMath.floor(Math.random()*2)
 
On May 1, 3:16*pm, "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.m...878f7a0aea0b90

<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 >= 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. ?

VK 05-01-2010 11:54 AM

Re: Math.random() and Math.round(Math.random()) andMath.floor(Math.random()*2)
 
On May 1, 3:37*pm, 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/Cor...ference/Object...
> > Returns the value of a number rounded to the nearest integer.

>
> >https://developer.mozilla.org/En/Cor...ference/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....wse_frm/thread...
>
>
>
> - 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.

VK 05-01-2010 12:17 PM

Re: Math.random() and Math.round(Math.random()) andMath.floor(Math.random()*2)
 
On May 1, 4:02*pm, "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() >= 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() ?



John G Harris 05-01-2010 05:21 PM

Re: Math.random() and Math.round(Math.random()) and Math.floor(Math.random()*2)
 
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/Cor...erence/Objects
>/Math/Round
> Returns the value of a number rounded to the nearest integer.
>
> https://developer.mozilla.org/En/Cor...erence/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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