About rand()

[Spiros Bousbouras]

The standard says that rand() should return a pseudo-random
number but what does pseudorandom mean ? If an implementation
of rand() always returned the same number would it be conforming ?
What if it always alternated between 2 values ?

On the practical side do you have any thoughts on what one
could realistically expect from the behaviour of rand() ? Could
for example one expect that eventually any value in the range
[0,RAND_MAX] will be returned ?

[Peter Nilsson]

Spiros Bousbouras wrote:

The standard says that rand() should return a pseudo-random
number but what does pseudorandom mean ? If an implementation
of rand() always returned the same number would it be conforming ?
What if it always alternated between 2 values ?

On the practical side do you have any thoughts on what one
could realistically expect from the behaviour of rand() ? Could
for example one expect that eventually any value in the range
[0,RAND_MAX] will be returned ?

It's entirely a QoI issue. Pragmatically, it is trivial to write a
rand()
that returns every value at some point, even if the distribution is
not perfect. [A few implementations I've seen copy the example
shown in K&R2.]

The FAQ has a number of comments on the issues of rand().

Anyone needing to use random numbers in a serious program will
likely roll their own routine from the plethora of PRNG's available on
the net. [E.g. http://www.stanford.edu/~blp/writings/clc/random.html.]

--
Peter

[Spiros Bousbouras]

Peter Nilsson wrote:

Spiros Bousbouras wrote:

The standard says that rand() should return a pseudo-random
number but what does pseudorandom mean ? If an implementation
of rand() always returned the same number would it be conforming ?
What if it always alternated between 2 values ?

On the practical side do you have any thoughts on what one
could realistically expect from the behaviour of rand() ? Could
for example one expect that eventually any value in the range
[0,RAND_MAX] will be returned ?

It's entirely a QoI issue. Pragmatically, it is trivial to write a
rand()
that returns every value at some point, even if the distribution is
not perfect. [A few implementations I've seen copy the example
shown in K&R2.]

By "perfect" distribution do you mean uniform distribution ?

[Walter Roberson]

In article <11************ **********@v45g 2000cwv.googleg roups.com>,
Spiros Bousbouras <sp****@gmail.c omwrote:

>The standard says that rand() should return a pseudo-random
number but what does pseudorandom mean ? If an implementation
of rand() always returned the same number would it be conforming ?
What if it always alternated between 2 values ?

It must produce a pseudo-random sequence in the range 0
to RAND_MAX, where RAND_MAX is at least 32767. If on a particular
implementation it can never produce RAND_MAX then RAND_MAX
for that implementation would be defined as the largest value that
it -could- produce, and if that value was not at least 32767 then
the implementation would be non-conforming.

One could similarily argue that if 0 cannot be produced that
the implementation is non-conforming; the argument is perhaps
a bit weaker.

If the implementation alternated between 0 and RAND_MAX then
it would be conforming.

>On the practical side do you have any thoughts on what one
could realistically expect from the behaviour of rand() ? Could
for example one expect that eventually any value in the range
[0,RAND_MAX] will be returned ?

I would not -expect- any self-respecting rand() to not be
able to produce one of the values in the range, eventually;
I would -expect- at worst the sample function given in the
standard. But it wouldn't shock me if some organization
that produced a C-like language used what they -thought-
was a good rand() but which turned out not to be able to produce
some set of values. [NB: the number of organizations that
produce C-like languages appears to far outnumber the ones that
produce conforming C.]

--
If you lie to the compiler, it will get its revenge. -- Henry Spencer

[Spiros Bousbouras]

Walter Roberson wrote:

In article <11************ **********@v45g 2000cwv.googleg roups.com>,
Spiros Bousbouras <sp****@gmail.c omwrote:

The standard says that rand() should return a pseudo-random
number but what does pseudorandom mean ? If an implementation
of rand() always returned the same number would it be conforming ?
What if it always alternated between 2 values ?

It must produce a pseudo-random sequence in the range 0
to RAND_MAX, where RAND_MAX is at least 32767. If on a particular
implementation it can never produce RAND_MAX then RAND_MAX
for that implementation would be defined as the largest value that
it -could- produce, and if that value was not at least 32767 then
the implementation would be non-conforming.

The standard says "The rand function computes a
sequence of pseudo-random numbers in the range
of 0 to RAND_MAX." I don't see how it follows from
that that the largest value which can be produced
will by definition be RAND_MAX.

[Richard Tobin]

In article <11************ **********@51g2 000cwl.googlegr oups.com>,
Spiros Bousbouras <sp****@gmail.c omwrote:

>The standard says "The rand function computes a
sequence of pseudo-random numbers in the range
of 0 to RAND_MAX." I don't see how it follows from
that that the largest value which can be produced
will by definition be RAND_MAX.

The standard is rather weak in its description of rand(). It makes
no mention of the distribution of random numbers, so an implementation
that returns 1 99.99999999% of the time could still be conforming.
Presumably this would be considered a quality of implementation issue,
and the same goes for an implementation that never produced RAND_MAX.

-- Richard

--
"Considerat ion shall be given to the need for as many as 32 characters
in some alphabets" - X3.4, 1963.

[user923005]

Spiros Bousbouras wrote:

Walter Roberson wrote:

In article <11************ **********@v45g 2000cwv.googleg roups.com>,
Spiros Bousbouras <sp****@gmail.c omwrote:

>The standard says that rand() should return a pseudo-random
>number but what does pseudorandom mean ? If an implementation
>of rand() always returned the same number would it be conforming ?
>What if it always alternated between 2 values ?

It must produce a pseudo-random sequence in the range 0
to RAND_MAX, where RAND_MAX is at least 32767. If on a particular
implementation it can never produce RAND_MAX then RAND_MAX
for that implementation would be defined as the largest value that
it -could- produce, and if that value was not at least 32767 then
the implementation would be non-conforming.

The standard says "The rand function computes a
sequence of pseudo-random numbers in the range
of 0 to RAND_MAX." I don't see how it follows from
that that the largest value which can be produced
will by definition be RAND_MAX.

According to that definition the sequence:
1,1,1,1...
seems to fit because 1 is between 0 and RAND_MAX.

The rand() function cannot produce negative numbers (by definition)
The rand() function cannot produce numbers larger than RAND_MAX (by
definition).

Generally speaking, a halfway-decent rand() implementation will
eventually produce every number between and including 0 .. RAND_MAX.

However, there is not guarantee in the standard that rand() is halfway
decent (e.g. that it passes Marsaglia's tests).

If you want good pseudo-random numbers, then use the Mersenne Twister.

[David T. Ashley]

"Spiros Bousbouras" <sp****@gmail.c omwrote in message
news:11******** **************@ v45g2000cwv.goo glegroups.com.. .

The standard says that rand() should return a pseudo-random
number but what does pseudorandom mean ? If an implementation
of rand() always returned the same number would it be conforming ?
What if it always alternated between 2 values ?

On the practical side do you have any thoughts on what one
could realistically expect from the behaviour of rand() ? Could
for example one expect that eventually any value in the range
[0,RAND_MAX] will be returned ?

Pseudo-random means that the next value of the output is a function of some
internal state. Often, the state and the returned value are the same thing.
Pseudo-random means that the next value is algorithmically predictable, i.e.
it isn't truly random where one could not predict.

http://en.wikipedia.org/wiki/Pseudo-random

The most common approach to pseudo-random generators is to use prime moduli.

http://en.wikipedia.org/wiki/Linear_...tial_generator

In fact, most people who implement their own random number generators are
pretty happy with the simple one at the link immediately above. I believe
as long as the requirement of coprimality between a couple of the parameters
is met, the generated sequence is guaranteed to hit every value in the
interval. I'm sure all the math is at the link above.

--
David T. Ashley (dt*@e3ft.com)
http://www.e3ft.com (Consulting Home Page)
http://www.dtashley.com (Personal Home Page)
http://gpl.e3ft.com (GPL Publications and Projects)

[CBFalconer]

"David T. Ashley" wrote:

>

.... snip ...

>
In fact, most people who implement their own random number
generators are pretty happy with the simple one at the link
immediately above. I believe as long as the requirement of
coprimality between a couple of the parameters is met, the
generated sequence is guaranteed to hit every value in the
interval. I'm sure all the math is at the link above.

Just read Knuth (TAOCP). He has a thorough treatment of linear
congruential generators, including some cookbook tables.

--
Chuck F (cbfalconer at maineline dot net)
Available for consulting/temporary embedded and systems.
<http://cbfalconer.home .att.net>

[David T. Ashley]

"CBFalconer " <cb********@yah oo.comwrote in message
news:45******** *******@yahoo.c om...

"David T. Ashley" wrote:

>>

... snip ...

>>
In fact, most people who implement their own random number
generators are pretty happy with the simple one at the link
immediately above. I believe as long as the requirement of
coprimality between a couple of the parameters is met, the
generated sequence is guaranteed to hit every value in the
interval. I'm sure all the math is at the link above.

Just read Knuth (TAOCP). He has a thorough treatment of linear
congruential generators, including some cookbook tables.

Thanks. I have those books on my shelves and actually didn't know that
random number generation was in it (I've used it most for extended-precision
arithmetic and searching and sorting).

I've always admired Knuth. He has a mathematician's gift for brevity.
There is a lot packed into those books.

--
David T. Ashley (dt*@e3ft.com)
http://www.e3ft.com (Consulting Home Page)
http://www.dtashley.com (Personal Home Page)
http://gpl.e3ft.com (GPL Publications and Projects)