Mersenne Twister -- A Revised C++ Implementation

[Scott Robert Ladd]

I've posted my revised C++ implementation of the Mersenne Twister at:

http://www.coyotegulch.com/libcoyote...istedRoad.html

This is "free-as-in-liberty" and "free-as-in-beer" code.

The Mersenne Twister is a "random number" generator invented by Makoto
Matsumoto and Takuji Nishimura; their website includes numerous
implementations of the algorithm.

Essentially, the Mersenne Twister is a very large linear-feedback shift
register. The algorithm operates on a 19,937 bit seed, stored in an
624-element array of 32-bit unsigned integers. The value 2^19937-1 is a
Mersenne prime; the technique for manipulating the seed is based on an
older "twisting" algorithm -- hence the name "Mersenne Twister".

An appealing aspect of the Mersenne Twister is its use of binary
operations -- as opposed to time-consuming multiplication -- for
generating numbers. The algorithm also has a very long period, and good
granularity. It is both fast and effective for non-cryptographic
applications.

--
Scott Robert Ladd
Coyote Gulch Productions (http://www.coyotegulch.com)
Software Invention for High-Performance Computing

[Stephen Howe]

> A random number generator that does not generate uniformly distributed

numbers is of very questionable use.

Not at all. I could have a random number generator returning doubles that
generates a random number between 0 and 1 with a Normal distribution, mean
0.5, standard deviation 1. I can think of a use for that. I can think of
other non-uniform random number generator distributions, all statistical
that are of use.

Your mathematical credentials are suspect. You seem to be way more
incompetent than the OP.

Stephen Howe

[Carsten Hansen]

"Stephen Howe" <NO**********@d ial.pipex.com> wrote in message
news:3f******** *************** @reading.news.p ipex.net...

A random number generator that does not generate uniformly distributed
numbers is of very questionable use.

Not at all. I could have a random number generator returning doubles that
generates a random number between 0 and 1 with a Normal distribution, mean
0.5, standard deviation 1. I can think of a use for that. I can think of
other non-uniform random number generator distributions, all statistical
that are of use.

Your mathematical credentials are suspect. You seem to be way more
incompetent than the OP.

Stephen Howe

A normal distribution has infinite range. So, generating random numbers
between 0 and 1 with a Normal distribution doesn't make sense.
Yes, you can have a truncated Normal distribution, but that is not what you
are writing.

I'm well aware that there are non-uniform random number distributions. In
the fall I corrected two errors in Knuth's Vol. 2 about non-uniform RNG. I
have the check to prove it.
I commented about the code which is intended to generate a uniform
distribution. I doesn't as others have pointed out.
As for my credentials, I have a Ph.D. in Mathematics (Penn State '89).

Carsten Hansen

[Stephen Howe]

> A normal distribution has infinite range. So, generating random numbers

between 0 and 1 with a Normal distribution doesn't make sense.

It does if you are returning cumulative probabilites. So

_ x
|
p(x) = 1.0 / (sqrt (2.0 * pi))I exp(- (x * x) / 2.0)
_I
-Inf

That will lie between 0.0 and 1.0.

Stephen Howe

[Carsten Hansen]

"Stephen Howe" <NO**********@d ial.pipex.com> wrote in message
news:3f******** *************** @news.dial.pipe x.com...

A normal distribution has infinite range. So, generating random numbers
between 0 and 1 with a Normal distribution doesn't make sense.

It does if you are returning cumulative probabilites. So

_ x
|
p(x) = 1.0 / (sqrt (2.0 * pi))I exp(- (x * x) / 2.0)
_I
-Inf

That will lie between 0.0 and 1.0.

Stephen Howe

That is not a distribution. That is a probability. You don't generate that.
You calculate that.
You talked about generating random numbers between 0 and 1 with a Normal
distribution.
Now you are changing it to cumulative probabilities. Something very
different.
But nice try. Maybe you will get partial credit.

Carsten Hansen

[Chris Theis]

"Carsten Hansen" <ha******@world net.att.net> wrote in message
news:4G******** ***********@bgt nsc05-news.ops.worldn et.att.net...

"Stephen Howe" <NO**********@d ial.pipex.com> wrote in message
news:3f******** *************** @news.dial.pipe x.com...

A normal distribution has infinite range. So, generating random numbers between 0 and 1 with a Normal distribution doesn't make sense.
It does if you are returning cumulative probabilites. So

_ x
|
p(x) = 1.0 / (sqrt (2.0 * pi))I exp(- (x * x) / 2.0)
_I
-Inf

That will lie between 0.0 and 1.0.

Stephen Howe

That is not a distribution. That is a probability. You don't generate

that. You calculate that.
IMHO you also "calculate" numbers following a distribution, don´t you? I
mean we´re talking about distributions given in analytical form and not some
stochastic processes.
You talked about generating random numbers between 0 and 1 with a Normal
distribution.
Now you are changing it to cumulative probabilities. Something very
different.
To be exact he is talking about cumulative distributions (CDF) and not
cumulative probabilities, though in principle you are right as the
discussion is about PDF and not CDF.
But nice try. Maybe you will get partial credit.

Thanks :-) But don´t you think that this discussion will lead to nowhere and
that comp.lang.c++ might not be the place to discuss statistical issues?

Regards
Chris

[Carsten Hansen]

"Chris Theis" <Ch************ *@nospam.cern.c h> wrote in message
news:vK******** *************@n ews.chello.at.. .

"Carsten Hansen" <ha******@world net.att.net> wrote in message
news:4G******** ***********@bgt nsc05-news.ops.worldn et.att.net...

"Stephen Howe" <NO**********@d ial.pipex.com> wrote in message
news:3f******** *************** @news.dial.pipe x.com...

> A normal distribution has infinite range. So, generating random numbers > between 0 and 1 with a Normal distribution doesn't make sense.

It does if you are returning cumulative probabilites. So

_ x
|
p(x) = 1.0 / (sqrt (2.0 * pi))I exp(- (x * x) / 2.0)
_I
-Inf

That will lie between 0.0 and 1.0.

Stephen Howe
That is not a distribution. That is a probability. You don't generate

that.

You calculate that.

IMHO you also "calculate" numbers following a distribution, don´t you? I
mean we´re talking about distributions given in analytical form and not

some stochastic processes.

You talked about generating random numbers between 0 and 1 with a Normal
distribution.
Now you are changing it to cumulative probabilities. Something very
different.

To be exact he is talking about cumulative distributions (CDF) and not
cumulative probabilities, though in principle you are right as the
discussion is about PDF and not CDF.

But nice try. Maybe you will get partial credit.
Thanks :-) But don´t you think that this discussion will lead to nowhere

and that comp.lang.c++ might not be the place to discuss statistical issues?

Regards
Chris

Generating random numbers with a given distribution has a well-established
meaning. Generating random numbers with a Normal distribution between 0 and
1 doesn't makes sense. I'm not supposed to correct that?

Carsten Hansen

[Chris Theis]

"Carsten Hansen" <ha******@world net.att.net> wrote in message
news:mPRKb.2745 $Ub6.81689@bgtn sc04-
[SNIP]

Generating random numbers with a given distribution has a well-established
meaning. Generating random numbers with a Normal distribution between 0 and 1 doesn't makes sense. I'm not supposed to correct that?

Carsten Hansen

Hi Carsten,

relax :-) Of course you should correct wrong statements, this is the way
that people reading these postings are supposed to obtain wider & better
knowledge. However, I wouldn´t be so quick to say that generating a normal
distribution between 0 & 1 (Stephen proposed a mean value of 0.5) doesn´t
make sense. If you want to study for example a special case of a biased
Wiener-Levy process you might resort to such random numbers (whether this
study makes any sense or not is a different thing!).

Chris

[Carsten Hansen]

"Chris Theis" <Ch************ *@nospam.cern.c h> wrote in message
news:jj******** *******@news.ch ello.at...

"Carsten Hansen" <ha******@world net.att.net> wrote in message
news:mPRKb.2745 $Ub6.81689@bgtn sc04-
[SNIP]

Generating random numbers with a given distribution has a well-established meaning. Generating random numbers with a Normal distribution between 0

and

1 doesn't makes sense. I'm not supposed to correct that?

Carsten Hansen

Hi Carsten,

relax :-) Of course you should correct wrong statements, this is the way
that people reading these postings are supposed to obtain wider & better
knowledge. However, I wouldn´t be so quick to say that generating a normal
distribution between 0 & 1 (Stephen proposed a mean value of 0.5) doesn´t
make sense. If you want to study for example a special case of a biased
Wiener-Levy process you might resort to such random numbers (whether this
study makes any sense or not is a different thing!).

Chris

Generating random numbers with a given distribution has a well-established
meaning.
Using that well-established meaning and given that a Normal distribution has
an infinite range, it does not make sense to talk about generating random
numbers with a Normal distribution between 0 and 1.
You can calculate other things. But if you use a well-established phrase,
you better qualify it.

That is all I'm saying.

Carsten Hansen

[kevin collins]

Carsten Hansen writes:

Generating random numbers with a given distribution has a well-established
meaning.
Using that well-established meaning and given that a Normal distribution has an infinite range, it does not make sense to talk about generating random
numbers with a Normal distribution between 0 and 1.
You can calculate other things. But if you use a well-established phrase,
you better qualify it.

I read Ladd's whole post as "good enough for government work". If I had
seen a similar thing in some high-falutin' mathematics journal, I would have
applied different standards. After all, the computers I have seen have
been unable to express infinity in a reasonable fashion, anyway, one of the
popular OSes limits RAM to only 2^29 bytes. Computers of the kind being
discussed here (that is, a machine, not a human) deal with approximations
for the real numbers encountered in the field of mathematics. C++, as used
here, does not deal with symbolic mathematics.

I saw, and see, no reason for further qualification as to the use of the
phrase, considering the context in which it was provided.

It is pretty clear that you are the kind of person that has to have the last
word. So post it, I don't expect to express any answer.

[Carsten Hansen]

"kevin collins" <ke********@hot mail.com> wrote in message
news:pXTKb.7668 83$Tr4.2203330@ attbi_s03...

Carsten Hansen writes:

Generating random numbers with a given distribution has a well-established meaning.
Using that well-established meaning and given that a Normal distribution has

an infinite range, it does not make sense to talk about generating random numbers with a Normal distribution between 0 and 1.
You can calculate other things. But if you use a well-established phrase, you better qualify it.

I read Ladd's whole post as "good enough for government work". If I had
seen a similar thing in some high-falutin' mathematics journal, I would

have applied different standards. After all, the computers I have seen have
been unable to express infinity in a reasonable fashion, anyway, one of the popular OSes limits RAM to only 2^29 bytes. Computers of the kind being
discussed here (that is, a machine, not a human) deal with approximations
for the real numbers encountered in the field of mathematics. C++, as used here, does not deal with symbolic mathematics.

I saw, and see, no reason for further qualification as to the use of the
phrase, considering the context in which it was provided.

It is pretty clear that you are the kind of person that has to have the last word. So post it, I don't expect to express any answer.

This has nothing to do with how big a number you can represent on a
computer. When you have an infinite range and you claim it falls between 0
and 1 you are talking nonsense.

Carsten Hansen