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

[Chris Theis]

"Carsten Hansen" <ha******@world net.att.net> wrote in message
news:_1******** ***********@bgt nsc05-news.ops.worldn et.att.net...

"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.

Okay if you want to stick to knit-picking then so be it. Stephen never
claimed that the infinite range falls between 0 and 1. He was only talking
about a normal distribution with mean 0.5 between the limits of 0 and 1. It
is of course correct that the Stiltjes-integral applied in mathematical
statistics is defined from -\inf to \inf. However, if you want to calculate
anything reasonable you will have to specify limits as infinity is a
mathematical construct that doesn´t play very well with practical
applications (to see this we only have to resort to Quantum Mechanics, which
is OT here and I don´t wanna get into that now). Specifying limits does
bring us back to numerical accuracy which depends on your machine and
therefore any applied limit is valid (see my previous post about the
Wiener-Levy process).

Regards
Chris

[Carsten Hansen]

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

"Carsten Hansen" <ha******@world net.att.net> wrote in message
news:_1******** ***********@bgt nsc05-news.ops.worldn et.att.net...

"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.

Okay if you want to stick to knit-picking then so be it. Stephen never
claimed that the infinite range falls between 0 and 1. He was only talking
about a normal distribution with mean 0.5 between the limits of 0 and 1.

It is of course correct that the Stiltjes-integral applied in mathematical
statistics is defined from -\inf to \inf. However, if you want to calculate anything reasonable you will have to specify limits as infinity is a
mathematical construct that doesn´t play very well with practical
applications (to see this we only have to resort to Quantum Mechanics, which is OT here and I don´t wanna get into that now). Specifying limits does
bring us back to numerical accuracy which depends on your machine and
therefore any applied limit is valid (see my previous post about the
Wiener-Levy process).

Regards
Chris

You can have a truncated normal distribution. If you do, you specify the
mean, the standard deviation and the limits for the truncation.
That is fine. But that is not what Stephen wrote. He is calculating
something else (a cumulative probability).
Using the same name, generating random numbers with a Normal distribution,
for two different things is confusing and misleading.
There are no numerical accuracy issues here.

Carsten Hansen