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Floating Point Random Number Generator

I know how to use rand() to generate random POSITIVE-INTEGER numbers.

But, I'd like to generate a random DOUBLE number in the range of 0.0 to 1.0
with resolution of a double (i.e., every possible double value in the range
could come up with equal probability). I'd also like to be able to seed this
generator (e.g., via the clock) so that the same sequence of random values
don't come up every time.

Anybody have an easy and fast (computationall y) way to do this? Thanks in
advance...!
Nov 17 '05 #1
5 3358
Peteroid wrote:
I know how to use rand() to generate random POSITIVE-INTEGER numbers.

But, I'd like to generate a random DOUBLE number in the range of 0.0
to 1.0 with resolution of a double (i.e., every possible double value
in the range could come up with equal probability). I'd also like to
be able to seed this generator (e.g., via the clock) so that the same
sequence of random values don't come up every time.


A double in [0.0,1.0) has 2^52 distinct values. To generate such doubles,
first generate a random integer in [0,2^52) and then divide it by 2^52.
Note that all such integers, including 2^52 can be represented exactly as
doubles.

You might want to look at boost::random (see
http://www.boost.org/libs/random/index.html for details) for pseudo-random
generators that are good enough to generate 2^52 numbers without cycles.
You need to use a long period generator such as a Mersenne twister to really
get 2^52 values out of it. Your generator will have to generate 64 bit
values of course.

-cd
Nov 17 '05 #2
Thanks, Carl!

You gave me a better way than I was going. I'll create a class that allows
me to generate a floating-point number in the range of [0.0.,1.0] (yes,
closed on both sides) of arbitray bit-count resolution up to a limit (51, or
possibly even 63, sounds good, based on your response).

Say the bit-count is N. Generate an N-bit random number by generating N/16
number of random 16-bit integers (using rand()), and possibly 1 more for the
N%16 remaining bits (which is masked off the apprograte number of high bits
to get correct number of bytes), and then append them into a double by
shifting and adding. Then divide by a double version of (2^N - 1) and that
should (for some values of N) produce the closed interval random
floating-point number expressed as a double!

The seed is nor just srand()...

Thanx again...! :)

[==Peteroid==]

"Carl Daniel [VC++ MVP]" <cp************ *************** **@mvps.org.nos pam>
wrote in message news:uM******** ******@TK2MSFTN GP14.phx.gbl...
Peteroid wrote:
I know how to use rand() to generate random POSITIVE-INTEGER numbers.

But, I'd like to generate a random DOUBLE number in the range of 0.0
to 1.0 with resolution of a double (i.e., every possible double value
in the range could come up with equal probability). I'd also like to
be able to seed this generator (e.g., via the clock) so that the same
sequence of random values don't come up every time.
A double in [0.0,1.0) has 2^52 distinct values. To generate such doubles,
first generate a random integer in [0,2^52) and then divide it by 2^52.
Note that all such integers, including 2^52 can be represented exactly as
doubles.

You might want to look at boost::random (see
http://www.boost.org/libs/random/index.html for details) for pseudo-random
generators that are good enough to generate 2^52 numbers without cycles.
You need to use a long period generator such as a Mersenne twister to

really get 2^52 values out of it. Your generator will have to generate 64 bit
values of course.

-cd

Nov 17 '05 #3
Peteroid wrote:
Thanks, Carl!

You gave me a better way than I was going. I'll create a class that
allows me to generate a floating-point number in the range of
[0.0.,1.0] (yes, closed on both sides) of arbitray bit-count
resolution up to a limit (51, or possibly even 63, sounds good, based
on your response).

Say the bit-count is N. Generate an N-bit random number by generating
N/16 number of random 16-bit integers (using rand()), and possibly 1
more for the N%16 remaining bits (which is masked off the apprograte
number of high bits to get correct number of bytes), and then append
them into a double by shifting and adding. Then divide by a double
version of (2^N - 1) and that should (for some values of N) produce
the closed interval random floating-point number expressed as a
double!


Just be aware that the resulting numbers will very likely not cover all
possible values. The period of a 52 bit number generated from concatenation
of 4 values from a 16 bit rng followed by a mask to 52 bits will be at most
2^18 - nowhere near 2^52.

-cd
Nov 17 '05 #4
TOM
You may want to read the section on random number generators in
"Numerical Recipes in C". The text is free and on-line in PDF format by
permission of the publisher, at:

http://www.nr.com/

It's very difficult to build a good random number generator. The text
illustrates the problems and some ways around it, but is focused
on float rather than double.

-- Tom

"Peteroid" <pe************ @msn.com> wrote in message
news:u2******** ******@TK2MSFTN GP11.phx.gbl...
Thanks, Carl!

You gave me a better way than I was going. I'll create a class that allows
me to generate a floating-point number in the range of [0.0.,1.0] (yes,
closed on both sides) of arbitray bit-count resolution up to a limit (51,
or
possibly even 63, sounds good, based on your response).

Say the bit-count is N. Generate an N-bit random number by generating N/16
number of random 16-bit integers (using rand()), and possibly 1 more for
the
N%16 remaining bits (which is masked off the apprograte number of high
bits
to get correct number of bytes), and then append them into a double by
shifting and adding. Then divide by a double version of (2^N - 1) and that
should (for some values of N) produce the closed interval random
floating-point number expressed as a double!

The seed is nor just srand()...

Thanx again...! :)

[==Peteroid==]

"Carl Daniel [VC++ MVP]" <cp************ *************** **@mvps.org.nos pam>
wrote in message news:uM******** ******@TK2MSFTN GP14.phx.gbl...
Peteroid wrote:
> I know how to use rand() to generate random POSITIVE-INTEGER numbers.
>
> But, I'd like to generate a random DOUBLE number in the range of 0.0
> to 1.0 with resolution of a double (i.e., every possible double value
> in the range could come up with equal probability). I'd also like to
> be able to seed this generator (e.g., via the clock) so that the same
> sequence of random values don't come up every time.


A double in [0.0,1.0) has 2^52 distinct values. To generate such
doubles,
first generate a random integer in [0,2^52) and then divide it by 2^52.
Note that all such integers, including 2^52 can be represented exactly as
doubles.

You might want to look at boost::random (see
http://www.boost.org/libs/random/index.html for details) for
pseudo-random
generators that are good enough to generate 2^52 numbers without cycles.
You need to use a long period generator such as a Mersenne twister to

really
get 2^52 values out of it. Your generator will have to generate 64 bit
values of course.

-cd


Nov 17 '05 #5
Thanks for the link Tom!

As it turns out (and unlike what I first asked), I don't actaully need for
every double floating-point number to be generated randomly that exists in
[0.0,1.0]. It turns out I'm able to determine the 'resolution' of the
generator that is good enough for my application for what it happens to be
doing at the moment. By 'resolution' I mean the number of possible
equally-spaced floating-point random values I need to generate in the
[0.0,1.0] range (e.g., resolution 3 would generate only these values: 0.0,
..5, 1.0).

So I created a class with a 'base' (= resolution-1) and let rand() generate
a random number from 0 to base, and then produce this number divided by
base to get it into the [0.0,1.0] range. This is sufficient for my
application.

I realized, based on the responses here, that any random number generator on
a digital computer will never return all possibly real numbers, so I had to
deal with a 'resolution' no matter what. The method I've created deals with
such any (not too big) resolution 'perfectly', and so it works!

Thanks!

[==Peteroid==]

"TOM" <no****@noprovi der.nodomain> wrote in message
news:%2******** ********@TK2MSF TNGP09.phx.gbl. ..
You may want to read the section on random number generators in
"Numerical Recipes in C". The text is free and on-line in PDF format by
permission of the publisher, at:

http://www.nr.com/

It's very difficult to build a good random number generator. The text
illustrates the problems and some ways around it, but is focused
on float rather than double.

-- Tom

"Peteroid" <pe************ @msn.com> wrote in message
news:u2******** ******@TK2MSFTN GP11.phx.gbl...
Thanks, Carl!

You gave me a better way than I was going. I'll create a class that allows me to generate a floating-point number in the range of [0.0.,1.0] (yes,
closed on both sides) of arbitray bit-count resolution up to a limit (51, or
possibly even 63, sounds good, based on your response).

Say the bit-count is N. Generate an N-bit random number by generating N/16 number of random 16-bit integers (using rand()), and possibly 1 more for
the
N%16 remaining bits (which is masked off the apprograte number of high
bits
to get correct number of bytes), and then append them into a double by
shifting and adding. Then divide by a double version of (2^N - 1) and that should (for some values of N) produce the closed interval random
floating-point number expressed as a double!

The seed is nor just srand()...

Thanx again...! :)

[==Peteroid==]

"Carl Daniel [VC++ MVP]" <cp************ *************** **@mvps.org.nos pam> wrote in message news:uM******** ******@TK2MSFTN GP14.phx.gbl...
Peteroid wrote:
> I know how to use rand() to generate random POSITIVE-INTEGER numbers.
>
> But, I'd like to generate a random DOUBLE number in the range of 0.0
> to 1.0 with resolution of a double (i.e., every possible double value
> in the range could come up with equal probability). I'd also like to
> be able to seed this generator (e.g., via the clock) so that the same
> sequence of random values don't come up every time.

A double in [0.0,1.0) has 2^52 distinct values. To generate such
doubles,
first generate a random integer in [0,2^52) and then divide it by 2^52.
Note that all such integers, including 2^52 can be represented exactly as doubles.

You might want to look at boost::random (see
http://www.boost.org/libs/random/index.html for details) for
pseudo-random
generators that are good enough to generate 2^52 numbers without cycles. You need to use a long period generator such as a Mersenne twister to

really
get 2^52 values out of it. Your generator will have to generate 64 bit
values of course.

-cd



Nov 17 '05 #6

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