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MathGroup Archive 2002

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Re: Random bits (generation)

  • To: mathgroup at smc.vnet.net
  • Subject: [mg35120] Re: [mg35045] Random bits (generation)
  • From: Daniel Lichtblau <danl at wolfram.com>
  • Date: Tue, 25 Jun 2002 03:42:35 -0400 (EDT)
  • References: <200206210354.XAA08580@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

"DIAMOND Mark R." wrote:
> 
> I am not sure whether anyone other than a Wolfram guru will know the answer
> to this. ...
> 
> (1) If I wish to generate a large number of random bits, what is the fastest
> way?
> (2) What is the safest way in the sense of being able to expect the bit
> sequence to pass Marsaglia's Diehard battery of tests Maurer's Universal
> Statistical Test.? or is this requirement impossible to meet with Random?
> 
> More specifically, to be sure that they are independent and random, should I
> use something like Random[Integer, {0,1}] or can one use *all the bits* of,
> say, Random[Integer, {0,2^32-1}] ... or even something  larger.
> 
> Cheers,
> 
> Mark Diamond

Probably best just to generate random bits using e.g.

randomBits[length_] := Table[Random[Integer], {length}]

This is reasonably fast and will give high quality random sequence. You
might get better speed by generating a bigger number and then extracting
bits, but you then run the risk of having a less "random" sequence.

More information as to what methods are used under what circumstances
may be found at:

http://library.wolfram.com/mathgroup/archive/2000/May/msg00088.html

Among other things it is noted at that link that the method above should
pass all the DIEHARD tests.


Daniel Lichtblau
Wolfram Research


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