Re: [Q] Can a good random bit sequence generator be a good random number sequence generator?

<sjtu.0992@xxxxxxxxx> wrote in message

I am looking for the comments or any references (books or papers)
regarding the subject title.


You have to look at the issue from a computer and programming view point.

If the bit sequence file from the generator say passes Diehard 3, then we
can assume that it has acceptable random bit sequences. There are several of
the Diehard tests that stress this characteristic. You can go to more severe
testing using L'Ecuyer's tests to assure this characteristic.

I have no idea if the mersine twister will pass L'Ecuyer's tests. It is
really is an old generator.

If 32 bit sequential segments of the sequence are cut out and taken as an
unsigned long integer, then we have a good random number sequence, between
2^32 and 0. If we convert to a signed long integer, the numbers are now
positive and negative, and the limits of the numbers as a uniform
distribution are 2^31 to -2^31-1. We still have a uniform distribution.

If however 64 bit sequences are taken and taken as a double precision
floating point number, then we have totally lost the two critical aspects, a
uniform distribution between a lower and upper limit and a random
characteristic of the number in a decimal sense. A double precision floating
point number really has 65 bits, where the extra bit is a hidden bit,
assigned a value of 1, and the 52 bit mantissa shifted left to assure that
the hidden bit is one.

David Heiser