Question

Consider the .NET Random stream:

var r = new Random(); 
while (true) 
{ 
    r.Next(); 
}

How long does it take to repeat?

Answer 1

According to the documentation:

Pseudo-random numbers are chosen with equal probability from a finite
set of numbers. The chosen numbers are
not completely random because a
definite mathematical algorithm is
used to select them, but they are
sufficiently random for practical
purposes. The current implementation
of the Random class is based on Donald
E. Knuth’s subtractive random number
generator algorithm. For more
information, see D. E. Knuth. “The Art
of Computer Programming, volume 2:
Seminumerical Algorithms”.
Addison-Wesley, Reading, MA, second
edition, 1981.

The subtractive generator (Knuth, Vol 2)
Xf,n = (Xf,n-k – Xf,n-j) mod 1.
See Knuth for a table of possible values of k and j. We choose k = 63, j = 31. This generator is interesting because:

• It has a long period. The period of the least significant bit in this sequence is 2^k-1. The actual period is much longer than this.
• With some mild restrictions, the floating point arithmetic involved is exact!

The second property holds when X is of the form
l 247
(0 � l < 247)
Single-precision arithmetic is exact on the Crays (48-bit mantissa) and as is double-precision arithmetic on IEEE-compliant machines.

This allows the basic random number sequence to be generated by the Fortran code

  x(n) = x(n-k) - x(n-j)
  if (x(n) < 0.0) x(n) = 1.0 + x(n)

In practice random numbers are generated in batches as needed and stored in an array which acts as a circular buffer.

The algorithm mentioned has a period that depends on the seed value – you can find more details here.