Talk:Lagged Fibonacci generator

Large number of cycles?

I don't believe that this statement is true, is it?

"any maximum period LFG has a large number of possible cycles, all different"

For example, many M-sequences have only two cycles, one of length 2^N-1, and one of length 1 (the element 0)

I also believe that many additive LFGs have only a very small number of cycles, with extremely long cycles.

Dubious claim?

"It is important that M be greater than 100 for the additive case"

This isn't true so I've removed it. OoS (talk) 11:49, 22 November 2007 (UTC)[reply]

Reference to The Art of Computer Programming

"Another list of possible values for j and k is on page 28 of volume 2 of The Art of Computer Programming"

Not in the third edition. In the third edition the list is as follows (table 1, page 29):

(24,55), (38,89), (37,100), (30, 127), (83,258), (107,378), (273,607), (1029,2281), (576,3217), (4187,9689), (7083,19937), (9739,23209)

OoS (talk) 17:43, 23 November 2007 (UTC)[reply]

Mention of Matlab

Matlab by default now uses the mersenne twister, article needs updating to clarify —Preceding unsigned comment added by 80.3.31.37 (talk) 12:33, 27 September 2010 (UTC)[reply]

Error in definition of the maximum period

In the article you can find the following error:

Lagged Fibonacci generators have a maximum period of (2k - 1)*2M-1 if addition or subtraction is used, and (2^k-1)*k if exclusive-or operations are used to combine the previous values.

Correct is the following:

In the case if the xor operation is used as binary operation in the Lagged Fibonacci generators the period p equals to (2^k-1)*k only if (gcd(2^k-1, k) = 1). In all other cases the period p equals to lcm(2^k-1, k).

The following table lists some examples for small values of k:

k	(2^k-1)*k	lcm(2^k-1, k)	gcd(2^k-1, k)
3	21	21	1
4	60	60	1
5	155	155	1
6	378	126	3
7	889	889	1
8	2040	2040	1
...
12	49140	16380	3
...
18	4718574	524286	9
19	9961453	9961453	1
20	20971500	4194300	5
21	44040171	6291453	7
...

Legend: (gcd: greatest common divisor; lcm: least common multiple)

--Aragorn321 (talk) 20:37, 15 February 2013 (UTC)[reply]

vandalized page

79.112.127.128 (talk) 21:13, 29 April 2013 (UTC)[reply]