<s>
A	O
Lagged	B-Algorithm
Fibonacci	I-Algorithm
generator	I-Algorithm
(	O
LFG	O
or	O
sometimes	O
LFib	O
)	O
is	O
an	O
example	O
of	O
a	O
pseudorandom	B-Algorithm
number	I-Algorithm
generator	I-Algorithm
.	O
</s>
<s>
This	O
class	O
of	O
random	O
number	O
generator	O
is	O
aimed	O
at	O
being	O
an	O
improvement	O
on	O
the	O
'	O
standard	O
 '	O
linear	B-Algorithm
congruential	I-Algorithm
generator	I-Algorithm
.	O
</s>
<s>
These	O
are	O
based	O
on	O
a	O
generalisation	O
of	O
the	O
Fibonacci	B-Algorithm
sequence	I-Algorithm
.	O
</s>
<s>
The	O
Fibonacci	B-Algorithm
sequence	I-Algorithm
may	O
be	O
described	O
by	O
the	O
recurrence	O
relation	O
:	O
</s>
<s>
This	O
may	O
be	O
either	O
addition	O
,	O
subtraction	O
,	O
multiplication	O
,	O
or	O
the	O
bitwise	O
exclusive-or	O
operator	O
(	O
XOR	B-Application
)	O
.	O
</s>
<s>
If	O
the	O
operation	O
used	O
is	O
addition	O
,	O
then	O
the	O
generator	O
is	O
described	O
as	O
an	O
Additive	O
Lagged	B-Algorithm
Fibonacci	I-Algorithm
Generator	I-Algorithm
or	O
ALFG	O
,	O
if	O
multiplication	O
is	O
used	O
,	O
it	O
is	O
a	O
Multiplicative	O
Lagged	B-Algorithm
Fibonacci	I-Algorithm
Generator	I-Algorithm
or	O
MLFG	O
,	O
and	O
if	O
the	O
XOR	B-Application
operation	O
is	O
used	O
,	O
it	O
is	O
called	O
a	O
Two-tap	O
generalised	B-Architecture
feedback	I-Architecture
shift	I-Architecture
register	I-Architecture
or	O
GFSR	B-Architecture
.	O
</s>
<s>
The	O
Mersenne	B-Algorithm
Twister	I-Algorithm
algorithm	O
is	O
a	O
variation	O
on	O
a	O
GFSR	B-Architecture
.	O
</s>
<s>
The	O
GFSR	B-Architecture
is	O
also	O
related	O
to	O
the	O
linear-feedback	B-Architecture
shift	I-Architecture
register	I-Architecture
,	O
or	O
LFSR	B-Architecture
.	O
</s>
<s>
The	O
maximum	O
period	O
of	O
lagged	B-Algorithm
Fibonacci	I-Algorithm
generators	I-Algorithm
depends	O
on	O
the	O
binary	O
operation	O
.	O
</s>
<s>
If	O
bitwise	O
xor	B-Application
is	O
used	O
,	O
the	O
maximum	O
period	O
is	O
2k	O
−	O
1	O
.	O
</s>
<s>
Another	O
list	O
of	O
possible	O
values	O
for	O
j	O
and	O
k	O
is	O
on	O
page	O
29	O
of	O
volume	O
2	O
of	O
The	B-General_Concept
Art	I-General_Concept
of	I-General_Concept
Computer	I-General_Concept
Programming	I-General_Concept
:	O
</s>
<s>
In	O
a	O
paper	O
on	O
four-tap	O
shift	O
registers	O
,	O
Robert	O
M	O
.	O
Ziff	O
,	O
referring	O
to	O
LFGs	O
that	O
use	O
the	O
XOR	B-Application
operator	O
,	O
states	O
that	O
"	O
It	O
is	O
now	O
widely	O
known	O
that	O
such	O
generators	O
,	O
in	O
particular	O
with	O
the	O
two-tap	O
rules	O
such	O
as	O
R(103, 250 )	O
,	O
have	O
serious	O
deficiencies	O
.	O
</s>
<s>
Freeciv	B-Application
uses	O
a	O
lagged	B-Algorithm
Fibonacci	I-Algorithm
generator	I-Algorithm
with	O
{	O
j	O
=	O
24	O
,	O
k	O
=	O
55}	O
for	O
its	O
random	O
number	O
generator	O
.	O
</s>
<s>
The	O
Boost	B-Language
library	I-Language
includes	O
an	O
implementation	O
of	O
a	O
lagged	B-Algorithm
Fibonacci	I-Algorithm
generator	I-Algorithm
.	O
</s>
<s>
Subtract	B-Algorithm
with	I-Algorithm
carry	I-Algorithm
,	O
a	O
lagged	B-Algorithm
Fibonacci	I-Algorithm
generator	I-Algorithm
engine	O
,	O
is	O
included	O
in	O
the	O
C++11	B-Language
library	O
.	O
</s>
<s>
The	O
Oracle	B-General_Concept
Database	I-General_Concept
implements	O
this	O
generator	O
in	O
its	O
DBMS_RANDOM	O
package	O
(	O
available	O
in	O
Oracle	B-General_Concept
8	O
and	O
newer	O
versions	O
)	O
.	O
</s>
