<s>
In	O
computer	B-General_Concept
science	I-General_Concept
,	O
the	O
Fibonacci	B-Algorithm
search	I-Algorithm
technique	I-Algorithm
is	O
a	O
method	O
of	O
searching	O
a	O
sorted	B-Data_Structure
array	I-Data_Structure
using	O
a	O
divide	B-Algorithm
and	I-Algorithm
conquer	I-Algorithm
algorithm	I-Algorithm
that	O
narrows	O
down	O
possible	O
locations	O
with	O
the	O
aid	O
of	O
Fibonacci	B-Algorithm
numbers	I-Algorithm
.	O
</s>
<s>
Compared	O
to	O
binary	O
search	O
where	O
the	O
sorted	B-Data_Structure
array	I-Data_Structure
is	O
divided	O
into	O
two	O
equal-sized	O
parts	O
,	O
one	O
of	O
which	O
is	O
examined	O
further	O
,	O
Fibonacci	B-Algorithm
search	I-Algorithm
divides	O
the	O
array	O
into	O
two	O
parts	O
that	O
have	O
sizes	O
that	O
are	O
consecutive	O
Fibonacci	B-Algorithm
numbers	I-Algorithm
.	O
</s>
<s>
On	O
average	O
,	O
this	O
leads	O
to	O
about	O
4%	O
more	O
comparisons	O
to	O
be	O
executed	O
,	O
but	O
it	O
has	O
the	O
advantage	O
that	O
one	O
only	O
needs	O
addition	O
and	O
subtraction	O
to	O
calculate	O
the	O
indices	O
of	O
the	O
accessed	O
array	O
elements	O
,	O
while	O
classical	O
binary	O
search	O
needs	O
bit-shift	O
(	O
see	O
Bitwise	O
operation	O
)	O
,	O
division	O
or	O
multiplication	O
,	O
operations	O
that	O
were	O
less	O
common	O
at	O
the	O
time	O
Fibonacci	B-Algorithm
search	I-Algorithm
was	O
first	O
published	O
.	O
</s>
<s>
Fibonacci	B-Algorithm
search	I-Algorithm
has	O
an	O
average	O
-	O
and	O
worst-case	O
complexity	O
of	O
O(log n )	O
(	O
see	O
Big	O
O	O
notation	O
)	O
.	O
</s>
<s>
The	O
Fibonacci	B-Algorithm
sequence	I-Algorithm
has	O
the	O
property	O
that	O
a	O
number	O
is	O
the	O
sum	O
of	O
its	O
two	O
predecessors	O
.	O
</s>
<s>
Fibonacci	B-Algorithm
search	I-Algorithm
can	O
divide	O
it	O
into	O
parts	O
approaching	O
1:1.618	O
while	O
using	O
the	O
simpler	O
operations	O
.	O
</s>
<s>
If	O
the	O
elements	O
being	O
searched	O
have	O
non-uniform	O
access	O
memory	O
storage	O
(	O
i	O
.	O
e.	O
,	O
the	O
time	O
needed	O
to	O
access	O
a	O
storage	O
location	O
varies	O
depending	O
on	O
the	O
location	O
accessed	O
)	O
,	O
the	O
Fibonacci	B-Algorithm
search	I-Algorithm
may	O
have	O
the	O
advantage	O
over	O
binary	O
search	O
in	O
slightly	O
reducing	O
the	O
average	O
time	O
needed	O
to	O
access	O
a	O
storage	O
location	O
.	O
</s>
<s>
If	O
the	O
machine	O
executing	O
the	O
search	O
has	O
a	O
direct	O
mapped	O
CPU	B-General_Concept
cache	I-General_Concept
,	O
binary	O
search	O
may	O
lead	O
to	O
more	O
cache	O
misses	O
because	O
the	O
elements	O
that	O
are	O
accessed	O
often	O
tend	O
to	O
gather	O
in	O
only	O
a	O
few	O
cache	O
lines	O
;	O
this	O
is	O
mitigated	O
by	O
splitting	O
the	O
array	O
in	O
parts	O
that	O
do	O
not	O
tend	O
to	O
be	O
powers	O
of	O
two	O
.	O
</s>
<s>
If	O
the	O
data	O
is	O
stored	O
on	O
a	O
magnetic	B-Architecture
tape	I-Architecture
where	O
seek	O
time	O
depends	O
on	O
the	O
current	O
head	O
position	O
,	O
a	O
tradeoff	O
between	O
longer	O
seek	O
time	O
and	O
more	O
comparisons	O
may	O
lead	O
to	O
a	O
search	B-Application
algorithm	I-Application
that	O
is	O
skewed	O
similarly	O
to	O
Fibonacci	B-Algorithm
search	I-Algorithm
.	O
</s>
<s>
Fibonacci	B-Algorithm
search	I-Algorithm
is	O
derived	O
from	O
Golden	B-Algorithm
section	I-Algorithm
search	I-Algorithm
,	O
an	O
algorithm	O
by	O
Jack	O
Kiefer	O
(	O
1953	O
)	O
to	O
search	O
for	O
the	O
maximum	O
or	O
minimum	O
of	O
a	O
unimodal	O
function	O
in	O
an	O
interval	O
.	O
</s>
<s>
Let	O
k	O
be	O
defined	O
as	O
an	O
element	O
in	O
F	O
,	O
the	O
array	O
of	O
Fibonacci	B-Algorithm
numbers	I-Algorithm
.	O
</s>
<s>
If	O
n	O
is	O
not	O
a	O
Fibonacci	B-Algorithm
number	I-Algorithm
,	O
let	O
Fm	O
be	O
the	O
smallest	O
number	O
in	O
F	O
that	O
is	O
greater	O
than	O
n	O
.	O
</s>
<s>
The	O
array	O
of	O
Fibonacci	B-Algorithm
numbers	I-Algorithm
is	O
defined	O
where	O
Fk+2	O
=	O
Fk+1+Fk	O
,	O
when	O
k≥0	O
,	O
F1	O
=	O
1	O
,	O
and	O
F0	O
=	O
1	O
.	O
</s>
<s>
This	O
has	O
the	O
advantage	O
that	O
the	O
new	O
i	O
is	O
closer	O
to	O
the	O
old	O
i	O
and	O
is	O
more	O
suitable	O
for	O
accelerating	O
searching	O
on	O
magnetic	B-Architecture
tape	I-Architecture
.	O
</s>
