<s>
Multiplicative	B-Algorithm
binary	I-Algorithm
search	I-Algorithm
was	O
first	O
described	O
by	O
Thomas	O
Standish	O
in	O
1980	O
.	O
</s>
<s>
On	O
modern	O
hardware	O
,	O
the	O
cache-friendly	O
nature	O
of	O
multiplicative	B-Algorithm
binary	I-Algorithm
search	I-Algorithm
makes	O
it	O
suitable	O
for	O
out-of-core	B-Application
search	O
on	O
block-oriented	B-General_Concept
storage	O
as	O
an	O
alternative	O
to	O
B-trees	B-Architecture
and	O
B+	O
trees	O
.	O
</s>
<s>
For	O
optimal	O
performance	O
,	O
the	O
branching	B-Data_Structure
factor	I-Data_Structure
of	O
a	O
B-tree	B-Architecture
or	O
B+	O
-tree	O
must	O
match	O
the	O
block	B-General_Concept
size	I-General_Concept
of	O
the	O
file	B-Application
system	I-Application
that	O
it	O
is	O
stored	O
on	O
.	O
</s>
<s>
The	O
permutation	O
used	O
by	O
multiplicative	B-Algorithm
binary	I-Algorithm
search	I-Algorithm
places	O
the	O
optimal	O
number	O
of	O
keys	O
in	O
the	O
first	O
(	O
root	O
)	O
block	O
,	O
regardless	O
of	O
block	B-General_Concept
size	I-General_Concept
.	O
</s>
<s>
Multiplicative	B-Algorithm
binary	I-Algorithm
search	I-Algorithm
is	O
used	O
by	O
some	O
optimizing	B-Application
compilers	I-Application
to	O
implement	O
switch	O
statements	O
.	O
</s>
<s>
Multiplicative	B-Algorithm
binary	I-Algorithm
search	I-Algorithm
operates	O
on	O
a	O
permuted	O
sorted	O
array	B-Data_Structure
.	O
</s>
<s>
Keys	O
are	O
stored	O
in	O
the	O
array	B-Data_Structure
in	O
level-order	O
sequence	O
of	O
the	O
corresponding	O
balanced	O
binary	B-Language
search	I-Language
tree	I-Language
.	O
</s>
<s>
This	O
places	O
the	O
first	O
pivot	O
of	O
a	O
binary	O
search	O
as	O
the	O
first	O
element	O
in	O
the	O
array	B-Data_Structure
.	O
</s>
<s>
Given	O
an	O
array	B-Data_Structure
A	O
of	O
n	O
elements	O
with	O
values	O
A0	O
...	O
An−1	O
,	O
and	O
target	O
value	O
T	O
,	O
the	O
following	O
subroutine	O
uses	O
multiplicative	B-Algorithm
binary	I-Algorithm
search	I-Algorithm
to	O
find	O
the	O
index	O
of	O
T	O
in	O
A	O
.	O
</s>
