<s>
In	O
modular	O
arithmetic	O
,	O
Barrett	B-Algorithm
reduction	I-Algorithm
is	O
a	O
reduction	O
algorithm	O
introduced	O
in	O
1986	O
by	O
P.D.	O
</s>
<s>
would	O
be	O
to	O
use	O
a	O
fast	O
division	B-Algorithm
algorithm	I-Algorithm
.	O
</s>
<s>
Barrett	B-Algorithm
reduction	I-Algorithm
is	O
an	O
algorithm	O
designed	O
to	O
optimize	O
this	O
operation	O
assuming	O
is	O
constant	O
,	O
and	O
,	O
replacing	O
divisions	O
by	O
multiplications	O
.	O
</s>
<s>
Let	O
be	O
the	O
inverse	O
of	O
as	O
a	O
floating	B-Algorithm
point	I-Algorithm
number	I-Algorithm
.	O
</s>
<s>
Thus	O
Barrett	B-Algorithm
reduction	I-Algorithm
approximates	O
with	O
a	O
value	O
because	O
division	O
by	O
is	O
just	O
a	O
right-shift	O
and	O
so	O
it	O
is	O
cheap	O
.	O
</s>
<s>
Barrett	O
's	O
primary	O
motivation	O
for	O
considering	O
reduction	O
was	O
the	O
implementation	O
of	O
RSA	B-Architecture
,	O
where	O
the	O
values	O
in	O
question	O
will	O
almost	O
certainly	O
exceed	O
the	O
size	O
of	O
a	O
machine	O
word	O
.	O
</s>
