<s>
The	O
BKM	B-Algorithm
algorithm	I-Algorithm
is	O
a	O
shift-and-add	B-Algorithm
algorithm	I-Algorithm
for	O
computing	O
elementary	O
functions	O
,	O
first	O
published	O
in	O
1994	O
by	O
Jean-Claude	O
Bajard	O
,	O
Sylvanus	O
Kla	O
,	O
and	O
Jean-Michel	O
Muller	O
.	O
</s>
<s>
By	O
using	O
a	O
precomputed	O
table	O
of	O
logarithms	O
of	O
negative	O
powers	O
of	O
two	O
,	O
the	O
BKM	B-Algorithm
algorithm	I-Algorithm
computes	O
elementary	O
functions	O
using	O
only	O
integer	O
add	O
,	O
shift	O
,	O
and	O
compare	O
operations	O
.	O
</s>
<s>
BKM	O
is	O
similar	O
to	O
CORDIC	B-Algorithm
,	O
but	O
uses	O
a	O
table	O
of	O
logarithms	O
rather	O
than	O
a	O
table	O
of	O
arctangents	O
.	O
</s>
<s>
On	O
each	O
iteration	O
,	O
a	O
choice	O
of	O
coefficient	O
is	O
made	O
from	O
a	O
set	O
of	O
nine	O
complex	O
numbers	O
,	O
1	O
,	O
0	O
,	O
−1	O
,	O
i	O
,	O
−i	O
,	O
1+i	O
,	O
1−i	O
,	O
−1+i	O
,	O
−1−i	O
,	O
rather	O
than	O
only	O
−1	O
or	O
+1	O
as	O
used	O
by	O
CORDIC	B-Algorithm
.	O
</s>
<s>
BKM	O
provides	O
a	O
simpler	O
method	O
of	O
computing	O
some	O
elementary	O
functions	O
,	O
and	O
unlike	O
CORDIC	B-Algorithm
,	O
BKM	O
needs	O
no	O
result	O
scaling	O
factor	O
.	O
</s>
<s>
The	O
convergence	O
rate	O
of	O
BKM	O
is	O
approximately	O
one	O
bit	O
per	O
iteration	O
,	O
like	O
CORDIC	B-Algorithm
,	O
but	O
BKM	O
requires	O
more	O
precomputed	O
table	O
elements	O
for	O
the	O
same	O
precision	O
because	O
the	O
table	O
stores	O
logarithms	O
of	O
complex	O
operands	O
.	O
</s>
<s>
a	O
barrel	O
shifter	O
)	O
or	O
hardware	O
floating	B-Algorithm
point	I-Algorithm
arithmetic	I-Algorithm
.	O
</s>
<s>
Working	O
in	O
either	O
base	O
,	O
the	O
multiplication	O
by	O
s	O
can	O
be	O
replaced	O
with	O
direct	O
modification	O
of	O
the	O
floating	B-Algorithm
point	I-Algorithm
exponent	O
,	O
subtracting	O
1	O
from	O
it	O
during	O
each	O
iteration	O
.	O
</s>
