<s>
CORDIC	B-Algorithm
(	O
for	O
"	O
coordinate	B-Algorithm
rotation	I-Algorithm
digital	I-Algorithm
computer	I-Algorithm
"	O
)	O
,	O
also	O
known	O
as	O
Volder	B-Algorithm
's	I-Algorithm
algorithm	I-Algorithm
,	O
or	O
:	O
Digit-by-digit	B-Algorithm
method	I-Algorithm
Circular	B-Algorithm
CORDIC	I-Algorithm
(	O
Jack	O
E	O
.	O
Volder	O
)	O
,	O
Linear	B-Algorithm
CORDIC	I-Algorithm
,	O
Hyperbolic	O
CORDIC	B-Algorithm
(	O
John	O
Stephen	O
Walther	O
)	O
,	O
and	O
Generalized	B-Algorithm
Hyperbolic	I-Algorithm
CORDIC	I-Algorithm
(	O
GH	B-Algorithm
CORDIC	I-Algorithm
)	O
(	O
Yuanyong	O
Luo	O
et	O
al	O
.	O
</s>
<s>
CORDIC	B-Algorithm
is	O
therefore	O
also	O
an	O
example	O
of	O
digit-by-digit	O
algorithms	O
.	O
</s>
<s>
CORDIC	B-Algorithm
and	O
closely	O
related	O
methods	O
known	O
as	O
pseudo-multiplication	O
and	O
pseudo-division	O
or	O
factor	O
combining	O
are	O
commonly	O
used	O
when	O
no	O
hardware	O
multiplier	O
is	O
available	O
(	O
e.g.	O
</s>
<s>
in	O
simple	O
microcontrollers	B-Architecture
and	O
FPGAs	B-Architecture
)	O
,	O
as	O
the	O
only	O
operations	O
it	O
requires	O
are	O
additions	O
,	O
subtractions	O
,	O
bitshift	O
and	O
lookup	B-Data_Structure
tables	I-Data_Structure
.	O
</s>
<s>
As	O
such	O
,	O
they	O
all	O
belong	O
to	O
the	O
class	O
of	O
shift-and-add	B-Algorithm
algorithms	I-Algorithm
.	O
</s>
<s>
In	O
computer	O
science	O
,	O
CORDIC	B-Algorithm
is	O
often	O
used	O
to	O
implement	O
floating-point	B-Algorithm
arithmetic	I-Algorithm
when	O
the	O
target	O
platform	O
lacks	O
hardware	O
multiply	O
for	O
cost	O
or	O
space	O
reasons	O
.	O
</s>
<s>
Similar	O
mathematical	O
techniques	O
were	O
published	O
by	O
Henry	O
Briggs	O
as	O
early	O
as	O
1624	O
and	O
RobertFlower	O
in	O
1771	O
,	O
but	O
CORDIC	B-Algorithm
is	O
better	O
optimized	O
for	O
low-complexity	O
finite-state	O
CPUs	O
.	O
</s>
<s>
CORDIC	B-Algorithm
was	O
conceived	O
in	O
1956	O
by	O
Jack	O
E	O
.	O
Volder	O
at	O
the	O
aeroelectronics	O
department	O
of	O
Convair	O
out	O
of	O
necessity	O
to	O
replace	O
the	O
analog	O
resolver	O
in	O
the	O
B-58	O
bomber	O
's	O
navigation	O
computer	O
with	O
a	O
more	O
accurate	O
and	O
faster	O
real-time	O
digital	O
solution	O
.	O
</s>
<s>
Therefore	O
,	O
CORDIC	B-Algorithm
is	O
sometimes	O
referred	O
to	O
as	O
a	O
digital	O
resolver	O
.	O
</s>
<s>
His	O
research	O
led	O
to	O
an	O
internal	O
technical	O
report	O
proposing	O
the	O
CORDIC	B-Algorithm
algorithm	I-Algorithm
to	O
solve	O
sine	O
and	O
cosine	O
functions	O
and	O
a	O
prototypical	O
computer	O
implementing	O
it	O
.	O
</s>
<s>
The	O
report	O
also	O
discussed	O
the	O
possibility	O
to	O
compute	O
hyperbolic	O
coordinate	B-General_Concept
rotation	I-General_Concept
,	O
logarithms	O
and	O
exponential	O
functions	O
with	O
modified	O
CORDIC	B-Algorithm
algorithms	I-Algorithm
.	O
</s>
<s>
Utilizing	O
CORDIC	B-Algorithm
for	O
multiplication	O
and	O
division	O
was	O
also	O
conceived	O
at	O
this	O
time	O
.	O
</s>
<s>
Based	O
on	O
the	O
CORDIC	B-Algorithm
principle	O
,	O
DanH.Daggett	O
,	O
a	O
colleague	O
of	O
Volder	O
at	O
Convair	O
,	O
developed	O
conversion	O
algorithms	O
between	O
binary	O
and	O
binary-coded	O
decimal	O
(	O
BCD	O
)	O
.	O
</s>
<s>
In	O
1958	O
,	O
Convair	O
finally	O
started	O
to	O
build	O
a	O
demonstration	O
system	O
to	O
solve	O
radar	O
fix-taking	O
problems	O
named	O
CORDIC	B-Algorithm
I	O
,	O
completed	O
in	O
1960	O
without	O
Volder	O
,	O
who	O
had	O
left	O
the	O
company	O
already	O
.	O
</s>
<s>
More	O
universal	O
CORDIC	B-Algorithm
II	O
models	O
A	O
(	O
stationary	O
)	O
and	O
B	O
(	O
airborne	O
)	O
were	O
built	O
and	O
tested	O
by	O
Daggett	O
and	O
Harry	O
Schuss	O
in	O
1962	O
.	O
</s>
<s>
Volder	B-Algorithm
's	I-Algorithm
CORDIC	I-Algorithm
algorithm	O
was	O
first	O
described	O
in	O
public	O
in	O
1959	O
,	O
which	O
caused	O
it	O
to	O
be	O
incorporated	O
into	O
navigation	O
computers	O
by	O
companies	O
including	O
Martin-Orlando	O
,	O
Computer	O
Control	O
,	O
Litton	O
,	O
Kearfott	O
,	O
Lear-Siegler	O
,	O
Sperry	O
,	O
Raytheon	O
,	O
and	O
Collins	O
Radio	O
.	O
</s>
<s>
Volder	O
teamed	O
up	O
with	O
Malcolm	O
McMillan	O
to	O
build	O
Athena	O
,	O
a	O
fixed-point	O
desktop	O
calculator	O
utilizing	O
his	O
binary	O
CORDIC	B-Algorithm
algorithm	I-Algorithm
.	O
</s>
<s>
Still	O
,	O
McMillan	O
introduced	O
David	O
S	O
.	O
Cochran	O
(	O
HP	O
)	O
to	O
Volder	B-Algorithm
's	I-Algorithm
algorithm	I-Algorithm
and	O
when	O
Cochran	O
later	O
met	O
Volder	O
he	O
referred	O
him	O
to	O
a	O
similar	O
approach	O
John	O
E	O
.	O
Meggitt	O
(	O
IBM	O
)	O
had	O
proposed	O
as	O
pseudo-multiplication	O
and	O
pseudo-division	O
in	O
1961	O
.	O
</s>
<s>
Meggitt	O
's	O
method	O
also	O
suggested	O
the	O
use	O
of	O
base	O
10	O
rather	O
than	O
base	O
2	O
,	O
as	O
used	O
by	O
Volder	B-Algorithm
's	I-Algorithm
CORDIC	I-Algorithm
so	O
far	O
.	O
</s>
<s>
These	O
efforts	O
led	O
to	O
the	O
ROMable	O
logic	O
implementation	O
of	O
a	O
decimal	O
CORDIC	B-Algorithm
prototype	O
machine	O
inside	O
of	O
Hewlett-Packard	O
in	O
1966	O
,	O
built	O
by	O
and	O
conceptually	O
derived	O
from	O
Thomas	O
E	O
.	O
Osborne	O
's	O
prototypical	O
Green	O
Machine	O
,	O
a	O
four-function	O
,	O
floating-point	B-Algorithm
desktop	O
calculator	O
he	O
had	O
completed	O
in	O
DTL	B-General_Concept
logic	O
in	O
December	O
1964	O
.	O
</s>
<s>
John	O
Stephen	O
Walther	O
at	O
Hewlett-Packard	O
generalized	O
the	O
algorithm	O
into	O
the	O
Unified	O
CORDIC	B-Algorithm
algorithm	I-Algorithm
in	O
1971	O
,	O
allowing	O
it	O
to	O
calculate	O
hyperbolic	O
functions	O
,	O
natural	O
exponentials	O
,	O
natural	O
logarithms	O
,	O
multiplications	O
,	O
divisions	O
,	O
and	O
square	O
roots	O
.	O
</s>
<s>
The	O
CORDIC	B-Algorithm
subroutines	O
for	O
trigonometric	O
and	O
hyperbolic	O
functions	O
could	O
share	O
most	O
of	O
their	O
code	O
.	O
</s>
<s>
This	O
development	O
resulted	O
in	O
the	O
first	O
scientific	O
handheld	O
calculator	O
,	O
the	O
HP-35	B-Device
in	O
1972	O
.	O
</s>
<s>
Based	O
on	O
hyperbolic	O
CORDIC	B-Algorithm
,	O
Yuanyong	O
Luo	O
et	O
al	O
.	O
</s>
<s>
further	O
proposed	O
a	O
Generalized	B-Algorithm
Hyperbolic	I-Algorithm
CORDIC	I-Algorithm
(	O
GH	B-Algorithm
CORDIC	I-Algorithm
)	O
to	O
directly	O
compute	O
logarithms	O
and	O
exponentials	O
with	O
an	O
arbitrary	O
fixed	O
base	O
in	O
2019	O
.	O
</s>
<s>
Theoretically	O
,	O
Hyperbolic	O
CORDIC	B-Algorithm
is	O
a	O
special	O
case	O
of	O
GH	B-Algorithm
CORDIC	I-Algorithm
.	O
</s>
<s>
Originally	O
,	O
CORDIC	B-Algorithm
was	O
implemented	O
only	O
using	O
the	O
binary	O
numeral	O
system	O
and	O
despite	O
Meggitt	O
suggesting	O
the	O
use	O
of	O
the	O
decimal	O
system	O
for	O
his	O
pseudo-multiplication	O
approach	O
,	O
decimal	O
CORDIC	B-Algorithm
continued	O
to	O
remain	O
mostly	O
unheard	O
of	O
for	O
several	O
more	O
years	O
,	O
so	O
that	O
Hermann	O
Schmid	O
and	O
Anthony	O
Bogacki	O
still	O
suggested	O
it	O
as	O
a	O
novelty	O
as	O
late	O
as	O
1973	O
and	O
it	O
was	O
found	O
only	O
later	O
that	O
Hewlett-Packard	O
had	O
implemented	O
it	O
in	O
1966	O
already	O
.	O
</s>
<s>
Decimal	O
CORDIC	B-Algorithm
became	O
widely	O
used	O
in	O
pocket	O
calculators	O
,	O
most	O
of	O
which	O
operate	O
in	O
binary-coded	O
decimal	O
(	O
BCD	O
)	O
rather	O
than	O
binary	O
.	O
</s>
<s>
This	O
change	O
in	O
the	O
input	O
and	O
output	O
format	O
did	O
not	O
alter	O
CORDIC	B-Algorithm
's	O
core	O
calculation	O
algorithms	O
.	O
</s>
<s>
CORDIC	B-Algorithm
is	O
particularly	O
well-suited	O
for	O
handheld	O
calculators	O
,	O
in	O
which	O
low	O
cost	O
–	O
and	O
thus	O
low	O
chip	O
gate	O
count	O
–	O
is	O
much	O
more	O
important	O
than	O
speed	O
.	O
</s>
<s>
CORDIC	B-Algorithm
has	O
been	O
implemented	O
in	O
the	O
ARM-based	B-Architecture
STM32G4	O
,	O
Intel	B-Device
8087	I-Device
,	O
80287	O
,	O
80387	O
up	O
to	O
the	O
80486	B-General_Concept
coprocessor	O
series	O
as	O
well	O
as	O
in	O
the	O
Motorola	B-General_Concept
68881	I-General_Concept
and	O
68882	B-General_Concept
for	O
some	O
kinds	O
of	O
floating-point	B-Algorithm
instructions	O
,	O
mainly	O
as	O
a	O
way	O
to	O
reduce	O
the	O
gate	O
counts	O
(	O
and	O
complexity	O
)	O
of	O
the	O
FPU	B-General_Concept
sub-system	O
.	O
</s>
<s>
CORDIC	B-Algorithm
uses	O
simple	O
shift-add	O
operations	O
for	O
several	O
computing	O
tasks	O
such	O
as	O
the	O
calculation	O
of	O
trigonometric	O
,	O
hyperbolic	O
and	O
logarithmic	O
functions	O
,	O
real	O
and	O
complex	O
multiplications	O
,	O
division	O
,	O
square-root	O
calculation	O
,	O
solution	O
of	O
linear	O
systems	O
,	O
eigenvalue	O
estimation	O
,	O
singular	O
value	O
decomposition	O
,	O
QR	O
factorization	O
and	O
many	O
others	O
.	O
</s>
<s>
As	O
a	O
consequence	O
,	O
CORDIC	B-Algorithm
has	O
been	O
used	O
for	O
applications	O
in	O
diverse	O
areas	O
such	O
as	O
signal	O
and	O
image	B-Algorithm
processing	I-Algorithm
,	O
communication	O
systems	O
,	O
robotics	O
and	O
3D	O
graphics	O
apart	O
from	O
general	O
scientific	O
and	O
technical	O
computation	O
.	O
</s>
<s>
CORDIC	B-Algorithm
was	O
used	O
to	O
implement	O
the	O
Intel	B-Device
8087	I-Device
math	B-General_Concept
coprocessor	I-General_Concept
in	O
1980	O
,	O
avoiding	O
the	O
need	O
to	O
implement	O
hardware	O
multiplication	O
.	O
</s>
<s>
CORDIC	B-Algorithm
is	O
generally	O
faster	O
than	O
other	O
approaches	O
when	O
a	O
hardware	O
multiplier	O
is	O
not	O
available	O
(	O
e.g.	O
,	O
a	O
microcontroller	B-Architecture
)	O
,	O
or	O
when	O
the	O
number	O
of	O
gates	O
required	O
to	O
implement	O
the	O
functions	O
it	O
supports	O
should	O
be	O
minimized	O
(	O
e.g.	O
,	O
in	O
an	O
FPGA	B-Architecture
or	O
ASIC	O
)	O
.	O
</s>
<s>
In	O
fact	O
,	O
CORDIC	B-Algorithm
is	O
a	O
standard	O
drop-in	O
IP	B-Architecture
in	O
FPGA	B-Architecture
development	O
applications	O
such	O
as	O
Vivado	O
for	O
Xilinx	O
,	O
while	O
a	O
power	O
series	O
implementation	O
is	O
not	O
due	O
to	O
the	O
specificity	O
of	O
such	O
an	O
IP	B-Architecture
,	O
i.e.	O
</s>
<s>
CORDIC	B-Algorithm
can	O
compute	O
many	O
different	O
functions	O
(	O
general	O
purpose	O
)	O
while	O
a	O
hardware	O
multiplier	O
configured	O
to	O
execute	O
power	O
series	O
implementations	O
can	O
only	O
compute	O
the	O
function	O
it	O
was	O
designed	O
for	O
.	O
</s>
<s>
On	O
the	O
other	O
hand	O
,	O
when	O
a	O
hardware	O
multiplier	O
is	O
available	O
(	O
e.g.	O
,	O
in	O
a	O
DSP	B-General_Concept
microprocessor	O
)	O
,	O
table-lookup	O
methods	O
and	O
power	O
series	O
are	O
generally	O
faster	O
than	O
CORDIC	B-Algorithm
.	O
</s>
<s>
In	O
recent	O
years	O
,	O
the	O
CORDIC	B-Algorithm
algorithm	I-Algorithm
has	O
been	O
used	O
extensively	O
for	O
various	O
biomedical	O
applications	O
,	O
especially	O
in	O
FPGA	B-Architecture
implementations	O
.	O
</s>
<s>
The	O
STM32G4	O
series	O
and	O
certain	O
STM32H7	O
series	O
of	O
MCUs	O
implement	O
a	O
CORDIC	B-Algorithm
module	O
to	O
accelerate	O
computations	O
in	O
various	O
mixed	O
signal	O
applications	O
such	O
as	O
graphics	O
for	O
human-machine	B-Application
interface	I-Application
and	O
field	O
oriented	O
control	O
of	O
motors	O
.	O
</s>
<s>
While	O
not	O
as	O
fast	O
as	O
a	O
power	O
series	O
approximation	O
,	O
CORDIC	B-Algorithm
is	O
indeed	O
faster	O
than	O
interpolating	O
table	O
based	O
implementations	O
such	O
as	O
the	O
ones	O
provided	O
by	O
the	O
ARM	O
CMSIS	O
and	O
C	O
standard	O
libraries	O
.	O
</s>
<s>
Though	O
the	O
results	O
may	O
be	O
slightly	O
less	O
accurate	O
as	O
the	O
CORDIC	B-Algorithm
modules	O
provided	O
only	O
achieve	O
20	O
bits	O
of	O
precision	O
in	O
the	O
result	O
.	O
</s>
<s>
For	O
example	O
,	O
most	O
of	O
the	O
performance	O
difference	O
compared	O
to	O
the	O
ARM	O
implementation	O
is	O
due	O
to	O
the	O
overhead	O
of	O
the	O
interpolation	O
algorithm	O
,	O
which	O
achieves	O
full	O
floating	B-Algorithm
point	I-Algorithm
precision	O
(	O
24	O
bits	O
)	O
and	O
can	O
likely	O
achieve	O
relative	O
error	O
to	O
that	O
precision	O
.	O
</s>
<s>
Another	O
benefit	O
is	O
that	O
the	O
CORDIC	B-Algorithm
module	O
is	O
a	O
coprocessor	O
and	O
can	O
be	O
run	O
in	O
parallel	O
with	O
other	O
CPU	O
tasks	O
.	O
</s>
<s>
Other	O
means	O
of	O
polynomial	O
approximation	O
,	O
such	O
as	O
minimax	B-Algorithm
optimization	O
,	O
may	O
be	O
used	O
to	O
control	O
both	O
kinds	O
of	O
error	O
.	O
</s>
<s>
Many	O
older	O
systems	O
with	O
integer-only	O
CPUs	O
have	O
implemented	O
CORDIC	B-Algorithm
to	O
varying	O
extents	O
as	O
part	O
of	O
their	O
IEEE	O
floating-point	B-Algorithm
libraries	O
.	O
</s>
<s>
As	O
most	O
modern	O
general-purpose	O
CPUs	O
have	O
floating-point	B-Algorithm
registers	O
with	O
common	O
operations	O
such	O
as	O
add	O
,	O
subtract	O
,	O
multiply	O
,	O
divide	O
,	O
sine	O
,	O
cosine	O
,	O
square	O
root	O
,	O
log10	O
,	O
natural	O
log	O
,	O
the	O
need	O
to	O
implement	O
CORDIC	B-Algorithm
in	O
them	O
with	O
software	O
is	O
nearly	O
non-existent	O
.	O
</s>
<s>
Only	O
microcontroller	B-Architecture
or	O
special	O
safety	O
and	O
time-constrained	O
software	O
applications	O
would	O
need	O
to	O
consider	O
using	O
CORDIC	B-Algorithm
.	O
</s>
<s>
CORDIC	B-Algorithm
can	O
be	O
used	O
to	O
calculate	O
a	O
number	O
of	O
different	O
functions	O
.	O
</s>
<s>
This	O
explanation	O
shows	O
how	O
to	O
use	O
CORDIC	B-Algorithm
in	O
rotation	O
mode	O
to	O
calculate	O
the	O
sine	O
and	O
cosine	O
of	O
an	O
angle	O
,	O
assuming	O
that	O
the	O
desired	O
angle	O
is	O
given	O
in	O
radians	O
and	O
represented	O
in	O
a	O
fixed-point	O
format	O
.	O
</s>
<s>
Using	O
CORDIC	B-Algorithm
,	O
one	O
would	O
start	O
with	O
the	O
vector	O
:	O
</s>
<s>
More	O
formally	O
,	O
every	O
iteration	O
calculates	O
a	O
rotation	O
,	O
which	O
is	O
performed	O
by	O
multiplying	O
the	O
vector	O
with	O
the	O
rotation	B-Algorithm
matrix	I-Algorithm
:	O
</s>
<s>
The	O
following	O
is	O
a	O
MATLAB/GNU	O
Octave	O
implementation	O
of	O
CORDIC	B-Algorithm
that	O
does	O
not	O
rely	O
on	O
any	O
transcendental	O
functions	O
except	O
in	O
the	O
precomputation	O
of	O
tables	O
.	O
</s>
<s>
With	O
MATLAB	B-Language
's	O
standard	O
double-precision	O
arithmetic	O
and	O
"	O
format	O
long	O
"	O
printout	O
,	O
the	O
results	O
increase	O
in	O
accuracy	O
for	O
n	O
up	O
to	O
about	O
48	O
.	O
</s>
<s>
In	O
Java	O
the	O
Math	O
class	O
has	O
a	O
scalb(double x,int scale )	O
method	O
to	O
perform	O
such	O
a	O
shift	O
,	O
C	O
has	O
the	O
ldexp	O
function	O
,	O
and	O
the	O
x86	O
class	O
of	O
processors	O
have	O
the	O
fscale	O
floating	B-Algorithm
point	I-Algorithm
operation	O
.	O
</s>
<s>
The	O
number	O
of	O
logic	O
gates	O
for	O
the	O
implementation	O
of	O
a	O
CORDIC	B-Algorithm
is	O
roughly	O
comparable	O
to	O
the	O
number	O
required	O
for	O
a	O
multiplier	O
as	O
both	O
require	O
combinations	O
of	O
shifts	O
and	O
additions	O
.	O
</s>
<s>
The	O
choice	O
for	O
a	O
multiplier-based	O
or	O
CORDIC-based	O
implementation	O
will	O
depend	O
on	O
the	O
context	O
.	O
</s>
<s>
The	O
multiplication	O
of	O
two	O
complex	O
numbers	O
represented	O
by	O
their	O
real	O
and	O
imaginary	O
components	O
(	O
rectangular	O
coordinates	O
)	O
,	O
for	O
example	O
,	O
requires	O
4	O
multiplications	O
,	O
but	O
could	O
be	O
realized	O
by	O
a	O
single	O
CORDIC	B-Algorithm
operating	O
on	O
complex	O
numbers	O
represented	O
by	O
their	O
polar	O
coordinates	O
,	O
especially	O
if	O
the	O
magnitude	O
of	O
the	O
numbers	O
is	O
not	O
relevant	O
(	O
multiplying	O
a	O
complex	O
vector	O
with	O
a	O
vector	O
on	O
the	O
unit	O
circle	O
actually	O
amounts	O
to	O
a	O
rotation	O
)	O
.	O
</s>
<s>
CORDICs	B-Algorithm
are	O
often	O
used	O
in	O
circuits	O
for	O
telecommunications	O
such	O
as	O
digital	B-Algorithm
down	I-Algorithm
converters	I-Algorithm
.	O
</s>
<s>
Double	O
iterations	O
method	O
consists	O
in	O
the	O
fact	O
that	O
unlike	O
the	O
classical	O
CORDIC	B-Algorithm
method	O
,	O
where	O
the	O
iteration	O
step	O
value	O
changes	O
EVERY	O
time	O
,	O
i.e.	O
</s>
<s>
The	O
generalization	O
of	O
the	O
CORDIC	B-Algorithm
convergence	O
problems	O
for	O
the	O
arbitrary	O
positional	O
number	O
system	O
with	O
Radix	O
R	O
showed	O
that	O
for	O
the	O
functions	O
sin	O
,	O
cos	O
,	O
arctg	O
,	O
it	O
is	O
enough	O
to	O
perform	O
(	O
R-1	O
)	O
iterations	O
for	O
each	O
value	O
of	O
i	O
(	O
i	O
=	O
0	O
or	O
1	O
to	O
n	O
,	O
where	O
n	O
is	O
the	O
number	O
of	O
digits	O
)	O
,	O
i.e.	O
</s>
<s>
CORDIC	B-Algorithm
is	O
part	O
of	O
the	O
class	O
of	O
"	O
shift-and-add	O
"	O
algorithms	O
,	O
as	O
are	O
the	O
logarithm	O
and	O
exponential	O
algorithms	O
derived	O
from	O
Henry	O
Briggs	O
 '	O
work	O
.	O
</s>
<s>
Another	O
shift-and-add	B-Algorithm
algorithm	I-Algorithm
which	O
can	O
be	O
used	O
for	O
computing	O
many	O
elementary	O
functions	O
is	O
the	O
BKM	B-Algorithm
algorithm	I-Algorithm
,	O
which	O
is	O
a	O
generalization	O
of	O
the	O
logarithm	O
and	O
exponential	O
algorithms	O
to	O
the	O
complex	O
plane	O
.	O
</s>
<s>
The	O
BKM	B-Algorithm
algorithm	I-Algorithm
is	O
slightly	O
more	O
complex	O
than	O
CORDIC	B-Algorithm
,	O
but	O
has	O
the	O
advantage	O
that	O
it	O
does	O
not	O
need	O
a	O
scaling	O
factor	O
(	O
K	O
)	O
.	O
</s>
