A High-Sp eed CORDIC Algorithm and
Architecture for DSP Applications
Martin Kuhlmann, Keshab K. Parhi
Dept. of Electrical and Computer Engineering
University of Minnesota, Minneap olis MN 55455, USA
Email:
f
kuhlmann, parhi
g
@ece.umn.edu
Abstract - This pap er presentsanovel CORDIC algorithm and ar-
chitecture for the rotation and vectoring mode in circular coordinate
systems in which the directions of all micro-rotations are precomputed
while maintaining a constant scale factor. Thus, an examination of the
sign of the angle or
y
-remainder after each iteration is no longer required.
By using Most-Signicant Digit (MSD) rst adder/multiplier, the criti-
cal path of the entire CORDIC architecture only requires
(1
:
5
n
+2)
and
(1
:
5
n
+ 10)
full-adders (
n
corresponds to the word-length of the inputs)
for rotation and vectoring mo des, respectively. This is a speed improve-
ment of ab out 30% compared to the previously fastest reported shared
rotation and vectoring mode implementations. Additionally, there is a
higher degree of freedom in choosing the pip eline cutsets due to the novel
independence of iteration i and i-1 in the CORDIC rotation. Optional
pipelining can lead for example to an on-line delay of three clo ck-cycles
where every clock cycles corresponds to a delayoftwelve full-adders.
1 Intro duction
CORDIC (COordinate Rotation DIgital Computer) [1, 2] is an iterative al-
gorithm for the calculation of the rotation of a two-dimensional vector, in
linear, circular or hyperb olic co ordinate systems, using only add and shift op-
erations. Its current applications are in the eld of digital signal processing,
image processing, ltering, matrix algebra, etc [3].
The CORDIC algorithm consists of two op erating modes, the rotation
mode and the vectoring mo de, respectively. In the rotation mo de, avector
(x,y) is rotated by an angle
to obtain the new vector (
x
;y
). In every
micro-rotation
i
, xed angles of the value arctan(2
,
i
) which are stored in a
ROM are subtracted or added from/to the angle remainder
i
, so that the
angle remainder approaches zero. In the vectoring mode, the length R and
the angle towards the x-axis
of a vector (x,y) are computed (see Fig. 1). For
this purp ose, the vector is rotated towards the x-axis so that the y-comp onent
This work was supported by the Defense Advanced Research Projects Agency under
contract number DA/DABT63-96-C-0050.
