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Note that the range of convergence of this algorithm is limited to [-99.99°, 99.99°],
which can be extended to entire coordinate space using the properties of sine and
cosine functions, using an extra iteration for full-range rotation. The overall scaling-
factor of above CORDIC iterations is given by (3).
1
12
⁄
(3)
2.2
Unified CORDIC Algorithm
Walther [7] has extended the scope of conventional CORDIC algorithm to include
linear and hyperbolic trajectory along with circular trajectory. Due to this extension,
the application and usefulness of CORDIC is broadened since computing of various
other functions such as exponential and logarithmic becomes possible. A variable (m)
for defining the trajectory was introduced to modify the basic CORDIC rotation
matrix and elementary angle 'ʱi' as:
·
1 ·
·2
·
·2
1
√1·2
and
1
1
√
√
·2
where,
1 circular
0 linear
1 hyperbolic
where
2.3
The Three Dimensional CORDIC Algorithm
The CORDIC algorithm is extended to three dimensional coordinate space by [8-9].
A vector in three dimensional space has Cartesian coordinates (X
i
, Y
i
, Z
i
) and
spherical coordinates (R
i
, θ
i
, ʦ
i
). The vector can be rotated by an angle ʱ
i
around the
z axis and by an angle ʲ
i
away from the z axis to become a new vector which has
coordinates (X
i+1
, Y
i+1
, Z
i+1
) and spherical coordinates (R
i
, θ
i
+ ʱ
i
, ʦ
i
+ ʲ
i
).
cos
sin
sin
sin
cos
(4)
