cordicatan2
CORDICbased four quadrant inverse tangent
Syntax
theta = cordicatan2(y,x)
theta = cordicatan2(y,x,niters)
Description
theta = cordicatan2(y,x) computes the four
quadrant arctangent of y and x using
a CORDIC algorithm approximation.
theta = cordicatan2(y,x,niters) performs niters iterations
of the algorithm.
y,x 
y,x are Cartesian coordinates. y and x must
be the same size. If they are not the same size, at least one value
must be a scalar value. Both y and x must
have the same data type.

niters 
niters is the number of iterations the
CORDIC algorithm performs. This is an optional argument. When specified, niters must
be a positive, integervalued scalar. If you do not specify niters or
if you specify a value that is too large, the algorithm uses a maximum
value. For fixedpoint operation, the maximum number of iterations
is one less than the word length of y or x.
For floatingpoint operation, the maximum value is 52 for double or
23 for single. Increasing the number of iterations can produce more
accurate results but also increases the expense of the computation
and adds latency.

Output Arguments
theta 
theta is the arctangent value, which is
in the range [pi, pi] radians. If y and x are
floatingpoint numbers, then theta has the same
data type as y and x. Otherwise, theta is
a fixedpoint data type with the same word length as y and x and
with a bestprecision fraction length for the [pi, pi] range.

Examples
Floatingpoint CORDIC arctangent calculation.
theta_cdat2_float = cordicatan2(0.5,0.5)
theta_cdat2_float =
2.3562
Fixed point CORDIC arctangent calculation.
theta_cdat2_fixpt = cordicatan2(fi(0.5,1,16,15),fi(0.5,1,16,15));
theta_cdat2_fixpt =
2.3562
DataTypeMode: Fixedpoint: binary point scaling
Signedness: Signed
WordLength: 16
FractionLength: 13
More About
expand all
CORDIC is an acronym for COordinate Rotation
DIgital Computer. The Givens rotationbased CORDIC algorithm is one
of the most hardwareefficient algorithms available because it requires
only iterative shiftadd operations (see References). The CORDIC algorithm
eliminates the need for explicit multipliers. Using CORDIC, you can
calculate various functions, such as sine, cosine, arc sine, arc cosine,
arc tangent, and vector magnitude. You can also use this algorithm
for divide, square root, hyperbolic, and logarithmic functions.
Increasing the number of CORDIC iterations can produce more
accurate results, but doing so also increases the expense of the computation
and adds latency.
Signal Flow Diagrams
CORDIC Vectoring Kernel
The accuracy of the CORDIC kernel depends on the choice of initial
values for X, Y, and Z.
This algorithm uses the following initial values:
fimath Propagation Rules
CORDIC functions discard any local fimath attached
to the input.
The CORDIC functions use their own internal fimath when
performing calculations:
OverflowAction—Wrap
RoundingMethod—Floor
The output has no attached fimath.
References
[1] Volder, JE. "The CORDIC Trigonometric
Computing Technique." IRE Transactions on Electronic
Computers. Vol. EC8, September 1959, pp. 330–334.
[2] Andraka, R. "A survey of CORDIC
algorithm for FPGA based computers." Proceedings
of the 1998 ACM/SIGDA sixth international symposium on Field programmable
gate arrays. Feb. 22–24, 1998, pp. 191–200.
[3] Walther, J.S. "A Unified Algorithm
for Elementary Functions." HewlettPackard Company, Palo Alto.
Spring Joint Computer Conference, 1971, pp. 379–386. (from
the collection of the Computer History Museum). www.computer.org/csdl/proceedings/afips/1971/5077/00/50770379.pdf
[4] Schelin, Charles W. "Calculator Function
Approximation." The American Mathematical Monthly.
Vol. 90, No. 5, May 1983, pp. 317–325.
See Also
atan2  atan2  cordiccos  cordicsin
Tutorials