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.

Input Arguments

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, integer-valued scalar. If you do not specify niters or
if you specify a value that is too large, the algorithm uses a maximum
value. For fixed-point operation, the maximum number of iterations
is one less than the word length of y or x.
For floating-point 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
floating-point numbers, then theta has the same
data type as y and x. Otherwise, theta is
a fixed-point data type with the same word length as y and x and
with a best-precision fraction length for the [-pi, pi] range.

CORDIC is an acronym for COordinate Rotation
DIgital Computer. The Givens rotation-based CORDIC algorithm is one
of the most hardware-efficient algorithms available because it requires
only iterative shift-add 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.

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. EC-8, 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." Hewlett-Packard 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.