theta = cordicangle(c) returns
the phase angles, in radians, of matrix c, which
contains complex elements.

theta = cordicangle(c,niters) performs niters iterations
of the algorithm.

Input Arguments

c

Matrix of complex numbers

niters

niters is the number of iterations the
CORDIC algorithm performs. This argument is optional. 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 the word length of r or one less than the
word length of theta, whichever is smaller. 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 contains the polar coordinates angle
values, which are in the range [–pi, pi] radians. If x and y are
floating-point, then theta has the same data
type as x and y. Otherwise, theta is
a fixed-point data type with the same word length as x and y and
with a best-precision fraction length for the [-pi, pi] range.

Examples

Phase angle for double-valued input and for fixed-point-valued
input.

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.

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. 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.