r = cordicabs(c) r = cordicabs(c,niters) r = cordicabs(c,niters,'ScaleOutput',b) r = cordicabs(c,'ScaleOutput',b)

Description

r = cordicabs(c) returns
the magnitude of the complex elements of C.

r = cordicabs(c,niters) performs niters iterations
of the algorithm.

r = cordicabs(c,niters,'ScaleOutput',b) specifies
both the number of iterations and, depending on the Boolean value
of b, whether to scale the output by the inverse
CORDIC gain value.

r = cordicabs(c,'ScaleOutput',b)
scales the output depending on the Boolean value of b.

Input Arguments

c

c is a vector of complex values.

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.

Name-Value Pair Arguments

Optional comma-separated pairs of Name,Value arguments,
where Name is the argument name and Value is
the corresponding value. Name must appear inside
single quotes ('').

'ScaleOutput'

ScaleOutput is a Boolean value that specifies
whether to scale the output by the inverse CORDIC gain factor. This
argument is optional. If you set ScaleOutput to true or 1,
the output values are multiplied by a constant, which incurs extra
computations. If you set ScaleOutput to false or 0,
the output is not scaled.

Default: true

Output Arguments

r

r contains the magnitude values of the
complex input values. If the inputs are fixed-point values, r is
also fixed point (and is always signed, with binary point scaling).
All input values must have the same data type. If the inputs are signed,
then the word length of r is the input word length
+ 2. If the inputs are unsigned, then the word length of r is
the input word length + 3. The fraction length of r is
always the same as the fraction length of the inputs.

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.