y = cordicsin(theta,niters) computes
the sine of theta using a CORDIC algorithm approximation.

Input Arguments

theta

theta can be a signed or unsigned scalar,
vector, matrix, or N-dimensional array containing
the angle values in radians. All values of theta must
be real and in the range [–2π 2π).

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 theta. 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 it also increases the expense of the computation and
adds latency.

Output Arguments

y

y is the CORDIC-based approximation
of the sine of theta. When the input to the function
is floating point, the output data type is the same as the input data
type. When the input is fixed point, the output has the same word
length as the input, and a fraction length equal to the WordLength – 2.

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.

X represents the sine, Y represents
the cosine, and Z represents theta. The accuracy
of the CORDIC rotation kernel depends on the choice of initial values
for X, Y, and Z.
This algorithm uses the following initial values:

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.