cordicangle

CORDIC-based phase angle

Syntax

theta = cordicangle(c)

theta = cordicangle(c,niters)

Description

theta = cordicangle(c) returns the phase angle in the interval [-π,π] for each element of a complex array c.

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

Examples

CORDIC-Based Phase Angle

Use the cordicangle function to compute the CORDIC-based phase angle for double-precision and fixed-point inputs.

dblRandomVals = complex(rand(5,4),rand(5,4));
theta_dbl_ref = angle(dblRandomVals);
theta_dbl_cdc = cordicangle(dblRandomVals)

theta_dbl_cdc = 5×4

    0.6777    1.4428    1.3512    1.4002
    0.0394    1.2122    0.0328    1.0252
    1.4223    0.6222    0.2816    0.3334
    0.7966    0.6003    0.0948    0.8758
    0.8208    0.1756    0.1208    0.0359

fxpRandomVals = fi(dblRandomVals);
theta_fxp_cdc = cordicangle(fxpRandomVals)

theta_fxp_cdc = 
    0.6777    1.4426    1.3513    1.4001
    0.0393    1.2122    0.0327    1.0254
    1.4224    0.6223    0.2817    0.3333
    0.7964    0.6003    0.0950    0.8757
    0.8208    0.1758    0.1208    0.0359

          DataTypeMode: Fixed-point: binary point scaling
            Signedness: Signed
            WordLength: 16
        FractionLength: 13

Input Arguments

c — Input array

scalar | vector | matrix | multidimensional array

Input array, specified as a scalar, vector, matrix, or multidimensional array. When the elements of c are nonnegative real numbers, cordicangle returns 0. When the elements of c are negative real numbers, cordicangle returns π.

Data Types: single | double | fi
Complex Number Support: Yes

niters — Number of iterations CORDIC algorithm performs

positive integer-valued scalar

Number of iterations the CORDIC algorithm performs, specified as a positive integer-valued scalar.

Increasing the number of iterations can produce more accurate results but also increases the expense of the computation and adds latency.

If you do not specify niters, or if you specify it as empty or nonfinite, the maximum allowed value is used. For fixed-point input, the maximum number of iterations is one less than the word length of c. For double-precision input, the maximum value is 52. For single-precision input, the maximum value is 23.

Data Types: single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64 | fi

Output Arguments

theta — Phase angle in radians

scalar | vector | matrix | multidimensional array

Phase angle in radians, returned as a scalar, vector, matrix, or multidimensional array.

If c is floating-point, then theta has the same data type as c. Otherwise, theta has a fixed-point data type with the same word length as c and with a best-precision fraction length.

Algorithms

CORDIC

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, arcsine, arccosine, arctangent, and vector magnitude. You can also use this algorithm for divide, square root, hyperbolic, and logarithmic functions.

The precision of the CORDIC algorithm is a function of the data type used and the maximum shift value or number of iterations of the CORDIC kernel. Using a data type with a larger word length and performing more iterations of the CORDIC algorithm can reduce the numeric error of the result. However, doing so also increases the latency of the computation and the utilizes more hardware resources. For more information, see How to Set CORDIC Input Word Length and Maximum Shift Value to Achieve Desired Precision.

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:

$$\begin{array}{l}{x}_0\text{ is initialized to the }x\text{ input value}\\ y_0\text{ is initialized to the }y\text{ input value}\\ z_0\text{ is initialized to }0\end{array}$$

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, Jack E. “The CORDIC Trigonometric Computing Technique.” IRE Transactions on Electronic Computers. EC-8, no. 3 (Sept. 1959): 330–334.

[2] Andraka, Ray. “A Survey of CORDIC Algorithm for FPGA Based Computers.” In Proceedings of the 1998 ACM/SIGDA Sixth International Symposium on Field Programmable Gate Arrays, 191–200. https://dl.acm.org/doi/10.1145/275107.275139.

[3] Walther, J.S. “A Unified Algorithm for Elementary Functions.” In Proceedings of the May 18-20, 1971 Spring Joint Computer Conference, 379–386. https://dl.acm.org/doi/10.1145/1478786.1478840.

[4] Schelin, Charles W. “Calculator Function Approximation.” The American Mathematical Monthly, no. 5 (May 1983): 317–325. https://doi.org/10.2307/2975781.

Extended Capabilities

C/C++ Code Generation

Generate C and C++ code using MATLAB® Coder™.

Usage notes and limitations:

• Variable-size signals are not supported.

• The number of iterations the CORDIC algorithm performs, niters, must be a constant.

HDL Code Generation

Generate VHDL, Verilog and SystemVerilog code for FPGA and ASIC designs using HDL Coder™.

The cordicangle function also supports to MATLAB^® to High-Level Synthesis (HLS) code generation.

Version History

Introduced in R2011b