CORDIC-based phase angle


theta = cordicangle(c)
theta = cordicangle(c,niters)


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


Matrix of complex numbers


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 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.


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

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

theta_dbl_cdc =

    1.0422    1.0987    1.2536    0.6122
    0.5893    0.8874    0.3580    0.2020
    0.5840    0.2113    0.8933    0.6355
    0.7212    0.2074    0.9820    0.8110
    1.3640    0.3288    1.4434    1.1291

theta_fxp_cdc =
    1.0422    1.0989    1.2534    0.6123
    0.5894    0.8872    0.3579    0.2019
    0.5840    0.2112    0.8931    0.6357
    0.7212    0.2075    0.9819    0.8110
    1.3640    0.3289    1.4434    1.1289

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

More About

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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.


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:

x0 is initialized to the x input valuey0 is initialized to the y input valuez0 is initialized to 0

fimath Propagation Rules

CORDIC functions discard any local fimath attached to the input.

The CORDIC functions use their own internal fimath when performing calculations:

  • OverflowActionWrap

  • RoundingMethodFloor

The output has no attached fimath.


[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).

[4] Schelin, Charles W. "Calculator Function Approximation." The American Mathematical Monthly. Vol. 90, No. 5, May 1983, pp. 317–325.

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