Main Content


CORDIC-based phase angle



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.


collapse all

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

collapse all

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

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

collapse all

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.

More About

collapse all


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.

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


collapse all

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, 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.

[3] Walther, J.S. “A Unified Algorithm for Elementary Functions.” In Proceedings of the May 18-20, 1971 Spring Joint Computer Conference, 379-386.

[4] Schelin, Charles W. “Calculator Function Approximation.” The American Mathematical Monthly, no. 5 (May 1983): 317-325.

Extended Capabilities

Version History

Introduced in R2011b