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cordicatan2

CORDIC-based four quadrant inverse tangent

Description

theta = cordicatan2(y,x) computes the four quadrant arctangent of y and x using a CORDIC algorithm approximation.

example

theta = cordicatan2(y,x,niters) performs niters iterations of the algorithm.

Examples

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Define floating-point Cartesian coordinates.

y = 0.5;
x = -0.5;

Use cordicatan2 to compute floating-point CORDIC arctangent. Compare the result to the arctangent computed using atan2.

theta_cdat2_float = cordicatan2(y,x)
theta_cdat2_float = 
2.3562
theta_atan2_float = atan2(y,x)
theta_atan2_float = 
2.3562

Define fixed-point Cartesian coordinates.

y = fi(0.5,1,16,15);
x = fi(-0.5,1,16,15);

Use cordicatan2 to compute fixed-point CORDIC arctangent. Compare the result to the arctangent computed using atan2.

theta_cdat2_fixpt = cordicatan2(y,x)
theta_cdat2_fixpt = 
    2.3562

          DataTypeMode: Fixed-point: binary point scaling
            Signedness: Signed
            WordLength: 16
        FractionLength: 13
theta_atan2_fixpt = atan2(y,x)
theta_atan2_fixpt = 
    2.3562

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

Input Arguments

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Cartesian y-coordinate, specified as a scalar, vector, matrix, or multidimensional array.

y and x must be the same size. If they are not the same size, at least one value must be a scalar value. y and x must have the same data type.

Data Types: single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64 | fi
Complex Number Support: Yes

Cartesian x-coordinate, specified as a scalar, vector, matrix, or multidimensional array.

y and x must be the same size. If they are not the same size, at least one value must be a scalar value. y and x must have the same data type.

Data Types: single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64 | fi
Complex Number Support: Yes

Number of iterations of CORDIC algorithm, 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 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 y or x.

  • For floating-point operation, the maximum value is 52 for double or 23 for single.

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

Output Arguments

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Arctangent value in the range [-pi, pi] radians, returned as a scalar, vector, matrix, or multidimensional array.

If y and x are floating-point numbers, then theta has the same data type as y and x. Otherwise, theta is a fixed-point data type with the same word length as y and x and with a best-precision fraction length for the [-pi, pi] range.

Algorithms

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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

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Version History

Introduced in R2011b