cordicsinhcosh

CORDIC-based approximation of hyperbolic sine and cosine

Since R2023b

Syntax

[S,C] = cordicsinhcosh(X)

[S,C] = cordicsinhcosh(X,N)

Description

[S,C] = cordicsinhcosh(X) returns the hyperbolic sine (sinh) S and hyperbolic cosine (cosh) C of the elements in X using a CORDIC-based approximation. The cordicsinhcosh function operates element-wise on arrays. All angles are in radians. The function uses the maximum number of CORDIC iterations for the numeric type of X.

[S,C] = cordicsinhcosh(X,N) additionally specifies the maximum shift value N in the CORDIC iterations. For fixed-point input X, the maximum shift value is limited by the word length minus one.

Examples

Hyperbolic Sine and Cosine of Fixed-Point fi Object

theta = fi(pi/4);
[s,c] = cordicsinhcosh(theta)

s = 
    0.8688

          DataTypeMode: Fixed-point: binary point scaling
            Signedness: Signed
            WordLength: 16
        FractionLength: 14

c = 
    1.3248

          DataTypeMode: Fixed-point: binary point scaling
            Signedness: Signed
            WordLength: 16
        FractionLength: 14

CORDIC Hyperbolic Cosine with Specified Number of Iterations

Compute the hyperbolic cosine of a double using a CORDIC-based approximation and specify the number of iterations the CORDIC kernel should perform. Plot the CORDIC approximation of the hyperbolic cosine with varying numbers of iterations.

x = -1:0.01:1;
for n = 5:5:20
    [s,c] = cordicsinhcosh(x,n);
    plot(x,c);
    hold on;
end
legend('n = 5','n = 10','n = 15','n = 20')

Input Arguments

X — Input angles in radians

scalar | vector | matrix | multidimensional array

Input angles in radians, specified as a scalar, vector, matrix, or multidimensional array. X must be a double, single, fixed-point fi, or scaled-double fi. If X is a fixed-point fi or scaled-double fi, then X must be signed and binary-point scaled.

If X is double or single, then S and C are double or single, respectively.

Data Types: single | double | fi

N — Maximum shift value in CORDIC iterations

real integer-valued scalar

Maximum shift value in CORDIC iterations, specified as a real integer-valued scalar.

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

Output Arguments

S — Hyperbolic sine

scalar | vector | matrix | multidimensional array

Hyperbolic sine (sinh), returned as a scalar, vector, matrix, or multidimensional array.

If X is double or single, then S and C are double or single, respectively.

If X is a fixed-point fi or scaled-double fi, then S and C have the same word length as X and fraction length equal to two less than the word length.

C — Hyperbolic cosine

scalar | vector | matrix | multidimensional array

Hyperbolic cosine (cosh), returned as a scalar, vector, matrix, or multidimensional array.

If X is double or single, then S and C are double or single, respectively.

If X is a fixed-point fi or scaled-double fi, then S and C have the same word length as X and fraction length equal to two less than the word length.

Limitations

• The cordicsinhcosh function returns an error if X is outside the domain of convergence for the CORDIC hyperbolic sine and cosine kernel. The domain of convergence is a function of the numeric type of X and the maximum CORDIC shift value n. The domain of convergence converges to around [-1.1182, +1.1182]. You can use the fixed.cordic.hyperbolic.domainOfConvergence function to compute the domain of convergence for a particular X and n.

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.

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 maximum shift value N in the CORDIC iterations must be a constant.

Version History

Introduced in R2023b