cordicsigmoid

CORDIC-based approximation of sigmoid activation

Since R2023b

Syntax

Y = cordicsigmoid(X)

Y = cordicsigmoid(X,N)

Description

Y = cordicsigmoid(X) computes the sigmoid activation of the numeric input X by applying the sigmoid transfer function. All values in Y are between 0 and 1.

To optimize the numerics for fixed-point input, the cordicsigmoid function implements the sigmoid activation using a CORDIC-based approximation of hyperbolic tangent, without computing the exponential.

$$Y=\frac{1}{1+\exp (-X)}=\frac{1-\tanh (-X/2)}{2}$$

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

Examples

Apply Sigmoid Activation

This example shows how to use the cordicsigmoid function to apply the sigmoid function to fixed-point input data.

x = fi(linspace(-10,10,100));
y = cordicsigmoid(x);
plot(x,y)

Apply Sigmoid Activation with Specified Maximum Shift Value in CORDIC Iterations

This example shows how to specify the maximum shift value in CORDIC iterations for the cordicsigmoid function.

wl = 11;
fl = 7;
nt = numerictype(1,wl,fl);

rDbl = range(nt);
nPts = min(2^18,2^wl);

xDbl = double(linspace(rDbl(1),rDbl(2),nPts));
x = fi(xDbl,nt);

for nIter = 5:5:10
    y = cordicsigmoid(x,nIter);
    plot(x,y);
    hold on;
end

yIdeal = 1 ./ ( 1 + exp(-double(x)));
plot(x,yIdeal);
hold off;

legend('N = 5','N = 10','Ideal')

Input Arguments

X — Input data

scalar | vector | matrix | multidimensional array

Input data, specified as a scalar, vector, matrix, or multidimensional array.

When X is fixed point, then it must use binary-point scaling.

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

Y — Sigmoid activations

vector

Sigmoid activations, returned as a vector. All values in Y are between 0 and 1.

When the input X is a floating-point data type, then the output Y has the same data type as the input X. When the input X is a fixed-point data type, then the output Y has a signed, fixed-point data type with the same word length as X and fraction length equal to two less than the word 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.

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™.

• Variable-size signals are not supported.

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

Version History

Introduced in R2023b