Hard Sigmoid

Perform the Hard Sigmoid activation function on an input matrix:

$$C[i][j] = \text{hard\_sigmoid}(A[i][j])$$

The Hard Sigmoid function is defined as:

$$\text{hard\_sigmoid}(x) = \begin{cases} 0 & \text{if } x \leq -3 \\ 1 & \text{if } x \geq 3 \\ \frac{x + 3}{6} & \text{otherwise} \end{cases}$$

Input:

• Matrix $A$ of size $M \times N$ containing floating-point values

Output:

• Matrix $C$ of size $M \times N$ containing the Hard Sigmoid activation values

Notes:

• Both matrices $\text{A}$ and $\text{C}$ are stored in row-major order
• The Hard Sigmoid function is a piecewise linear approximation of the standard Sigmoid function