Sigmoid

The quantized sigmoid function is defined as follows:

$\sigma_Q(x) = \dfrac{Q}{1 + 2^{-x}}$

where $Q$ is the quantization (scaling) factor. We use $2$ instead of $e$ to avoid floating point operations.

Implementation

Step	Operation	Description
1	VirtualConst(0)	Create constant zero tensor for comparisons
2	Gte	Compute ge0 = (z >= 0) to track sign of input
3	Sub	Compute neg_z = -z for absolute value calculation
4	Select	Compute abs_z = select(ge0, z, -z) (absolute value)
5	VirtualPow2	Compute `pow2 = 2^{
6	VirtualConst(Q)	Load quantization constant Q
7	Mul	Compute Q² = Q * Q
8	Div	Compute `div_Q_pow = Q / 2^{
9	Mul	Compute `mul_Q_pow = Q * 2^{
10	Select	Compute a = select(ge0, div_Q_pow, mul_Q_pow) (choose branch based on sign of z)
11	Add	Compute b = Q + a
12	Div	Compute c = Q² / b → final quantized sigmoid output σ_Q(z)
13	VirtualMove	Move final tensor c to output destination