QFunctional

Quantized element-wise merges — each result fake-quantized to one grid.

The converted, inference-time form of FloatFunctional, installed by lucid.quantization.convert (or built via from_float). It exposes the identical surface — add, mul, add_relu, cat, add_scalar, mul_scalar — but every call now fake-quantizes its output onto the single (scale, zero_point) grid the source FloatFunctional observed during calibration.

This is what makes residual quantization correct. A skip-add feeds two branches that were quantized on their own scales; requantizing the sum to one calibrated grid re-aligns them, so the block's output matches int8 numerics instead of drifting off at full precision. Under the sidecar representation (design B) the requantized result is carried as float32 with int8 numerics — no packed-integer container is produced.

Every merge routes its raw float result $t$ through

with the calibrated (scale, zero_point) $S, Z$ and grid bounds $q_{\min}, q_{\max}$ (0, 255 for the default quint8). Only the output is snapped; add_relu applies the ReLU before this step so the grid matches the post-ReLU range calibration saw.