quantfixpoint

confirmedcertificateC++Inference & servingJuly 13, 2026

the question

Is ggml's q8_0 dequantize-then-requantize a fixed point, and is the per-element reconstruction error strictly bounded by d/2?

what came out

Confirmed. Dequant-then-requant fixes exactly the rail blocks (max|q|==127) and the canonical zero block; over 5,000,000 random inputs the quantizer emitted zero non-rail nonzero blocks, so its whole output range is stable. The d/2 error bound is not strict: fp16 storage of the scale inflates the worst case to about 1.6x d/2.

method & receipts

Result: confirmed
Pre-registered — the prediction was written down and committed before the run.
Reproducible — one script re-runs the whole thing from scratch.
Tested — a correctness/benchmark suite ships alongside the code.

→ read the code and re-run it

github.com/v-code01/quantfixpoint