Order-1 Scale AC

The Order1ScaleAC codec is a specialized arithmetic coder designed specifically for the SCALE planes of MXFP4 / NVFP4 microscaled tensors.

Theory

While standard block scales are pure 8-bit exponents, FP8 scale formats (like E4M3 or E5M2) contain mantissa bits. These bits produce a continuous distribution with strong autocorrelation along the row.

Order1ScaleAC exploits this by modeling a per-row lag-1 Probability Mass Function (PMF) over the scale bytes. It fits a conditional table during compression, serializes it into the codec state, and uses a range coder to compress the sequence based on the previous byte's context.

To minimize trial-encode overhead, the codec uses a fast marginal-entropy pre-screen. If the data is near-uniform (entropy ≥ 7.5 bits/byte), the codec aborts early, as row conditioning cannot recover the overhead of storing the per-row PMF table.

Usage

This codec strictly requires Byte-width Scale or GlobalScale planes with a Rows layout and an FP8 scale format (E4M3 or E5M2).

References

• This codec is an original adaptation of Order-1 Arithmetic Coding tailored for the scale distributions in MXFP4 and NVFP4 formats.