.M4A File Format – Prediction and entropy

Adaptive Golomb decoding

The coder keeps a running mean of the values it has seen, mb, and derives each code’s parameter from it. It starts at the cookie’s mb value. The adaptation rate is pb × pbFactor ÷ 4, from the cookie’s pb and the element’s pbFactor.

For each value:

1. m = mb >> QBSHIFT, and k is ⌊log₂(m + 3)⌋, capped at the cookie’s kb. Then m = (1 << k) − 1.
2. Count the 1 bits up to a 0: this is the prefix.
3. A prefix of 9 or more is an escape: the value follows as a raw field as wide as the channel’s predicted bits.
4. Otherwise, if k is 1, the value is the prefix. If not, peek at k bits as v; the value is prefix × m. If v is under 2, only k − 1 bits are consumed. If not, all k are, and v − 1 is added.
5. Add zmode (below). A set low bit means negative: the residual is −(n + 1) ÷ 2 when odd and n ÷ 2 when even.
6. Update the mean: mb = pb × n + mb − ((pb × mb) >> QBSHIFT), with n including zmode. If n exceeds 0xFFFF, the mean becomes 0xFFFF.

Zero runs

After a value, zmode resets to 0. If mb × 4 is below 512 and samples remain, a run follows: zmode becomes 1, then the run length is read with the same coding, using k = lead(mb) − 24 + ((mb + 16) >> 6), where lead is the number of leading zero bits in 32 bits. That many zero residuals follow. If the length is 65535 or more, zmode returns to 0. The mean then becomes 0.

The adaptive predictor

The predictor runs over the residuals with the element’s num coefficients and denShift.

• The first sample is the first residual, unchanged.
• With no coefficients the remaining samples are the residuals, unchanged.
• With 31 coefficients the code is a plain first-order integrator: each output is the previous output plus the residual, wrapped to the channel’s bit width. The first pass when mode is not 0 runs this way.
• Otherwise the first num samples after the first use that same first-order rule. Full prediction starts at the next sample.

For sample j, with top the sample num + 1 places back:

prediction = top + ((Σ coef[k] × (out[j−1−k] − top) + half) >> denShift)
out[j]     = wrap(residual[j] + prediction)

Here half is 1 << (denShift − 1), and wrap discards the bits above the channel’s width and sign-extends.

Coefficient adaptation

Each coefficient steps by 1 according to the sign of the residual and the sign of its difference from top. Steps run from the oldest coefficient towards the newest, and each updated coefficient subtracts its weighted contribution from a running budget that starts as the residual. When the budget crosses zero, the remaining coefficients stay as they are. A zero residual changes nothing.

The stereo matrix

A CPE decodes two channels, U and V. With mixRes not zero:

L = U + V − ((mixRes × V) >> mixBits)
R = L − V

With mixRes zero, L is U and R is V. Any shifted-off bits are put back after this step.

Output by bit depth