Monkey’s Audio entropy coding

Each channel’s values are the outputs that the filters consume. The way they are coded has changed several times, so the decoder chooses by file version. This page follows FFmpeg’s decoder; Monkey’s Audio has no written specification of it.

Coders by version

Version	Coder	Tables
Below 3860	Adaptive Rice coding, read through a bit reader	None
3860 to 3899	Adaptive Rice coding with overflow handling; above 3880, a loop that raises `k`	None
3900 to 3929	Range coder; stereo channels coded one after the other	`counts_3970`
3930 to 3989	Range coder; stereo Y and X values interleaved. Mono is as for 3900	`counts_3970`
3990 and later	Range coder with an adaptive pivot	`counts_3980`

The history records: 3.86 rewrote the bitstream, 3.89 made it more robust, 3.90 introduced the new format, 3.96 corrected it for rare failures and 3.99 improved the entropy coder. Both Rice states start at k = 10 at the start of every frame.

The range coder

From version 3900 a frame’s data goes through a byte-oriented range coder.

Constant	Value
CODE_BITS	32
TOP_VALUE	1 << 31
SHIFT_BITS	23
EXTRA_BITS	7
BOTTOM_VALUE	TOP_VALUE >> 8
MODEL_ELEMENTS	64; the symbol value 63 is an escape

Start: read one byte, then set low to that byte shifted right by 1, and range to 128.
Normalise: while range is at most 2²³, read another byte and scale.
Decode: for a total frequency tot, help = range ÷ tot and the cumulative frequency is low ÷ help. A power-of-two total uses a shift instead.
Update: low −= help × lt and range = help × sy, with the symbol’s cumulative start and width.

A symbol is found by locating the cumulative frequency in the tables below. In the 3900 stereo path the decoder backs up one byte between channels and restarts the range coder, to match the reference implementation.

Symbol tables

counts holds each symbol’s cumulative start, and counts_diff its width. A 16-bit cumulative frequency above 65492 is outside the tables: it is its own symbol, frequency − 65535 + 63, with a width of 1. Symbol 63 is the escape.

Symbol	counts_3970	counts_diff_3970	counts_3980	counts_diff_3980
0	0	14824	0	19578
1	14824	13400	19578	16582
2	28224	11124	36160	12257
3	39348	8507	48417	7906
4	47855	6139	56323	4576
5	53994	4177	60899	2366
6	58171	2755	63265	1170
7	60926	1756	64435	536
8	62682	1104	64971	261
9	63786	677	65232	119
10	64463	415	65351	65
11	64878	248	65416	31
12	65126	150	65447	19
13	65276	89	65466	10
14	65365	54	65476	6
15	65419	31	65482	3
16	65450	19	65485	3
17	65469	11	65488	2
18	65480	7	65490	1
19	65487	4	65491	1
20	65491	2	65492	1
21	65493		65493

Decoding a value, 3900 to 3989

Read a symbol using counts_3970; this is the overflow. If it is the escape, read 5 more bits as tmpk and set the overflow to 0; otherwise tmpk is k − 1, or 0 if that is negative. Then read tmpk bits as x, in two parts above 16 bits, and add overflow << tmpk. The update of k and the sign mapping are as for 3990, below.

Decoding a value, 3990

pivot is ksum >> 5, at least 1.
Read the overflow with counts_3980. On the escape, it is rebuilt from two 16-bit reads.
Read base with a total of pivot. A pivot of 65536 or more is reduced to 16 bits and read in two steps.
x = base + overflow × pivot.
Update: lim is 1 << (k + 4), or 0 when k is 0; ksum += (x + 1) ÷ 2 − ((ksum + 16) >> 5). If ksum is below lim, lower k; otherwise, if it is at least 1 << (k + 5) and k is under 24, raise k.
The sign: ((x >> 1) ^ ((x & 1) − 1)) + 1. An even value gives a negative result and an odd value a positive one.

.APE File Format – Entropy coding

Coders by version

The range coder

Symbol tables

Decoding a value, 3900 to 3989

Decoding a value, 3990