Compression — measured

Spherical harmonics dominate a coloured scene's bytes, and the format lets a writer pick a bit depth per band. This page is what that buys, in numbers, measured rather than asserted: every row is the size of a file this package wrote and the error between the coefficients that went in and the ones that came back out of it. Reproduce the whole table with

python3 python/tools/rd_benchmark.py            # to stdout
python3 python/tools/rd_benchmark.py --csv out.csv

What is being measured, and what is not

The scene is synthetic and its spherical harmonics are the point of it: coefficients drawn from a low-frequency function of position plus noise, with band energy falling by degree — the property a real fit has and the one both the quantizer and the entropy coder act on. (The conformance corpus fills coefficients with a counter, which deflate codes almost perfectly and coarser quantization only disturbs; measuring rate on that fixture would say quantizing makes files bigger, which is true of the counter and false of everything else.)

These numbers are against this format's own 8-bit deflate baseline. Nothing here is a comparison with another format. file vs base and SH vs base are ratios to the first row; SH PSNR is the peak signal-to-noise of the reconstructed coefficients; max err is the largest single byte-level deviation; in bounds confirms the encoder's declared per-band bound held on every gaussian.

Degree-3 scene, deflate (the default codec)

On this scene the spherical harmonics are 49% of the file at full precision (14,740 of 29,929 bytes), so the bit depth is where the bytes are.

SH bits	file bytes	SH bytes	file vs base	SH vs base	SH PSNR	max err	in bounds
8 (base)	29,929	14,740	1.000	1.000	lossless	0	yes
7	27,415	12,171	0.916	0.826	51.2 dB	1	yes
6	24,740	9,496	0.827	0.644	46.3 dB	2	yes
5	21,732	6,488	0.726	0.440	41.1 dB	4	yes
4	20,159	4,915	0.674	0.333	34.1 dB	8	yes
3	19,540	4,292	0.653	0.291	26.6 dB	16	yes
balanced	24,229	8,985	0.810	0.610	44.0 dB	4	yes
aggressive	21,267	6,021	0.711	0.408	28.5 dB	16	yes

balanced and aggressive are the per-band ladders: they spend more bits on the low-degree bands that carry most of the energy and fewer on the high-degree bands that carry little, so at a given file size they hold more PSNR than a uniform cut does — the balanced row is smaller than uniform-6 and higher-quality than uniform-5.

Degree-3 scene, zstd

The zstd rows tell the same story with a stronger backstop coder. At level 3 zstd trails deflate slightly on this already-quantized data (the byte-plane shuffle leaves little for the entropy stage); at level 19 it pulls ahead — uniform-5 reaches 0.691 of the baseline file where deflate reaches 0.726, at identical error, because the error is set by the bit depth and only the residual coding differs.

SH bits	zstd-3 file	zstd-3 vs base	zstd-19 file	zstd-19 vs base	SH PSNR
8	30,173	1.008	29,406	0.983	lossless
7	27,619	0.923	26,275	0.878	51.2 dB
6	25,285	0.845	23,483	0.785	46.3 dB
5	22,549	0.753	20,677	0.691	41.1 dB
4	21,182	0.708	19,068	0.637	34.1 dB
3	20,656	0.690	18,563	0.620	26.6 dB

Reading the trade

The error is the bit depth's, not the codec's: every codec column at a given depth shares one SH PSNR and one max err, because quantization sets the error and compression only codes what is left. So the choice is two independent dials — pick the bit depth for the quality you will accept, then pick the codec and level for how hard you want to squeeze the result. On this scene, dropping SH from 8 to 5 bits costs about 41 dB of headroom (visually lossless for most content) and returns a quarter of the whole file; 5-bit with zstd-19 returns nearly a third. The in bounds column is the guarantee underneath all of it: the deviation the file declares is the deviation it holds, verified per gaussian at encode.