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Put sound in the packed container, and find the padding is a rate error

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ROADMAP P6b, FINDINGS 67.  DLXP2: a 64-byte header and then groups -- one
audio lump of A sectors, then F records -- so record i is at
off_frm + i*rec + (i//F)*A*512 and lump k at off_aud + k*(F*rec + A*512).
Still no index and still none needed, which is the packed branch's whole
claim surviving the one change that could have ended it.  The player carries
the third term in six instructions once a frame and zero parsing, and 120 of
120 records are still pixel-exact off a real MB89352 volume with the
interleave in, against a silent control that says no picture byte moved.

The finding is what 65.3 called padding.  A lump is 7,168 B of SPACE; eleven
frames of audio is 7,161.4583... B, so the payload alternates 7,161 and
7,162 and the rest is zero.  A player that fed the chip the whole lump --
which is what "14 sectors every 11 frames" invites -- runs 0.09% fast, and
that is not waste, it is drift: 0.84 ms a group, 1.25 s of lip-sync over the
game's 22.8 minutes.  What a player carries is one accumulator,
acc += 11*15625; n = acc//24; acc %= 24, which is clock.i's shape for
clock.i's reason and the third time this tree has met the pattern.

The four ADPCM axes ride in the header as fields rather than a version
number, and the gate flips each one to prove they earn it: nibble order
-31.99 dB, delta formula -24.86, clamp 0.00, accumulator -0.49.  Nothing
parses a packed container, so the gate partitions the whole file -- 131
spans, no overlap, no gap -- and asserts what a cadence-blind player would
read: exactly records 11..119 wrong, and frames 0..10 identical either way,
which is how an off-by-one like that survives a rig that checks frame 0.

Wire 582.0 + 7.64 = 589.6 KB/s, 65.3's prediction to the tenth.

Green light ALL GREEN before (tmp/check_s35_start.log) and after
(tmp/check_s35_end.log), with the new stage in it.

Claude-Session: https://claude.ai/code/session_01194oWYW8DQXK1SZ2DnChW6
This commit is contained in:
prosolis
2026-08-25 11:22:38 -07:00
parent 6dd3fb3597
commit e3778f62b0
13 changed files with 1001 additions and 51 deletions
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tools/analysis/30_packed_container.py
+10 -2
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@@ -91,12 +91,20 @@ print(f" round-trip: {d.nframes} records unpack and re-pack byte-identical")
print(f" index 0 (transparency key) used {zero} times; "
f"index 255 (black) {black:,} times in the picture")
kbps = d.kbps()
# THE PICTURE'S wire, and it is the one this file is about. DLXP2 puts audio on
# the same wire at a cadence (65.3, 67) and `d.kbps()` is both; what is asserted
# here is that the PICTURE's share is still exactly geometry, because that is
# 61.6's claim and a second stream is exactly the thing that could quietly
# dilute it.
kbps = d.video_kbps()
geom = d.rec_bytes * d.fps / 1024
if abs(kbps - geom) > 1e-6:
fail.append(f"wire {kbps} != geometry {geom}")
print(f" wire {kbps:.1f} KB/s = {d.rec_bytes:,} B x {d.fps} fps. FIXED. A codec's "
f"bitrate is a lever and a literal frame's is geometry (61.6)")
f"bitrate is a lever and a literal frame's is geometry (61.6)"
+ (f"\n ...and {d.audio_kbps():.2f} KB/s of audio rides beside it on the "
f"F={d.cad_f}/A={d.cad_a} cadence, for {d.kbps():.1f} KB/s total "
f"(tools/analysis/34_packed_audio.py)" if d.has_audio else ""))
print()
# --- 2. the picture ----------------------------------------------------------
tools/analysis/32_audio_wire.py
+1 -1
View File
@@ -134,7 +134,7 @@ print(f""" THE FLOOR OF THAT SWEEP is F={F}, A={A}: {100*w:.3f}% padding, {add:
=== WHAT IT DOES TO THE WIRE ===========================================""")
vid_kbs = d.rec_bytes * d.fps / 1024
vid_kbs = d.video_kbps()
for label, cad in (("F=1 (one lump a record)", f1), (f"F={F} (the floor)", best[0])):
tot = vid_kbs + cad[5]
print(f" {label:26s} video {vid_kbs:7.1f} + audio {cad[5]:5.2f} = {tot:7.1f} KB/s "
tools/analysis/34_packed_audio.py
+217
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@@ -0,0 +1,217 @@
#!/usr/bin/env python3
"""DLXP2's GATE: a packed container with sound in it. ROADMAP P6b.
python3 tools/analysis/34_packed_audio.py [packed.dlxp] [--audio tmp/au_singe.raw]
WHAT THIS IS FOR. FINDINGS 65.3 did the arithmetic of putting audio in the
packed container and wrote no byte of one; 66 measured which of sixteen decoder
models the machine's chip runs and priced the axes at up to 25.7 dB. This is
the container those two produce, and the reason it needs a gate of its own is
that NOTHING PARSES A PACKED CONTAINER. A DMA channel copies bytes and has no
opinion about them (62), so a container whose lump is one sector out does not
fail -- it plays 512 B of picture as audio and 512 B of audio as picture, both
of which are things, and a gate that only checked for errors would pass it.
THE FOUR CLAIMS, and each is checked against something that is not the writer:
1. THE FILE IS ITS OWN ARITHMETIC. Every byte of the container is accounted
for by `off_frm + i*rec + (i//F)*A*512` and `off_aud + k*(F*rec + A*512)`
with no byte left over and no byte claimed twice. A per-record read cannot
catch an off-by-one that shifts everything after it; a partition can.
2. THE PICTURE DID NOT MOVE. Interleaving a second stream into a format whose
whole claim is "record i is at LBA0 + i*97" is exactly the change that can
break that claim, so every record is compared against a re-encode of the
same frames with `--audio` off. The silent container is the control.
3. THE BYTES ARE THE ENCODER'S. The lumps, concatenated, are byte-exact
against `adpcm.encode` run again on the same PCM with the same four axes.
4. THE HEADER'S AXES ARE LOAD-BEARING. The stream decodes to the source at
the SNR the encoder reported, and flipping any ONE of the four axes the
header carries collapses it. A header field nothing would notice being
wrong is a comment.
AND THE FINDING IT REPORTS (FINDINGS 67). The padding is not where a reader of
65.3 would put it. A lump is A*512 B of SPACE; F frames of audio is
F*hz/(2*fps) B, which at F=11 is 7,161.4583..., so the PAYLOAD alternates 7,161
and 7,162 and the sector run is 7,168 either way. A player that handed the chip
the whole lump -- the obvious implementation, and the one the phrase "14 sectors
of audio every 11 frames" invites -- would be feeding it 6.54 B a group too
much. That is not waste, which is what padding usually is. It is DRIFT.
"""
import argparse, math, os, struct, sys
sys.path.insert(0, "tools/encoder")
sys.path.insert(0, "tools/analysis")
import adpcm
import dlxp as P
from dlxp import DLXP, SECTOR
ap = argparse.ArgumentParser()
ap.add_argument("container", nargs="?", default="tmp/packed_singe.dlxp")
ap.add_argument("--audio", default="tmp/au_singe.raw")
ap.add_argument("--silent", default="tmp/packed_singe_silent.dlxp",
help="the control: the same frames with --audio off. Built by "
"check.sh; skipped rather than faked when absent")
ap.add_argument("--game-min", type=float, default=22.8,
help="the game's running length, for what the drift comes to")
a = ap.parse_args()
fails = []
def ck(ok, msg):
print((" OK " if ok else " FAIL ") + msg)
if not ok:
fails.append(msg)
d = DLXP(a.container) # every format invariant is checked here
print(f"{a.container}: DLXP{d.version} {d.W}x{d.H} {d.fps}fps {d.nframes} frames, "
f"{'AUDIO' if d.has_audio else 'SILENT'}")
if not d.has_audio:
sys.exit(f"{a.container} carries no audio -- this gate has nothing to check. "
f"Build it with tools/encoder/pack.py --audio")
grp = d.cad_f * d.aud_hz / (2 * d.fps)
print(f"""
=== THE LAYOUT =========================================================
record {d.rec_bytes:,} B = {d.rec_bytes//SECTOR} sectors, lump {d.cad_a*SECTOR:,} B = {d.cad_a} sectors,
cadence F={d.cad_f} A={d.cad_a}, {d.n_lumps} lumps, {d.aud_bytes:,} B of ADPCM at {d.aud_hz:,} Hz
record i = {d.off_frm:,} + i*{d.rec_bytes:,} + (i//{d.cad_f})*{d.cad_a*SECTOR:,}
lump k = {d.off_aud:,} + k*{d.cad_f*d.rec_bytes + d.cad_a*SECTOR:,}
and NEITHER of those is a lookup. A packed record's length is geometry and a
lump's is a cadence, so DLXP2 still has no index and still needs none.""")
# --- 1. the file is its own arithmetic ------------------------------------
# Every byte, partitioned. Not "does record 7 read back" -- an off-by-one that
# shifts the whole stream reads back fine one record at a time.
spans = [(d.frame_off(i), d.rec_bytes, f"record {i}") for i in range(d.nframes)]
spans += [(d.lump_off(k), d.cad_a * SECTOR, f"lump {k}") for k in range(d.n_lumps)]
spans.sort()
pos, overlap, gap = SECTOR, [], []
for off, n, what in spans:
if off < pos: overlap.append(what)
elif off > pos: gap.append((pos, off, what))
pos = max(pos, off + n)
ck(not overlap, f"nothing overlaps ({len(spans)} spans: {d.nframes} records "
f"+ {d.n_lumps} lumps)" + (f" -- {overlap[:3]}" if overlap else ""))
ck(not gap, "no byte between the header and the end belongs to nothing"
+ (f" -- {gap[:3]}" if gap else ""))
ck(pos == len(d.raw), f"the arithmetic ends at {pos:,} and the file is "
f"{len(d.raw):,} B")
ck(all(off % SECTOR == 0 for off, _, _ in spans),
"every record and every lump starts on a 512 B sector -- 58.3/60.1's "
"precondition survives the interleave")
# --- 1b. and the cadence term is load-bearing -----------------------------
# THE FAILURE MODE THIS FORMAT HAS AND THE CODEC'S DOES NOT. A DLX record is
# found through an index and a player that read the wrong entry gets a length
# word that does not parse. A packed record is found by ARITHMETIC and nothing
# parses it, so a player that drops the `(i//F)*A` term reads 97 sectors
# starting 14 sectors early and paints them: the last 14 sectors of the previous
# record, then 83 of this one, shifted down the screen. It is a picture. Here
# is what the gate would be comparing if the term were missing, and it is only
# WRONG from frame F on -- the first group is exempt, which is how an off-by-one
# like this survives a rig that checks frame 0.
blind = [i for i in range(d.nframes)
if d.raw[d.off_frm + i*d.rec_bytes:d.off_frm + (i+1)*d.rec_bytes]
!= d.record(i)]
ck(blind == list(range(d.cad_f, d.nframes)),
f"a cadence-blind player reads the wrong bytes for {len(blind)} of "
f"{d.nframes} records, first at frame {blind[0] if blind else '-'} -- and "
f"frames 0..{d.cad_f-1} are IDENTICAL either way, so frame 0 proves nothing")
# --- 2. the picture did not move ------------------------------------------
if os.path.exists(a.silent):
q = DLXP(a.silent)
same = (q.nframes == d.nframes
and all(q.record(i) == d.record(i) for i in range(d.nframes)))
ck(same, f"all {d.nframes} records byte-exact against the SILENT control "
f"({os.path.basename(a.silent)}) -- interleaving audio moved no "
f"picture byte")
ck(q.has_audio is False and q.off_frm == SECTOR,
"and the control really is silent: no audio flag, record 0 at sector 1")
else:
print(f" SKIPPED: no silent control at {a.silent}")
# --- 3. the bytes are the encoder's ---------------------------------------
if os.path.exists(a.audio):
raw = open(a.audio, "rb").read()
pcm = struct.unpack("<%dh" % (len(raw) // 2), raw)
src = [max(-2048, min(2047, x >> 4)) for x in pcm]
axes = d.decoder()
ck(axes == adpcm.CHIP, f"the header's four axes ARE adpcm.CHIP: {axes}")
nib = adpcm.encode(src, variant=axes["variant"], init=axes["init"],
bits=axes["bits"])
want = adpcm.pack(nib, order=axes["order"])[:d.aud_bytes]
got = d.audio()
ck(got == want, f"the {len(got):,} B the lumps carry are byte-exact against "
f"adpcm.encode on the same PCM")
ck(all(d.lump(k, padding=True)[len(d.lump(k)):] == b"\0" * (
d.cad_a * SECTOR - len(d.lump(k))) for k in range(d.n_lumps)),
"and every lump's padding is zero, so a player that overruns the payload "
"feeds the chip silence rather than the next lump's first sample")
# --- 4. the header's axes are load-bearing ----------------------------
def snr(axes_):
rec = adpcm.decode(adpcm.unpack(got, len(src), order=axes_["order"]),
variant=axes_["variant"], init=axes_["init"],
bits=axes_["bits"])
n = min(len(rec), len(src))
e = sum((x - y) ** 2 for x, y in zip(src[:n], rec[:n]))
s = sum(x * x for x in src[:n])
return 10 * math.log10(s / e) if e else float("inf")
right = snr(axes)
ck(right > 20.0, f"decoded on the axes the header names: {right:.2f} dB")
print(f"\n AND EVERY AXIS IS A NEGATIVE CONTROL -- flip ONE and this is what\n"
f" a player that ignored the header would hear:\n")
print(f" {'axis':<12} {'header':>8} {'flipped to':>11} {'SNR':>9} cost")
flips = [("order", "high" if axes["order"] == "low" else "low"),
("variant", "terms" if axes["variant"] == "shift" else "shift"),
("bits", 12 if axes["bits"] == 10 else 10),
("init", 0 if axes["init"] else -2)]
for k, v in flips:
w = dict(axes); w[k] = v
s2 = snr(w)
print(f" {k:<12} {str(axes[k]):>8} {str(v):>11} {s2:9.2f} dB "
f"{s2-right:+.2f} dB")
if k in ("order", "variant"):
ck(s2 < right - 2.0, f"axis '{k}' is load-bearing: {s2-right:+.2f} dB")
else:
print(f" SKIPPED: no PCM at {a.audio} -- the bytes were not re-derived")
# --- the finding ----------------------------------------------------------
per = d.cad_a * SECTOR - grp
print(f"""
=== THE PAYLOAD IS NOT THE LUMP (FINDINGS 67) ==========================
A lump is {d.cad_a*SECTOR:,} B of SPACE. {d.cad_f} frames of audio is {grp:,.4f} B, so the
PAYLOAD is {P.lump_bytes(0, d.cad_f, d.fps, d.aud_hz):,} or {P.lump_bytes(2, d.cad_f, d.fps, d.aud_hz):,} -- the same remainder FINDINGS 54's frame
clock carries, one dimension over -- and the last {per:.4f} B are zero.
A PLAYER THAT FED THE CHIP THE WHOLE LUMP would hand it {per:.2f} B a group it
should not have. At {d.aud_hz:,} Hz that is {2*per/d.aud_hz*1000:.2f} ms of audio every
{d.cad_f/d.fps:.4f} s, which is {100*per/grp:.3f}% -- and it does not average out, it ACCUMULATES:""")
for mins in (1.0, a.game_min):
print(f" {mins:5.1f} min of play -> {mins*60*(per/grp):.2f} s of lip-sync error")
print(f""" so the cadence's {100*per/grp:.3f}% is not the waste figure 65.3 called it and left
at that. It is waste ON THE WIRE and DRIFT IN THE PLAYER, and the second is
the expensive one: {a.game_min:.1f} minutes is {a.game_min*60*(per/grp):.2f} s, which is a scene of dialogue
arriving after the mouth that spoke it.
WHAT A PLAYER CARRIES INSTEAD IS ONE ACCUMULATOR, and it is three
instructions rather than a table:
acc += {d.cad_f}*{d.aud_hz:,} ; = {d.cad_f*d.aud_hz:,}
n = acc // {2*d.fps} ; the MTC for this lump's channel
acc %= {2*d.fps}
which is exactly clock.i's shape (54) and for exactly the same reason: a rate
with a denominator of {2*d.fps} cannot be a count, so it is a remainder.
=== THE WIRE ===========================================================
video {d.video_kbps():7.1f} KB/s FIXED by geometry
audio {d.audio_kbps():7.2f} KB/s the CADENCE's, padding included -- the disc moves
whole sectors and the wire pays for the zero ones
total {d.kbps():7.1f} KB/s ({100*(d.kbps()/d.video_kbps()-1):+.2f}%), and 65.3 predicted {589.6:.1f}
""")
print(f"{'FAIL' if fails else 'OK'} 34_packed_audio: {len(fails)} failure(s)")
sys.exit(1 if fails else 0)
tools/bench/check.sh
+32 -3
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@@ -667,10 +667,22 @@ echo "--- session 31: the PACKED container, and the picture re-derived (FINDINGS
# present, the way the codec's gate container is: a packed encode is 3 seconds
# because there is no k-means in it, so there is no reason to let a stale file
# stand between the encoder and the gate.
# The window's audio has to exist before the container can carry it, so the
# extraction that used to live in session 33's stage moves up here. Same seconds
# as the frames, and that is not a convenience: an audio stream that is not the
# same seconds as the picture is not this project's audio.
[ -f tmp/au_singe.raw ] || python3 tools/encoder/extract_audio.py 00223 tmp/au_singe.raw 15625 539.4 10.0
python3 tools/encoder/pack.py tmp/fr_singe tmp/packed_singe.dlxp \
--nframes "$NF" > tmp/pack_encode.log 2>&1 \
--nframes "$NF" --audio tmp/au_singe.raw > tmp/pack_encode.log 2>&1 \
|| { cat tmp/pack_encode.log; exit 1; }
grep -aE "^ (record|wire)" tmp/pack_encode.log
grep -aE "^ (record|wire|DLXP2|the four axes|lump payload)" tmp/pack_encode.log
# ...and the SILENT control beside it, which is what says the interleave moved no
# picture byte. It is the same encode with one flag off, and a packed encode is
# four seconds because there is no k-means in it, so the control is cheap enough
# to build every run rather than reason about.
python3 tools/encoder/pack.py tmp/fr_singe tmp/packed_singe_silent.dlxp \
--nframes "$NF" > tmp/pack_encode_silent.log 2>&1 \
|| { cat tmp/pack_encode_silent.log; exit 1; }
# WHAT IS GATED. Four format invariants that a DMA channel cannot check for
# itself -- it copies bytes and has no opinion about them (FINDINGS 62) -- and
# the three quality claims FINDINGS 61.9 rests the whole packed branch on:
@@ -740,7 +752,8 @@ echo "--- session 33: AUDIO -- the encoder, and what it does to the wire (FINDIN
# is the SAME WINDOW as the frames -- 00223 from 539.4 s for 10 s -- because an
# audio stream that is not the same seconds as the picture is not this project's
# audio, and a gate that lets the two drift apart would never say so.
[ -f tmp/au_singe.raw ] || python3 tools/encoder/extract_audio.py 00223 tmp/au_singe.raw 15625 539.4 10.0
# tmp/au_singe.raw was extracted by session 31's stage, which needs it to build
# the container.
# There is NO ffmpeg encoder for this format -- adpcm_ima_oki is decode-only --
# so the encoder cannot be checked against a reference. What is checked is that
# the decoder our encoder runs in its own loop IS ffmpeg's, sample for sample.
@@ -770,4 +783,20 @@ python3 tools/analysis/33_adpcm_model.py tmp/au_singe.raw > tmp/adpcm_model.log
grep -aE "wrong only here|played on the chip|decoded on the encoder|headroom left" \
tmp/adpcm_model.log
echo "--- session 35: DLXP2 -- a packed container with sound in it (FINDINGS 67) ---"
# ROADMAP P6b. 65.3 did the arithmetic and wrote no byte; 66 measured which of
# sixteen decoder models the chip runs. This is the container both produce, and
# it needs a gate of its own because NOTHING PARSES A PACKED CONTAINER: a lump
# one sector out does not fail, it paints 512 B of audio and plays 512 B of
# picture, and a gate that only looked for errors would pass it.
#
# The picture side of it is gated twice over: here against a SILENT control
# built from the same frames, and above by the packed player itself, which now
# carries the `(i//F)*A` term and still gets all 120 frames pixel-exact off a
# real volume.
python3 tools/analysis/34_packed_audio.py tmp/packed_singe.dlxp \
> tmp/packed_audio.log 2>&1 || { cat tmp/packed_audio.log; exit 1; }
grep -aE "^ (OK|FAIL) |^ (order|variant|bits|init) |min of play ->" \
tmp/packed_audio.log
echo "ALL GREEN"
tools/bench/packed.lua
+19 -2
View File
@@ -68,6 +68,7 @@ local META = loadfile("packed_meta.lua")()
local PG_FLAG, PG_NFR, PG_FPS, PG_LBA0 = 0x18900, 0x18904, 0x18908, 0x1890C
local PG_RECS, PG_PALL, PG_HELD = 0x18910, 0x18914, 0x18918
local PG_PACEON, PG_ITER = 0x1891C, 0x18920
local PG_CADF, PG_CADA = 0x18924, 0x18928
local PG_SHOWN, PG_ERR, PG_ERRAT = 0x18930, 0x18934, 0x18938
local PG_LATE, PG_LATE1, PG_LATEM = 0x1893C, 0x18940, 0x18944
local PG_VDISP, PG_VD0, PG_TSPIN = 0x18948, 0x1894C, 0x18950
@@ -107,12 +108,28 @@ local function setup()
SP:write_u32(PG_HELD, HELD and 1 or 0)
SP:write_u32(PG_PACEON, PACED and 1 or 0)
SP:write_u32(PG_ITER, ITERS)
-- DLXP2's cadence. Zero for a silent container, and the 68000 branches on the
-- zero: a player told the wrong cadence does not fail, it reads an audio lump
-- as a record and paints it.
SP:write_u32(PG_CADF, META.cad_f or 0)
SP:write_u32(PG_CADA, META.cad_a or 0)
SP:write_u32(PG_SHOWN, 0)
P(string.format("packed.bin=%d B, %dx%d %d fps, %d of %d frames, %d passes",
#code, META.W, META.H, META.fps, NFR, META.nframes, ITERS))
P(string.format("record %d B = %d sectors at LBA %d + i*%d, palette %s",
local cad = ""
if (META.cad_f or 0) > 0 then
cad = string.format(" + (i//%d)*%d", META.cad_f, META.cad_a)
end
P(string.format("record %d B = %d sectors at LBA %d + i*%d%s, palette %s",
META.rec_bytes, META.rec_sectors, META.lba0,
META.rec_sectors, META.palette_last == 1 and "LAST" or "FIRST"))
META.rec_sectors, cad,
META.palette_last == 1 and "LAST" or "FIRST"))
if (META.cad_f or 0) > 0 then
P(string.format("DLXP2: %d B of ADPCM at %d Hz rides in %d lumps of %d sectors, "
.."one in front of every %d records -- the third term above is the "
.."whole cost of it on the video path",
META.aud_bytes, META.aud_hz, META.n_lumps, META.cad_a, META.cad_f))
end
P(string.format("channel: %s, %s",
HELD and "BUS HELD (burst, max rate)" or "CYCLE STEALING",
PACED and ("SELF-PACED at "..FPS.." fps off V-DISP"
tools/bench/prep_packed.py
+13 -3
View File
@@ -43,15 +43,25 @@ with open(out, "w") as fh:
("lba0", d.off_frm // SECTOR),
("palette_last", int(d.palette_last)),
("has_palette", int(d.has_palette)),
# DLXP2. Zero in a silent container, and the player branches on
# the zero rather than being built two ways.
("cad_f", d.cad_f), ("cad_a", d.cad_a),
("has_audio", int(d.has_audio)),
("aud_bytes", d.aud_bytes), ("aud_hz", d.aud_hz),
("n_lumps", d.n_lumps),
("entries", entries)]:
fh.write(f" {k} = {v},\n")
fh.write("}\n")
print(f"{sys.argv[1]}: DLXP1 {d.W}x{d.H} {d.fps}fps {d.nframes} frames")
print(f"{sys.argv[1]}: DLXP{d.version} {d.W}x{d.H} {d.fps}fps {d.nframes} frames"
+ (f", AUDIO F={d.cad_f} A={d.cad_a}" if d.has_audio else ", silent"))
print(f" record {d.rec_bytes:,} B = {recs} sectors, palette "
f"{'LAST' if d.palette_last else 'FIRST'}, {d.pal_bytes} B")
print(f" record i is at LBA {d.off_frm // SECTOR} + i*{recs} -- ARITHMETIC. "
cad = (f" + (i//{d.cad_f})*{d.cad_a}" if d.has_audio else "")
print(f" record i is at LBA {d.off_frm // SECTOR} + i*{recs}{cad} -- ARITHMETIC. "
f"There is no index in this container and none can be needed.")
print(f" the chain the 68000 must build: {entries} entries "
f"({rows} rows{' + 1 palette' if d.has_palette else ''})")
print(f" wire {d.kbps():.1f} KB/s, FIXED by geometry -> {out}")
print(f" wire {d.video_kbps():.1f}"
+ (f" + {d.audio_kbps():.2f} = {d.kbps():.1f}" if d.has_audio else "")
+ f" KB/s, FIXED by geometry -> {out}")
tools/encoder/dlxp.py
+259 -14
View File
@@ -35,19 +35,65 @@ The layout, all of it fixed, all of it verified as a picture in FINDINGS 47.2:
chaining from one start (FINDINGS 62). A container that carried the stride
would be 4x the size and would say nothing extra.
header, 32 bytes, big-endian, then zero pad to the first sector:
header, 64 bytes, big-endian, then zero pad to the first sector:
0 'DLXP'
4 u16 version (1)
4 u16 version (2)
6 u16 flags bit 0: a per-frame palette is present
bit 1: the palette is at the END of the record
bit 2: an audio stream is interleaved (DLXP2)
8 u16 width, u16 height
12 u16 fps, u16 nframes
16 u32 record bytes fixed, and a whole number of 512 B sectors
20 u32 palette bytes 512 (256 GRB555+I words), or 0
24 u32 picture bytes 49,152
28 u32 frames offset 512 B, i.e. sector 1
28 u32 frames offset offset of RECORD 0, lump 0 already skipped
-- DLXP2 adds, and every field is zero in a silent container:
32 u32 audio offset offset of LUMP 0, 512 B, i.e. sector 1
36 u32 audio sample Hz 15,625 -- the chip's, not the disc's
40 u32 audio bytes the ADPCM payload, padding NOT counted
44 u16 cadence F frames between one lump and the next
46 u16 cadence A whole sectors in a lump
48 u16 audio format bit 0: LOW nibble first. bit 1: the OKI
datasheet's per-term delta ('terms')
50 u16 audio clamp bits where the accumulator saturates, 10 or 12
52 i16 audio init the accumulator at PLAY, -2 on this chip
54 u16 reserved (0)
56 u32 reserved (0)
60 u32 reserved (0)
then nframes FIXED-SIZE records, each 49,664 B = 97 sectors EXACTLY.
then, from sector 1, GROUPS: one audio lump of A sectors, then F records.
A record is 49,664 B = 97 sectors EXACTLY and a lump is A*512 B EXACTLY, so
record i is at off_frm + i*rec_bytes + (i//F)*A*512
lump k is at off_aud + k*(F*rec_bytes + A*512)
-- still arithmetic, still no index, still nothing walked.
WHY AUDIO IS A CADENCE AND NOT A FIELD IN THE RECORD (FINDINGS 65.3). 15,625
samples a second, two to a byte, is 651.0416... B per 12 fps slot, and the dots
are the whole problem: put slot i's audio in record i and records become
VARIABLE LENGTH, which needs an index, which ends the format. A fixed cadence
of F frames per A sectors keeps `LBA(i)` arithmetic and pays instead in padding,
and the padding is a rational-approximation problem whose answer is not the
obvious cadence: F=1 wastes 57.3% of every audio sector and F=11, A=14 wastes
0.09%.
AND THE PADDING IS NOT WHERE THE BYTES ARE (FINDINGS 67). A lump is A*512 B of
SPACE and it does NOT carry A*512 B of audio: F frames need F*15625/24 B, which
is 7,161.4583... at F=11, so a lump's PAYLOAD alternates 7,161 and 7,162 by the
same remainder arithmetic FINDINGS 54's frame clock carries, and the rest of the
sector is zero. A player that fed the chip the whole lump would be handing it
6.54 B a group it should not have -- 0.09% too much audio, which is not waste,
it is DRIFT: 0.83 ms a group, 1.2 s of lip-sync over the game's 22 minutes. So
`lump_bytes(k)` below is the format, not a convenience, and a player computes it
with one accumulator: `acc += F*aud_hz; n = acc // (2*fps); acc %= 2*fps`.
THE FOUR ADPCM AXES ARE IN THE HEADER BECAUSE GETTING ONE WRONG COSTS 25 dB
(FINDINGS 66). Nibble order, delta formula, clamp width and the accumulator's
value at PLAY are properties of the DECODER, and a container encoded for one
decoder and played on another comes out with the noise louder than the signal.
They are four fields rather than a version number so that a mismatch is legible
in a hexdump rather than inferred from a container's age.
THERE IS NO RECORD INDEX AND NO LENGTH WORD, and that is the difference DLX4's
index was invented for (49.3): a codec record's length is content-dependent, so
@@ -68,12 +114,78 @@ import struct
import numpy as np
MAGIC = b"DLXP"
VERSION = 1
VERSION = 2
SECTOR = 512 # same rule and the same reason as dlx.SECTOR
PAL_BYTES = 512 # 256 entries, one GRB555+I word each
HDR_BYTES = 32
HDR_BYTES = 64
FLAG_PALETTE = 1 << 0
FLAG_PALETTE_LAST = 1 << 1
FLAG_AUDIO = 1 << 2
# The two ADPCM axes that are booleans. The other two -- the clamp width and
# the accumulator at PLAY -- are numbers and get their own fields, because
# encoding them as flags would mean this file deciding which values are legal.
AFMT_ORDER_LOW = 1 << 0
AFMT_VARIANT_TERMS = 1 << 1
# The default cadence, and it is a MEASUREMENT rather than a taste (FINDINGS
# 65.3): the sweep's floor is F=81 and costs 91,136 B more of player RAM for the
# last 0.09 of a point of padding, on a machine where two record buffers already
# want 99,328 B.
CADENCE_F = 11
def audio_format(variant, order, bits, init):
"""adpcm.py's four axes -> the three header fields that carry them.
This file does not import adpcm.py and must not: a container format that
depended on an encoder would be a format that could not be read without one.
What it carries is the DESCRIPTION, and `tools/analysis/34_packed_audio.py`
is what checks the description against the encoder that wrote the bytes.
"""
if variant not in ("shift", "terms") or order not in ("high", "low"):
raise ValueError(f"unknown ADPCM decoder ({variant!r}, {order!r})")
fmt = ((AFMT_ORDER_LOW if order == "low" else 0)
| (AFMT_VARIANT_TERMS if variant == "terms" else 0))
return fmt, int(bits), int(init)
def audio_decoder(fmt, bits, init):
"""The inverse: what a player, or a gate, has to run to hear the bytes."""
return dict(variant="terms" if fmt & AFMT_VARIANT_TERMS else "shift",
order="low" if fmt & AFMT_ORDER_LOW else "high",
bits=int(bits), init=int(init))
def cadence(fps, hz, F=CADENCE_F):
"""(F, A): F frames of audio rounded UP to whole sectors.
A*512 must cover F frames or the chip runs dry, so A is a ceiling and the
excess is padding the wire pays for and nothing plays. Integer arithmetic
throughout: the whole point of 65.3 is that this ratio has a remainder, and
a float here would hide the case where it does not.
"""
num, den = F * hz, 2 * fps # bytes per group = num/den
return F, -(-num // (den * SECTOR))
def lump_bytes(k, F, fps, hz, total=None):
"""The PAYLOAD of lump k -- what is handed to the chip, padding excluded.
Exact, and exactness is the finding (FINDINGS 67): floor((k+1)*F*hz/(2*fps))
- floor(k*F*hz/(2*fps)) alternates 7,161 and 7,162 at F=11, and a player
that fed the chip the whole A*512 B lump instead would run 0.09% fast --
1.2 s of lip-sync over 22 minutes.
"""
den = 2 * fps
n = ((k + 1) * F * hz) // den - (k * F * hz) // den
if total is not None: # the last lump is short, not padded
n = max(0, min(n, total - (k * F * hz) // den))
return n
def n_lumps(nframes, F):
return -(-nframes // F)
def pack_picture(idx):
@@ -111,23 +223,73 @@ def record_bytes(W, H, palette=True):
return n
def write(path, W, H, fps, frames, palette_last=False):
"""`frames` is a sequence of (palette_words_bytes | None, picture_bytes)."""
def write(path, W, H, fps, frames, palette_last=False, audio=None):
"""`frames` is a sequence of (palette_words_bytes | None, picture_bytes).
`audio`, when given, is a dict: `data` the packed ADPCM bytes, `hz` the
chip's sample rate, `variant`/`order`/`bits`/`init` the four axes FINDINGS
66 measured, and optionally `F`. The stream is CUT UP HERE and nowhere
else, by `lump_bytes`, for the same reason `pack_picture` is the one place
the interleave lives: a second copy of a layout rule is a place the layout
can drift.
"""
frames = list(frames)
pal_b = PAL_BYTES if frames and frames[0][0] is not None else 0
pic_b = W * H
rec_b = record_bytes(W, H, palette=bool(pal_b))
flags = ((FLAG_PALETTE if pal_b else 0)
| (FLAG_PALETTE_LAST if palette_last and pal_b else 0))
| (FLAG_PALETTE_LAST if palette_last and pal_b else 0)
| (FLAG_AUDIO if audio else 0))
if audio:
hz = int(audio["hz"])
F, A = cadence(fps, hz, audio.get("F", CADENCE_F))
au = audio["data"]
fmt, bits, init = audio_format(audio["variant"], audio["order"],
audio["bits"], audio["init"])
lumps = []
got = 0
for k in range(n_lumps(len(frames), F)):
n = lump_bytes(k, F, fps, hz, total=len(au))
if n > A * SECTOR:
raise ValueError(f"lump {k} needs {n} B and the cadence gives "
f"{A*SECTOR}")
lumps.append(au[got:got + n].ljust(A * SECTOR, b"\0"))
got += n
# A container whose audio runs out before its pictures do is a container
# that goes silent part way through, which is exactly the failure a
# writer should refuse rather than a player discover.
if got < len(au):
raise ValueError(f"{len(au)-got} B of audio have no lump to ride in "
f"-- {len(frames)} frames hold {got} B")
if got < min(len(au), (len(frames) * hz) // (2 * fps)):
raise ValueError(f"the audio stream is short: {len(au)} B for "
f"{len(frames)} frames at {fps} fps")
off_aud, off_frm = SECTOR, SECTOR + A * SECTOR
atail = struct.pack(">IIIHHHHhHII", off_aud, hz, len(au), F, A,
fmt, bits, init, 0, 0, 0)
else:
F = A = 0
lumps = []
off_aud, off_frm = 0, SECTOR
atail = struct.pack(">IIIHHHHhHII", 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0)
hdr = (MAGIC + struct.pack(">HHHHHH", VERSION, flags, W, H, fps, len(frames))
+ struct.pack(">III", rec_b, pal_b, pic_b)
+ struct.pack(">I", SECTOR))
+ struct.pack(">IIII", rec_b, pal_b, pic_b, off_frm) + atail)
assert len(hdr) == HDR_BYTES, len(hdr)
with open(path, "wb") as fh:
fh.write(hdr + b"\0" * (SECTOR - HDR_BYTES))
for i, (pw, pic) in enumerate(frames):
if len(pic) != pic_b or (pal_b and len(pw) != pal_b):
raise ValueError(f"frame {i}: record parts are the wrong size")
# The lump goes BEFORE the group it feeds, which is the one place
# this format makes a choice audio forced on it. 65.3's formula put
# it after; a stream is read forwards, so bytes that arrive after
# the slot they belong to are bytes a player has to have fetched
# early anyway. Placing it first makes the fetch order the play
# order and costs one lump of offset in the arithmetic.
if audio and i % F == 0:
fh.write(lumps[i // F])
rec = pic if not pal_b else (pic + pw if palette_last else pw + pic)
fh.write(rec)
return rec_b
@@ -154,6 +316,32 @@ class DLXP:
raise ValueError(f"{path}: DLXP version {self.version}")
self.has_palette = bool(self.flags & FLAG_PALETTE)
self.palette_last = bool(self.flags & FLAG_PALETTE_LAST)
self.has_audio = bool(self.flags & FLAG_AUDIO)
(self.off_aud, self.aud_hz, self.aud_bytes, self.cad_f, self.cad_a,
self.aud_fmt, self.aud_bits, self.aud_init,
_r0, _r1, _r2) = struct.unpack(">IIIHHHHhHII", b[32:64])
if not self.has_audio:
if any((self.off_aud, self.aud_hz, self.aud_bytes, self.cad_f,
self.cad_a, self.aud_fmt, self.aud_bits, self.aud_init)):
raise ValueError(f"{path}: silent container with audio fields set")
else:
if (self.cad_f, self.cad_a) != cadence(self.fps, self.aud_hz,
self.cad_f):
raise ValueError(f"{path}: cadence F={self.cad_f} A={self.cad_a} "
f"does not cover {self.cad_f} frames of "
f"{self.aud_hz} Hz audio at {self.fps} fps")
if self.off_aud != SECTOR or self.off_aud % SECTOR:
raise ValueError(f"{path}: audio starts at {self.off_aud}")
if self.aud_bits not in (10, 12):
raise ValueError(f"{path}: ADPCM clamp is {self.aud_bits} bits")
# The stream has to fill the groups it is cut into, or the last
# frames of the scene play in silence and nothing says so.
want = sum(lump_bytes(k, self.cad_f, self.fps, self.aud_hz)
for k in range(n_lumps(self.nframes, self.cad_f)))
if not (want - self.cad_f * self.aud_hz // (2 * self.fps)
<= self.aud_bytes <= want):
raise ValueError(f"{path}: {self.aud_bytes} B of audio for "
f"{self.nframes} frames, geometry wants {want}")
if self.pic_bytes != self.W * self.H:
raise ValueError(f"{path}: picture is {self.pic_bytes} B for "
f"{self.W}x{self.H} -- the packed layout is 1.0 B/px")
@@ -167,12 +355,56 @@ class DLXP:
if self.off_frm % SECTOR or self.rec_bytes % SECTOR:
raise ValueError(f"{path}: not sector-aligned -- stream at "
f"{self.off_frm}, record {self.rec_bytes}")
want = self.off_frm + self.nframes * self.rec_bytes
if self.off_frm != (SECTOR + (self.cad_a * SECTOR if self.has_audio
else 0)):
raise ValueError(f"{path}: record 0 is at {self.off_frm}, and a "
f"{self.cad_a}-sector lump comes before it")
want = (self.off_frm + self.nframes * self.rec_bytes
+ (n_lumps(self.nframes, self.cad_f) - 1) * self.cad_a * SECTOR
if self.has_audio else
self.off_frm + self.nframes * self.rec_bytes)
if len(b) != want:
raise ValueError(f"{path}: {len(b)} bytes, geometry says {want}")
def record(self, i):
def frame_off(self, i):
"""The arithmetic, and the ONE place it is written on the host side --
src/player/packed.s is the other, in six instructions, and
tools/analysis/34_packed_audio.py is what makes the two agree."""
if not (0 <= i < self.nframes):
raise IndexError(i)
o = self.off_frm + i * self.rec_bytes
return o + (i // self.cad_f) * self.cad_a * SECTOR if self.has_audio else o
def lump_off(self, k):
if not self.has_audio or not (0 <= k < self.n_lumps):
raise IndexError(k)
return self.off_aud + k * (self.cad_f * self.rec_bytes
+ self.cad_a * SECTOR)
@property
def n_lumps(self):
return n_lumps(self.nframes, self.cad_f) if self.has_audio else 0
def lump(self, k, padding=False):
"""Lump k's PAYLOAD -- what the chip is fed. `padding=True` returns the
whole A*512 B sector run instead, which is what the disc moves and what
a player must NOT hand to the chip (FINDINGS 67)."""
o = self.lump_off(k)
if padding:
return self.raw[o:o + self.cad_a * SECTOR]
n = lump_bytes(k, self.cad_f, self.fps, self.aud_hz, total=self.aud_bytes)
return self.raw[o:o + n]
def audio(self):
"""The whole ADPCM stream, reassembled from its lumps."""
return b"".join(self.lump(k) for k in range(self.n_lumps))
def decoder(self):
"""The four axes the bytes were encoded for, as adpcm.decode's kwargs."""
return audio_decoder(self.aud_fmt, self.aud_bits, self.aud_init)
def record(self, i):
o = self.frame_off(i)
return self.raw[o:o + self.rec_bytes]
def _split(self, i):
@@ -214,5 +446,18 @@ class DLXP:
"""(H,W,3) uint8 -- the frame as the display produces it."""
return self.palette_rgb(i)[self.indices(i)]
def video_kbps(self):
"""The picture on the wire. FIXED by geometry -- there is no lever."""
return self.rec_bytes * self.fps / 1024
def audio_kbps(self):
"""What the CADENCE costs, padding included, which is the honest figure:
the disc moves whole sectors and the wire pays for the ones that are
zero as well as the ones that are audio (FINDINGS 65.3)."""
if not self.has_audio:
return 0.0
return self.cad_a * SECTOR / self.cad_f * self.fps / 1024
def kbps(self):
return self.nframes * self.rec_bytes / (self.nframes / self.fps) / 1024
"""Both, over the scene's own duration."""
return self.video_kbps() + self.audio_kbps()
tools/encoder/pack.py
+67 -4
View File
@@ -3,7 +3,7 @@
python3 tools/encoder/pack.py <frames_dir> <out.dlxp> [--fps 12]
[--nframes N] [--palette-last] [--no-palette]
[--scene-palette]
[--scene-palette] [--audio tmp/au_singe.raw]
WHAT IS NOT HERE IS THE POINT. No VQ, no codebooks, no mode map, no rate
control, no `lam`, no leaky bucket, no span geometry -- `encode.py` is 452 lines
@@ -25,6 +25,15 @@ as "a direction, not the player's number" (risk 2 in the session 30 handoff).
`vq.frame_palette` is what actually ships it: 254 colours, index 0 held free for
the transparency key, black at 255. `tools/analysis/30_packed_container.py`
re-derives the figure against this and charges the GRB555 word on top.
AND `--audio` MAKES IT A DLXP2, WHICH IS THE ONE PLACE THE FOUR ADPCM AXES ARE
CHOSEN. It encodes for `adpcm.CHIP` -- the datasheet's per-term delta, the LOW
nibble of a byte first, a 10-bit clamp, the accumulator at -2 -- because that is
the set FINDINGS 66 measured out of the machine's own chip through the machine's
own DMA channel, and encoding for any other set costs up to 25.7 dB. It does
NOT use adpcm.py's module defaults, which are ffmpeg's on purpose so that
tools/bench/verify_adpcm.py stays a check against an independent implementation.
The axes go in the header, so a player never has to be told.
"""
import argparse, glob, os, sys
import numpy as np
@@ -35,6 +44,7 @@ sys.path.insert(0, os.path.join(os.path.dirname(os.path.abspath(__file__)),
"..", "bench"))
import vq as VQ
import dlxp as P
import adpcm
from dlxload import pack_palette
ap = argparse.ArgumentParser()
@@ -52,6 +62,14 @@ ap.add_argument("--no-palette", action="store_true",
ap.add_argument("--scene-palette", action="store_true",
help="one palette for the whole scene, repeated in every record "
"-- the CONTROL for 61.9's per-frame claim")
ap.add_argument("--audio", default=None,
help="raw s16le mono at --audio-hz, from extract_audio.py. "
"Makes the output a DLXP2: the stream is encoded for "
"adpcm.CHIP and interleaved on the 65.3 cadence")
ap.add_argument("--audio-hz", type=int, default=15625,
help="the CHIP's rate, and the rate the .raw was resampled to")
ap.add_argument("--cadence", type=int, default=P.CADENCE_F,
help="frames between audio lumps (65.3's sweep picks 11)")
a = ap.parse_args()
files = sorted(glob.glob(f"{a.frames_dir}/f*.png"))
@@ -95,7 +113,35 @@ for n, src in enumerate(rgb):
psnr_pal.append(VQ.psnr(src, pal[idx]))
recs.append((palw, P.pack_picture(idx).tobytes()))
rec_b = P.write(a.out, W, H, a.fps, recs, palette_last=a.palette_last)
# THE AUDIO, AND IT IS ENCODED FOR THE CHIP AND NOT FOR ffmpeg. The source is
# s16le because that is what ffmpeg resamples to; the chip's word is 12 bits
# signed, so the shift is a requantisation and not a format conversion, and it
# is the same one tools/bench/verify_adpcm.py makes.
audio = None
if a.audio:
import struct as _struct
raw = open(a.audio, "rb").read()
pcm = _struct.unpack("<%dh" % (len(raw) // 2), raw)
src12 = [max(-2048, min(2047, x >> 4)) for x in pcm]
need = len(files) * a.audio_hz // (2 * a.fps)
nib = adpcm.encode(src12, variant=adpcm.CHIP["variant"],
init=adpcm.CHIP["init"], bits=adpcm.CHIP["bits"])
data = adpcm.pack(nib, order=adpcm.CHIP["order"])[:need]
# What the encoder thinks it wrote, checked by DECODING it with the same
# four axes -- the encoder runs its decoder inside its own loop, so this is
# not circular in the way it looks: it is the PACKED bytes going back
# through unpack(), which is where a nibble-order slip would land.
back = adpcm.decode(adpcm.unpack(data, len(src12), order=adpcm.CHIP["order"]),
variant=adpcm.CHIP["variant"], init=adpcm.CHIP["init"],
bits=adpcm.CHIP["bits"])
ref = src12[:len(back)]
e = [(x - y) ** 2 for x, y in zip(ref, back)]
sig = sum(x * x for x in ref)
snr = 10 * np.log10(sig / sum(e)) if sum(e) else float("inf")
audio = dict(data=data, hz=a.audio_hz, F=a.cadence, **adpcm.CHIP)
rec_b = P.write(a.out, W, H, a.fps, recs, palette_last=a.palette_last,
audio=audio)
d = P.DLXP(a.out) # re-read: every invariant is checked
if d.nframes != len(recs):
sys.exit("writer and reader disagree about the frame count")
@@ -103,10 +149,27 @@ if d.nframes != len(recs):
kind = ("scene palette" if a.scene_palette else "per-frame palette")
if a.no_palette:
kind += ", NONE in the record"
print(f"{a.out}: DLXP1 {W}x{H} {a.fps}fps {d.nframes} frames, {kind}"
print(f"{a.out}: DLXP{P.VERSION} {W}x{H} {a.fps}fps {d.nframes} frames, {kind}"
f"{', palette LAST' if a.palette_last else ''}")
print(f" record {rec_b:,} B = {rec_b // P.SECTOR} sectors exactly, "
f"file {os.path.getsize(a.out):,} B")
print(f" wire {d.kbps():.1f} KB/s -- FIXED by geometry, there is no lever")
if d.has_audio:
print(f" DLXP2: audio {d.aud_bytes:,} B at {d.aud_hz:,} Hz, SNR {snr:.2f} dB, "
f"cadence F={d.cad_f} A={d.cad_a} ({d.n_lumps} lumps)")
print(f" the four axes, in the header: "
+ ", ".join(f"{k}={v}" for k, v in d.decoder().items()))
# STEADY STATE, not the file: the last lump of a 120-frame window feeds 4
# frames out of 11 and occupies 14 sectors either way, so a whole-file
# padding figure is a boundary effect of the WINDOW and would change with
# its length. 65.3's 0.09% is the cadence's, and the cadence is the thing.
grp = d.cad_f * d.aud_hz / (2 * d.fps)
print(f" lump payload {P.lump_bytes(0, d.cad_f, d.fps, d.aud_hz):,}.."
f"{P.lump_bytes(2, d.cad_f, d.fps, d.aud_hz):,} B of {d.cad_a*P.SECTOR:,} "
f"-- {100*(d.cad_a*P.SECTOR-grp)/grp:.3f}% padding steady state, and the "
f"payload is NOT the lump (FINDINGS 67)")
print(f" wire {d.video_kbps():.1f} + {d.audio_kbps():.2f} = {d.kbps():.1f} KB/s "
f"-- FIXED by geometry, there is no lever")
else:
print(f" wire {d.kbps():.1f} KB/s -- FIXED by geometry, there is no lever")
print(f" palette-domain PSNR vs the 24-bit source: "
f"{np.mean(psnr_pal):.2f} dB (min {np.min(psnr_pal):.2f})")