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Roger Dannenberg's explanatory comments for new MidiTime function

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Paul Licameli 2017-09-23 18:36:26 -04:00
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src/AudioIO.cpp
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@ -81,6 +81,78 @@
speed at mTime. This effectively integrates speed to get position.
Negative speeds are allowed too, for instance in scrubbing.
\par The Big Picture
@verbatim
Sample
Time (in seconds, = total_sample_count / sample_rate)
^
| / /
| y=x-mSystemTimeMinusAudioTime / /
| / # /
| / /
| / # <- callbacks (#) showing
| /# / lots of timing jitter.
| top line is "full buffer" / / Some are later,
| condition / / indicating buffer is
| / / getting low. Plot
| / # / shows sample time
| / # / (based on how many
| / # / samples previously
| / / *written*) vs. real
| / # / time.
| /<------->/ audio latency
| /# v/
| / / bottom line is "empty buffer"
| / # / condition = DAC output time =
| / /
| / # <-- rapid callbacks as buffer is filled
| / /
0 +...+---------#---------------------------------------------------->
0 ^ | | real time
| | first callback time
| mSystemMinusAudioTime
|
Probably the actual real times shown in this graph are very large
in practice (> 350,000 sec.), so the X "origin" might be when
the computer was booted or 1970 or something.
@endverbatim
To estimate the true DAC time (needed to synchronize MIDI), we need
a mapping from track time to DAC time. The estimate is the theoretical
time of the full buffer (top diagonal line) + audio latency. To
estimate the top diagonal line, we "draw" the line to be at least
as high as any sample time corresponding to a callback (#), and we
slowly lower the line in case the sample clock is slow or the system
clock is fast, preventing the estimated line from drifting too far
from the actual callback observations. The line is occasionally
"bumped" up by new callback observations, but continuously
"lowered" at a very low rate. All adjustment is accomplished
by changing mSystemMinusAudioTime, shown here as the X-intercept.\n
theoreticalFullBufferTime = realTime - mSystemMinusAudioTime\n
To estimate audio latency, notice that the first callback happens on
an empty buffer, but the buffer soon fills up. This will cause a rapid
re-estimation of mSystemMinusAudioTime. (The first estimate of
mSystemMinusAudioTime will simply be the real time of the first
callback time.) By watching these changes, which happen within ms of
starting, we can estimate the buffer size and thus audio latency.
So, to map from track time to real time, we compute:\n
DACoutputTime = trackTime + mSystemMinusAudioTime\n
There are some additional details to avoid counting samples while
paused or while waiting for initialization, MIDI latency, etc.
Also, in the code, track time is measured with respect to the track
origin, so there's an extra term to add (mT0) if you start somewhere
in the middle of the track.
Finally, when a callback occurs, you might expect there is room in
the output buffer for the requested frames, so maybe the "full buffer"
sample time should be based not on the first sample of the callback, but
the last sample time + 1 sample. I suspect, at least on Linux, that the
callback occurs as soon as the last callback completes, so the buffer is
really full, and the callback thread is going to block waiting for space
in the output buffer.
\par Midi Time
MIDI is not warped according to the speed control. This might be
something that should be changed. (Editorial note: Wouldn't it
@ -95,33 +167,61 @@
\par
Therefore, we define the following interface for MIDI timing:
\li \c AudioTime() is the time based on all samples written so far, including zeros output during pauses. AudioTime() is based on the start location mT0, not zero.
\li \c PauseTime() is the amount of time spent paused, based on a count of zero samples output.
\li \c MidiTime() is an estimate in milliseconds of the current audio output time + 1s. In other words, what audacity track time corresponds to the audio (including pause insertions) at the output?
\li \c PauseTime() is the amount of time spent paused, based on a count of zero-padding samples output.
\li \c MidiTime() is an estimate in milliseconds of the current audio output time + 1s. In other words, what audacity track time corresponds to the audio (plus pause insertions) at the DAC output?
\par AudioTime() and PauseTime() computation
AudioTime() is simply mT0 + mNumFrames / mRate.
mNumFrames is incremented in each audio callback. Similarly, PauseTime()
is mNumPauseFrames / mRate. mNumPauseFrames is also incremented in
each audio callback when a pause is in effect.
each audio callback when a pause is in effect or audio output is ready to start.
\par MidiTime() computation
MidiTime() is computed based on information from PortAudio's callback,
which estimates the system time at which the current audio buffer will
be output. Consider the (unimplemented) function RealToTrack() that
maps real time to track time. If outputTime is PortAudio's time
estimate for the most recent output buffer, then \n
RealToTrack(outputTime) = AudioTime() - PauseTime() - bufferDuration \n
We want to know RealToTrack of the current time, so we use this
approximation for small d: \n
RealToTrack(t + d) = RealToTrack(t) + d \n
Letting t = outputTime and d = (systemTime - outputTime), we can
maps real audio write time to track time. If writeTime is the system
time for the first sample of the current output buffer, and
if we are in the callback, so AudioTime() also refers to the first sample
of the buffer, then \n
RealToTrack(writeTime) = AudioTime() - PauseTime()\n
We want to know RealToTrack of the current time (when we are not in the
callback, so we use this approximation for small d: \n
RealToTrack(t + d) = RealToTrack(t) + d, or \n
Letting t = writeTime and d = (systemTime - writeTime), we can
substitute to get:\n
RealToTrack(systemTime) = AudioTime() - PauseTime() - bufferduration + (systemTime - outputTime) \n
MidiTime() should include pause time, so add PauseTime() to both sides of
the equation. Also MidiTime() is offset by 1 second to avoid negative
time at startup, so add 1 to both sides:
MidiTime() in seconds = RealToTrack(systemTime) + PauseTime() + 1 = \n
AudioTime() - bufferduration + (systemTime - outputTime) + 1
RealToTrack(systemTime)
= RealToTrack(writeTime) + systemTime - writeTime\n
= AudioTime() - PauseTime() + (systemTime - writeTime) \n
MidiTime() should include pause time, so that it increases smoothly,
and audioLatency so that MidiTime() corresponds to the time of audio
output rather than audio write times. Also MidiTime() is offset by 1
second to avoid negative time at startup, so add 1: \n
MidiTime(systemTime) in seconds\n
= RealToTrack(systemTime) + PauseTime() - audioLatency + 1 \n
= AudioTime() + (systemTime - writeTime) - audioLatency + 1 \n
(Note that audioLatency is called mAudioOutLatency in the code.)
When we schedule a MIDI event with track time TT, we need
to map TT to a PortMidi timestamp. The PortMidi timestamp is exactly
MidiTime(systemTime) in ms units, and \n
MidiTime(x) = RealToTrack(x) + PauseTime() + 1, so \n
timestamp = TT + PauseTime() + 1 - midiLatency \n
Note 1: The timestamp is incremented by the PortMidi stream latency
(midiLatency) so we subtract midiLatency here for the timestamp
passed to PortMidi. \n
Note 2: Here, we're setting x to the time at which RealToTrack(x) = TT,
so then MidiTime(x) is the desired timestamp. To be completely
correct, we should assume that MidiTime(x + d) = MidiTime(x) + d,
and consider that we compute MidiTime(systemTime) based on the
*current* system time, but we really want the MidiTime(x) for some
future time corresponding when MidiTime(x) = TT.)
\par
Also, we should assume PortMidi was opened with mMidiLatency, and that
MIDI messages become sound with a delay of mSynthLatency. Therefore,
the final timestamp calculation is: \n
timestamp = TT + PauseTime() + 1 - (mMidiLatency + mSynthLatency) \n
(All units here are seconds; some conversion is needed in the code.)
\par
The difference AudioTime() - PauseTime() is the time "cursor" for
@ -129,34 +229,92 @@
unsynchronized. In particular, MIDI will not be synchronized with
the visual cursor, which moves with scaled time reported in mTime.
\par Midi Synchronization
The goal of MIDI playback is to deliver MIDI messages synchronized to
audio (assuming no speed variation for now). If a midi event has time
tmidi, then the timestamp for that message should be \n
timestamp (in seconds) = tmidi + PauseTime() + 1.0 - latency.\n
(This is actually off by 1ms; see "PortMidi Latency Parameter" below for
more detail.)
Notice the extra 1.0, added because MidiTime() is offset by 1s to avoid
starting at a negative value. Also notice that we subtract latency.
The user must set device latency using preferences. Some software
synthesizers have very high latency (on the order of 100ms), so unless
we lower timestamps and send messages early, the final output will not
be synchronized.
This timestamp is interpreted by PortMidi relative to MidiTime(), which
is synchronized to audio output. So the only thing we need to do is
output Midi messages shortly before they will be played with the correct
timestamp. We will take "shortly before" to mean "at about the same time
as corresponding audio". Based on this, output the event when
AudioTime() - PauseTime() > mtime - latency,
adjusting the event time by adding PauseTime() + 1 - latency.
This gives at least mAudioOutputLatency for
the MIDI output to be generated (we want to generate MIDI output before
the actual output time because events generated early are accurately timed
according to their timestamp). However, the MIDI thread sleeps for
MIDI_SLEEP in its polling loop, so the worst case is really
mAudioOutputLatency + MIDI_SLEEP. In case the audio output latency is
very low, we will output events when
AudioTime() + MIDI_SLEEP - PauseTime() > mtime - latency.
\par Timing in Linux
It seems we cannot get much info from Linux. We can read the time
when we get a callback, and we get a variable frame count (it changes
from one callback to the next). Returning to the RealToTrack()
equations above: \n
RealToTrack(outputTime) = AudioTime() - PauseTime() - bufferDuration \n
where outputTime should be PortAudio's estimate for the most recent output
buffer, but at least on my Dell Latitude E7450, PortAudio is getting zero
from ALSA, so we need to find a proxy for this.
\par Estimating outputTime (Plan A, assuming double-buffered, fixed-size buffers, please skip to Plan B)
One can expect the audio callback to happen as soon as there is room in
the output for another block of samples, so we could just measure system
time at the top of the callback. Then we could add the maximum delay
buffered in the system. E.g. if there is simple double buffering and the
callback is computing one of the buffers, the callback happens just as
one of the buffers empties, meaning the other buffer is full, so we have
exactly one buffer delay before the next computed sample is output.
If computation falls behind a bit, the callback will be later, so the
delay to play the next computed sample will be less. I think a reasonable
way to estimate the actual output time is to assume that the computer is
mostly keeping up and that *most* callbacks will occur immediately when
there is space. Note that the most likely reason for the high-priority
audio thread to fall behind is the callback itself, but the start of the
callback should be pretty consistently keeping up.
Also, we do not have to have a perfect estimate of the time. Suppose we
estimate a linear mapping from sample count to system time by saying
that the sample count maps to the system time at the most recent callback,
and set the slope to 1% slower than real time (as if the sample clock is
slow). Now, at each callback, if the callback seems to occur earlier than
expected, we can adjust the mapping to be earlier. The earlier the
callback, the more accurate it must be. On the other hand, if the callback
is later than predicted, it must be a delayed callback (or else the
sample clock is more than 1% slow, which is really a hardware problem.)
How bad can this be? Assuming callbacks every 30ms (this seems to be what
I'm observing in a default setup), you'll be a maximum of 1ms off even if
2 out of 3 callbacks are late. This is pretty reasonable given that
PortMIDI clock precision is 1ms. If buffers are larger and callback timing
is more erratic, errors will be larger, but even a few ms error is
probably OK.
\par Estimating outputTime (Plan B, variable framesPerBuffer in callback, please skip to Plan C)
ALSA is complicated because we get varying values of
framesPerBuffer from callback to callback. Assume you get more frames
when the callback is later (because there is more accumulated input to
deliver and more more accumulated room in the output buffers). So take
the current time and subtract the duration of the frame count in the
current callback. This should be a time position that is relatively
jitter free (because we estimated the lateness by frame count and
subtracted that out). This time position intuitively represents the
current ADC time, or if no input, the time of the tail of the output
buffer. If we wanted DAC time, we'd have to add the total output
buffer duration, which should be reported by PortAudio. (If PortAudio
is wrong, we'll be systematically shifted in time by the error.)
Since there is still bound to be jitter, we can smooth these estimates.
First, we will assume a linear mapping from system time to audio time
with slope = 1, so really it's just the offset we need, which is going
to be a double that we can read/write atomically without locks or
anything fancy. (Maybe it should be "volatile".)
To improve the estimate, we get a new offset every callback, so we can
create a "smooth" offset by using a simple regression model (also
this could be seen as a first order filter). The following formula
updates smooth_offset with a new offset estimate in the callback:
smooth_offset = smooth_offset * 0.9 + new_offset_estimate * 0.1
Since this is smooth, we'll have to be careful to give it a good initial
value to avoid a long convergence.
\par Estimating outputTime (Plan C)
ALSA is complicated because we get varying values of
framesPerBuffer from callback to callback. It seems there is a lot
of variation in callback times and buffer space. One solution would
be to go to fixed size double buffer, but Audacity seems to work
better as is, so Plan C is to rely on one invariant which is that
the output buffer cannot overflow, so there's a limit to how far
ahead of the DAC time we can be writing samples into the
buffer. Therefore, we'll assume that the audio clock runs slow by
about 0.2% and we'll assume we're computing at that rate. If the
actual output position is ever ahead of the computed position, we'll
increase the computed position to the actual position. Thus whenever
the buffer is less than near full, we'll stay ahead of DAC time,
falling back at a rate of about 0.2% until eventually there's
another near-full buffer callback that will push the time back ahead.
\par Interaction between MIDI, Audio, and Pause
When Pause is used, PauseTime() will increase at the same rate as