Discontinuities in sample-exact automation in high tempo, resulting in crackles

[PhysSong]

(Originally reported by @LostRobotMusic on Discord)

Bug Summary

• Sample-exact automation doesn't work well if a tick is shorter than the buffer size. Some jump discontinuities are observed in the automation.
  Note this bug depends on your sample rate and buffer size settings. If you can't reproduce the bug, try higher tempo, larger buffer size and lower sample rate.

Steps to reproduce

• Set tempo to sufficiently high value(300 is enough for sample rate 44100Hz and buffer size 256)
• Add any instrument, and add amplifier effect in the track
• Connect the gain of the amplifier to an automation pattern with linear progression
• Render to a file

Here's an example project file:
bug.mmp.zip

Expected behavior

Smooth automation

Actual behavior

Discontinuity observed, resulting in audible crackles

Affected LMMS versions

Not sure

[PhysSong]

In AutomatableModel::valueBuffer, this part handles sample-exact automation:

lmms/src/core/AutomatableModel.cpp

Lines 670 to 672 in 679d632

	if( m_oldValue != val )
	{
	m_valueBuffer.interpolate( m_oldValue, val );

In Song::processNextBuffer, automation is handled at the beginning of every tick:

lmms/src/core/Song.cpp

Lines 338 to 341 in 679d632

	if (static_cast<f_cnt_t>(frameOffsetInTick) == 0)
	{
	// First frame of tick: process automation and play tracks
	processAutomations(trackList, getPlayPos(), framesToPlay);

If two or more beginning of ticks present in a rendering buffer, the interpolation logic doesn't work as expected.