Piano: New timing system and zoomable piano roll

This patch allows roll notes to be of different sizes. This necessitates
a new internal representation of time. BPM and time signatures are
mostly implemented but not exposed.

Roll notes are now sample-accurate and the grid is aligned to 60 BPM
4/4. The roll is divided by the time signature raised to some power of
2, giving the musical divisions of (in the case of 4/4) 16, 32, 64 etc.

Before, our timing was derived from the buffer size and we relied on
that to implement delay. Delay has been rewritten to be sample-granular.
It's now exposed as the proper "divisions of a beat".
Something to be wary of is that the last buffer in the loop is also used
for the start of the next loop. In other words, we loop mid-buffer. This
means we write WAVs with a tiny bit of silence due to breaking the loop
after filling half a buffer.

The data structure for the roll is an array of SinglyLinkedLists of
RollNotes. Separating by pitch (via the array layout) makes insertion
much simpler and faster. Using sorted lists (and thus
SinglyLinkedListIterators) to do lookups is very quick as you know the
sample of the next note and can just compare it to the current sample. I
implemented this with HashMaps and the cost of lookups was abysmal. I
also tried a single SinglyLinkedList and the insertion code got even
more complicated than it already is.

Applications/Piano/AudioEngine.h

@@ -30,9 +30,11 @@
 #include "Music.h"
 #include <AK/FixedArray.h>
 #include <AK/Noncopyable.h>
-#include <AK/Queue.h>
+#include <AK/SinglyLinkedList.h>
 #include <LibAudio/Buffer.h>
 
+typedef AK::SinglyLinkedListIterator<SinglyLinkedList<RollNote>, RollNote> RollIter;
+
 class AudioEngine {
     AK_MAKE_NONCOPYABLE(AudioEngine)
     AK_MAKE_NONMOVABLE(AudioEngine)
@@ -42,8 +44,7 @@ public:
 
     const FixedArray<Sample>& buffer() const { return *m_front_buffer_ptr; }
     const Vector<Audio::Sample>& recorded_sample() const { return m_recorded_sample; }
-    Switch roll_note(int y, int x) const { return m_roll_notes[y][x]; }
-    int current_column() const { return m_current_column; }
+    const SinglyLinkedList<RollNote>& roll_notes(int note) const { return m_roll_notes[note]; }
     int octave() const { return m_octave; }
     int octave_base() const { return (m_octave - octave_min) * 12; }
     int wave() const { return m_wave; }
@@ -53,14 +54,14 @@ public:
     int release() const { return m_release; }
     int delay() const { return m_delay; }
     int time() const { return m_time; }
-    int tick() const { return m_tick; }
 
     void fill_buffer(FixedArray<Sample>& buffer);
     void reset();
+    void set_should_loop(bool b) { m_should_loop = b; }
     String set_recorded_sample(const StringView& path);
     void set_note(int note, Switch);
     void set_note_current_octave(int note, Switch);
-    void set_roll_note(int y, int x, Switch);
+    void set_roll_note(int note, u32 on_sample, u32 off_sample);
     void set_octave(Direction);
     void set_wave(int wave);
     void set_wave(Direction);
@@ -78,9 +79,7 @@ private:
     Audio::Sample noise() const;
     Audio::Sample recorded_sample(size_t note);
 
-    void update_roll();
-    void set_notes_from_roll();
-
+    void sync_roll(int note);
     void set_sustain_impl(int sustain);
 
     FixedArray<Sample> m_front_buffer { sample_count };
@@ -88,7 +87,7 @@ private:
     FixedArray<Sample>* m_front_buffer_ptr { &m_front_buffer };
     FixedArray<Sample>* m_back_buffer_ptr { &m_back_buffer };
 
-    Queue<NonnullOwnPtr<FixedArray<Sample>>> m_delay_buffers;
+    Vector<Sample> m_delay_buffer;
 
     Vector<Audio::Sample> m_recorded_sample;
 
@@ -108,11 +107,13 @@ private:
     int m_release;
     double m_release_step[note_count];
     int m_delay { 0 };
+    size_t m_delay_samples { 0 };
+    size_t m_delay_index { 0 };
 
-    int m_time { 0 };
-    int m_tick { 8 };
+    u32 m_time { 0 };
 
-    Switch m_roll_notes[note_count][horizontal_notes] { { Off } };
-    int m_current_column { 0 };
-    int m_previous_column { horizontal_notes - 1 };
+    bool m_should_loop { true };
+
+    SinglyLinkedList<RollNote> m_roll_notes[note_count];
+    RollIter m_roll_iters[note_count];
 };