+void
+
+TempoSection::update_bar_offset_from_bbt (const Meter& m)
+{
+ _bar_offset = ((start().beats - 1) * BBT_Time::ticks_per_beat + start().ticks) /
+ (m.divisions_per_bar() * BBT_Time::ticks_per_beat);
+
+ DEBUG_TRACE (DEBUG::TempoMath, string_compose ("Tempo set bar offset to %1 from %2 w/%3\n", _bar_offset, start(), m.divisions_per_bar()));
+}
+
+void
+TempoSection::set_type (TempoSectionType type)
+{
+ _type = type;
+}
+
+double
+TempoSection::tempo_at_frame (framepos_t frame, double end_bpm, framepos_t end_frame, framecnt_t frame_rate) const
+{
+
+ if (_type == Constant) {
+ return beats_per_minute();
+ }
+
+ return tick_tempo_at_time (frame_to_minute (frame, frame_rate), end_bpm * BBT_Time::ticks_per_beat, frame_to_minute (end_frame, frame_rate)) / BBT_Time::ticks_per_beat;
+}
+
+framepos_t
+TempoSection::frame_at_tempo (double tempo, double end_bpm, framepos_t end_frame, framecnt_t frame_rate) const
+{
+ if (_type == Constant) {
+ return 0;
+ }
+
+ return minute_to_frame (time_at_tick_tempo (tempo * BBT_Time::ticks_per_beat, end_bpm * BBT_Time::ticks_per_beat, frame_to_minute (end_frame, frame_rate)), frame_rate);
+}
+
+double
+TempoSection::tick_at_frame (framepos_t frame, double end_bpm, framepos_t end_frame, framecnt_t frame_rate) const
+{
+ if (_type == Constant) {
+ return frame / frames_per_beat (frame_rate);
+ }
+
+ return tick_at_time (frame_to_minute (frame, frame_rate), end_bpm * BBT_Time::ticks_per_beat, frame_to_minute (end_frame, frame_rate));
+}
+
+framepos_t
+TempoSection::frame_at_tick (double tick, double end_bpm, framepos_t end_frame, framecnt_t frame_rate) const
+{
+ if (_type == Constant) {
+ return (framepos_t) floor (tick * frames_per_beat(frame_rate));
+ }
+
+ return minute_to_frame (time_at_tick (tick, end_bpm * BBT_Time::ticks_per_beat, frame_to_minute (end_frame, frame_rate)), frame_rate);
+}
+
+double TempoSection::beat_at_frame (framepos_t frame, double end_bpm, framepos_t end_frame, framecnt_t frame_rate) const
+{
+ return tick_at_frame (frame, end_bpm, end_frame, frame_rate) / BBT_Time::ticks_per_beat;
+}
+
+framepos_t TempoSection::frame_at_beat (double beat, double end_bpm, framepos_t end_frame, framecnt_t frame_rate) const
+{
+ return frame_at_tick (beat * BBT_Time::ticks_per_beat, end_bpm, end_frame, frame_rate);
+}
+
+framecnt_t
+TempoSection::minute_to_frame (double time, framecnt_t frame_rate) const
+{
+ return time * 60.0 * frame_rate;
+}
+
+double
+TempoSection::frame_to_minute (framecnt_t frame, framecnt_t frame_rate) const
+{
+ return (frame / (double) frame_rate) / 60.0;
+}
+
+/* constant for exp */
+double
+TempoSection::a_func (double begin_tpm, double end_tpm, double end_time) const
+{
+ return log (end_tpm / ticks_per_minute()) / c_func (end_tpm, end_time);
+}
+double
+TempoSection::c_func (double end_tpm, double end_time) const
+{
+ return log (end_tpm / ticks_per_minute()) / end_time;
+}
+
+/* tempo in tpm at time in minutes */
+double
+TempoSection::tick_tempo_at_time (double time, double end_tpm, double end_time) const
+{
+ return exp (c_func (end_tpm, end_time) * time) * ticks_per_minute();
+}
+
+/* time in minutes at tempo in tpm */
+double
+TempoSection::time_at_tick_tempo (double tick_tempo, double end_tpm, double end_time) const
+{
+ return log (tick_tempo / ticks_per_minute()) / c_func (end_tpm, end_time);
+}
+
+/* tempo in bpm at time in minutes */
+double
+TempoSection::tempo_at_time (double time, double end_bpm, double end_time) const
+{
+ return tick_tempo_at_time (time, end_bpm * BBT_Time::ticks_per_beat, end_time) / BBT_Time::ticks_per_beat;
+}
+
+/* time in minutes at tempo in bpm */
+double
+TempoSection::time_at_tempo (double tempo, double end_bpm, double end_time) const
+{
+ return time_at_tick_tempo (tempo * BBT_Time::ticks_per_beat, end_bpm * BBT_Time::ticks_per_beat, end_time);
+}
+
+/* tick at time in minutes */
+double
+TempoSection::tick_at_time (double time, double end_tpm, double end_time) const
+{
+ return ((exp (c_func (end_tpm, end_time) * time)) - 1) * ticks_per_minute() / c_func (end_tpm, end_time);
+}
+
+/* time in minutes at tick */
+double
+TempoSection::time_at_tick (double tick, double end_tpm, double end_time) const
+{
+ return log (((c_func (end_tpm, end_time) * tick) / ticks_per_minute()) + 1) / c_func (end_tpm, end_time);
+}
+
+/* beat at time in minutes */
+double
+TempoSection::beat_at_time (double time, double end_tpm, double end_time) const
+{
+ return tick_at_time (time, end_tpm, end_time) / BBT_Time::ticks_per_beat;
+}
+
+/* time in munutes at beat */
+double
+TempoSection::time_at_beat (double beat, double end_tpm, double end_time) const
+{
+ return time_at_tick (beat * BBT_Time::ticks_per_beat, end_tpm, end_time);
+}
+
+void
+TempoSection::update_bbt_time_from_bar_offset (const Meter& meter)
+{
+ BBT_Time new_start;
+
+ if (_bar_offset < 0.0) {
+ /* not set yet */
+ return;
+ }
+
+ new_start.bars = start().bars;
+
+ double ticks = BBT_Time::ticks_per_beat * meter.divisions_per_bar() * _bar_offset;
+ new_start.beats = (uint32_t) floor (ticks/BBT_Time::ticks_per_beat);
+ new_start.ticks = 0; /* (uint32_t) fmod (ticks, BBT_Time::ticks_per_beat); */
+
+ /* remember the 1-based counting properties of beats */
+ new_start.beats += 1;
+ DEBUG_TRACE (DEBUG::TempoMath, string_compose ("from bar offset %1 and dpb %2, ticks = %3->%4 beats = %5\n",
+ _bar_offset, meter.divisions_per_bar(), ticks, new_start.ticks, new_start.beats));
+
+ set_start (new_start);
+}
+