livetrax/libs/temporal/tempo.cc

/*
    Copyright (C) 2017 Paul Davis

    This program is free software; you can redistribute it and/or modify
    it under the terms of the GNU General Public License as published by
    the Free Software Foundation; either version 2 of the License, or
    (at your option) any later version.

    This program is distributed in the hope that it will be useful,
    but WITHOUT ANY WARRANTY; without even the implied warranty of
    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
    GNU General Public License for more details.

    You should have received a copy of the GNU General Public License
    along with this program; if not, write to the Free Software
    Foundation, Inc., 675 Mass Ave, Cambridge, MA 02139, USA.
*/

#include <algorithm>
#include <vector>

#include <inttypes.h>

#include "pbd/compose.h"
#include "pbd/convert.h"
#include "pbd/enumwriter.h"
#include "pbd/error.h"
#include "pbd/failed_constructor.h"
#include "pbd/stacktrace.h"
#include "pbd/string_convert.h"

#include "temporal/debug.h"
#include "temporal/tempo.h"
#include "temporal/types_convert.h"

#include "pbd/i18n.h"

using namespace PBD;
using namespace Temporal;
using std::cerr;
using std::cout;
using std::endl;
using Temporal::superclock_t;

std::string Tempo::xml_node_name = X_("Tempo");
std::string Meter::xml_node_name = X_("Meter");

SerializedRCUManager<TempoMap> TempoMap::_map_mgr (0);
thread_local TempoMap::WritableSharedPtr TempoMap::_tempo_map_p;
PBD::Signal0<void> TempoMap::MapChanged;

void
Point::add_state (XMLNode & node) const
{
	node.set_property (X_("sclock"), _sclock);
	node.set_property (X_("quarters"), _quarters);
	node.set_property (X_("bbt"), _bbt);
}

Point::Point (TempoMap const & map, XMLNode const & node)
	: MapOwned (map)
{
	if (!node.get_property (X_("sclock"), _sclock)) {
		throw failed_constructor();
	}
	if (!node.get_property (X_("quarters"), _quarters)) {
		throw failed_constructor();
	}
	if (!node.get_property (X_("bbt"), _bbt)) {
		throw failed_constructor();
	}
}

#if 0
samplepos_t
Point::sample() const
{
	return superclock_to_samples (_sclock, _map->sample_rate());
}
#endif

Tempo::Tempo (XMLNode const & node)
{
	assert (node.name() == xml_node_name);


	node.get_property (X_("npm"), _npm);
	node.get_property (X_("enpm"), _enpm);

	_superclocks_per_note_type = double_npm_to_scpn (_npm);
	_end_superclocks_per_note_type = double_npm_to_scpn (_enpm);

	_super_note_type_per_second = double_npm_to_snps (_npm);
	_end_super_note_type_per_second = double_npm_to_snps (_enpm);

	if (!node.get_property (X_("note-type"), _note_type)) {
		throw failed_constructor ();
	}

	if (!node.get_property (X_("active"), _active)) {
		throw failed_constructor ();
	}
	if (!node.get_property (X_("locked-to-meter"), _locked_to_meter)) {
		_locked_to_meter = true;
	}

	/* older versions used "clamped" as the property name here */

	if (!node.get_property (X_("continuing"), _continuing) && !node.get_property (X_("clamped"), _continuing)) {
		_continuing = false;
	}
}

void
Tempo::set_note_types_per_minute (double npm)
{
	_npm = npm;
	_superclocks_per_note_type = double_npm_to_scpn (_npm);
	_super_note_type_per_second = double_npm_to_snps (_npm);
}

void
Tempo::set_end_npm (double npm)
{
	_enpm = npm;
	_end_super_note_type_per_second = double_npm_to_snps (_enpm);
	_end_superclocks_per_note_type = double_npm_to_scpn (_enpm);
}

void
Tempo::set_continuing (bool yn)
{
	_continuing = yn;
}

XMLNode&
Tempo::get_state () const
{
	XMLNode* node = new XMLNode (xml_node_name);

	node->set_property (X_("npm"), note_types_per_minute());
	node->set_property (X_("enpm"), end_note_types_per_minute());
	node->set_property (X_("note-type"), note_type());
	node->set_property (X_("type"), type());
	node->set_property (X_("active"), active());
	node->set_property (X_("locked-to-meter"), _locked_to_meter);
	node->set_property (X_("continuing"), _continuing);

	return *node;
}

int
Tempo::set_state (XMLNode const & node, int /*version*/)
{
	if (node.name() != xml_node_name) {
		return -1;
	}

	node.get_property (X_("npm"), _npm);
	node.get_property (X_("enpm"), _enpm);

	_superclocks_per_note_type = double_npm_to_scpn (_npm);
	_end_superclocks_per_note_type = double_npm_to_scpn (_enpm);
	_super_note_type_per_second = double_npm_to_snps (_npm);
	_end_super_note_type_per_second = double_npm_to_snps (_enpm);

	node.get_property (X_("note-type"), _note_type);
	node.get_property (X_("active"), _active);

	if (!node.get_property (X_("locked-to-meter"), _locked_to_meter)) {
		_locked_to_meter = true;
	}

	/* older versions used "clamped" as the property name here */

	if (!node.get_property (X_("continuing"), _continuing) && !node.get_property (X_("continuing"), _continuing)) {
		_continuing = false;
	}

	return 0;
}

Meter::Meter (XMLNode const & node)
{
	assert (node.name() == xml_node_name);
	if (!node.get_property (X_("note-value"), _note_value)) {
		throw failed_constructor ();
	}
	if (!node.get_property (X_("divisions-per-bar"), _divisions_per_bar)) {
		throw failed_constructor ();
	}
}

XMLNode&
Meter::get_state () const
{
	XMLNode* node = new XMLNode (xml_node_name);
	node->set_property (X_("note-value"), note_value());
	node->set_property (X_("divisions-per-bar"), divisions_per_bar());
	return *node;
}

int
Meter::set_state (XMLNode const & node, int /* version */)
{
	if (node.name() != xml_node_name) {
		return -1;
	}

	node.get_property (X_("note-value"), _note_value);
	node.get_property (X_("divisions-per-bar"), _divisions_per_bar);

	return 0;
}

Temporal::BBT_Time
Meter::bbt_add (Temporal::BBT_Time const & bbt, Temporal::BBT_Offset const & add) const
{
	int32_t bars = bbt.bars;
	int32_t beats = bbt.beats;
	int32_t ticks = bbt.ticks;

	if ((bars ^ add.bars) < 0) {
		/* signed-ness varies */
		if (abs(add.bars) >= abs(bars)) {
			/* addition will change which side of "zero" the answer is on;
			   adjust bbt.bars towards zero to deal with "unusual" BBT math
			*/
			if (bars < 0) {
				bars++;
			} else {
				bars--;
			}
		}
	}

	if ((beats ^ add.beats) < 0) {
		/* signed-ness varies */
		if (abs (add.beats) >= abs (beats)) {
			/* adjust bbt.beats towards zero to deal with "unusual" BBT math */
			if (beats < 0) {
				beats++;
			} else {
				beats--;
			}
		}
	}

	Temporal::BBT_Offset r (bars + add.bars, beats + add.beats, ticks + add.ticks);

	/* ticks-per-bar-division; PPQN is ticks-per-quarter note */

	const int32_t tpg = ticks_per_grid ();

	if (r.ticks >= tpg) {

		/* ticks per bar */
		const int32_t tpb = tpg * _divisions_per_bar;

		if (r.ticks >= tpb) {
			r.bars += r.ticks / tpb;
			r.ticks %= tpb;
		}

		if (r.ticks >= tpg) {
			r.beats += r.ticks / tpg;
			r.ticks %= tpg;
		}
	}

	if (r.beats > _divisions_per_bar) {

		/* adjust to zero-based math, since that's what C++ operators expect */

		r.beats -= 1;
		r.bars += r.beats / _divisions_per_bar;
		r.beats %= _divisions_per_bar;

		/* adjust back */

		r.beats += 1;
	}

	if (r.bars == 0) {
		r.bars = 1;
	}

	return Temporal::BBT_Time (r.bars, r.beats, r.ticks);
}

Temporal::BBT_Time
Meter::bbt_subtract (Temporal::BBT_Time const & bbt, Temporal::BBT_Offset const & sub) const
{
	int32_t bars = bbt.bars;
	int32_t beats = bbt.beats;
	int32_t ticks = bbt.ticks;

	if ((bars ^ sub.bars) < 0) {
		/* signed-ness varies */
		if (abs (sub.bars) >= abs (bars)) {
			/* adjust bbt.bars towards zero to deal with "unusual" BBT math */
			if (bars < 0) {
				bars++;
			} else {
				bars--;
			}
		}
	}

	if ((beats ^ sub.beats) < 0) {
		/* signed-ness varies */
		if (abs (sub.beats) >= abs (beats)) {
			/* adjust bbt.beats towards zero to deal with "unusual" BBT math */
			if (beats < 0) {
				beats++;
			} else {
				beats--;
			}
		}
	}

	Temporal::BBT_Offset r (bars - sub.bars, beats - sub.beats, ticks - sub.ticks);

	/* ticks-per-bar-division; PPQN is ticks-per-quarter note */

	const int32_t tpg = ticks_per_grid ();

	if (r.ticks < 0) {
		r.beats += floor ((double) r.ticks / tpg);
		r.ticks = tpg + (r.ticks % Temporal::Beats::PPQN);
	}

	if (r.beats <= 0) {
		r.bars += floor ((r.beats - 1.0) / _divisions_per_bar);
		r.beats = _divisions_per_bar + (r.beats % _divisions_per_bar);
	}

	if (r.bars <= 0) {
		r.bars -= 1;
	}

	return Temporal::BBT_Time (r.bars, r.beats, r.ticks);
}

Temporal::BBT_Time
Meter::round_to_bar (Temporal::BBT_Time const & bbt) const
{
	Beats b (bbt.beats, bbt.ticks);
	Beats half (Beats::ticks (Beats::PPQN + ((_divisions_per_bar * Beats::PPQN / 2))));

	if (b >= half) {
		return BBT_Time (bbt.bars+1, 1, 0);
	}

	return BBT_Time (bbt.bars, 1, 0);
}

Temporal::BBT_Time
Meter::round_up_to_beat (Temporal::BBT_Time const & bbt) const
{
	Temporal::BBT_Time b = bbt.round_up_to_beat ();
	if (b.beats > _divisions_per_bar) {
		b.bars++;
		b.beats = 1;
	}
	return b;
}

Temporal::BBT_Time
Meter::round_to_beat (Temporal::BBT_Time const & bbt) const
{
	Temporal::BBT_Time b = bbt.round_to_beat ();
	if (b.beats > _divisions_per_bar) {
		b.bars++;
		b.beats = 1;
	}
	return b;
}

Temporal::Beats
Meter::to_quarters (Temporal::BBT_Offset const & offset) const
{
	int64_t ticks = 0;

	ticks += (Beats::PPQN * offset.bars * _divisions_per_bar * 4) / _note_value;
	ticks += (Beats::PPQN * offset.beats * 4) / _note_value;

	/* "parts per bar division" */

	const int tpg = ticks_per_grid ();

	if (offset.ticks > tpg) {
		ticks += Beats::PPQN * offset.ticks / tpg;
		ticks += offset.ticks % tpg;
	} else {
		ticks += offset.ticks;
	}

	return Beats (ticks/Beats::PPQN, ticks%Beats::PPQN);
}

int
TempoPoint::set_state (XMLNode const & node, int version)
{
	int ret;

	if ((ret = Tempo::set_state (node, version)) == 0) {
		if (node.get_property (X_("omega"), _omega)) {
			/* XXX ?? */
		}
	}

	return ret;
}

XMLNode&
TempoPoint::get_state () const
{
	XMLNode& base (Tempo::get_state());
	Point::add_state (base);
	base.set_property (X_("omega"), _omega);
	return base;
}

TempoPoint::TempoPoint (TempoMap const & map, XMLNode const & node)
	: Point (map, node)
	, Tempo (node)
	, _omega (0)
{
	node.get_property (X_("omega"), _omega);
}

/* To understand the math(s) behind ramping, see the file doc/tempo.{pdf,tex}
 */

void
TempoPoint::compute_omega_from_next_tempo (TempoPoint const & next)
{
	compute_omega_from_distance_and_next_tempo (next.beats() - beats(), next);
}

void
TempoPoint::compute_omega_from_distance_and_next_tempo (Beats const & quarter_duration, TempoPoint const & next)
{
	superclock_t end_scpqn;

	if (!_continuing) {
		/* tempo is defined by our own start and end */
		end_scpqn = end_superclocks_per_quarter_note();
	} else {
		/* tempo is defined by our own start the start of the next tempo */
		end_scpqn = next.superclocks_per_quarter_note ();
	}

	if (superclocks_per_quarter_note () == end_scpqn) {
		_omega = 0.0;
		return;
	}

	compute_omega_from_quarter_duration (quarter_duration, end_scpqn);
}

void
TempoPoint::compute_omega_from_quarter_duration (Beats const & quarter_duration, superclock_t end_scpqn)
{
	_omega = ((1.0/end_scpqn) - (1.0/superclocks_per_quarter_note())) / DoubleableBeats (quarter_duration).to_double();
	DEBUG_TRACE (DEBUG::TemporalMap, string_compose ("quarter-computed omega from qtr duration = %1 dur was %2 start speed %3 end speed [%4]\n", _omega, quarter_duration.str(), superclocks_per_quarter_note(), end_scpqn));
}

void
TempoPoint::compute_omega_from_audio_duration (samplecnt_t audio_duration, superclock_t end_scpqn)
{
	_omega = (1.0 / (samples_to_superclock (audio_duration, TEMPORAL_SAMPLE_RATE))) * log ((double) superclocks_per_note_type() / end_scpqn);
	DEBUG_TRACE (DEBUG::TemporalMap, string_compose ("computed omega from audio duration= %1%2 dur was %3\n", std::setprecision(12), _omega, audio_duration));
}

superclock_t
TempoPoint::superclock_at (Temporal::Beats const & qn) const
{
	if (qn == _quarters) {
		return _sclock;
	}

	if (qn < Beats()) {
		/* negative */
		assert (_quarters == Beats());
	} else {
		/* positive */
		assert (qn >= _quarters);
	}

	if (!actually_ramped()) {
		/* not ramped, use linear */
		const Beats delta = qn - _quarters;
		const superclock_t spqn = superclocks_per_quarter_note ();
		return _sclock + (spqn * delta.get_beats()) + int_div_round ((spqn * delta.get_ticks()), superclock_t (Temporal::ticks_per_beat));
	}

	superclock_t r;
	const double log_expr = superclocks_per_quarter_note() * _omega * DoubleableBeats (qn - _quarters).to_double();

	if (log_expr < -1) {
		r = _sclock + llrint (log (-log_expr - 1.0) / -_omega);

		if (r < 0) {
			std::cerr << "CASE 1: " << *this << endl << " scpqn = " << superclocks_per_quarter_note() << std::endl;
			std::cerr << " for " << qn << " @ " << _quarters << " | " << _sclock << " + log (" << log_expr << ") "
			          << log (-log_expr - 1.0)
			          << " - omega = " << -_omega
			          << " => "
			          << r << std::endl;
			abort ();
		}

	} else {
		r = _sclock + llrint (log1p (log_expr) / _omega);

		if (r < 0) {
			std::cerr << "CASE 2: scpqn = " << superclocks_per_quarter_note() << std::endl;
			std::cerr << " for " << qn << " @ " << _quarters << " | " << _sclock << " + log1p (" << superclocks_per_quarter_note() * _omega * DoubleableBeats (qn - _quarters).to_double() << " = "
			          << log1p (superclocks_per_quarter_note() * _omega * DoubleableBeats (qn - _quarters).to_double())
			          << " => "
			          << r << std::endl;
			abort ();
		}
	}

	return r;
}

superclock_t
TempoPoint::superclocks_per_note_type_at (timepos_t const &pos) const
{
	if (!actually_ramped()) {
		return _superclocks_per_note_type;
	}

	return _superclocks_per_note_type * exp (-_omega * (pos.superclocks() - sclock()));
}

Temporal::Beats
TempoPoint::quarters_at_superclock (superclock_t sc) const
{
	/* catch a special case. The maximum superclock_t value cannot be
	   converted into a 32bit beat + 32 bit tick value for common tempos.
	   Obviously, values less than this can also cause overflow, but are
	   unlikely to be encountered.

	   A longer term/big picture solution for this is likely required in
	   order to deal with longer sessions. Still, even at 300bpm, a 32 bit
	   integer should cover 165 days. The problem is that a 62 bit (int62_t)
	   superclock counter can cover 105064 days, so the theoretical
	   potential for errors here is real.
	*/

	if (sc >= int62_t::max) {
		return std::numeric_limits<Beats>::max();
	}

	if (!actually_ramped()) {

		// assert (sc >= _sclock);
		superclock_t sc_delta = sc - _sclock;

		/* convert sc into superbeats, given that sc represents some number of seconds */
		const superclock_t whole_seconds = sc_delta / superclock_ticks_per_second();
		const superclock_t remainder = sc_delta - (whole_seconds * superclock_ticks_per_second());

		const int64_t supernotes = ((_super_note_type_per_second) * whole_seconds) + int_div_round (superclock_t ((_super_note_type_per_second) * remainder), superclock_ticks_per_second());
		/* multiply after divide to reduce overflow risk */
		const int64_t superbeats = int_div_round (supernotes, (superclock_t) _note_type) * 4;

		/* convert superbeats to beats:ticks */
		int32_t b;
		int32_t t;

		Tempo::superbeats_to_beats_ticks (superbeats, b, t);

		DEBUG_TRACE (DEBUG::TemporalMap, string_compose ("%8 => \nsc %1 delta %9 = %2 secs rem = %3 rem snotes %4 sbeats = %5 => %6 : %7\n", sc, whole_seconds, remainder, supernotes, superbeats, b , t, *this, sc_delta));

		const Beats ret = _quarters + Beats (b, t);

		/* positive superclock can never generate negative beats unless
		 * it is too large. If that happens, handle it the same way as
		 * the opening special case in this method.
		 */

		if (sc >= 0 && ret < Beats()) {
			return std::numeric_limits<Beats>::max();
		}

		return ret;
	}

	const double b = (exp (_omega * (sc - _sclock)) - 1) / (superclocks_per_quarter_note() * _omega);
	return _quarters + Beats::from_double (b);
}

MeterPoint::MeterPoint (TempoMap const & map, XMLNode const & node)
	: Point (map, node)
	, Meter (node)
{
}

/* Given a time in BBT_Time, compute the equivalent Beat Time.
 *
 * Computation assumes that the Meter is in effect at the time specified as
 * BBT_Time (i.e. there is no other MeterPoint between this one and the specified
 * time.
 */
Temporal::Beats
MeterPoint::quarters_at (Temporal::BBT_Time const & bbt) const
{
	Temporal::BBT_Offset offset = bbt_delta (bbt, _bbt);
	return _quarters + to_quarters (offset);
}

/* Given a time in Beats, compute the equivalent BBT Time.
 *
 * Computation assumes that the Meter is in effect at the time specified in
 * Beats (i.e. there is no other MeterPoint between this one and the specified
 * time.
 */

Temporal::BBT_Time
MeterPoint::bbt_at (Temporal::Beats const & qn) const
{
	return bbt_add (_bbt, Temporal::BBT_Offset (0, 0,  (qn - _quarters).to_ticks()));
}

XMLNode&
MeterPoint::get_state () const
{
	XMLNode& base (Meter::get_state());
	Point::add_state (base);
	return base;
}

Temporal::BBT_Time
TempoMetric::bbt_at (timepos_t const & pos) const
{
	if (pos.is_beats()) {
		return bbt_at (pos.beats());
	}

	superclock_t sc = pos.superclocks();

	/* Use the later of the tempo or meter as the reference point to
	 * compute the BBT distance. All map points are fully defined by all 3
	 * time types, but we need the latest one to avoid incorrect
	 * computations of quarter duration.
	 */

	const Point* reference_point;

	if (_tempo->beats() < _meter->beats()) {
		reference_point = _meter;
	} else {
		reference_point = _tempo;
	}

	const Beats dq = _tempo->quarters_at_superclock (sc) - reference_point->beats();

	DEBUG_TRACE (DEBUG::TemporalMap, string_compose ("qn @ %1 = %2, meter @ %3 , delta %4\n", sc, _tempo->quarters_at_superclock (sc), _meter->beats(), dq));

	/* dq is delta in quarters (beats). Convert to delta in note types of
	   the current meter, which we'll call "grid"
	*/

	const int64_t note_value_count = int_div_round (dq.get_beats() * _meter->note_value(), int64_t (4));

	/* now construct a BBT_Offset using the count in grid units */

	const BBT_Offset bbt_offset (0, note_value_count, dq.get_ticks());

	DEBUG_TRACE (DEBUG::TemporalMap, string_compose ("BBT offset from %3 @ %1: %2\n", (_tempo->beats() < _meter->beats() ?  _meter->bbt() : _tempo->bbt()), bbt_offset,
	                                                 (_tempo->beats() < _meter->beats() ? "meter" : "tempo")));
	return _meter->bbt_add (reference_point->bbt(), bbt_offset);
}

superclock_t
TempoMetric::superclock_at (BBT_Time const & bbt) const
{
	DEBUG_TRACE (DEBUG::TemporalMap, string_compose ("get quarters for %1 = %2 using %3\n", bbt, _meter->quarters_at (bbt), *this));
	return _tempo->superclock_at (_meter->quarters_at (bbt));
}

MusicTimePoint::MusicTimePoint (TempoMap const & map, XMLNode const & node)
	: Point (map, node)
	, TempoPoint (map, *node.child (Tempo::xml_node_name.c_str()))
	, MeterPoint (map, *node.child (Meter::xml_node_name.c_str()))
{
	node.get_property (X_("name"), _name); /* may fail, leaves name empty */
}

XMLNode&
MusicTimePoint::get_state () const
{
	XMLNode* node = new XMLNode (X_("MusicTime"));

	Point::add_state (*node);

	node->add_child_nocopy (Tempo::get_state());
	node->add_child_nocopy (Meter::get_state());

	node->set_property (X_("name"), _name); /* failure is OK */

	return *node;
}

void
MusicTimePoint::set_name (std::string const & str)
{
	_name = str;
	/* XXX need a signal or something to announce change */
}


void
TempoMapPoint::start_float ()
{
	_floating = true;
}

void
TempoMapPoint::end_float ()
{
	_floating = false;
}

/* TEMPOMAP */

TempoMap::TempoMap (Tempo const & initial_tempo, Meter const & initial_meter)
{
	TempoPoint* tp = new TempoPoint (*this, initial_tempo, 0, Beats(), BBT_Time());
	MeterPoint* mp = new MeterPoint (*this, initial_meter, 0, Beats(), BBT_Time());

	_tempos.push_back   (*tp);
	_meters.push_back   (*mp);

	_points.push_back (*tp);
	_points.push_back (*mp);
}

TempoMap::~TempoMap()
{
}

TempoMap::TempoMap (XMLNode const & node, int version)
{
	set_state (node, version);
}

TempoMap::TempoMap (TempoMap const & other)
{
	copy_points (other);
}

TempoMap&
TempoMap::operator= (TempoMap const & other)
{
	copy_points (other);
	return *this;
}

void
TempoMap::copy_points (TempoMap const & other)
{
	std::vector<Point*> p;

	p.reserve (other._meters.size() + other._tempos.size() + other._bartimes.size());

	for (Meters::const_iterator m = other._meters.begin(); m != other._meters.end(); ++m) {
		if (dynamic_cast<MusicTimePoint const *> (&*m)) {
			continue;
		}
		MeterPoint* mp = new MeterPoint (*m);
		_meters.push_back (*mp);
		p.push_back (mp);
	}

	for (Tempos::const_iterator t = other._tempos.begin(); t != other._tempos.end(); ++t) {
		if (dynamic_cast<MusicTimePoint const *> (&*t)) {
			continue;
		}
		TempoPoint* tp = new TempoPoint (*t);
		_tempos.push_back (*tp);
		p.push_back (tp);
	}

	for (MusicTimes::const_iterator mt = other._bartimes.begin(); mt != other._bartimes.end(); ++mt) {
		MusicTimePoint* mtp = new MusicTimePoint (*mt);
		_bartimes.push_back (*mtp);
		_tempos.push_back (*mtp);
		_meters.push_back (*mtp);
		p.push_back (mtp);
	}

	sort (p.begin(), p.end(), Point::ptr_sclock_comparator());

	for (auto & pi : p) {
		pi->set_map (*this);
		_points.push_back (*pi);
	}
}

MeterPoint*
TempoMap::add_meter (MeterPoint* mp)
{
	bool replaced;
	MeterPoint* ret = core_add_meter (mp, replaced);

	if (!replaced) {
		core_add_point (mp);
	} else {
		delete mp;
	}

	reset_starting_at (ret->sclock());
	return ret;
}

void
TempoMap::change_tempo (TempoPoint & p, Tempo const & t)
{
	*((Tempo*)&p) = t;
	reset_starting_at (p.sclock());
}

TempoPoint &
TempoMap::set_tempo (Tempo const & t, BBT_Time const & bbt)
{
	return set_tempo (t, timepos_t (quarters_at (bbt)));
}

TempoPoint &
TempoMap::set_tempo (Tempo const & t, timepos_t const & time)
{
	TempoPoint * ret;

	DEBUG_TRACE (DEBUG::TemporalMap, string_compose ("Set tempo @ %1 to %2\n", time, t));

	if (time.is_beats()) {


		/* tempo changes are required to be on-beat */

		Beats on_beat = time.beats().round_to_beat();
		superclock_t sc;
		BBT_Time bbt;

		TempoMetric metric (metric_at (on_beat, false));

		bbt = metric.bbt_at (on_beat);
		sc = metric.superclock_at (on_beat);

		TempoPoint* tp = new TempoPoint (*this, t, sc, on_beat, bbt);
		ret = add_tempo (tp);

	} else {

		Beats beats;
		BBT_Time bbt;
		superclock_t sc = time.superclocks();

		TempoMetric tm (metric_at (sc, false));

		/* tempo changes must be on beat */

		beats = tm.quarters_at_superclock (sc).round_to_beat ();
		bbt = tm.bbt_at (beats);

		/* recompute superclock position of rounded beat */
		sc = tm.superclock_at (beats);

		TempoPoint* tp = new TempoPoint (*this, t, sc, beats, bbt);
		ret = add_tempo (tp);

	}

#ifndef NDEBUG
	if (DEBUG_ENABLED (DEBUG::TemporalMap)) {
		dump (cerr);
	}
#endif

	return *ret;
}

void
TempoMap::core_add_point (Point* pp)
{
	Points::iterator p;
	const Beats beats_limit = pp->beats();

	for (p = _points.begin(); p != _points.end() && p->beats() < beats_limit; ++p);
	_points.insert (p, *pp);
}

TempoPoint*
TempoMap::core_add_tempo (TempoPoint* tp, bool& replaced)
{
	Tempos::iterator t;
	const superclock_t sclock_limit = tp->sclock();
	const Beats beats_limit = tp->beats ();

	for (t = _tempos.begin(); t != _tempos.end() && t->beats() < beats_limit; ++t);

	if (t != _tempos.end()) {
		if (t->sclock() == sclock_limit) {
			/* overwrite Tempo part of this point */
			*((Tempo*)&(*t)) = *tp;
			/* caller must delete tp when replaced is true */
			DEBUG_TRACE (DEBUG::TemporalMap, string_compose ("overwrote old tempo with %1\n", *tp));
			replaced = true;
			return &(*t);
		}
	}

	DEBUG_TRACE (DEBUG::TemporalMap, string_compose ("inserted tempo %1\n", *tp));

	replaced = false;
	return &(* _tempos.insert (t, *tp));
}

MeterPoint*
TempoMap::core_add_meter (MeterPoint* mp, bool& replaced)
{
	Meters::iterator m;
	const superclock_t sclock_limit = mp->sclock();
	const Beats beats_limit = mp->beats ();

	for (m = _meters.begin(); m != _meters.end() && m->beats() < beats_limit; ++m);

	if (m != _meters.end()) {
		if (m->sclock() == sclock_limit) {
			/* overwrite Meter part of this point */
			*((Meter*)&(*m)) = *mp;
			/* caller must delete mp when replaced is true */
			replaced = true;
			return &(*m);
		}
	}

	replaced = false;
	return &(*(_meters.insert (m, *mp)));
}

MusicTimePoint*
TempoMap::core_add_bartime (MusicTimePoint* mtp, bool& replaced)
{
	MusicTimes::iterator m;
	const superclock_t sclock_limit = mtp->sclock();

	for (m = _bartimes.begin(); m != _bartimes.end() && m->sclock() < sclock_limit; ++m);

	if (m != _bartimes.end()) {
		if (m->sclock() == sclock_limit) {
			/* overwrite Tempo part of this point */
			*m = *mtp;
			/* caller must delete mtp when replaced is true */
			DEBUG_TRACE (DEBUG::TemporalMap, string_compose ("overwrote old bartime with %1\n", mtp));
			replaced = true;
			return &(*m);
		}
	}

	DEBUG_TRACE (DEBUG::TemporalMap, string_compose ("inserted bartime %1\n", mtp));

	replaced = false;
	return &(* _bartimes.insert (m, *mtp));
}

TempoPoint*
TempoMap::add_tempo (TempoPoint * tp)
{
	bool replaced;
	TempoPoint* ret = core_add_tempo (tp, replaced);

	if (!replaced) {
		core_add_point (tp);
	} else {
		delete tp;
	}

	reset_starting_at (ret->sclock());
	return ret;
}

void
TempoMap::remove_tempo (TempoPoint const & tp)
{
	superclock_t sc (tp.sclock());
	Tempos::iterator t;

	assert (_tempos.size() > 1);

	/* the argument is likely to be a Point-derived object that doesn't
	 * actually exist in this TempoMap, since the caller called
	 * TempoMap::write_copy() in order to perform an RCU operation, but
	 * will be removing an element known from the original map.
	 *
	 * However, since we do not allow points of the same type (Tempo,
	 * Meter, BarTime) at the same time, we can effectively search here
	 * using what is effectively a duple of (type,time) for the
	 * comparison.
	 *
	 * Once/if found, we will have a pointer to the actual Point-derived
	 * object in this TempoMap, and we can then remove that from the
	 * _points list.
	 */

	for (t = _tempos.begin(); t != _tempos.end() && t->sclock() < tp.sclock(); ++t);

	if (t == _tempos.end()) {
		/* not found */
		return;
	}

	if (t->sclock() != tp.sclock()) {
		/* error ... no tempo point at the time of tp */
		return;
	}

	Tempos::iterator nxt = _tempos.begin();
	Tempos::iterator prev = _tempos.end();

	if (t != _tempos.end()) {
		nxt = t;
		++nxt;
	}

	if (t != _tempos.begin()) {
		prev = t;
		--prev;
	}

	const bool was_end = (nxt == _tempos.end());

	_tempos.erase (t);
	remove_point (*t);

	if (prev != _tempos.end() && was_end) {
		prev->set_end_npm (prev->note_types_per_minute()); /* remove any ramp */
	} else {
		reset_starting_at (sc);
	}
}

void
TempoMap::set_bartime (BBT_Time const & bbt, timepos_t const & pos, std::string name)
{
	assert (pos.time_domain() == AudioTime);

	superclock_t sc (pos.superclocks());
	TempoMetric metric (metric_at (sc));
	MusicTimePoint* tp = new MusicTimePoint (*this, sc, metric.quarters_at_superclock (sc), bbt, metric.tempo(), metric.meter(), name);

	add_or_replace_bartime (tp);
}

MusicTimePoint*
TempoMap::add_or_replace_bartime (MusicTimePoint* mtp)
{
	bool replaced;
	MusicTimePoint* ret = core_add_bartime (mtp, replaced);

	if (!replaced) {
		bool ignore;
		(void) core_add_tempo (mtp, ignore);
		(void) core_add_meter (mtp, ignore);
		core_add_point (mtp);
	} else {
		delete mtp;
	}

	reset_starting_at (ret->sclock());

	return ret;
}

void
TempoMap::remove_bartime (MusicTimePoint const & tp)
{
	superclock_t sc (tp.sclock());
	MusicTimes::iterator m;

	/* the argument is likely to be a Point-derived object that doesn't
	 * actually exist in this TempoMap, since the caller called
	 * TempoMap::write_copy() in order to perform an RCU operation, but
	 * will be removing an element known from the original map.
	 *
	 * However, since we do not allow points of the same type (Tempo,
	 * Meter, BarTime) at the same time, we can effectively search here
	 * using what is effectively a duple of (type,time) for the
	 * comparison.
	 *
	 * Once/if found, we will have a pointer to the actual Point-derived
	 * object in this TempoMap, and we can then remove that from the
	 * _points list.
	 */

	for (m = _bartimes.begin(); m != _bartimes.end() && m->sclock() < tp.sclock(); ++m);

	if (m->sclock() != tp.sclock()) {
		/* error ... no music time point at the time of tp */
		return;
	}

	_bartimes.erase (m);
	remove_point (*m);
	reset_starting_at (sc);
}

void
TempoMap::remove_point (Point const & point)
{
	Points::iterator p;
	Point const * tpp (&point);

	/* note that the point passed here must be an element of the _points
	 * list, which is not true for the point passed to the callees
	 * (remove_tempo(), remove_meter(), remove_bartime().
	 *
	 * in those methods, we effectively search for a match on a duple of
	 * (type, time), but here we are comparing pointer addresses.
	 */

	for (p = _points.begin(); p != _points.end(); ++p) {
		if (&(*p) == tpp) {
			// XXX need to fix this leak delete tpp;
			_points.erase (p);
			break;
		}
	}
}

void
TempoMap::reset_starting_at (superclock_t sc)
{
	DEBUG_TRACE (DEBUG::MapReset, string_compose ("reset starting at %1\n", sc));
#ifndef NDEBUG
	if (DEBUG_ENABLED(DEBUG::MapReset)) {
		dump (std::cerr);
	}
#endif

	assert (!_tempos.empty());
	assert (!_meters.empty());


	TempoPoint*     tp;
	TempoPoint*     nxt_tempo = 0;
	MeterPoint*     mp;
	MusicTimePoint* mtp;
	TempoMetric metric (_tempos.front(), _meters.front());
	Points::iterator p;
	bool need_initial_ramp_reset = false;

	DEBUG_TRACE (DEBUG::MapReset, string_compose ("we begin at %1 with metric %2\n", sc, metric));

	/* We will reset the superclock (audio) and beat time based on the BBT
	 * time of each point. To make sure this works correctly, sort them by
	 * BBT time first. If we do not do this, then we will use points as
	 * TempoMetrics in a (potentially) incorrect order.
	 */

	Point::bbt_comparator cmp;
	_points.sort (cmp);

#ifndef NDEBUG
	if (DEBUG_ENABLED(DEBUG::MapReset)) {
		std::cerr << "\nPOST SORT:\n";
		dump (std::cerr);
	}
#endif
	/* Setup the metric that is in effect at the starting point */

	for (p = _points.begin(); p != _points.end(); ++p) {

		DEBUG_TRACE (DEBUG::MapReset, string_compose ("Now looking at %1 => %2 \n", &(*p), *p));

		if (p->sclock() > sc) {
			break;
		}

		mtp = 0;
		tp = 0;
		mp = 0;

		if ((mtp = dynamic_cast<MusicTimePoint*> (&*p)) != 0) {

			/* nothing to do here. We do not reset music time (bar
			 * time) points since everything about their position is set
			 * by the user. The only time we would change them is
			 * if we alter the time domain of the tempo map.
			 */

			metric = TempoMetric (*mtp, *mtp);
			DEBUG_TRACE (DEBUG::MapReset, string_compose ("Bartime!, used tempo @ %1\n", (TempoPoint*) mtp));
			need_initial_ramp_reset = false;
		} else if ((tp = dynamic_cast<TempoPoint*> (&*p)) != 0) {
			metric = TempoMetric (*tp, metric.meter());
			if (tp->ramped()) {
				need_initial_ramp_reset = true;
			} else {
				need_initial_ramp_reset = true;
			}
			DEBUG_TRACE (DEBUG::MapReset, string_compose ("Tempo! @ %1, metric's tempo is %2\n", tp, &metric.tempo()));
		} else if ((mp = dynamic_cast<MeterPoint*> (&*p)) != 0) {
			metric = TempoMetric (metric.tempo(), *mp);
			DEBUG_TRACE (DEBUG::MapReset, "Meter!\n");
		}
	}

	/* if the tempo point the defines our starting metric for position
	 * @param sc is ramped, recompute its omega value based on the beat
	 * time of the following tempo point. If we do not do this before we
	 * start, then ::superclock_at() for subsequent points will be
	 * incorrect.
	 */

	if (need_initial_ramp_reset) {
		const TempoPoint *nxt = next_tempo (metric.tempo());
		if (nxt) {
			const_cast<TempoPoint*> (&metric.tempo())->compute_omega_from_next_tempo (*nxt);
		}
		need_initial_ramp_reset = false;
	}

	/* Now iterate over remaining points and recompute their audio time
	 * and beat time positions.
	 */

	for ( ; p != _points.end(); ++p) {


		mtp = 0;
		tp = 0;
		mp = 0;

		if ((mtp = dynamic_cast<MusicTimePoint*> (&*p)) == 0) {
			if ((tp = dynamic_cast<TempoPoint*> (&*p)) == 0) {
				mp = dynamic_cast<MeterPoint*> (&*p);
			}
		}

		DEBUG_TRACE (DEBUG::MapReset, string_compose ("workong on it! tp = %1\n", tp));

		if (tp) {

			Points::iterator pp = p;
			nxt_tempo = 0;
			++pp;

			while (pp != _points.end()) {
				TempoPoint* nt = dynamic_cast<TempoPoint*> (&*pp);
				if (nt) {
					nxt_tempo = nt;
					break;
				}
				++pp;
			}

			DEBUG_TRACE (DEBUG::MapReset, string_compose ("considering omega comp for %1 with nxt = %2\n", *tp, nxt_tempo));
			if (tp->ramped() && nxt_tempo) {
				tp->compute_omega_from_next_tempo (*nxt_tempo);
			}
		}

		if (!mtp) {
			DEBUG_TRACE (DEBUG::MapReset, string_compose ("recompute %1 using %2\n", p->bbt(), metric));
			superclock_t sc = metric.superclock_at (p->bbt());
			DEBUG_TRACE (DEBUG::MapReset, string_compose ("\tbased on %1 move to %2,%3\n", p->bbt(), sc, metric.meter().quarters_at (p->bbt())));
			p->set (sc, metric.meter().quarters_at (p->bbt()), p->bbt());
		} else {
			DEBUG_TRACE (DEBUG::MapReset, "\tnot recomputing this one\n");
		}

		/* Now ensure that metric is correct moving forward */

		if ((mtp = dynamic_cast<MusicTimePoint*> (&*p)) != 0) {
			metric = TempoMetric (*mtp, *mtp);
		} else if ((tp = dynamic_cast<TempoPoint*> (&*p)) != 0) {
			metric = TempoMetric (*tp, metric.meter());
		} else if ((mp = dynamic_cast<MeterPoint*> (&*p)) != 0) {
			metric = TempoMetric (metric.tempo(), *mp);
		}
	}

	DEBUG_TRACE (DEBUG::MapReset, "RESET DONE\n");
#ifndef NDEBUG
	if (DEBUG_ENABLED(DEBUG::MapReset)) {
		dump (std::cerr);
	}
#endif
}

bool
TempoMap::move_meter (MeterPoint const & mp, timepos_t const & when, bool earlier, bool push)
{
	assert (!_tempos.empty());
	assert (!_meters.empty());

	if (_meters.size() < 2 || mp == _meters.front()) {
		/* not movable */
		return false;
	}

	superclock_t sc;
	Beats beats;
	BBT_Time bbt;
	bool round_up;

	beats = when.beats ();

	if (earlier) {
		round_up = false;
	} else {
		round_up = true;
	}

	/* Do not allow moving a meter marker to the same position as
	 * an existing one.
	 */

	Tempos::iterator t, prev_t;
	Meters::iterator m, prev_m;

	/* meter changes must be on bar */
	for (t = _tempos.begin(), prev_t = _tempos.end(); t != _tempos.end() && t->beats() < beats; ++t) { prev_t = t; }
	for (m = _meters.begin(), prev_m = _meters.end(); m != _meters.end() && m->beats() < beats && *m != mp; ++m) { prev_m = m; }

	if (prev_m == _meters.end()) {
		return false;
	}

	if (prev_t == _tempos.end()) {
		prev_t = _tempos.begin();
	}

	TempoMetric metric (*prev_t, *prev_m);
	bbt = metric.bbt_at (beats);

	if (round_up) {
		bbt = bbt.round_up_to_bar ();
	} else {
		bbt = bbt.round_down_to_bar ();
	}

	for (t = _tempos.begin(), prev_t = _tempos.end(); t != _tempos.end() && t->bbt() < bbt; ++t) { prev_t = t; }
	for (m = _meters.begin(), prev_m = _meters.end(); m != _meters.end() && m->bbt() < bbt && *m != mp; ++m) { prev_m = m; }

	if (prev_m == _meters.end()) {
		return false;
	}

	if (prev_t == _tempos.end()) {
		prev_t = _tempos.begin();
	}

	metric = TempoMetric (*prev_t, *prev_m);
	beats = metric.quarters_at (bbt);

	for (m = _meters.begin(), prev_m = _meters.end(); m != _meters.end(); ++m) {
		if (&*m != &mp) {
			if (m->beats() == beats) {
				return false;
			}
		}
	}

	sc = metric.superclock_at (bbt);

	if (mp.sclock() == sc && mp.beats() == beats && mp.bbt() == bbt) {
		return false;
	}

	const superclock_t old_sc = mp.sclock();

	/* reset position of this meter */
	const_cast<MeterPoint*> (&mp)->set (sc, beats, bbt);

	{

		Meters::iterator current = _meters.end();
		Meters::iterator insert_before = _meters.end();

		for (Meters::iterator m = _meters.begin(); m != _meters.end(); ++m) {
			if (*m == mp) {
				current = m;
			}
			if (insert_before == _meters.end() && (m->sclock() > sc)) {
				insert_before = m;
			}
		}

		/* existing meter must have been found */
		assert (current != _meters.end());

		/* reposition in list */
		_meters.splice (insert_before, _meters, current);

	}

	{

		Points::iterator current = _points.end();
		Points::iterator insert_before = _points.end();

		for (Points::iterator m = _points.begin(); m != _points.end(); ++m) {
			if (*m == mp) {
				current = m;
			}
			if (insert_before == _points.end() && (m->sclock() > sc)) {
				insert_before = m;
			}
		}

		/* existing meter must have been found */
		assert (current != _points.end());

		/* reposition in list */
		_points.splice (insert_before, _points, current);

	}

	/* recompute 3 domain positions for everything after this */
	reset_starting_at (std::min (sc, old_sc));

	return true;
}

bool
TempoMap::move_tempo (TempoPoint const & tp, timepos_t const & when, bool push)
{
	assert (!_tempos.empty());
	assert (!_meters.empty());

	if (_tempos.size() < 2 || tp == _tempos.front()) {
		/* not movable */
		return false;
	}

	superclock_t sc;
	Beats beats;
	BBT_Time bbt;

	/* tempo changes must be on beat */

	beats = when.beats();

	/* XXX need to assert that meter note value is >= 4 */

	MeterPoint const & mm (meter_at (beats));

	beats.round_to_subdivision (mm.note_value() / 4, RoundNearest);

	/* Do not allow moving a tempo marker to the same position as
	 * an existing one.
	 */

	Tempos::iterator t, prev_t;
	Meters::iterator m, prev_m;

	/* find tempo & meter in effect at the new target location */

	for (t = _tempos.begin(), prev_t = _tempos.end(); t != _tempos.end() && t->beats() <= beats && *t != tp; ++t) { prev_t = t; }
	for (m = _meters.begin(), prev_m = _meters.end(); m != _meters.end() && m->beats() <= beats; ++m) { prev_m = m; }

	if (prev_t == _tempos.end()) {
		/* moved earlier than first, no movement */
		return false;
	}

	if (prev_m == _meters.end()) {
		/* moved earlier than first, no movement */
		return false;
	}

	/* If the previous tempo is ramped, we need to recompute its omega
	 * constant to cover the (new) duration of the ramp.
	 */

	if (prev_t->actually_ramped()) {
		prev_t->compute_omega_from_distance_and_next_tempo (beats - prev_t->beats(), tp);
	}

	TempoMetric metric (*prev_t, *prev_m);

	const Beats delta ((beats - tp.beats()).abs());

	if (delta < Beats::ticks (metric.meter().ticks_per_grid())) {
		return false;
	}

	sc = metric.superclock_at (beats);
	bbt = metric.bbt_at (beats);

	if (tp.sclock() == sc && tp.beats() == beats && tp.bbt() == bbt) {
		return false;
	}

	const superclock_t old_sc = tp.sclock();
	/* reset position of this tempo */
	const_cast<TempoPoint*> (&tp)->set (sc, beats, bbt);

	/* move to correct position in tempo list */

	{
		Tempos::iterator current = _tempos.end();
		Tempos::iterator insert_before = _tempos.end();

		for (Tempos::iterator t = _tempos.begin(); t != _tempos.end(); ++t) {
			if (*t == tp) {
				current = t;
			}
			if (insert_before == _tempos.end() && (t->sclock() > sc)) {
				insert_before = t;
			}
		}

		/* existing tempo must have been found */
		assert (current != _tempos.end());
		/* reposition in list */
		_tempos.splice (insert_before, _tempos, current);
	}

	/* move to correct position in points list */

	{
		Points::iterator current = _points.end();
		Points::iterator insert_before = _points.end();

		for (Points::iterator t = _points.begin(); t != _points.end(); ++t) {
			if (*t == tp) {
				current = t;
			}
			if (insert_before == _points.end() && (t->sclock() > sc)) {
				insert_before = t;
			}
		}

		/* existing tempo must have been found */
		assert (current != _points.end());

		/* reposition in list */
		_points.splice (insert_before, _points, current);
	}

	/* recompute 3 domain positions for everything after this */
	reset_starting_at (std::min (sc, old_sc));

	return true;
}

MeterPoint &
TempoMap::set_meter (Meter const & m, timepos_t const & time)
{
	MeterPoint * ret = 0;

	DEBUG_TRACE (DEBUG::TemporalMap, string_compose ("Set meter @ %1 to %2\n", time, m));

	if (time.is_beats()) {

		Beats beats (time.beats());
		TempoMetric metric (metric_at (beats));

		/* meter changes are required to be on-bar */

		BBT_Time rounded_bbt = metric.bbt_at (beats);
		rounded_bbt = metric.round_to_bar (rounded_bbt);

		const Beats rounded_beats = metric.quarters_at (rounded_bbt);
		const superclock_t sc = metric.superclock_at (rounded_beats);

		MeterPoint* mp = new MeterPoint (*this, m, sc, rounded_beats, rounded_bbt);

		ret = add_meter (mp);

	} else {

		superclock_t sc (time.superclocks());
		Beats beats;
		BBT_Time bbt;

		TempoMetric metric (metric_at (sc));

		/* meter changes must be on bar */

		bbt = metric.bbt_at (time);
		bbt = metric.round_to_bar (bbt);

		/* compute beat position */
		beats = metric.quarters_at (bbt);

		/* recompute superclock position of bar-rounded position */
		sc = metric.superclock_at (beats);

		MeterPoint* mp = new MeterPoint (*this, m, sc, beats, bbt);

		ret = add_meter (mp);
	}

	return *ret;
}

MeterPoint &
TempoMap::set_meter (Meter const & t, BBT_Time const & bbt)
{
	return set_meter (t, timepos_t (quarters_at (bbt)));
}

void
TempoMap::remove_meter (MeterPoint const & mp)
{
	superclock_t sc = mp.sclock();
	Meters::iterator m;

	/* the argument is likely to be a Point-derived object that doesn't
	 * actually exist in this TempoMap, since the caller called
	 * TempoMap::write_copy() in order to perform an RCU operation, but
	 * will be removing an element known from the original map.
	 *
	 * However, since we do not allow points of the same type (Tempo,
	 * Meter, BarTime) at the same time, we can effectively search here
	 * using what is effectively a duple of (type,time) for the
	 * comparison.
	 *
	 * Once/if found, we will have a pointer to the actual Point-derived
	 * object in this TempoMap, and we can then remove that from the
	 * _points list.
	 */

	for (m = _meters.begin(); m != _meters.end() && m->sclock() < mp.sclock(); ++m);

	if (m == _meters.end()) {
		/* not found */
		return;
	}

	if (m->sclock() != mp.sclock()) {
		/* error ... no meter point at the time of mp */
		return;
	}

	_meters.erase (m);
	remove_point (*m);
	reset_starting_at (sc);
}

Temporal::BBT_Time
TempoMap::bbt_at (timepos_t const & pos) const
{
	if (pos.is_beats()) {
		return bbt_at (pos.beats());
	}
	return bbt_at (pos.superclocks());
}

Temporal::BBT_Time
TempoMap::bbt_at (superclock_t s) const
{
	return metric_at (s).bbt_at (timepos_t::from_superclock (s));
}

Temporal::BBT_Time
TempoMap::bbt_at (Temporal::Beats const & qn) const
{
	return metric_at (qn).bbt_at (qn);
}

#if 0
samplepos_t
TempoMap::sample_at (Temporal::Beats const & qn) const
{
	return superclock_to_samples (metric_at (qn).superclock_at (qn), TEMPORAL_SAMPLE_RATE);
}

samplepos_t
TempoMap::sample_at (Temporal::BBT_Time const & bbt) const
{
	return samples_to_superclock (metric_at (bbt).superclock_at (bbt), TEMPORAL_SAMPLE_RATE);
}

samplepos_t
TempoMap::sample_at (timepos_t const & pos) const
{
	if (pos.is_beat()) {
		return sample_at (pos.beats ());
	}

	/* somewhat nonsensical to call this under these conditions but ... */

	return pos.superclocks();
}
#endif

superclock_t
TempoMap::superclock_at (Temporal::Beats const & qn) const
{
	return metric_at (qn).superclock_at (qn);
}

superclock_t
TempoMap::superclock_at (Temporal::BBT_Time const & bbt) const
{
	return metric_at (bbt).superclock_at (bbt);
}

superclock_t
TempoMap::superclock_at (timepos_t const & pos) const
{
	if (pos.is_beats()) {
		return superclock_at (pos.beats ());
	}

	/* somewhat nonsensical to call this under these conditions but ... */

	return pos.superclocks();
}

#define S2Sc(s) (samples_to_superclock ((s), TEMPORAL_SAMPLE_RATE))
#define Sc2S(s) (superclock_to_samples ((s), TEMPORAL_SAMPLE_RATE))

/** Count the number of beats that are equivalent to distance when going forward,
    starting at pos.
*/
Temporal::Beats
TempoMap::scwalk_to_quarters (superclock_t pos, superclock_t distance) const
{
	TempoMetric first (metric_at (pos));
	TempoMetric last (metric_at (pos+distance));
	Temporal::Beats a = first.quarters_at_superclock (pos);
	Temporal::Beats b = last.quarters_at_superclock (pos+distance);
	return b - a;
}

Temporal::Beats
TempoMap::scwalk_to_quarters (Temporal::Beats const & pos, superclock_t distance) const
{
	/* XXX this converts from beats to superclock and back to beats... which is OK (reversible) */
	superclock_t s = metric_at (pos).superclock_at (pos);
	s += distance;
	return metric_at (s).quarters_at_superclock (s);

}

Temporal::Beats
TempoMap::bbtwalk_to_quarters (Beats const & pos, BBT_Offset const & distance) const
{
	return quarters_at (bbt_walk (bbt_at (pos), distance)) - pos;
}

Temporal::Beats
TempoMap::bbtwalk_to_quarters (BBT_Time const & pos, BBT_Offset const & distance) const
{
	return quarters_at (bbt_walk (pos, distance)) - quarters_at (pos);
}

void
TempoMap::sample_rate_changed (samplecnt_t new_sr)
{
	const double ratio = new_sr / (double) TEMPORAL_SAMPLE_RATE;

	for (Tempos::iterator t = _tempos.begin(); t != _tempos.end(); ++t) {
		t->map_reset_set_sclock_for_sr_change (llrint (ratio * t->sclock()));
	}

	for (Meters::iterator m = _meters.begin(); m != _meters.end(); ++m) {
		m->map_reset_set_sclock_for_sr_change (llrint (ratio * m->sclock()));
	}

	for (MusicTimes::iterator p = _bartimes.begin(); p != _bartimes.end(); ++p) {
		p->map_reset_set_sclock_for_sr_change (llrint (ratio * p->sclock()));
	}
}

void
TempoMap::dump (std::ostream& ostr) const
{
	ostr << "\n\nTEMPO MAP @ " << this << ":\n" << std::dec;
	ostr << "... tempos...\n";
	for (Tempos::const_iterator t = _tempos.begin(); t != _tempos.end(); ++t) {
		ostr << &*t << ' ' << *t << endl;
	}

	ostr << "... meters...\n";
	for (Meters::const_iterator m = _meters.begin(); m != _meters.end(); ++m) {
		ostr << &*m << ' ' << *m << endl;
	}

	ostr << "... bartimes...\n";
	for (MusicTimes::const_iterator m = _bartimes.begin(); m != _bartimes.end(); ++m) {
		ostr << &*m << ' ' << *m << endl;
	}
	ostr << "... all points ...\n";
	for (Points::const_iterator p = _points.begin(); p != _points.end(); ++p) {
		ostr << &*p << ' ' << *p;
		if (dynamic_cast<MusicTimePoint const *> (&(*p))) {
			ostr << " BarTime";
		}

		if (dynamic_cast<TempoPoint const *> (&(*p))) {
			ostr << " Tempo";
		}

		if (dynamic_cast<MeterPoint const *> (&(*p))) {
			ostr << " Meter";
		}
		ostr << endl;
	}
	ostr << "------------\n\n\n";
}

template<class const_traits_t>  typename const_traits_t::iterator_type
TempoMap::_get_tempo_and_meter (typename const_traits_t::tempo_point_type & tp,
                                typename const_traits_t::meter_point_type & mp,
                                typename const_traits_t::time_reference (Point::*method)() const,
                                typename const_traits_t::time_type arg,
                                typename const_traits_t::iterator_type begini,
                                typename const_traits_t::iterator_type endi,
                                typename const_traits_t::tempo_point_type tstart,
                                typename const_traits_t::meter_point_type mstart,
                                bool can_match, bool ret_iterator_after_not_at) const
{
	typename const_traits_t::iterator_type p;
	typename const_traits_t::iterator_type last_used = endi;
	bool tempo_done = false;
	bool meter_done = false;

	assert (!_tempos.empty());
	assert (!_meters.empty());
	assert (!_points.empty());

	/* If the starting position is the beginning of the timeline (indicated
	 * by the default constructor value for the time_type (superclock_t,
	 * Beats, BBT_Time), then we are always allowed to use the tempo &
	 * meter at that position.
	 *
	 * Without this, it would be necessary to special case "can_match" in
	 * the caller if the start is "zero". Instead we do that here, since
	 * common cases (e.g. ::get_grid()) will use can_match = false, but may
	 * pass in a zero start point.
	 */

	can_match = (can_match || arg == typename const_traits_t::time_type ());

	/* Set return tempo and meter points by value using the starting tempo
	 * and meter passed in.
	 *
	 * Then advance through all points, resetting either tempo and/or meter
	 * until we find a point beyond (or equal to, if @p can_match is
	 * true) the @p arg (end time)
	 */

	for (tp = tstart, mp = mstart, p = begini; p != endi; ++p) {

		typename const_traits_t::tempo_point_type tpp;
		typename const_traits_t::meter_point_type mpp;

		if (!tempo_done && (tpp = dynamic_cast<typename const_traits_t::tempo_point_type> (&(*p))) != 0) {
			if ((can_match && (((*p).*method)() > arg)) || (!can_match && (((*p).*method)() >= arg))) {
				tempo_done = true;
			} else {
				tp = tpp;
				last_used = p;
			}
		}

		if (!meter_done && (mpp = dynamic_cast<typename const_traits_t::meter_point_type> (&(*p))) != 0) {
			if ((can_match && (((*p).*method)() > arg)) || (!can_match && (((*p).*method)() >= arg))) {
				meter_done = true;
			} else {
				mp = mpp;
				last_used = p;
			}
		}

		if (meter_done && tempo_done) {
			break;
		}
	}

	if (!tp || !mp) {
		return endi;
	}

	if (ret_iterator_after_not_at) {

		p = last_used;

		if (can_match) {
			while ((p != endi) && ((*p).*method)() <= arg) ++p;
		} else {
			while ((p != endi) && ((*p).*method)() < arg) ++p;
		}

		return p;
	}

	return last_used;
}

void
TempoMap::get_grid (TempoMapPoints& ret, superclock_t start, superclock_t end, uint32_t bar_mod, uint32_t beat_div) const
{
	/* note: @p bar_mod is "bar modulo", and describes the N in "give
	   me every Nth bar". If the caller wants every 4th bar, bar_mod ==
	   4. If we want every point defined by the tempo note type (e.g. every
	   quarter not, then bar_mod is zero.
	*/

	assert (!_tempos.empty());
	assert (!_meters.empty());
	assert (!_points.empty());

#ifndef NDEBUG
	if (DEBUG_ENABLED (DEBUG::Grid)) {
		dump (std::cout);
	}
#endif
	DEBUG_TRACE (DEBUG::Grid, string_compose (">>> GRID START %1 .. %2 (barmod = %3)\n", start, end, bar_mod));

	TempoPoint const * tp = 0;
	MeterPoint const * mp = 0;
	Points::const_iterator p = _points.begin();
	BBT_Time bbt;
	Beats beats;

	/* Find relevant meter for nominal start point */

	p = get_tempo_and_meter (tp, mp, start, true, true);

	/* p now points to either the point *after* start, or the end of the
	 * _points list.
	 *
	 * metric is the TempoMetric that is in effect at start
	 */

	TempoMetric metric = TempoMetric (*tp, *mp);

	DEBUG_TRACE (DEBUG::Grid, string_compose ("metric in effect at %1 = %2\n", start, metric));

	/* determine the BBT at start */

	bbt = metric.bbt_at (timepos_t::from_superclock (start));

	/* first task: get to the right starting point for the requested
	 * grid. if bar_mod is zero, then we'll start on the next beat after
	 * @param start. if bar_mod is non-zero, we'll start on the first bar
	 * after @p start. This bar position may or may not be a part of the
	 * grid, depending on whether or not it is a multiple of bar_mod.
	 *
	 * final argument = true means "return the iterator corresponding the
	 * point after the latter of the tempo/meter points"
	 */


	DEBUG_TRACE (DEBUG::Grid, string_compose ("start %1 is %2\n", start, bbt));

	if (bar_mod == 0) {

		/* round to next beat, then find the tempo/meter/bartime points
		 * in effect at that time.
		 */

		const BBT_Time new_bbt = metric.meter().round_up_to_beat (bbt);

		if (new_bbt != bbt) {

			bbt = new_bbt;

			/* rounded up, determine new starting superclock position */

			p = get_tempo_and_meter (tp, mp, bbt, false, true);

			metric = TempoMetric (*tp, *mp);

			DEBUG_TRACE (DEBUG::Grid, string_compose ("metric in effect(2) at %1 = %2\n", bbt, metric));

			/* recompute superclock position */

			superclock_t new_start = metric.superclock_at (bbt);

			DEBUG_TRACE (DEBUG::Grid, string_compose ("metric %1 says that %2 is at %3\n", metric, bbt, new_start));

			if (new_start < start) {
				DEBUG_TRACE (DEBUG::Grid, string_compose ("we've gone backwards, new is %1 start is %2\n", new_start, start));
				abort ();
			}

			start = new_start;

		} else {
			DEBUG_TRACE (DEBUG::Grid, string_compose ("%1 was on a beat, no rounding up necessary\n", bbt));
		}

	} else {

		BBT_Time bar = bbt.round_down_to_bar ();

		/* adjust to match bar_mod (e.g. we only want every 4th bar)
		 */

		if (bar_mod != 1) {
			bar.bars -= bar.bars % bar_mod;
			++bar.bars;
		}

		/* the rounding we've just done cannot change the meter in
		   effect, because it remains within the bar. But it could
		   change the tempo (which are only quantized to grid positions
		   within a bar). So if it has generated a new BBT time,
		   recompute the metric.
		*/

		if (bar != bbt) {

			bbt = bar;


			/* rebuild metric */

			p = get_tempo_and_meter (tp, mp, bbt, true, true);
			metric = TempoMetric (*tp, *mp);


			DEBUG_TRACE (DEBUG::Grid, string_compose ("metric in effect(3) at %1 = %2\n", start, metric));
			start = metric.superclock_at (bbt);

		} else {
			DEBUG_TRACE (DEBUG::Grid, string_compose ("%1 was on a bar, no round down to bar necessary\n", bbt));
		}
	}

	/* at this point:
	 *
	 * - metric is a TempoMetric that describes the situation at the adjusted start time
	 * - p is an iterator pointin to either the end of the _points list, or
	 *   the next point in the list after start.
	 */


	while (p != _points.end() && start < end) {

		bool next_point_is_bbt_marker = (dynamic_cast<MusicTimePoint const *> (&*p));

		/* Generate grid points (either actual meter-defined
		 * beats, or bars based on bar_mod) up until the next point
		 * in the map
		 */

		if (bar_mod != 0) {
			if (bbt.is_bar() && (bar_mod == 1 || ((bbt.bars % bar_mod == 1)))) {
				ret.push_back (TempoMapPoint (*this, metric, start, beats, bbt));
				DEBUG_TRACE (DEBUG::Grid, string_compose ("G %1\t       [%2]\n", metric, ret.back()));
			} else {
				DEBUG_TRACE (DEBUG::Grid, string_compose ("-- skip %1 not on bar_mod %2\n", bbt, bar_mod));
			}

			/* Advance by the number of bars specified by bar_mod */

			bbt.bars += bar_mod;

		} else {

			ret.push_back (TempoMapPoint (*this, metric, start, beats, bbt));
			DEBUG_TRACE (DEBUG::Grid, string_compose ("G %1\t       [%2]\n", metric, ret.back()));

			/* Advance beats by 1 meter-defined "beat */

			if (beat_div == 1) {
				bbt = metric.bbt_add (bbt, BBT_Offset (0, 1, 0));
			} else {
				bbt = metric.bbt_add (bbt, BBT_Offset (0, 0, Temporal::ticks_per_beat / beat_div));
			}
		}

		start = metric.superclock_at (bbt);

		DEBUG_TRACE (DEBUG::Grid, string_compose ("check overrun of next point with bbt @ %1 audio %2 point %3\n", bbt, start, *p));

		if ((!next_point_is_bbt_marker && bbt >= p->bbt()) || (start >= p->sclock())) {

			DEBUG_TRACE (DEBUG::Grid, string_compose ("we've reached/passed the next point, BBT %1 audio %2 point %3\n", bbt, start, *p));

			/* reset our sense of "now" to be wherever the point is */

			start = p->sclock();
			bbt = p->bbt();
			beats = p->beats();

			/* If we just arrived at a point (indicated by bbt ==
			 * p->bbt()), use all points at the same location to
			 * potentially reconstruct the metric. Note that a BBT point is
			 * both a tempo and a meter point, which is why we do test each
			 * point found at this location as both.
			 */

			bool rebuild_metric = false;

			while (p->bbt() == bbt) {

				TempoPoint const * tpp;
				MeterPoint const * mpp;

				if ((tpp = dynamic_cast<TempoPoint const *> (&(*p))) != 0) {
					rebuild_metric = true;
					tp = tpp;
				}

				if ((mpp = dynamic_cast<MeterPoint const *> (&(*p))) != 0) {
					rebuild_metric = true;
					mp = mpp;
				}

				++p;
			}

			/* reset the metric to use the most recent tempo & meter */

			if (rebuild_metric) {
				metric = TempoMetric (*tp, *mp);
				DEBUG_TRACE (DEBUG::Grid, string_compose ("second| with start = %1 aka %2 rebuilt metric from points, now %3\n", start, bbt, metric));
			}

		}

		/* Update the quarter-note time value to match the BBT and
		 * audio time positions
		 */

		beats = metric.quarters_at (bbt);

		DEBUG_TRACE (DEBUG::Grid, string_compose ("bar mod %1 moved to %2 qn %3 sc %4)\n", bar_mod, bbt, beats, start));

	}

	/* reached the end or no more points to consider, so just
	 * finish by filling the grid to the end, if necessary.
	 */

	if (start < end) {

		/* note: if start < end, then p == _points.end(). This means there are
		 * no more Points beyond the current value of start.
		 *
		 * Since there are no more Points beyond start, the current metric
		 * cannot involve a ramp, so the step size per grid element is
		 * constant. metric will also remain constant until we finish.
		 */

		DEBUG_TRACE (DEBUG::Grid, string_compose ("reached end, no more map points, use %5 to finish between %1 .. %2 initial bbt %3, beats %4\n", start, end, bbt, beats.str(), metric));

		while (start < end) {

			DEBUG_TRACE (DEBUG::Grid, string_compose ("bar mod %1 moved to %2 qn %3 sc %4)\n", bar_mod, bbt, beats, start));

			/* It is possible we already added the current BBT
			 * point, so check to avoid doubling up
			 */

			if (bar_mod != 0) {
				if (bbt.is_bar() && (bar_mod == 1 || ((bbt.bars % bar_mod == 0)))) {
					ret.push_back (TempoMapPoint (*this, metric, start, beats, bbt));
					DEBUG_TRACE (DEBUG::Grid, string_compose ("GendA %1\t       %2\n", metric, ret.back()));
				}

				/* Advance by the number of bars specified by
				   bar_mod, then recompute the beats and
				   superclock position corresponding to that
				   BBT time.
				*/

				bbt.bars += bar_mod;

			} else {
				ret.push_back (TempoMapPoint (*this, metric, start, beats, bbt));
				DEBUG_TRACE (DEBUG::Grid, string_compose ("GendB %1\t       %2\n", metric, ret.back()));

				/* move on by 1 meter-defined "beat" */

				if (beat_div == 1) {
					bbt = metric.bbt_add (bbt, BBT_Offset (0, 1, 0));
				} else {
					bbt = metric.bbt_add (bbt, BBT_Offset (0, 0, Temporal::ticks_per_beat / beat_div));
				}
			}

			/* compute audio and quarter-note time from the new BBT position */

			start = metric.superclock_at (bbt);
			beats = metric.quarters_at (bbt);
		}

		/* all done */

	} else {
		if (p == _points.end()) {
			DEBUG_TRACE (DEBUG::Grid, string_compose ("ended loop with start %1 end %2, p @ END\n", start, end));
		} else {
			DEBUG_TRACE (DEBUG::Grid, string_compose ("ended loop with start %1 end %2, p=> %3\n", start, end, *p));
		}
	}

	DEBUG_TRACE (DEBUG::Grid, "<<< GRID DONE\n");
}

uint32_t
TempoMap::count_bars (Beats const & start, Beats const & end) const
{
	TempoMapPoints bar_grid;
	superclock_t s (superclock_at (start));
	superclock_t e (superclock_at (end));
	get_grid (bar_grid, s, e, 1);
	return bar_grid.size();
}

std::ostream&
std::operator<<(std::ostream& str, Meter const & m)
{
	return str << m.divisions_per_bar() << '/' << m.note_value();
}

std::ostream&
std::operator<<(std::ostream& str, Tempo const & t)
{
	if (t.ramped()) {
		return str << t.note_types_per_minute() << " .. " << t.end_note_types_per_minute() << " 1/" << t.note_type() << " RAMPED notes per minute [ " << t.super_note_type_per_second() << " => " << t.end_super_note_type_per_second() << " sntpm ] (" << t.superclocks_per_note_type() << " sc-per-1/" << t.note_type() << ')';
	} else {
		return str << t.note_types_per_minute() << " 1/" << t.note_type() << " notes per minute [" << t.super_note_type_per_second() << " sntpm] (" << t.superclocks_per_note_type() << " sc-per-1/" << t.note_type() << ')';
	}
}

std::ostream&
std::operator<<(std::ostream& str, Point const & p)
{
	return str << "P@" << p.sclock() << '/' << p.beats() << '/' << p.bbt();
}

std::ostream&
std::operator<<(std::ostream& str, MeterPoint const & m)
{
	return str << *((Meter const *) &m) << ' ' << *((Point const *) &m);
}

std::ostream&
std::operator<<(std::ostream& str, TempoPoint const & t)
{
	str << *((Tempo const *) &t) << ' '  << *((Point const *) &t);
	if (t.ramped()) {
		if (t.actually_ramped()) {
			str << ' ' << " ramp to " << t.end_note_types_per_minute();
		} else {
			str << ' ' << " !ramp to " << t.end_note_types_per_minute();
		}
		str << " omega = " << std::setprecision(12) << t.omega();
	}
	return str;
}

std::ostream&
std::operator<<(std::ostream& str, MusicTimePoint const & p)
{
	str << "MP @ ";
	str << *((Point const *) &p);
	str << *((Tempo const *) &p);
	str << *((Meter const *) &p);
	return str;
}

std::ostream&
std::operator<<(std::ostream& str, TempoMetric const & tm)
{
	return str << tm.tempo() << ' '  << tm.meter();
}

std::ostream&
std::operator<<(std::ostream& str, TempoMapPoint const & tmp)
{
	str << '@' << std::setw (12) << tmp.sclock() << ' ' << tmp.sclock() / (double) superclock_ticks_per_second()
	    << " secs " << tmp.sample (TEMPORAL_SAMPLE_RATE) << " samples"
	    << (tmp.is_explicit_tempo() ? " EXP-T" : " imp-t")
	    << (tmp.is_explicit_meter() ? " EXP-M" : " imp-m")
	    << (tmp.is_explicit_position() ? " EXP-P" : " imp-p")
	    << " qn " << tmp.beats ()
	    << " bbt " << tmp.bbt()
		;

	if (tmp.is_explicit_tempo()) {
		str << " tempo " << tmp.tempo();
	}

	if (tmp.is_explicit_meter()) {
		str << " meter " << tmp.meter();
	}

	if (tmp.is_explicit_tempo() && tmp.tempo().ramped()) {
		str << " ramp omega = " << tmp.tempo().omega();
	}

	return str;
}

BBT_Time
TempoMap::bbt_walk (BBT_Time const & bbt, BBT_Offset const & o) const
{
	BBT_Offset offset (o);
	BBT_Time start (bbt);
	Tempos::const_iterator t, prev_t, next_t;
	Meters::const_iterator m, prev_m, next_m;

	assert (!_tempos.empty());
	assert (!_meters.empty());

	/* trivial (and common) case: single tempo, single meter */

	if (_tempos.size() == 1 && _meters.size() == 1) {
		return _meters.front().bbt_add (bbt, o);
	}

	/* Find tempo,meter pair for bbt, and also for the next tempo and meter
	 * after each (if any)
	 */

	/* Yes, linear search because the typical size of _tempos and _meters
	 * is 1, and extreme sizes are on the order of 10
	 */

	next_t = _tempos.end();
	next_m = _meters.end();

	for (t = _tempos.begin(), prev_t = t; t != _tempos.end() && t->bbt() < bbt;) {
		prev_t = t;
		++t;

		if (t != _tempos.end()) {
			next_t = t;
			++next_t;
		}
	}

	for (m = _meters.begin(), prev_m = m; m != _meters.end() && m->bbt() < bbt;) {
		prev_m = m;
		++m;

		if (m != _meters.end()) {
			next_m = m;
			++next_m;
		}
	}

	/* may have found tempo and/or meter precisely at the time given */

	if (t != _tempos.end() && t->bbt() == bbt) {
		prev_t = t;
	}

	if (m != _meters.end() && m->bbt() == bbt) {
		prev_m = m;
	}

	/* see ::metric_at() for comments about the use of const_cast here
	 */

	TempoMetric metric (*const_cast<TempoPoint*>(&*prev_t), *const_cast<MeterPoint*>(&*prev_m));


	/* normalize possibly too-large ticks count */

	const int32_t tpg = metric.meter().ticks_per_grid ();

	if (offset.ticks > tpg) {
		/* normalize */
		offset.beats += offset.ticks / tpg;
		offset.ticks %= tpg;
	}

	/* add each beat, 1 by 1, rechecking to see if there's a new
	 * TempoMetric in effect after each addition
	 */

#define TEMPO_CHECK_FOR_NEW_METRIC                                      \
	if (((next_t != _tempos.end()) && (start >= next_t->bbt())) || \
	    ((next_m != _meters.end()) && (start >= next_m->bbt()))) { \
		/* need new metric */ \
		if (start >= next_t->bbt()) { \
			if (start >= next_m->bbt()) { \
				metric = TempoMetric (*const_cast<TempoPoint*>(&*next_t), *const_cast<MeterPoint*>(&*next_m)); \
				++next_t; \
				++next_m; \
			} else { \
				metric = TempoMetric (*const_cast<TempoPoint*>(&*next_t), metric.meter()); \
				++next_t; \
			} \
		} else if (start >= next_m->bbt()) { \
			metric = TempoMetric (metric.tempo(), *const_cast<MeterPoint*>(&*next_m)); \
			++next_m; \
		} \
	}

	for (int32_t b = 0; b < offset.bars; ++b) {

		TEMPO_CHECK_FOR_NEW_METRIC;
		start.bars += 1;
	}

	for (int32_t b = 0; b < offset.beats; ++b) {

		TEMPO_CHECK_FOR_NEW_METRIC;
		start.beats += 1;
		if (start.beats > metric.divisions_per_bar()) {
			start.bars += 1;
			start.beats = 1;
		}
	}

	start.ticks += offset.ticks;

	if (start.ticks >= ticks_per_beat) {
		start.beats += 1;
		start.ticks %= ticks_per_beat;
	}


	return start;
}

Temporal::Beats
TempoMap::quarters_at (timepos_t const & pos) const
{
	if (pos.is_beats()) {
		/* a bit redundant */
		return pos.beats();
	}
	return quarters_at_superclock (pos.superclocks());
}

Temporal::Beats
TempoMap::quarters_at (Temporal::BBT_Time const & bbt) const
{
	return metric_at (bbt).quarters_at (bbt);
}

Temporal::Beats
TempoMap::quarters_at_superclock (superclock_t pos) const
{
	return metric_at (pos).quarters_at_superclock (pos);
}

XMLNode&
TempoMap::get_state () const
{
	XMLNode* node = new XMLNode (X_("TempoMap"));

	node->set_property (X_("superclocks-per-second"), superclock_ticks_per_second());

	XMLNode* children;

	children = new XMLNode (X_("Tempos"));
	node->add_child_nocopy (*children);
	for (Tempos::const_iterator t = _tempos.begin(); t != _tempos.end(); ++t) {
		if (!dynamic_cast<MusicTimePoint const *> (&(*t))) {
			children->add_child_nocopy (t->get_state());
		}
	}

	children = new XMLNode (X_("Meters"));
	node->add_child_nocopy (*children);
	for (Meters::const_iterator m = _meters.begin(); m != _meters.end(); ++m) {
		if (!dynamic_cast<MusicTimePoint const *> (& (*m))) {
			children->add_child_nocopy (m->get_state());
		}
	}

	children = new XMLNode (X_("MusicTimes"));
	node->add_child_nocopy (*children);
	for (MusicTimes::const_iterator b = _bartimes.begin(); b != _bartimes.end(); ++b) {
		children->add_child_nocopy (b->get_state());
	}

	return *node;
}

int
TempoMap::set_state (XMLNode const & node, int version)
{
	if (version <= 6000) {
		return set_state_3x (node);
	}

	/* global map properties */

	/* XXX this should probably be at the global level in the session file
	 * because it is the time unit for anything in the audio time domain,
	 * and affects a lot more than just the tempo map
	 */
	superclock_t sc;
	if (node.get_property (X_("superclocks-per-second"), sc)) {
		set_superclock_ticks_per_second (sc);
	}

	XMLNodeList const & children (node.children());

	/* XXX might be good to have a recovery mechanism in case setting
	 * things from XML fails. Not very likely, however.
	 */

	_tempos.clear ();
	_meters.clear ();
	_bartimes.clear ();
	_points.clear ();

	for (XMLNodeList::const_iterator c = children.begin(); c != children.end(); ++c) {
		if ((*c)->name() == X_("Tempos")) {
			if (set_tempos_from_state (**c)) {
				return -1;
			}
		}

		if ((*c)->name() == X_("Meters")) {
			if (set_meters_from_state (**c)) {
				return -1;
			}
		}

		if ((*c)->name() == X_("MusicTimes")) {
			if (set_music_times_from_state (**c)) {
				return -1;
			}
		}
	}

	return 0;
}

int
TempoMap::set_music_times_from_state (XMLNode const& mt_node)
{
	XMLNodeList const & children (mt_node.children());

	try {
		for (XMLNodeList::const_iterator c = children.begin(); c != children.end(); ++c) {
			MusicTimePoint* mp = new MusicTimePoint (*this, **c);
			add_or_replace_bartime (mp);
		}
	} catch (...) {
		_bartimes.clear (); /* remove any that were created */
		return -1;
	}

	return 0;
}

int
TempoMap::set_tempos_from_state (XMLNode const& tempos_node)
{
	XMLNodeList const & children (tempos_node.children());
	bool ignore;

	try {
		for (XMLNodeList::const_iterator c = children.begin(); c != children.end(); ++c) {
			TempoPoint* tp = new TempoPoint (*this, **c);
			core_add_tempo (tp, ignore);
			core_add_point (tp);
		}
	} catch (...) {
		_tempos.clear (); /* remove any that were created */
		return -1;
	}

	return 0;
}

int
TempoMap::set_meters_from_state (XMLNode const& meters_node)
{
	XMLNodeList const & children (meters_node.children());
	bool ignore;

	try {
		for (XMLNodeList::const_iterator c = children.begin(); c != children.end(); ++c) {
			MeterPoint* mp = new MeterPoint (*this, **c);
			core_add_meter (mp, ignore);
			core_add_point (mp);
		}
	} catch (...) {
		_meters.clear (); /* remove any that were created */
		return -1;
	}

	return 0;
}

bool
TempoMap::can_remove (TempoPoint const & t) const
{
	return !is_initial (t);
}

bool
TempoMap::is_initial (TempoPoint const & t) const
{
	return t.sclock() == 0;
}

bool
TempoMap::is_initial (MeterPoint const & m) const
{
	return m.sclock() == 0;
}

bool
TempoMap::can_remove (MeterPoint const & m) const
{
	return !is_initial (m);
}

/** returns the duration (using the domain of @p pos) of the supplied BBT time at a specified sample position in the tempo map.
 * @param pos the frame position in the tempo map.
 * @param bbt the distance in BBT time from pos to calculate.
 * @param dir the rounding direction..
 * @return the timecnt_t that @p bbt represents when starting at @p pos, in
 * the time domain of @p pos
*/
timecnt_t
TempoMap::bbt_duration_at (timepos_t const & pos, BBT_Offset const & dur) const
{
	if (pos.time_domain() == AudioTime) {
		return timecnt_t::from_superclock (superclock_at (bbt_walk (bbt_at (pos), dur)) - pos.superclocks(), pos);
	}
	return timecnt_t (bbtwalk_to_quarters (pos.beats(), dur), pos);

}

/** Takes a position and distance (both in any time domain), and returns a timecnt_t
 * that describes that distance from that position in a specified time domain.
 *
 * This method is used when converting a (distance,pos) pair (a timecnt_t) into
 * (distance,pos') in a different time domain. For an english example: "given a
 * distance of N beats from position P, what is that same distance measured in
 * superclocks from P' ?"
 *
 * A different example: "given a distance N superclocks from position P, what
 * is that same distance measured in beats from P' ?"
 *
 * There is a trivial case in which the requested return domain is the same as
 * the domain for the distance. In english: "given a distance of N beats from
 * P, what is the same distance measured in beats from P' ?" In this case, we
 * can simply construct a new timecnt_t that uses P' instead of P, since the
 * distance component must necessarily be same. Notice that this true no matter
 * what domain is used.
 */

timecnt_t
TempoMap::convert_duration (timecnt_t const & duration, timepos_t const & new_position, TimeDomain return_domain) const
{
	timepos_t p (return_domain);
	Beats b;
	superclock_t s;

	if (return_domain == duration.time_domain()) {
		/* new timecnt_t: same distance, but new position */
		return timecnt_t (duration.distance(), new_position);
	}

	switch (return_domain) {
	case AudioTime:
		switch (duration.time_domain()) {
		case AudioTime:
			/*NOTREACHED*/
			break;
		case BeatTime:
			/* duration is in beats but we're asked to return superclocks */
			switch (new_position.time_domain()) {
			case BeatTime:
				/* new_position is already in beats */
				p = new_position;
				break;
			case AudioTime:
				/* Determine beats at sc pos, so that we can add beats */
				p = timepos_t (metric_at (new_position).quarters_at_superclock (new_position.superclocks()));
				break;
			}
			/* add beats */
			p += duration;
			/* determine superclocks */
			s = metric_at (p).superclock_at (p.beats());
			/* return duration in sc */
			return timecnt_t::from_superclock (s - new_position.superclocks(), new_position);
			break;
		}
		break;

	case BeatTime:
		switch (duration.time_domain()) {
		case AudioTime:
			/* duration is in superclocks but we're asked to return beats */
			switch (new_position.time_domain ()) {
			case AudioTime:
				/* pos is already in superclocks */
				p = new_position;
				break;
			case BeatTime:
				/* determined sc at beat position so we can add superclocks */
				p = timepos_t (metric_at (new_position).sample_at (new_position.beats()));
				break;
			}
			/* add superclocks */
			p += duration;
			/* determine beats */
			b = metric_at (p).quarters_at_superclock (p.superclocks());
			/* return duration in beats */
			return timecnt_t (b - new_position.beats(), new_position);
			break;
		case BeatTime:
			/*NOTREACHED*/
			break;
		}
		break;
	}

	/*NOTREACHED*/
	abort ();
	/*NOTREACHED*/

	return timecnt_t::from_superclock (0);

}


uint32_t
TempoMap::n_meters () const
{
	return _meters.size();
}

uint32_t
TempoMap::n_tempos () const
{
	return _tempos.size();
}

void
TempoMap::insert_time (timepos_t const & pos, timecnt_t const & duration)
{
	assert (!_tempos.empty());
	assert (!_meters.empty());

	if (pos == std::numeric_limits<timepos_t>::min()) {
		/* can't insert time at the front of the map: those entries are fixed */
		return;
	}

	Tempos::iterator     t (_tempos.begin());
	Meters::iterator     m (_meters.begin());
	MusicTimes::iterator b (_bartimes.begin());

	TempoPoint current_tempo = *t;
	MeterPoint current_meter = *m;
	MusicTimePoint current_time_point (*this, 0, Beats(), BBT_Time(), current_tempo, current_meter);

	if (_bartimes.size() > 0) {
		current_time_point = *b;
	}

	superclock_t sc;
	Beats beats;
	BBT_Time bbt;

	/* set these to true so that we set current_* on our first pass
	 * through the while loop(s)
	 */

	bool moved_tempo = true;
	bool moved_meter = true;
	bool moved_bartime = true;

	switch (duration.time_domain()) {
	case AudioTime:
		sc = pos.superclocks();

		/* handle a common case quickly */

		if ((_tempos.size() < 2 || sc > _tempos.back().sclock()) &&
		    (_meters.size() < 2 || sc > _meters.back().sclock()) &&
		    (_bartimes.size() < 2 || (_bartimes.empty() || sc > _bartimes.back().sclock()))) {

			/* only one tempo, plus one meter and zero or
			   one bartimes, or insertion point is after last
			   item. nothing to do here.
			*/

			return;
		}

		/* advance fundamental iterators to correct position */

		while (t != _tempos.end()   && t->sclock() < sc) ++t;
		while (m != _meters.end()   && m->sclock() < sc) ++m;
		while (b != _bartimes.end() && b->sclock() < sc) ++b;

		while (t != _tempos.end() && m != _meters.end() && b != _bartimes.end()) {

			if (moved_tempo && t != _tempos.end()) {
				current_tempo = *t;
				moved_tempo = false;
			}
			if (moved_meter && m != _meters.end()) {
				current_meter = *m;
				moved_meter = false;
			}
			if (moved_bartime && b != _bartimes.end()) {
				current_time_point = *b;
				moved_bartime = false;
			}

			/* for each of t, m and b:

			   if the point is earlier than the other two,
			   recompute the superclock, beat and bbt
			   positions, and reset the point.
			*/

			if (t->sclock() < m->sclock() && t->sclock() < b->sclock()) {

				sc = t->sclock() + duration.superclocks();
				beats = current_tempo.quarters_at_superclock (sc);
				/* round tempo to beats */
				beats = beats.round_to_beat ();
				sc = current_tempo.superclock_at (beats);
				bbt = current_meter.bbt_at (beats);

				t->set (sc, beats, bbt);
				++t;
				moved_tempo = true;
			}

			if (m->sclock() < t->sclock() && m->sclock() < b->sclock()) {

				sc = m->sclock() + duration.superclocks();
				beats = current_tempo.quarters_at_superclock (sc);
				/* round meter to bars */
				bbt = current_meter.bbt_at (beats);
				beats = current_meter.quarters_at (current_meter.round_to_bar(bbt));
				/* recompute */
				sc = current_tempo.superclock_at (beats);

				m->set (sc, beats, bbt);
				++m;
				moved_meter = true;
			}

			if (b->sclock() < t->sclock() && b->sclock() < m->sclock()) {

				sc = b->sclock() + duration.superclocks();
				beats = current_tempo.quarters_at_superclock (sc);
				/* round bartime to beats */
				beats = beats.round_to_beat();
				sc = current_tempo.superclock_at (beats);
				bbt = current_meter.bbt_at (beats);

				m->set (sc, beats, bbt);
				++m;
				moved_meter = true;
			}

		}
		break;

	case BeatTime:
		break;
	}
}

bool
TempoMap::remove_time (timepos_t const & pos, timecnt_t const & duration)
{
	superclock_t start (pos.superclocks());
	superclock_t end ((pos + duration).superclocks());
	superclock_t shift (duration.superclocks());

	TempoPoint* last_tempo = 0;
	MeterPoint* last_meter = 0;
	TempoPoint* tempo_after = 0;
	MeterPoint* meter_after = 0;

	bool moved = false;

	for (Tempos::iterator t = _tempos.begin(); t != _tempos.end(); ) {

		if (t->sclock() >= start && t->sclock() < end) {

			last_tempo = &*t;
			t = _tempos.erase (t);
			moved = true;

		} else if (t->sclock() >= start) {
			t->set (t->sclock() - shift, t->beats(), t->bbt());
			moved = true;
			if (t->sclock() == start) {
				tempo_after = &*t;
			}
			++t;
		}
	}

	for (Meters::iterator m = _meters.begin(); m != _meters.end(); ) {

		if (m->sclock() >= start && m->sclock() < end) {

			last_meter = &*m;
			m = _meters.erase (m);
			moved = true;

		} else if (m->sclock() >= start) {
			m->set (m->sclock() - shift, m->beats(), m->bbt());
			moved = true;
			if (m->sclock() == start) {
				meter_after = &*m;
			}
			++m;
		}
	}

	if (last_tempo && !tempo_after) {
		last_tempo->set (start, last_tempo->beats(), last_tempo->bbt());
		moved = true;
	}

	if (last_meter && !meter_after) {
		last_tempo->set (start, last_meter->beats(), last_meter->bbt());
		moved = true;
	}

	if (moved) {
		reset_starting_at (start);
	}

	return moved;
}

TempoPoint const *
TempoMap::next_tempo (TempoPoint const & t) const
{
	Tempos::const_iterator i = _tempos.iterator_to (t);
	++i;

	if (i != _tempos.end()) {
		return &(*i);
	}

	return 0;
}

TempoPoint const *
TempoMap::previous_tempo (TempoPoint const & point) const
{
	Tempos::const_iterator i = _tempos.iterator_to (point);

	if (i == _tempos.begin()) {
		return 0;
	}

	--i;

	return &(*i);
}

double
TempoMap::quarters_per_minute_at (timepos_t const & pos) const
{
	TempoPoint const & tp (tempo_at (pos));
	const double val = tp.note_types_per_minute_at_DOUBLE (pos) * (4.0 / tp.note_type());
	return val;
}


TempoPoint const &
TempoMap::tempo_at (timepos_t const & pos) const
{
	return pos.is_beats() ? tempo_at (pos.beats()) : tempo_at (pos.superclocks());
}

MeterPoint const &
TempoMap::meter_at (timepos_t const & pos) const
{
	return pos.is_beats() ? meter_at (pos.beats()) : meter_at (pos.superclocks());
}

TempoMetric
TempoMap::metric_at (timepos_t const & pos) const
{
	if (pos.is_beats()) {
		return metric_at (pos.beats());
	}

	return metric_at (pos.superclocks());
}

TempoMetric
TempoMap::metric_at (superclock_t sc, bool can_match) const
{
	TempoPoint const * tp = 0;
	MeterPoint const * mp = 0;

	(void) get_tempo_and_meter (tp, mp, sc, can_match, false);

	return TempoMetric (*tp,* mp);
}

TempoMetric
TempoMap::metric_at (Beats const & b, bool can_match) const
{
	TempoPoint const * tp = 0;
	MeterPoint const * mp = 0;

	(void) get_tempo_and_meter (tp, mp, b, can_match, false);

	return TempoMetric (*tp, *mp);
}

TempoMetric
TempoMap::metric_at (BBT_Time const & bbt, bool can_match) const
{
	TempoPoint const * tp = 0;
	MeterPoint const * mp = 0;

	(void) get_tempo_and_meter (tp, mp, bbt, can_match, false);

	return TempoMetric (*tp, *mp);
}

bool
TempoMap::set_ramped (TempoPoint & tp, bool yn)
{
	assert (!_tempos.empty());

	if (tp.ramped() == yn) {
		return false;
	}

	Tempos::iterator nxt = _tempos.begin();
	++nxt;

	for (Tempos::iterator t = _tempos.begin(); nxt != _tempos.end(); ++t, ++nxt) {
		if (tp == *t) {
			break;
		}
	}

	if (nxt == _tempos.end()) {
		return false;
	}

	if (yn) {
		tp.set_end_npm (nxt->end_note_types_per_minute());
	} else {
		tp.set_end_npm (tp.note_types_per_minute());
	}

	reset_starting_at (tp.sclock());

	return true;
}

bool
TempoMap::set_continuing (TempoPoint& tp, bool yn)
{
	if (!yn) {
		tp.set_continuing (false);
		return true; /* change made */
	}

	TempoPoint const * prev = previous_tempo (tp);

	if (!prev) {
		return false;
	}

	tp.set_note_types_per_minute (prev->note_types_per_minute());

	return true;
}

void
TempoMap::stretch_tempo (TempoPoint* ts, samplepos_t sample, samplepos_t end_sample, Beats const & start_qnote, Beats const & end_qnote)
{
	/*
	  Ts (future prev_t)   Tnext
	  |                    |
	  |     [drag^]        |
	  |----------|----------
	        e_f  qn_beats(sample)
	*/

	if (!ts) {
		return;
	}

	superclock_t start_sclock = samples_to_superclock (sample, TEMPORAL_SAMPLE_RATE);
	superclock_t end_sclock = samples_to_superclock (end_sample, TEMPORAL_SAMPLE_RATE);

	/* minimum allowed measurement distance in samples */
	const superclock_t min_delta_sclock = samples_to_superclock (2, TEMPORAL_SAMPLE_RATE);
	double new_bpm;

	if (ts->continuing()) {

		/* this tempo point is required to start using the same bpm
		 * that the previous tempo ended with.
		 */

		TempoPoint* next_t = const_cast<TempoPoint*> (next_tempo (*ts));
		TempoPoint* prev_to_ts = const_cast<TempoPoint*> (previous_tempo (*ts));
		assert (prev_to_ts);
		/* the change in samples is the result of changing the slope of at most 2 previous tempo sections.
		 * constant to constant is straightforward, as the tempo prev to ts has constant slope.
		 */
		double contribution = 0.0;
		if (next_t && prev_to_ts->ramped()) {
			const DoubleableBeats delta_tp = ts->beats() - prev_to_ts->beats();
			const DoubleableBeats delta_np = next_t->beats() - prev_to_ts->beats();
			contribution = delta_tp.to_double() / delta_np.to_double();
		}
		samplepos_t const fr_off = end_sclock - start_sclock;
		sampleoffset_t const ts_sample_contribution = fr_off - (contribution * (double) fr_off);

		if (start_sclock > prev_to_ts->sclock() + min_delta_sclock && (start_sclock + ts_sample_contribution) > prev_to_ts->sclock() + min_delta_sclock) {
			DoubleableBeats delta_sp = start_qnote - prev_to_ts->beats();
			DoubleableBeats delta_ep = end_qnote - prev_to_ts->beats();
			new_bpm = ts->note_types_per_minute() * (delta_sp.to_double() / delta_ep.to_double());
		} else {
			new_bpm = ts->note_types_per_minute();
		}

	} else {

		/* ts is free to have it's bpm changed to any value (within limits) */

		if (start_sclock > ts->sclock() + min_delta_sclock && end_sclock > ts->sclock() + min_delta_sclock) {
			new_bpm = ts->note_types_per_minute() * ((start_sclock - ts->sclock()) / (double) (end_sclock - ts->sclock()));
		} else {
			new_bpm = ts->note_types_per_minute();
		}

		new_bpm = std::min (new_bpm, 1000.0);
	}
	/* don't clamp and proceed here.
	   testing has revealed that this can go negative,
	   which is an entirely different thing to just being too low.
	*/

	if (new_bpm < 0.5) {
		return;
	}

	ts->set_note_types_per_minute (new_bpm);

	if (ts->continuing()) {
		TempoPoint* prev = 0;
		if ((prev = const_cast<TempoPoint*> (previous_tempo (*ts))) != 0) {
			prev->set_end_npm (ts->end_note_types_per_minute());
		}
	}

	reset_starting_at (ts->sclock() + 1);
}

void
TempoMap::stretch_tempo_end (TempoPoint* ts, samplepos_t sample, samplepos_t end_sample)
{
	/*
	  Ts (future prev_t)   Tnext
	  |                    |
	  |     [drag^]        |
	  |----------|----------
	        e_f  qn_beats(sample)
	*/

	if (!ts) {
		return;
	}

	const superclock_t start_sclock = samples_to_superclock (sample, TEMPORAL_SAMPLE_RATE);
	const superclock_t end_sclock = samples_to_superclock (end_sample, TEMPORAL_SAMPLE_RATE);

	TempoPoint * prev_t = const_cast<TempoPoint*> (previous_tempo (*ts));

	if (!prev_t) {
		return;
	}

	/* minimum allowed measurement distance in superclocks */
	const superclock_t min_delta_sclock = samples_to_superclock (2, TEMPORAL_SAMPLE_RATE);
	double new_bpm;

	if (start_sclock > prev_t->sclock() + min_delta_sclock && end_sclock > prev_t->sclock() + min_delta_sclock) {
		new_bpm = prev_t->end_note_types_per_minute() * ((prev_t->sclock() - start_sclock) / (double) (prev_t->sclock() - end_sclock));
	} else {
		new_bpm = prev_t->end_note_types_per_minute();
	}

	new_bpm = std::min (new_bpm, (double) 1000.0);

	if (new_bpm < 0.5) {
		return;
	}

	prev_t->set_end_npm (new_bpm);

	if (ts->continuing()) {
		ts->set_note_types_per_minute (prev_t->note_types_per_minute());
	}

	reset_starting_at (prev_t->sclock());
}
void
TempoMap::twist_tempi (TempoPoint* ts, samplepos_t start_sample, samplepos_t end_sample)
{
	if (!ts) {
		return;
	}

	TempoPoint* next_t = 0;
	TempoPoint* next_to_next_t = 0;

	/* minimum allowed measurement distance in superclocks */
	const superclock_t min_delta_sclock = samples_to_superclock (2, TEMPORAL_SAMPLE_RATE);
	const superclock_t start_sclock = samples_to_superclock (start_sample, TEMPORAL_SAMPLE_RATE);
	const superclock_t end_sclock = samples_to_superclock (end_sample, TEMPORAL_SAMPLE_RATE);

	TempoPoint* prev_t = 0;
	const superclock_t sclock_offset = end_sclock - start_sclock;


	if (ts->beats() > Beats()) {
		prev_t = const_cast<TempoPoint*> (previous_tempo (*ts));
	}

	next_t = const_cast<TempoPoint*> (next_tempo (*ts));

	if (!next_t) {
		return;
	}

	next_to_next_t = const_cast<TempoPoint*> (next_tempo (*next_t));

	if (!next_to_next_t) {
		return;
	}

	double prev_contribution = 0.0;

	if (next_t && prev_t && prev_t->type() == TempoPoint::Ramped) {
		prev_contribution = (ts->sclock() - prev_t->sclock()) / (double) (next_t->sclock() - prev_t->sclock());
	}

	const sampleoffset_t ts_sclock_contribution = sclock_offset - (prev_contribution * (double) sclock_offset);

	superclock_t old_tc_sclock = ts->sclock();
	superclock_t old_next_sclock = next_t->sclock();
	superclock_t old_next_to_next_sclock = next_to_next_t->sclock();

	double new_bpm;
	double new_next_bpm;
	double new_copy_end_bpm;

	if (start_sclock > ts->sclock() + min_delta_sclock && (start_sclock + ts_sclock_contribution) > ts->sclock() + min_delta_sclock) {
		new_bpm = ts->note_types_per_minute() * ((start_sclock - ts->sclock()) / (double) (end_sclock - ts->sclock()));
	} else {
		new_bpm = ts->note_types_per_minute();
	}

	/* don't clamp and proceed here.
	   testing has revealed that this can go negative,
	   which is an entirely different thing to just being too low.
	*/

	if (new_bpm < 0.5) {
		return;
	}

	new_bpm = std::min (new_bpm, (double) 1000.0);

	bool was_constant = (ts->type() == TempoPoint::Constant);

	ts->set_note_types_per_minute (new_bpm);

	if (was_constant) {
		ts->set_end_npm (new_bpm);
	}

	if (!next_t->actually_ramped()) {

		if (start_sclock > ts->sclock() + min_delta_sclock && end_sclock > ts->sclock() + min_delta_sclock) {
			new_next_bpm = next_t->note_types_per_minute() * ((next_to_next_t->sclock() - old_next_sclock) / (double) ((old_next_to_next_sclock) - old_next_sclock));
		} else {
			new_next_bpm = next_t->note_types_per_minute();
		}

		next_t->set_note_types_per_minute (new_next_bpm);

	} else {

		double next_sclock_ratio = 1.0;
		double copy_sclock_ratio = 1.0;

		if (next_to_next_t) {
			next_sclock_ratio = (next_to_next_t->sclock() - old_next_sclock) / (double) (old_next_to_next_sclock -  old_next_sclock);
			copy_sclock_ratio = ((old_tc_sclock - next_t->sclock()) / (double) (old_tc_sclock - old_next_sclock));
		}

		new_next_bpm = next_t->note_types_per_minute() * next_sclock_ratio;
		new_copy_end_bpm = ts->end_note_types_per_minute() * copy_sclock_ratio;

		ts->set_end_npm (new_copy_end_bpm);

		if (next_t->continuing()) {
			next_t->set_note_types_per_minute (new_copy_end_bpm);
		} else {
			next_t->set_note_types_per_minute (new_next_bpm);
		}

		ts->set_end_npm (new_copy_end_bpm);
	}

	reset_starting_at (ts->sclock());
}

void
TempoMap::init ()
{
	WritableSharedPtr new_map (new TempoMap (Tempo (120, 4), Meter (4, 4)));
	_map_mgr.init (new_map);
	fetch ();
}

TempoMap::WritableSharedPtr
TempoMap::write_copy()
{
	return _map_mgr.write_copy();
}

int
TempoMap::update (TempoMap::WritableSharedPtr m)
{
	if (!_map_mgr.update (m)) {
		return -1;
	}

	/* update thread local map pointer in the calling thread */
	update_thread_tempo_map ();

#ifndef NDEBUG
	if (DEBUG_ENABLED (DEBUG::TemporalMap)) {
		m->dump (std::cerr);
	}
#endif

	MapChanged (); /* EMIT SIGNAL */

	return 0;
}

void
TempoMap::abort_update ()
{
	/* drop lock taken by write_copy() */
	_map_mgr.abort ();
	/* update thread local map pointer in calling thread. Note that this
	   will reset _tempo_map_p, which is (almost guaranteed to be) the only
	   reference to the copy of the map made in ::write_copy(), so it will
	   be destroyed here.
	*/
	TempoMap::fetch ();
}

void
TempoMap::midi_clock_beat_at_or_after (samplepos_t const pos, samplepos_t& clk_pos, uint32_t& clk_beat) const
{
	/* Sequences are always assumed to start on a MIDI Beat of 0 (ie, the downbeat).
	 *
	 * There are 24 MIDI clock per quarter note (1 Temporal::Beat)
	 *
	 * from http://midi.teragonaudio.com/tech/midispec/seq.htm
	 */

	Temporal::Beats b = (quarters_at_sample (pos)).round_up_to_beat ();

	/* We cannot use
	 *    clk_pos = sample_at (b);
	 * because in this case we have to round up to the start
	 * of the next tick, not round to to the current tick.
	 * (compare to 14da117bc88)
	 */
	clk_pos = PBD::muldiv_round (superclock_at (b), TEMPORAL_SAMPLE_RATE, superclock_ticks_per_second ());
	clk_beat = b.get_beats () * 24;

	assert (clk_pos >= pos);
}

/******** OLD STATE LOADING CODE SECTION *************/

#if 0
static bool
bbt_time_to_string (const BBT_Time& bbt, std::string& str)
{
	char buf[256];
	int retval = snprintf (buf, sizeof(buf), "%" PRIu32 "|%" PRIu32 "|%" PRIu32, bbt.bars, bbt.beats,
	                       bbt.ticks);

	if (retval <= 0 || retval >= (int)sizeof(buf)) {
		return false;
	}

	str = buf;
	return true;
}
#endif

static bool
string_to_bbt_time (const std::string& str, BBT_Time& bbt)
{
	if (sscanf (str.c_str (), "%" PRIu32 "|%" PRIu32 "|%" PRIu32, &bbt.bars, &bbt.beats,
	            &bbt.ticks) == 3) {
		return true;
	}
	return false;
}

int
TempoMap::parse_tempo_state_3x (const XMLNode& node, LegacyTempoState& lts)
{
	BBT_Time bbt;
	std::string start_bbt;

	// _legacy_bbt.bars = 0; // legacy session check compars .bars != 0; default BBT_Time c'tor uses 1.

	if (node.get_property ("start", start_bbt)) {
		if (string_to_bbt_time (start_bbt, bbt)) {
			/* legacy session - start used to be in bbt*/
			// _legacy_bbt = bbt;
			// set_pulse(-1.0);
			info << _("Legacy session detected. TempoSection XML node will be altered.") << endmsg;
		}
	}

	/* position is the only data we extract from older XML */

	if (!node.get_property ("frame", lts.sample)) {
		error << _("Legacy tempo section XML does not have a \"frame\" node - map will be ignored") << endmsg;
		cerr << _("Legacy tempo section XML does not have a \"frame\" node - map will be ignored") << endl;
		return -1;
	}

	if (node.get_property ("beats-per-minute", lts.note_types_per_minute)) {
		if (lts.note_types_per_minute < 0.0) {
			error << _("TempoSection XML node has an illegal \"beats_per_minute\" value") << endmsg;
			return -1;
		}
	}

	if (!node.get_property ("note-type", lts.note_type)) {
		if (lts.note_type < 1.0) {
			error << _("TempoSection XML node has an illegal \"note-type\" value") << endmsg;
			return -1;
		}
	} else {
		/* older session, make note type be quarter by default */
		lts.note_type = 4.0;
	}

	/* older versions used "clamped" as the property name here */

	if (!node.get_property ("clamped", lts.continuing)) {
		lts.continuing = false;
	}

	if (node.get_property ("end-beats-per-minute", lts.end_note_types_per_minute)) {
		if (lts.end_note_types_per_minute < 0.0) {
			info << _("TempoSection XML node has an illegal \"end-beats-per-minute\" value") << endmsg;
			return -1;
		}
	}

	Tempo::Type old_type;
	if (node.get_property ("tempo-type", old_type)) {
		/* sessions with a tempo-type node contain no end-beats-per-minute.
		   if the legacy node indicates a constant tempo, simply fill this in with the
		   start tempo. otherwise we need the next neighbour to know what it will be.
		*/

		if (old_type == Tempo::Constant) {
			lts.end_note_types_per_minute = lts.note_types_per_minute;
		} else {
			lts.end_note_types_per_minute = -1.0;
		}
	}

	if (!node.get_property ("active", lts.active)) {
		warning << _("TempoSection XML node has no \"active\" property") << endmsg;
		lts.active = true;
	}

	return 0;
}

int
TempoMap::parse_meter_state_3x (const XMLNode& node, LegacyMeterState& lms)
{
	std::string bbt_str;
	if (node.get_property ("start", bbt_str)) {
		if (string_to_bbt_time (bbt_str, lms.bbt)) {
			/* legacy session - start used to be in bbt*/
			info << _("Legacy session detected - MeterSection XML node will be altered.") << endmsg;
			// set_pulse (-1.0);
		} else {
			error << _("MeterSection XML node has an illegal \"start\" value") << endmsg;
		}
	}

	/* position is the only data we extract from older XML */

	if (!node.get_property ("frame", lms.sample)) {
		error << _("Legacy tempo section XML does not have a \"frame\" node - map will be ignored") << endmsg;
		return -1;
	}

	if (!node.get_property ("beat", lms.beat)) {
		lms.beat = 0.0;
	}

	if (node.get_property ("bbt", bbt_str)) {
		if (!string_to_bbt_time (bbt_str, lms.bbt)) {
			error << _("MeterSection XML node has an illegal \"bbt\" value") << endmsg;
			return -1;
		}
	} else {
		warning << _("MeterSection XML node has no \"bbt\" property") << endmsg;
	}

	/* beats-per-bar is old; divisions-per-bar is new */

	if (!node.get_property ("divisions-per-bar", lms.divisions_per_bar)) {
		if (!node.get_property ("beats-per-bar", lms.divisions_per_bar)) {
			error << _("MeterSection XML node has no \"beats-per-bar\" or \"divisions-per-bar\" property") << endmsg;
			return -1;
		}
	}

	if (lms.divisions_per_bar < 0.0) {
		error << _("MeterSection XML node has an illegal \"divisions-per-bar\" value") << endmsg;
		return -1;
	}

	if (!node.get_property ("note-type", lms.note_type)) {
		error << _("MeterSection XML node has no \"note-type\" property") << endmsg;
		return -1;
	}

	if (lms.note_type < 0.0) {
		error << _("MeterSection XML node has an illegal \"note-type\" value") << endmsg;
		return -1;
	}

	return 0;
}

int
TempoMap::set_state_3x (const XMLNode& node)
{
	XMLNodeList nlist;
	XMLNodeConstIterator niter;

	nlist = node.children();

	/* Need initial tempo & meter points, because subsequent ones will use
	 * set_tempo() and set_meter() which require pre-existing data
	 */

	int32_t initial_tempo_index = -1;
	int32_t initial_meter_index = -1;
	int32_t index;
	bool need_points_clear = true;
	bool initial_tempo_at_zero = true;
	bool initial_meter_at_zero = true;

	for (niter = nlist.begin(), index = 0; niter != nlist.end(); ++niter, ++index) {
		XMLNode* child = *niter;

		if ((initial_tempo_index < 0) && (child->name() == Tempo::xml_node_name)) {

			LegacyTempoState lts;

			if (parse_tempo_state_3x (*child, lts)) {
				error << _("Tempo map: could not set new state, restoring old one.") << endmsg;
				break;
			}

			if (lts.sample != 0) {
				initial_tempo_at_zero = false;
			}

			Tempo t (lts.note_types_per_minute,
			         lts.end_note_types_per_minute,
			         lts.note_type);
			TempoPoint* tp = new TempoPoint (*this, t, samples_to_superclock (0, TEMPORAL_SAMPLE_RATE), Beats(), BBT_Time());

			tp->set_continuing (lts.continuing);

			_tempos.clear ();
			if (need_points_clear) {
				_points.clear ();
				need_points_clear = false;
			}
			_tempos.push_back (*tp);
			_points.push_back (*tp);
			initial_tempo_index = index;

		}

		if ((initial_meter_index < 0) && (child->name() == Meter::xml_node_name)) {

			LegacyMeterState lms;

			if (parse_meter_state_3x (*child, lms)) {
				error << _("Tempo map: could not use old meter state, restoring old one.") << endmsg;
				break;
			}

			if (lms.sample != 0) {
				initial_meter_at_zero = false;
			}

			Meter m (lms.divisions_per_bar, lms.note_type);
			MeterPoint *mp = new MeterPoint (*this, m, 0, Beats(), BBT_Time());
			_meters.clear();
			if (need_points_clear) {
				_points.clear ();
				need_points_clear = false;
			}
			_meters.push_back (*mp);
			_points.push_back (*mp);
			initial_meter_index = index;
		}

		if (initial_tempo_index >= 0 && initial_meter_index >= 0) {
			break;
		}
	}

	if (initial_tempo_index < 0 || initial_meter_index < 0) {
		error << _("Old tempo map information is missing either tempo or meter information - ignored") << endmsg;
		return -1;
	}

	for (niter = nlist.begin(), index = 0; niter != nlist.end(); ++niter, ++index) {
		XMLNode* child = *niter;

		if (child->name() == Tempo::xml_node_name) {

			LegacyTempoState lts;

			if (parse_tempo_state_3x (*child, lts)) {
				error << _("Tempo map: could not set new state, restoring old one.") << endmsg;
				break;
			}

			if (index == initial_tempo_index) {
				/* already added */
				continue;
			}
			if (index == initial_tempo_index) {
				if (!initial_tempo_at_zero) {
					/* already added */
					continue;
				}
			}

			Tempo t (lts.note_types_per_minute,
			         lts.end_note_types_per_minute,
			         lts.note_type);

			set_tempo (t, timepos_t (lts.sample));

		} else if (child->name() == Meter::xml_node_name) {

			LegacyMeterState lms;

			if (parse_meter_state_3x (*child, lms)) {
				error << _("Tempo map: could not use old meter state, restoring old one.") << endmsg;
				break;
			}

			if (index == initial_meter_index) {
				if (!initial_meter_at_zero) {
					/* Add a BBT point to fix the meter location */
					set_bartime (lms.bbt, timepos_t (lms.sample));
				} else {
					continue;
				}
			}

			Meter m (lms.divisions_per_bar, lms.note_type);
			set_meter (m, timepos_t (lms.sample));
		}
	}

#if 0
	/* check for legacy sessions where bbt was the base musical unit for tempo */
	for (Metrics::const_iterator i = _metrics.begin(); i != _metrics.end(); ++i) {
		TempoSection* t;
		if ((t = dynamic_cast<TempoSection*> (*i)) != 0) {
			if (t->legacy_bbt().bars != 0) {
				fix_legacy_session();
				break;
			}

			if (t->end_note_types_per_minute() < 0.0) {
				fix_legacy_end_session();
				break;
			}
		}
	}

	if (niter == nlist.end()) {
		MetricSectionSorter cmp;
		_metrics.sort (cmp);
	}
#endif
#if 0

	/* check for multiple tempo/meters at the same location, which
	   ardour2 somehow allowed.
	*/

	{
		Tempos::iterator prev = _tempos.end();
		for (Tempos::iterator i = _tempos.begin(); i != _tempos.end(); ++i) {
			if (prev != _tempos.end()) {
			MeterSection* ms;
			MeterSection* prev_m;
			TempoSection* ts;
			TempoSection* prev_t;
			if ((prev_m = dynamic_cast<MeterSection*>(*prev)) != 0 && (ms = dynamic_cast<MeterSection*>(*i)) != 0) {
				if (prev_m->beat() == ms->beat()) {
					error << string_compose (_("Multiple meter definitions found at %1"), prev_m->beat()) << endmsg;
					return -1;
				}
			} else if ((prev_t = dynamic_cast<TempoSection*>(*prev)) != 0 && (ts = dynamic_cast<TempoSection*>(*i)) != 0) {
				if (prev_t->pulse() == ts->pulse()) {
					error << string_compose (_("Multiple tempo definitions found at %1"), prev_t->pulse()) << endmsg;
					return -1;
				}
			}
		}
		prev = i;
	}
#endif

	return 0;
}



#if 0
void
TempoMap::fix_legacy_session ()
{
	MeterSection* prev_m = 0;
	TempoSection* prev_t = 0;
	bool have_initial_t = false;

	for (Metrics::iterator i = _metrics.begin(); i != _metrics.end(); ++i) {
		MeterSection* m;
		TempoSection* t;

		if ((m = dynamic_cast<MeterSection*>(*i)) != 0) {
			if (m->initial()) {
				pair<double, BBT_Time> bbt = make_pair (0.0, BBT_Time (1, 1, 0));
				m->set_beat (bbt);
				m->set_pulse (0.0);
				m->set_minute (0.0);
				m->set_position_lock_style (AudioTime);
				prev_m = m;
				continue;
			}
			if (prev_m) {
				pair<double, BBT_Time> start = make_pair (((m->bbt().bars - 1) * prev_m->note_divisor())
									  + (m->bbt().beats - 1)
									  + (m->bbt().ticks / BBT_Time::ticks_per_beat)
									  , m->bbt());
				m->set_beat (start);
				const double start_beat = ((m->bbt().bars - 1) * prev_m->note_divisor())
					+ (m->bbt().beats - 1)
					+ (m->bbt().ticks / BBT_Time::ticks_per_beat);
				m->set_pulse (start_beat / prev_m->note_divisor());
			}
			prev_m = m;
		} else if ((t = dynamic_cast<TempoSection*>(*i)) != 0) {

			if (!t->active()) {
				continue;
			}
			/* Ramp type never existed in the era of this tempo section */
			t->set_end_npm (t->note_types_per_minute());

			if (t->initial()) {
				t->set_pulse (0.0);
				t->set_minute (0.0);
				t->set_position_lock_style (AudioTime);
				prev_t = t;
				have_initial_t = true;
				continue;
			}

			if (prev_t) {
				/* some 4.x sessions have no initial (non-movable) tempo. */
				if (!have_initial_t) {
					prev_t->set_pulse (0.0);
					prev_t->set_minute (0.0);
					prev_t->set_position_lock_style (AudioTime);
					prev_t->set_initial (true);
					prev_t->set_locked_to_meter (true);
					have_initial_t = true;
				}

				const double beat = ((t->legacy_bbt().bars - 1) * ((prev_m) ? prev_m->note_divisor() : 4.0))
					+ (t->legacy_bbt().beats - 1)
					+ (t->legacy_bbt().ticks / BBT_Time::ticks_per_beat);
				if (prev_m) {
					t->set_pulse (beat / prev_m->note_divisor());
				} else {
					/* really shouldn't happen but.. */
					t->set_pulse (beat / 4.0);
				}
			}
			prev_t = t;
		}
	}
}
void
TempoMap::fix_legacy_end_session ()
{
	TempoSection* prev_t = 0;

	for (Metrics::iterator i = _metrics.begin(); i != _metrics.end(); ++i) {
		TempoSection* t;

		if ((t = dynamic_cast<TempoSection*>(*i)) != 0) {

			if (!t->active()) {
				continue;
			}

			if (prev_t) {
				if (prev_t->end_note_types_per_minute() < 0.0) {
					prev_t->set_end_npm (t->note_types_per_minute());
				}
			}

			prev_t = t;
		}
	}

	if (prev_t) {
		prev_t->set_end_npm (prev_t->note_types_per_minute());
	}
}

#endif

TempoCommand::TempoCommand (XMLNode const & node)
	: _before (0)
	, _after (0)
{
	if (!node.get_property (X_("name"), _name)) {
		throw failed_constructor();
	}

	XMLNodeList const & children (node.children());
	for (XMLNodeList::const_iterator n = children.begin(); n != children.end(); ++n) {
		if ((*n)->name() == X_("before")) {
			if ((*n)->children().empty()) {
				throw failed_constructor();
			}
			_before = new XMLNode (*(*n)->children().front());
		} else if ((*n)->name() == X_("after")) {
			if ((*n)->children().empty()) {
				throw failed_constructor();
			}
			_after = new XMLNode (*(*n)->children().front());
		}
	}

	if (!_before || !_after) {
		throw failed_constructor();
	}
}

TempoCommand::TempoCommand (std::string const & str, XMLNode const * before, XMLNode const * after)
	: _name (str)
	, _before (before)
	, _after (after)
{

}

TempoCommand::~TempoCommand ()
{
	delete _before;
	delete _after;
}

XMLNode&
TempoCommand::get_state() const
{
	XMLNode* node = new XMLNode (X_("TempoCommand"));
	node->set_property (X_("name"), _name);

	if (_before) {
		XMLNode* b = new XMLNode (X_("before"));
		b->add_child_copy (*_before);
		node->add_child_nocopy (*b);
	}

	if (_after) {
		XMLNode* a = new XMLNode (X_("after"));
		a->add_child_copy (*_after);
		node->add_child_nocopy (*a);
	}

	return *node;
}

void
TempoCommand::undo ()
{
	if (!_before) {
		return;
	}

	TempoMap::WritableSharedPtr map (TempoMap::write_copy());
	map->set_state (*_before, Stateful::current_state_version);
	TempoMap::update (map);
}

void
TempoCommand::operator() ()
{
	if (!_after) {
		return;
	}

	TempoMap::WritableSharedPtr map (TempoMap::write_copy());
	map->set_state (*_after, Stateful::current_state_version);
	TempoMap::update (map);
}