ardour/libs/evoral/ControlList.cc

/*
 * Copyright (C) 2008-2009 Hans Baier <hansfbaier@googlemail.com>
 * Copyright (C) 2008-2012 Carl Hetherington <carl@carlh.net>
 * Copyright (C) 2008-2015 David Robillard <d@drobilla.net>
 * Copyright (C) 2010-2017 Paul Davis <paul@linuxaudiosystems.com>
 * Copyright (C) 2014-2018 Robin Gareus <robin@gareus.org>
 * Copyright (C) 2014 Ben Loftis <ben@harrisonconsoles.com>
 * Copyright (C) 2015 Nick Mainsbridge <mainsbridge@gmail.com>
 *
 * 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.,
 * 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
 */

#include <cmath>

#ifdef COMPILER_MSVC
#include <float.h>

// 'std::isnan()' is not available in MSVC.
#define isnan_local(val) (bool)_isnan((double)val)
#else
#define isnan_local std::isnan
#endif

#define GUARD_POINT_DELTA Temporal::timecnt_t (64)

#include <cassert>
#include <cmath>
#include <iostream>
#include <utility>

#include "evoral/ControlList.h"
#include "evoral/Curve.h"
#include "evoral/ParameterDescriptor.h"
#include "evoral/TypeMap.h"
#include "evoral/types.h"

#include "pbd/control_math.h"
#include "pbd/compose.h"
#include "pbd/error.h"
#include "pbd/i18n.h"
#include "pbd/debug.h"

using namespace std;
using namespace PBD;
using namespace Temporal;

namespace Evoral {

inline bool event_time_less_than (ControlEvent* a, ControlEvent* b)
{
	return a->when < b->when;
}

ControlList::ControlList (const Parameter& id, const ParameterDescriptor& desc, TimeDomain ts)
	: _parameter(id)
	, _desc(desc)
	, _interpolation (default_interpolation ())
	, _time_domain (ts)
	, _curve(0)
{
	_frozen = 0;
	_changed_when_thawed = false;
	_lookup_cache.left = timepos_t::max (_time_domain);
	_lookup_cache.range.first = _events.end();
	_lookup_cache.range.second = _events.end();
	_search_cache.left = timepos_t::max (_time_domain);
	_search_cache.first = _events.end();
	_sort_pending = false;
	new_write_pass = true;
	_in_write_pass = false;
	did_write_during_pass = false;
	insert_position = timepos_t::max (_time_domain);
	most_recent_insert_iterator = _events.end();
}

ControlList::ControlList (const ControlList& other)
	: _parameter(other._parameter)
	, _desc(other._desc)
	, _interpolation(other._interpolation)
	, _time_domain (other._time_domain)
	, _curve(0)
{
	_frozen = 0;
	_changed_when_thawed = false;
	_lookup_cache.range.first = _events.end();
	_lookup_cache.range.second = _events.end();
	_search_cache.first = _events.end();
	_sort_pending = false;
	new_write_pass = true;
	_in_write_pass = false;
	did_write_during_pass = false;
	insert_position = timepos_t::max (_time_domain);
	most_recent_insert_iterator = _events.end();

	// XXX copy_events() emits Dirty, but this is just assignment copy/construction
	copy_events (other);
}

ControlList::ControlList (const ControlList& other, timepos_t const & start, timepos_t const & end)
	: _parameter(other._parameter)
	, _desc(other._desc)
	, _interpolation(other._interpolation)
	, _time_domain (other._time_domain)
	, _curve(0)
{
	_frozen = 0;
	_changed_when_thawed = false;
	_lookup_cache.range.first = _events.end();
	_lookup_cache.range.second = _events.end();
	_search_cache.first = _events.end();
	_sort_pending = false;

	/* now grab the relevant points, and shift them back if necessary */

	boost::shared_ptr<ControlList> section = const_cast<ControlList*>(&other)->copy (start, end);

	if (!section->empty()) {
		// XXX copy_events() emits Dirty, but this is just assignment copy/construction
		copy_events (*(section.get()));
	}

	new_write_pass = true;
	_in_write_pass = false;
	did_write_during_pass = false;
	insert_position = timepos_t::max (_time_domain);
	most_recent_insert_iterator = _events.end();

	mark_dirty ();
}

ControlList::~ControlList()
{
	for (EventList::iterator x = _events.begin(); x != _events.end(); ++x) {
		delete (*x);
	}
	_events.clear ();

	delete _curve;
}

boost::shared_ptr<ControlList>
ControlList::create(const Parameter& id, const ParameterDescriptor& desc, TimeDomain time_style)
{
	return boost::shared_ptr<ControlList>(new ControlList(id, desc, time_style));
}

bool
ControlList::operator== (const ControlList& other)
{
	return _events == other._events;
}

ControlList&
ControlList::operator= (const ControlList& other)
{
	if (this != &other) {
		/* list should be frozen before assignment */
		assert (_frozen > 0);
		_changed_when_thawed = false;
		_sort_pending = false;

		insert_position = other.insert_position;
		new_write_pass = true;
		_in_write_pass = false;
		did_write_during_pass = false;
		insert_position = timepos_t::max (_time_domain);

		_parameter = other._parameter;
		_desc = other._desc;
		_interpolation = other._interpolation;

		copy_events (other);
	}

	return *this;
}

void
ControlList::copy_events (const ControlList& other)
{
	{
		Glib::Threads::RWLock::WriterLock lm (_lock);
		for (EventList::iterator x = _events.begin(); x != _events.end(); ++x) {
			delete (*x);
		}
		_events.clear ();
		Glib::Threads::RWLock::ReaderLock olm (other._lock);
		for (const_iterator i = other.begin(); i != other.end(); ++i) {
			_events.push_back (new ControlEvent ((*i)->when, (*i)->value));
		}
		unlocked_invalidate_insert_iterator ();
		mark_dirty ();
	}
	maybe_signal_changed ();
}

void
ControlList::create_curve()
{
	_curve = new Curve(*this);
}

void
ControlList::destroy_curve()
{
	delete _curve;
	_curve = NULL;
}

ControlList::InterpolationStyle
ControlList::default_interpolation () const
{
	if (_desc.toggled) {
		return Discrete;
	} else if (_desc.logarithmic) {
		return Logarithmic;
	}
	return Linear;
}

void
ControlList::maybe_signal_changed ()
{
	if (_frozen) {
		_changed_when_thawed = true;
	} else {
		Dirty (); /* EMIT SIGNAL */
	}
}

void
ControlList::clear ()
{
	{
		Glib::Threads::RWLock::WriterLock lm (_lock);
		for (EventList::iterator x = _events.begin(); x != _events.end(); ++x) {
			delete (*x);
		}
		_events.clear ();
		unlocked_invalidate_insert_iterator ();
		mark_dirty ();
	}

	maybe_signal_changed ();
}

void
ControlList::x_scale (ratio_t const & factor)
{
	Glib::Threads::RWLock::WriterLock lm (_lock);
	_x_scale (factor);
}

timepos_t
ControlList::ensure_time_domain (timepos_t const & val) const
{
	if (val.time_domain() != _time_domain) {
		switch (_time_domain) {
		case Temporal::AudioTime:
			return timepos_t (val.samples());
			break;
		case Temporal::BeatTime:
			return timepos_t (val.beats());
			break;
		}
	}
	return val;
}

bool
ControlList::extend_to (timepos_t const & end)
{
	timepos_t actual_end = ensure_time_domain (end);

	Glib::Threads::RWLock::WriterLock lm (_lock);

	if (_events.empty() || _events.back()->when == actual_end) {
		return false;
	}

	ratio_t factor (actual_end.val(), _events.back()->when.val());
	_x_scale (factor);

	return true;
}

void
ControlList::y_transform (boost::function<double(double)> callback)
{
	{
		Glib::Threads::RWLock::WriterLock lm (_lock);
		for (iterator i = _events.begin(); i != _events.end(); ++i) {
			(*i)->value = callback ((*i)->value);
		}
		mark_dirty ();
	}
	maybe_signal_changed ();
}

void
ControlList::list_merge (ControlList const& other, boost::function<double(double, double)> callback)
{
	{
		Glib::Threads::RWLock::WriterLock lm (_lock);
		EventList nel;
		/* First scale existing events, copy into a new list.
		 * The original list is needed later to interpolate
		 * for new events only present in the master list.
		 */
		for (iterator i = _events.begin(); i != _events.end(); ++i) {
			float val = callback ((*i)->value, other.eval ((*i)->when));
			nel.push_back (new ControlEvent ((*i)->when , val));
		}
		/* Now add events which are only present in the master-list. */
		const EventList& evl (other.events());
		for (const_iterator i = evl.begin(); i != evl.end(); ++i) {
			bool found = false;
			// TODO: optimize, remember last matching iterator (lists are sorted)
			for (iterator j = _events.begin(); j != _events.end(); ++j) {
				if ((*i)->when == (*j)->when) {
					found = true;
					break;
				}
			}
			/* skip events that have already been merge in the first pass */
			if (found) {
				continue;
			}
			float val = callback (unlocked_eval ((*i)->when), (*i)->value);
			nel.push_back (new ControlEvent ((*i)->when, val));
		}
		nel.sort (event_time_less_than);

		for (EventList::iterator x = _events.begin(); x != _events.end(); ++x) {
			delete (*x);
		}
		_events.clear ();
		_events = nel;

		unlocked_remove_duplicates ();
		unlocked_invalidate_insert_iterator ();
		mark_dirty ();
	}
	maybe_signal_changed ();
}

void
ControlList::_x_scale (ratio_t const & factor)
{
	for (iterator i = _events.begin(); i != _events.end(); ++i) {
		(*i)->when = (*i)->when.scale (factor);
	}

	mark_dirty ();
}

struct ControlEventTimeComparator {
	bool operator() (ControlEvent* a, ControlEvent* b) {
		return a->when < b->when;
	}
};

void
ControlList::thin (double thinning_factor)
{
	if (thinning_factor == 0.0 || _desc.toggled) {
		return;
	}

	assert (is_sorted ());

	bool changed = false;

	{
		Glib::Threads::RWLock::WriterLock lm (_lock);

		ControlEvent* prevprev = 0;
		ControlEvent* cur = 0;
		ControlEvent* prev = 0;
		iterator pprev;
		int counter = 0;

		DEBUG_TRACE (DEBUG::ControlList, string_compose ("@%1 thin from %2 events\n", this, _events.size()));

		for (iterator i = _events.begin(); i != _events.end(); ++i) {

			cur = *i;
			counter++;

			if (counter > 2) {

				/* compute the area of the triangle formed by 3 points
				 */

				const double ppw = prevprev->when.val();
				const double pw = prev->when.val();
				const double cw = cur->when.val();

				double area = fabs ((ppw * (prev->value - cur->value)) +
						    (pw * (cur->value - prevprev->value)) +
						    (cw * (prevprev->value - prev->value)));

				if (area < thinning_factor) {
					iterator tmp = pprev;

					/* pprev will change to current
					   i is incremented to the next event
					   as we loop.
					*/

					pprev = i;
					_events.erase (tmp);
					changed = true;
					continue;
				}
			}

			prevprev = prev;
			prev = cur;
			pprev = i;
		}

		DEBUG_TRACE (DEBUG::ControlList, string_compose ("@%1 thin => %2 events\n", this, _events.size()));

		if (changed) {
			unlocked_invalidate_insert_iterator ();
			mark_dirty ();
		}
	}

	if (changed) {
		maybe_signal_changed ();
	}
}

void
ControlList::fast_simple_add (timepos_t const & time, double value)
{
	Glib::Threads::RWLock::WriterLock lm (_lock);
	/* to be used only for loading pre-sorted data from saved state */

	_events.insert (_events.end(), new ControlEvent (ensure_time_domain (time), value));

	mark_dirty ();
	if (_frozen) {
		_sort_pending = true;
	}
}

void
ControlList::invalidate_insert_iterator ()
{
	Glib::Threads::RWLock::WriterLock lm (_lock);
	unlocked_invalidate_insert_iterator ();
}

void
ControlList::unlocked_invalidate_insert_iterator ()
{
	most_recent_insert_iterator = _events.end();
}

void
ControlList::unlocked_remove_duplicates ()
{
	if (_events.size() < 2) {
		return;
	}
	iterator i = _events.begin();
	iterator prev = i++;
	while (i != _events.end()) {
		if ((*prev)->when == (*i)->when && (*prev)->value == (*i)->value) {
			i = _events.erase (i);
		} else {
			++prev;
			++i;
		}
	}
}

void
ControlList::start_write_pass (timepos_t const & time)
{
	Glib::Threads::RWLock::WriterLock lm (_lock);
	timepos_t when = ensure_time_domain (time);

	DEBUG_TRACE (DEBUG::ControlList, string_compose ("%1: setup write pass @ %2\n", this, when));

	insert_position = when;

	/* leave the insert iterator invalid, so that we will do the lookup
	   of where it should be in a "lazy" way - deferring it until
	   we actually add the first point (which may never happen).
	*/

	unlocked_invalidate_insert_iterator ();

	/* except if we're already in an active write-pass.
	 *
	 * invalid iterator == end() the iterator is set to the correct
	 * position in ControlList::add IFF (_in_write_pass && new_write_pass)
	 */
	if (_in_write_pass && !new_write_pass) {
#if 1
		add_guard_point (when, timecnt_t (_time_domain)); // also sets most_recent_insert_iterator
#else
		const ControlEvent cp (when, 0.0);
		most_recent_insert_iterator = lower_bound (_events.begin(), _events.end(), &cp, time_comparator);
#endif
	}
}

void
ControlList::write_pass_finished (timepos_t const & /*when*/, double thinning_factor)
{
	DEBUG_TRACE (DEBUG::ControlList, "write pass finished\n");

	if (did_write_during_pass) {
		thin (thinning_factor);
		did_write_during_pass = false;
	}
	new_write_pass = true;
	_in_write_pass = false;
}

void
ControlList::set_in_write_pass (bool yn, bool add_point, timepos_t when)
{
	DEBUG_TRACE (DEBUG::ControlList, string_compose ("set_in_write_pass: in-write: %1 @ %2 add point? %3\n", yn, when, add_point));

	_in_write_pass = yn;

	if (yn && add_point) {
		Glib::Threads::RWLock::WriterLock lm (_lock);
		add_guard_point (when, timecnt_t (_time_domain));
	}
}

void
ControlList::add_guard_point (timepos_t const & time, timecnt_t const & offset)
{
	/* we do not convert this yet */
	assert (offset.time_domain() == _time_domain);

	timepos_t when = ensure_time_domain (time);

	// caller needs to hold writer-lock

	if (offset.is_negative() && when < offset) {
		return;
	}

	if (offset.is_negative()) {
		/* check if there are points between when + offset .. when */
		ControlEvent cp (when + offset, 0.0);
		iterator s;
		iterator e;
		if ((s = lower_bound (_events.begin(), _events.end(), &cp, time_comparator)) != _events.end()) {
			cp.when = when;
			e = lower_bound (_events.begin(), _events.end(), &cp, time_comparator);
			if (s != e) {
				DEBUG_TRACE (DEBUG::ControlList, string_compose ("@%1 add_guard_point, none added, found event between %2 and %3\n", this, when.earlier (offset), when));
				return;
			}
		}
	} else {
		/* check if there are points between when + offset .. when */
		ControlEvent cp (when + offset, 0.0);
		iterator s;
		iterator e;
		if ((s = upper_bound (_events.begin(), _events.end(), &cp, time_comparator)) != _events.end()) {
			cp.when = when;
			e = upper_bound (_events.begin(), _events.end(), &cp, time_comparator);
			if (s != e) {
				DEBUG_TRACE (DEBUG::ControlList, string_compose ("@%1 add_guard_point, none added, found event between %2 and %3\n", this, when.earlier (offset), when));
				return;
			}
		}
	}

	/* don't do this again till the next write pass,
	 * unless we're not in a write-pass (transport stopped)
	 */
	if (_in_write_pass && new_write_pass) {
		WritePassStarted (); /* EMIT SIGNAL w/WriteLock */
		new_write_pass = false;
	}

	when += offset;

	ControlEvent cp (when, 0.0);
	most_recent_insert_iterator = lower_bound (_events.begin(), _events.end(), &cp, time_comparator);

	double eval_value = unlocked_eval (when);

	if (most_recent_insert_iterator == _events.end()) {

		DEBUG_TRACE (DEBUG::ControlList, string_compose ("@%1 insert iterator at end, adding eval-value there %2\n", this, eval_value));
		_events.push_back (new ControlEvent (when, eval_value));
		/* leave insert iterator at the end */

	} else if ((*most_recent_insert_iterator)->when == when) {

		DEBUG_TRACE (DEBUG::ControlList, string_compose ("@%1 insert iterator at existing point, setting eval-value there %2\n", this, eval_value));

		/* most_recent_insert_iterator points to a control event
		   already at the insert position, so there is
		   nothing to do.

		   ... except ...

		   advance most_recent_insert_iterator so that the "real"
		   insert occurs in the right place, since it
		   points to the control event just inserted.
		*/

		++most_recent_insert_iterator;
	} else {

		/* insert a new control event at the right spot */

		DEBUG_TRACE (DEBUG::ControlList, string_compose ("@%1 insert eval-value %2 just before iterator @ %3\n",
								 this, eval_value, (*most_recent_insert_iterator)->when));

		most_recent_insert_iterator = _events.insert (most_recent_insert_iterator, new ControlEvent (when, eval_value));

		/* advance most_recent_insert_iterator so that the "real"
		 * insert occurs in the right place, since it
		 * points to the control event just inserted.
		 */

		++most_recent_insert_iterator;
	}
}

bool
ControlList::in_write_pass () const
{
	return _in_write_pass;
}

bool
ControlList::editor_add (timepos_t const & time, double value, bool with_guard)
{
	/* this is for making changes from a graphical line editor */
	{
		Glib::Threads::RWLock::WriterLock lm (_lock);
		timepos_t when = ensure_time_domain (time);

		ControlEvent cp (when, 0.0f);
		iterator i = lower_bound (_events.begin(), _events.end(), &cp, time_comparator);

		if (i != _events.end () && (*i)->when == when) {
			return false;
		}

		/* clamp new value to allowed range */
		value = std::min ((double)_desc.upper, std::max ((double)_desc.lower, value));

		if (_events.empty()) {

			/* as long as the point we're adding is not at zero,
			 * add an "anchor" point there.
			 */

			if (when >= 1) {
				_events.insert (_events.end(), new ControlEvent (timepos_t (_time_domain), value));
				DEBUG_TRACE (DEBUG::ControlList, string_compose ("@%1 added value %2 at zero\n", this, value));
			}
		}

		insert_position = when;
		if (with_guard) {
			add_guard_point (when, -GUARD_POINT_DELTA);
			maybe_add_insert_guard (when);
			i = lower_bound (_events.begin(), _events.end(), &cp, time_comparator);
		}

		iterator result;
		DEBUG_TRACE (DEBUG::ControlList, string_compose ("editor_add: actually add when= %1 value= %2\n", when, value));
		result = _events.insert (i, new ControlEvent (when, value));

		if (i == result) {
			return false;
		}

		mark_dirty ();
	}
	maybe_signal_changed ();

	return true;
}

void
ControlList::maybe_add_insert_guard (timepos_t const & time)
{
	timepos_t when = ensure_time_domain (time);
	// caller needs to hold writer-lock
	if (most_recent_insert_iterator != _events.end()) {
		if ((*most_recent_insert_iterator)->when.earlier (when) > GUARD_POINT_DELTA) {
			/* Next control point is some distance from where our new point is
			   going to go, so add a new point to avoid changing the shape of
			   the line too much.  The insert iterator needs to point to the
			   new control point so that our insert will happen correctly. */
			most_recent_insert_iterator = _events.insert ( most_recent_insert_iterator,
					new ControlEvent (when + GUARD_POINT_DELTA, (*most_recent_insert_iterator)->value));

			DEBUG_TRACE (DEBUG::ControlList, string_compose ("@%1 added insert guard point @ %2 = %3\n",
			                                                 this, when + GUARD_POINT_DELTA,
			                                                 (*most_recent_insert_iterator)->value));
		}
	}
}

/** If we would just be adding to a straight line, move the previous point instead. */
bool
ControlList::maybe_insert_straight_line (timepos_t const & time, double value)
{
	timepos_t when = ensure_time_domain (time);

	// caller needs to hold writer-lock
	if (_events.empty()) {
		return false;
	}

	if (_events.back()->value == value) {
		// Point b at the final point, which we know exists
		EventList::iterator b = _events.end();
		--b;
		if (b == _events.begin()) {
			return false;  // No previous point
		}

		// Check the previous point's value
		--b;
		if ((*b)->value == value) {
			/* At least two points with the exact same value (straight
			   line), just move the final point to the new time. */
			_events.back()->when = when;
			DEBUG_TRACE (DEBUG::ControlList, string_compose ("final value of %1 moved to %2\n", value, when));
			return true;
		}
	}
	return false;
}

ControlList::iterator
ControlList::erase_from_iterator_to (iterator iter, timepos_t const & time)
{
	timepos_t when = ensure_time_domain (time);

	// caller needs to hold writer-lock
	while (iter != _events.end()) {
		if ((*iter)->when < when) {
			DEBUG_TRACE (DEBUG::ControlList, string_compose ("@%1 erase existing @ %2\n", this, (*iter)->when));
			delete *iter;
			iter = _events.erase (iter);
			continue;
		} else if ((*iter)->when >= when) {
			break;
		}
		++iter;
	}
	return iter;
}

/* this is for making changes from some kind of user interface or
 * control surface (GUI, MIDI, OSC etc)
 */
void
ControlList::add (timepos_t const & time, double value, bool with_guards, bool with_initial)
{
	timepos_t when = ensure_time_domain (time);

	/* clamp new value to allowed range */
	value = std::min ((double)_desc.upper, std::max ((double)_desc.lower, value));

	DEBUG_TRACE (DEBUG::ControlList,
	             string_compose ("@%1 add %2 at %3 guards = %4 write pass = %5 (new? %6) at end? %7\n",
	                             this, value, when, with_guards, _in_write_pass, new_write_pass,
	                             (most_recent_insert_iterator == _events.end())));
	{
		Glib::Threads::RWLock::WriterLock lm (_lock);
		ControlEvent cp (when, 0.0f);
		iterator insertion_point;

		if (_events.empty() && with_initial) {

			/* empty: add an "anchor" point if the point we're adding past time 0 */

			if (when >= 1) {
				if (_desc.toggled) {
					const double opp_val = ((value >= 0.5) ? 1.0 : 0.0);
					_events.insert (_events.end(), new ControlEvent (timepos_t (_time_domain), opp_val));
					DEBUG_TRACE (DEBUG::ControlList, string_compose ("@%1 added toggled value %2 at zero\n", this, opp_val));

				} else {
					_events.insert (_events.end(), new ControlEvent (timepos_t (_time_domain), value));
					DEBUG_TRACE (DEBUG::ControlList, string_compose ("@%1 added default value %2 at zero\n", this, _desc.normal));
				}
			}
		}

		if (_in_write_pass && new_write_pass) {

			/* first write in a write pass: add guard point if requested */

			if (with_guards) {
				add_guard_point (insert_position, timecnt_t (_time_domain));
				did_write_during_pass = true;
			} else {
				/* not adding a guard, but we need to set iterator appropriately */
				const ControlEvent cp (when, 0.0);
				most_recent_insert_iterator = lower_bound (_events.begin(), _events.end(), &cp, time_comparator);
			}
			WritePassStarted (); /* EMIT SIGNAL w/WriteLock */
			new_write_pass = false;

		} else if (_in_write_pass &&
		           (most_recent_insert_iterator == _events.end() || when > (*most_recent_insert_iterator)->when)) {

			/* in write pass: erase from most recent insert to now */

			if (most_recent_insert_iterator != _events.end()) {
				/* advance to avoid deleting the last inserted point itself. */
				++most_recent_insert_iterator;
			}

			if (with_guards) {
				most_recent_insert_iterator = erase_from_iterator_to (most_recent_insert_iterator, when + GUARD_POINT_DELTA);
				maybe_add_insert_guard (when);
			} else {
				most_recent_insert_iterator = erase_from_iterator_to(most_recent_insert_iterator, when);
			}

		} else if (!_in_write_pass) {

			/* not in a write pass: figure out the iterator we should insert in front of */

			DEBUG_TRACE (DEBUG::ControlList, string_compose ("compute(b) MRI for position %1\n", when));
			ControlEvent cp (when, 0.0f);
			most_recent_insert_iterator = lower_bound (_events.begin(), _events.end(), &cp, time_comparator);
		}

		/* OK, now we're really ready to add a new point */

		if (most_recent_insert_iterator == _events.end()) {
			DEBUG_TRACE (DEBUG::ControlList, string_compose ("@%1 appending new point at end\n", this));

			const bool done = maybe_insert_straight_line (when, value);
			if (!done) {
				_events.push_back (new ControlEvent (when, value));
				DEBUG_TRACE (DEBUG::ControlList, string_compose ("\tactually appended, size now %1\n", _events.size()));
			}

			most_recent_insert_iterator = _events.end();
			--most_recent_insert_iterator;

		} else if ((*most_recent_insert_iterator)->when == when) {

			if ((*most_recent_insert_iterator)->value != value) {
				DEBUG_TRACE (DEBUG::ControlList, string_compose ("@%1 reset existing point to new value %2\n", this, value));

				/* only one point allowed per time point, so add a guard point
				 * before it if needed then reset the value of the point.
				 */

				(*most_recent_insert_iterator)->value = value;

				/* if we modified the final value, then its as
				 * if we inserted a new point as far as the
				 * next addition, so make sure we know that.
				 */

				if (_events.back()->when == when) {
					most_recent_insert_iterator = _events.end();
				}

			} else {
				DEBUG_TRACE (DEBUG::ControlList, string_compose ("@%1 same time %2, same value value %3\n", this, when, value));
			}

		} else {
			DEBUG_TRACE (DEBUG::ControlList, string_compose ("@%1 insert new point at %2 at iterator at %3\n", this, when, (*most_recent_insert_iterator)->when));
			bool done = false;
			/* check for possible straight line here until maybe_insert_straight_line () handles the insert iterator properly*/
			if (most_recent_insert_iterator != _events.begin ()) {
				bool have_point2 = false;
				--most_recent_insert_iterator;
				const bool have_point1 = (*most_recent_insert_iterator)->value == value;

				if (most_recent_insert_iterator != _events.begin ()) {
					--most_recent_insert_iterator;
					have_point2 = (*most_recent_insert_iterator)->value == value;
					++most_recent_insert_iterator;
				}

				if (have_point1 && have_point2) {
					DEBUG_TRACE (DEBUG::ControlList, string_compose ("@%1 no change: move existing at %3 to %2\n", this, when, (*most_recent_insert_iterator)->when));
					(*most_recent_insert_iterator)->when = when;
					done = true;
				} else {
					++most_recent_insert_iterator;
				}
			}

			/* if the transport is stopped, add guard points */
			if (!done && !_in_write_pass) {
				add_guard_point (when, -GUARD_POINT_DELTA);
				maybe_add_insert_guard (when);
			} else if (with_guards) {
				maybe_add_insert_guard (when);
			}

			if (!done) {
				EventList::iterator x = _events.insert (most_recent_insert_iterator, new ControlEvent (when, value));
				DEBUG_TRACE (DEBUG::ControlList, string_compose ("@%1 inserted new value before MRI, size now %2\n", this, _events.size()));
				most_recent_insert_iterator = x;
			}
		}

		mark_dirty ();
	}
	maybe_signal_changed ();
}

void
ControlList::erase (iterator i)
{
	{
		Glib::Threads::RWLock::WriterLock lm (_lock);
		if (most_recent_insert_iterator == i) {
			unlocked_invalidate_insert_iterator ();
		}
		_events.erase (i);
		mark_dirty ();
	}
	maybe_signal_changed ();
}

void
ControlList::erase (iterator start, iterator end)
{
	{
		Glib::Threads::RWLock::WriterLock lm (_lock);
		_events.erase (start, end);
		unlocked_invalidate_insert_iterator ();
		mark_dirty ();
	}
	maybe_signal_changed ();
}

/** Erase the first event which matches the given time and value */
void
ControlList::erase (timepos_t const & time, double value)
{
	{
		Glib::Threads::RWLock::WriterLock lm (_lock);
		timepos_t when = ensure_time_domain (time);

		iterator i = begin ();
		while (i != end() && ((*i)->when != when || (*i)->value != value)) {
			++i;
		}

		if (i != end ()) {
			_events.erase (i);
			if (most_recent_insert_iterator == i) {
				unlocked_invalidate_insert_iterator ();
			}
		}

		mark_dirty ();
	}
	maybe_signal_changed ();
}

void
ControlList::erase_range (timepos_t const & start, timepos_t const & endt)
{
	bool erased = false;

	{
		Glib::Threads::RWLock::WriterLock lm (_lock);

		erased = erase_range_internal (start, endt, _events);

		if (erased) {
			mark_dirty ();
		}
	}

	if (erased) {
		maybe_signal_changed ();
	}
}

bool
ControlList::erase_range_internal (timepos_t const & start, timepos_t const & endt, EventList & events)
{
	bool erased = false;
	iterator s;
	iterator e;

	/* This is where we have to pick the time domain to be used when
	 * defining the control points.
	 *
	 * start/endt retain their values no matter what the time domain is,
	 * but the location of the control point is specified as a single
	 * integer value that represents either samples or beats. The sample
	 * position and beat position, while representing the same position on
	 * the timeline, will be numerically different anywhere (except perhaps
	 * zero).
	 *
	 * eg. start = 1000000 samples == 12.34 beats
	 *     cp.when = 100000 if ControlList uses AudioTime
	 *     cp.when = 23074  if ControlList uses BeatTime (see Beats::to_ticks())
	 *
	 */

	ControlEvent cp (start, 0.0f);

	if ((s = lower_bound (events.begin(), events.end(), &cp, time_comparator)) != events.end()) {

		cp.when = endt;
		e = upper_bound (events.begin(), events.end(), &cp, time_comparator);
		events.erase (s, e);
		if (s != e) {
			unlocked_invalidate_insert_iterator ();
			erased = true;
		}
	}

	return erased;
}

void
ControlList::slide (iterator before, timecnt_t const & distance)
{
	{
		Glib::Threads::RWLock::WriterLock lm (_lock);

		if (before == _events.end()) {
			return;
		}

		timecnt_t wd = distance;

		while (before != _events.end()) {
			(*before)->when += wd;
			++before;
		}

		mark_dirty ();
	}
	maybe_signal_changed ();
}

void
ControlList::shift (timepos_t const & time, timecnt_t const & distance)
{
	timepos_t pos = time;

	{
		Glib::Threads::RWLock::WriterLock lm (_lock);
		double v0, v1;

		if (distance.is_negative()) {
			/* Route::shift () with negative shift is used
			 * for "remove time". The time [pos.. pos-frames] is removed.
			 * and everyhing after, moved backwards.
			 */
			v0 = unlocked_eval (pos);
			v1 = unlocked_eval (pos.earlier (distance));
			erase_range_internal (pos, pos.earlier (distance), _events);
		} else {
			v0 = v1 = unlocked_eval (pos);
		}

		bool dst_guard_exists = false;

		for (iterator i = _events.begin(); i != _events.end(); ++i) {
			if ((*i)->when == pos) {
				dst_guard_exists = true;
			}
			if ((*i)->when >= pos) {
				(*i)->when += distance;
			}
		}

		/* add guard-points to retain shape, if needed */
		if (distance.is_positive()) {
			ControlEvent cp (pos, 0.0);
			iterator s = lower_bound (_events.begin(), _events.end(), &cp, time_comparator);
			if (s != _events.end ()) {
				_events.insert (s, new ControlEvent (pos, v0));
			}
			pos += distance;
		} else if (distance.is_negative() && pos > 0) {
			ControlEvent cp (pos.decrement(), 0.0);
			iterator s = lower_bound (_events.begin(), _events.end(), &cp, time_comparator);
			if (s != _events.end ()) {
				_events.insert (s, new ControlEvent (pos.decrement(), v0));
			}
		}
		if (!dst_guard_exists) {
			ControlEvent cp (pos, 0.0);
			iterator s = lower_bound (_events.begin(), _events.end(), &cp, time_comparator);
			_events.insert (s, new ControlEvent (pos, s == _events.end () ? v0 : v1));
		}


		mark_dirty ();
	}
	maybe_signal_changed ();
}

void
ControlList::modify (iterator iter, timepos_t const & time, double val)
{
	/* note: we assume higher level logic is in place to avoid this
	 * reordering the time-order of control events in the list. ie. all
	 * points after *iter are later than when.
	 */

	/* catch possible float/double rounding errors from higher levels */
	val = std::min ((double)_desc.upper, std::max ((double)_desc.lower, val));

	{
		Glib::Threads::RWLock::WriterLock lm (_lock);
		timepos_t when = ensure_time_domain (time);

		(*iter)->when = when;
		(*iter)->value = val;
		if (isnan_local (val)) {
			abort ();
		}

		if (!_frozen) {
			_events.sort (event_time_less_than);
			unlocked_remove_duplicates ();
			unlocked_invalidate_insert_iterator ();
		} else {
			_sort_pending = true;
		}

		mark_dirty ();
	}
	maybe_signal_changed ();
}

std::pair<ControlList::iterator,ControlList::iterator>
ControlList::control_points_adjacent (timepos_t const & xtime)
{
	Glib::Threads::RWLock::ReaderLock lm (_lock);
	iterator i;
	timepos_t xval = xtime;
	ControlEvent cp (xval, 0.0f);
	std::pair<iterator,iterator> ret;

	ret.first = _events.end();
	ret.second = _events.end();

	for (i = lower_bound (_events.begin(), _events.end(), &cp, time_comparator); i != _events.end(); ++i) {

		if (ret.first == _events.end()) {
			if ((*i)->when >= xval) {
				if (i != _events.begin()) {
					ret.first = i;
					--ret.first;
				} else {
					return ret;
				}
			}
		}

		if ((*i)->when > xval) {
			ret.second = i;
			break;
		}
	}

	return ret;
}

void
ControlList::freeze ()
{
	_frozen++;
}

void
ControlList::thaw ()
{
	assert(_frozen > 0);

	if (--_frozen > 0) {
		return;
	}

	{
		Glib::Threads::RWLock::WriterLock lm (_lock);

		if (_sort_pending) {
			_events.sort (event_time_less_than);
			unlocked_remove_duplicates ();
			unlocked_invalidate_insert_iterator ();
			_sort_pending = false;
		}
	}
	maybe_signal_changed ();
}

void
ControlList::mark_dirty () const
{
	_lookup_cache.left = timepos_t::max (_time_domain);
	_lookup_cache.range.first = _events.end();
	_lookup_cache.range.second = _events.end();
	_search_cache.left = timepos_t::max (_time_domain);
	_search_cache.first = _events.end();

	if (_curve) {
		_curve->mark_dirty();
	}
}

void
ControlList::truncate_end (timepos_t const & last_time)
{
	{
		Glib::Threads::RWLock::WriterLock lm (_lock);
		timepos_t last_coordinate = last_time;
		ControlEvent cp (last_coordinate, 0);
		ControlList::reverse_iterator i;
		double last_val;

		if (_events.empty()) {
			return;
		}

		if (last_coordinate == _events.back()->when) {
			return;
		}

		if (last_coordinate > _events.back()->when) {

			/* extending end:
			 */

			iterator foo = _events.begin();
			bool lessthantwo;

			if (foo == _events.end()) {
				lessthantwo = true;
			} else if (++foo == _events.end()) {
				lessthantwo = true;
			} else {
				lessthantwo = false;
			}

			if (lessthantwo) {
				/* less than 2 points: add a new point */
				_events.push_back (new ControlEvent (last_coordinate, _events.back()->value));
			} else {

				/* more than 2 points: check to see if the last 2 values
				   are equal. if so, just move the position of the
				   last point. otherwise, add a new point.
				*/

				iterator penultimate = _events.end();
				--penultimate; /* points at last point */
				--penultimate; /* points at the penultimate point */

				if (_events.back()->value == (*penultimate)->value) {
					_events.back()->when = last_coordinate;
				} else {
					_events.push_back (new ControlEvent (last_coordinate, _events.back()->value));
				}
			}

		} else {

			/* shortening end */

			last_val = unlocked_eval (last_coordinate);
			last_val = max ((double) _desc.lower, last_val);
			last_val = min ((double) _desc.upper, last_val);

			i = _events.rbegin();

			/* make i point to the last control point */

			++i;

			/* now go backwards, removing control points that are
			   beyond the new last coordinate.
			*/

			// FIXME: SLOW! (size() == O(n))

			uint32_t sz = _events.size();

			while (i != _events.rend() && sz > 2) {
				ControlList::reverse_iterator tmp;

				tmp = i;
				++tmp;

				if ((*i)->when < last_coordinate) {
					break;
				}

				_events.erase (i.base());
				--sz;

				i = tmp;
			}

			_events.back()->when = last_coordinate;
			_events.back()->value = last_val;
		}

		unlocked_invalidate_insert_iterator ();
		mark_dirty();
	}
	maybe_signal_changed ();
}

void
ControlList::truncate_start (timecnt_t const & overall)
{
	{
		Glib::Threads::RWLock::WriterLock lm (_lock);
		iterator i;
		double first_legal_value;
		timepos_t first_legal_coordinate;
		timepos_t overall_length (overall);

		if (_events.empty()) {
			/* nothing to truncate */
			return;
		} else if (overall_length == _events.back()->when) {
			/* no change in overall length */
			return;
		}

		if (overall_length > _events.back()->when) {

			/* growing at front: duplicate first point. shift all others */

			timepos_t shift (_events.back()->when.distance (overall_length));
			uint32_t np;

			for (np = 0, i = _events.begin(); i != _events.end(); ++i, ++np) {
				(*i)->when += shift;
			}

			if (np < 2) {

				/* less than 2 points: add a new point */
				_events.push_front (new ControlEvent (timepos_t (_time_domain), _events.front()->value));

			} else {

				/* more than 2 points: check to see if the first 2 values
				   are equal. if so, just move the position of the
				   first point. otherwise, add a new point.
				*/

				iterator second = _events.begin();
				++second; /* points at the second point */

				if (_events.front()->value == (*second)->value) {
					/* first segment is flat, just move start point back to zero */
					_events.front()->when = timepos_t (_time_domain);
				} else {
					/* leave non-flat segment in place, add a new leading point. */
					_events.push_front (new ControlEvent (timepos_t (_time_domain), _events.front()->value));
				}
			}

		} else {

			/* shrinking at front */

			first_legal_coordinate = _events.back()->when.earlier (overall_length);
			first_legal_value = unlocked_eval (first_legal_coordinate);
			first_legal_value = max ((double)_desc.lower, first_legal_value);
			first_legal_value = min ((double)_desc.upper, first_legal_value);

			/* remove all events earlier than the new "front" */

			i = _events.begin();

			while (i != _events.end() && !_events.empty()) {
				ControlList::iterator tmp;

				tmp = i;
				++tmp;

				if ((*i)->when > first_legal_coordinate) {
					break;
				}

				_events.erase (i);

				i = tmp;
			}


			/* shift all remaining points left to keep their same
			   relative position
			*/

			for (i = _events.begin(); i != _events.end(); ++i) {
				(*i)->when.shift_earlier (timecnt_t (first_legal_coordinate, timepos_t()));
			}

			/* add a new point for the interpolated new value */

			_events.push_front (new ControlEvent (timepos_t (_time_domain), first_legal_value));
		}

		unlocked_invalidate_insert_iterator ();
		mark_dirty();
	}
	maybe_signal_changed ();
}

double
ControlList::unlocked_eval (timepos_t const & xtime) const
{
	pair<EventList::iterator,EventList::iterator> range;
	int32_t npoints;
	timepos_t lpos, upos;
	double lval, uval;
	double fraction;
	double xx;
	double ll;

	const_iterator length_check_iter = _events.begin();
	for (npoints = 0; npoints < 4; ++npoints, ++length_check_iter) {
		if (length_check_iter == _events.end()) {
			break;
		}
	}

	switch (npoints) {
	case 0:
		return _desc.normal;

	case 1:
		return _events.front()->value;

	case 2:
		if (xtime >= _events.back()->when) {
			return _events.back()->value;
		} else if (xtime <= _events.front()->when) {
			return _events.front()->value;
		}

		lpos = _events.front()->when;
		lval = _events.front()->value;
		upos = _events.back()->when;
		uval = _events.back()->value;

		xx = lpos.distance (xtime).distance().val();
		ll = lpos.distance (upos).distance().val();

		fraction = xx / ll;

		switch (_interpolation) {
			case Discrete:
				return lval;
			case Logarithmic:
				return interpolate_logarithmic (lval, uval, fraction, _desc.lower, _desc.upper);
			case Exponential:
				return interpolate_gain (lval, uval, fraction, _desc.upper);
			case Curved:
				/* only used x-fade curves, never direct eval */
				assert (0);
			default: // Linear
				return interpolate_linear (lval, uval, fraction);
		}

	default:
		if (xtime >= _events.back()->when) {
			return _events.back()->value;
		} else if (xtime <= _events.front()->when) {
			return _events.front()->value;
		}

		return multipoint_eval (xtime);
	}

	abort(); /*NOTREACHED*/ /* stupid gcc */
	return _desc.normal;
}

double
ControlList::multipoint_eval (timepos_t const & xtime) const
{
	timepos_t upos, lpos;
	double uval, lval;
	double fraction;

	/* "Stepped" lookup (no interpolation) */
	/* FIXME: no cache.  significant? */
	if (_interpolation == Discrete) {
		const ControlEvent cp (xtime, 0);
		EventList::const_iterator i = lower_bound (_events.begin(), _events.end(), &cp, time_comparator);

		// shouldn't have made it to multipoint_eval
		assert(i != _events.end());

		if (i == _events.begin() || (*i)->when == xtime)
			return (*i)->value;
		else
			return (*(--i))->value;
	}

	/* Only do the range lookup if xtime is in a different range than last time
	 * this was called (or if the lookup cache has been marked "dirty" (left<0) */
	if ((_lookup_cache.left == timepos_t::max (_time_domain)) ||
	    ((_lookup_cache.left > xtime) ||
	     (_lookup_cache.range.first == _events.end()) ||
	     ((*_lookup_cache.range.second)->when < xtime))) {

		const ControlEvent cp (xtime, 0);

		_lookup_cache.range = equal_range (_events.begin(), _events.end(), &cp, time_comparator);
	}

	pair<const_iterator,const_iterator> range = _lookup_cache.range;

	if (range.first == range.second) {

		/* x does not exist within the list as a control point */

		_lookup_cache.left = xtime;

		if (range.first != _events.begin()) {
			--range.first;
			lpos = (*range.first)->when;
			lval = (*range.first)->value;
		}  else {
			/* we're before the first point */
			// return _default_value;
			return _events.front()->value;
		}

		if (range.second == _events.end()) {
			/* we're after the last point */
			return _events.back()->value;
		}

		upos = (*range.second)->when;
		uval = (*range.second)->value;

		fraction = (double) lpos.distance (xtime).distance().val() / (double) lpos.distance (upos).distance().val();

		switch (_interpolation) {
			case Logarithmic:
				return interpolate_logarithmic (lval, uval, fraction, _desc.lower, _desc.upper);
			case Exponential:
				return interpolate_gain (lval, uval, fraction, _desc.upper);
			case Discrete:
				/* should not reach here */
				assert (0);
			case Curved:
				/* only used x-fade curves, never direct eval */
				assert (0);
			default: // Linear
				return interpolate_linear (lval, uval, fraction);
				break;
		}
		assert (0);
	}

	/* x is a control point in the data */
	_lookup_cache.left = timepos_t::max (_time_domain);
	return (*range.first)->value;
}

void
ControlList::build_search_cache_if_necessary (timepos_t const & start_time) const
{
	timepos_t start = start_time;

	if (_events.empty()) {
		/* Empty, nothing to cache, move to end. */
		_search_cache.first = _events.end();
		_search_cache.left = timepos_t::max (_time_domain);
		return;
	} else if ((_search_cache.left == timepos_t::max (_time_domain)) || (_search_cache.left > start)) {
		/* Marked dirty (left == max), or we're too far forward, re-search. */

		const ControlEvent start_point (start, 0);

		_search_cache.first = lower_bound (_events.begin(), _events.end(), &start_point, time_comparator);
		_search_cache.left = start;
	}

	/* We now have a search cache that is not too far right, but it may be too
	   far left and need to be advanced. */

	while (_search_cache.first != end() && (*_search_cache.first)->when < start) {
		++_search_cache.first;
	}
	_search_cache.left = start;
}

/** Get the earliest event after \a start without interpolation.
 *
 * If an event is found, \a x and \a y are set to its coordinates.
 *
 * \param inclusive Include events with timestamp exactly equal to \a start
 * \return true if event is found (and \a x and \a y are valid).
 */
bool
ControlList::rt_safe_earliest_event_discrete_unlocked (timepos_t const & start_time, timepos_t & x, double& y, bool inclusive) const
{
	timepos_t start = start_time;

	build_search_cache_if_necessary (start);

	if (_search_cache.first != _events.end()) {
		const ControlEvent* const first = *_search_cache.first;

		const bool past_start = (inclusive ? first->when >= start : first->when > start);

		/* Earliest points is in range, return it */
		if (past_start) {

			x = first->when;
			y = first->value;

			/* Move left of cache to this point
			 * (Optimize for immediate call this cycle within range) */
			_search_cache.left = first->when;
			++_search_cache.first;

			assert(x >= start);
			return true;

		} else {
			return false;
		}

		/* No points in range */
	} else {
		return false;
	}
}

/** Get the earliest time the line crosses an integer (Linear interpolation).
 *
 * If an event is found, \a x and \a y are set to its coordinates.
 *
 * \param inclusive Include events with timestamp exactly equal to \a start
 * \return true if event is found (and \a x and \a y are valid).
 */
bool
ControlList::rt_safe_earliest_event_linear_unlocked (Temporal::timepos_t const & start_time, Temporal::timepos_t & x, double& y, bool inclusive, Temporal::timecnt_t min_x_delta) const
{
	timepos_t start = start_time;

	/* the max value is given as an out-of-bounds default value, when the
	   true default is zero, but the time-domain is not known at compile
	   time. This allows us to reset it to zero with the correct time
	   domain (equality comparisons across time domains where the actual
	   scalar value is zero should always be cheap, but that's not true of
	   other operators such as >, < etc.)
	*/

	if (min_x_delta == Temporal::timecnt_t::max()) {
		min_x_delta = Temporal::timecnt_t (time_domain());
	}

	// cout << "earliest_event(start: " << start << ", x: " << x << ", y: " << y << ", inclusive: " << inclusive <<  ") mxd " << min_x_delta << endl;

	const_iterator length_check_iter = _events.begin();
	if (_events.empty()) {
		/* no events, so we cannot interpolate */
		return false;
	} else if (_events.end() == ++length_check_iter) {
		/* one event, which decomposes to the same logic as the discrete one */
		return rt_safe_earliest_event_discrete_unlocked (start + min_x_delta, x, y, inclusive);
	}

	if (min_x_delta > 0) {
		/* if there is an event between [start ... start + min_x_delta], use it,
		 */
		build_search_cache_if_necessary (start);
		const ControlEvent* first = *_search_cache.first;
		if (_search_cache.first != _events.end()) {
			if (((first->when > start) || (inclusive && first->when == start)) && first->when < start + min_x_delta) {
				x = first->when;
				y = first->value;
				/* Move left of cache to this point
				 * (Optimize for immediate call this cycle within range) */
				_search_cache.left = x;
				return true;
			}
		}
	}

	/* No event between start and start + min_x_delta, so otherwise
	 * interpolate at start + min_x_delta
	 */

	start += min_x_delta;

	// Hack to avoid infinitely repeating the same event
	build_search_cache_if_necessary (start);

	if (_search_cache.first == _events.end()) {
		/* No points in the future, so no steps (towards them) in the future */
		return false;
	}

	const ControlEvent* first = NULL;
	const ControlEvent* next = NULL;

	if (_search_cache.first == _events.begin() || (*_search_cache.first)->when <= start) {
		/* Start is after first */
		first = *_search_cache.first;
		++_search_cache.first;
		if (_search_cache.first == _events.end()) {
			/* no later events, nothing to interpolate towards */
			return false;
		}
		next = *_search_cache.first;

	} else {
		/* Start is before first */
		assert (_search_cache.first != _events.begin());
		const_iterator prev = _search_cache.first;
		--prev;
		first = *prev;
		next = *_search_cache.first;
	}

	if (inclusive && first->when == start) {
		/* existing point matches start */

		x = first->when;
		y = first->value;
		/* Move left of cache to this point
		 * (Optimize for immediate call this cycle within range)
		 */
		_search_cache.left = first->when;
		return true;
	} else if (next->when < start || (!inclusive && next->when == start)) {
		/* "Next" is before the start, no points left. */
		return false;
	}

	if (fabs (first->value - next->value) <= 1) {

		/* delta between the two spanning points is <= 1,
		   consider the next point as the answer, but only if the next
		   point is actually beyond @param start.
		*/

		if (next->when > start) {
			x = next->when;
			y = next->value;
			/* Move left of cache to this point
			 * (Optimize for immediate call this cycle within range) */
			_search_cache.left = next->when;
			return true;
		} else {
			/* no suitable point can be determined */
			return false;
		}
	}

	const double slope = (next->value - first->value) / (double) first->when.distance (next->when).distance().val();

	//cerr << "start y: " << start_y << endl;

	//y = first->value + (slope * fabs(start - first->when));
	y = first->value;

	if (first->value < next->value) { // ramping up
		y = ceil(y);
	} else { // ramping down
		y = floor(y);
	}

	if (_time_domain == AudioTime) {
		x = first->when + timepos_t (samplepos_t ((y - first->value) / (double)slope));
	} else {
		x = first->when + timepos_t::from_ticks ((y - first->value) / (double)slope);
	}

	/* Now iterate until x has a suitable relationship to start (depending
	 * on the value of @param inclusive. Either less than @param start or
	 * less-than-or-equal with y not yet reaching the value of the next
	 * point.
	 */

	const double delta = (first->value < next->value) ? 1.0 /* ramping up */ : -1.0; /* ramping down */

	while ((inclusive && x < start) || (x <= start && y != next->value)) {

		y += delta;

		if (_time_domain == AudioTime) {
			x = first->when + timepos_t (samplepos_t ((y - first->value) / (double)slope));
		} else {
			x = first->when + timepos_t::from_ticks (int64_t ((y - first->value) / (double)slope));
		}
	}

	assert ((y >= first->value && y <= next->value) || (y <= first->value && y >= next->value) );

	const bool past_start = (inclusive ? x >= start : x > start);

	if (past_start) {
		/* Move left of cache to this point
		 * (Optimize for immediate call this cycle within range) */
		_search_cache.left = x;
		assert(inclusive ? x >= start : x > start);
		return true;
	}

	if (inclusive) {
		x = next->when;
		_search_cache.left = next->when;
	} else {
		x = start;
		_search_cache.left = x;
	}

	return true;
}


/** @param start Start position in model coordinates.
 *  @param end End position in model coordinates.
 *  @param op 0 = cut, 1 = copy, 2 = clear.
 */
boost::shared_ptr<ControlList>
ControlList::cut_copy_clear (timepos_t const & start_time, timepos_t const & end_time, int op)
{
	boost::shared_ptr<ControlList> nal = create (_parameter, _desc, _time_domain);
	iterator s, e;
	timepos_t start = start_time;
	timepos_t end = end_time;
	ControlEvent cp (start, 0.0);

	{
		Glib::Threads::RWLock::WriterLock lm (_lock);

		/* first, determine s & e, two iterators that define the range of points
		   affected by this operation
		*/

		if ((s = lower_bound (_events.begin(), _events.end(), &cp, time_comparator)) == _events.end()) {
			return nal;
		}

		/* and the last that is at or after `end' */
		cp.when = end;
		e = upper_bound (_events.begin(), _events.end(), &cp, time_comparator);


		/* if "start" isn't the location of an existing point,
		   evaluate the curve to get a value for the start. Add a point to
		   both the existing event list, and if its not a "clear" operation,
		   to the copy ("nal") as well.

		   Note that the time positions of the points in each list are different
		   because we want the copy ("nal") to have a zero time reference.
		*/


		/* before we begin any cut/clear operations, get the value of the curve
		   at "end".
		*/

		double end_value = unlocked_eval (end);

		if ((*s)->when != start) {

			double val = unlocked_eval (start);

			if (op != 1) { // cut/clear
				if (start > _events.front()->when) {
					_events.insert (s, (new ControlEvent (start, val)));
				}
			}

			if (op != 2) { // ! clear
				nal->_events.push_back (new ControlEvent (timepos_t (_time_domain), val));
			}
		}

		for (iterator x = s; x != e; ) {

			/* adjust new points to be relative to start, which
			   has been set to zero.
			*/

			if (op != 2) {
				nal->_events.push_back (new ControlEvent (timepos_t (start.distance ((*x)->when)), (*x)->value));
			}

			if (op != 1) {
				x = _events.erase (x);
			} else {
				++x;
			}
		}

		if (e == _events.end() || (*e)->when != end) {

			if (op != 1) { // cut/clear
				_events.insert (e, new ControlEvent (end, end_value));
			}

			if (op != 2) { // cut/copy
				nal->_events.push_back (new ControlEvent (timepos_t (start.distance (end)), end_value));
			}
		}

		unlocked_invalidate_insert_iterator ();
		mark_dirty ();
	}

	if (op != 1) {
		maybe_signal_changed ();
	}

	return nal;
}


boost::shared_ptr<ControlList>
ControlList::cut (timepos_t const & start, timepos_t const & end)
{
	return cut_copy_clear (start, end, 0);
}

boost::shared_ptr<ControlList>
ControlList::copy (timepos_t const & start, timepos_t const & end)
{
	return cut_copy_clear (start, end, 1);
}

void
ControlList::clear (timepos_t const & start, timepos_t const & end)
{
	cut_copy_clear (start, end, 2);
}

/** @param pos Position in model coordinates */
bool
ControlList::paste (const ControlList& alist, timepos_t const &  time)
{
	if (alist._events.empty()) {
		return false;
	}

	/* when pasting a range of automation, first add guard points so the automation data before and after this range is retained */
	const ControlEvent* last = alist.back();
	add_guard_point (time, -GUARD_POINT_DELTA);
	add_guard_point (time + last->when, GUARD_POINT_DELTA);

	{
		Glib::Threads::RWLock::WriterLock lm (_lock);
		iterator where;
		iterator prev;
		timepos_t end;
		timepos_t pos = time;
		ControlEvent cp (pos, 0.0);

		where = upper_bound (_events.begin(), _events.end(), &cp, time_comparator);

		for (const_iterator i = alist.begin();i != alist.end(); ++i) {
			double value = (*i)->value;
			if (alist.parameter() != parameter()) {
				const ParameterDescriptor& src_desc = alist.descriptor();

				// This does not work for logscale and will probably also not do
				// the right thing for integer_step and sr_dependent parameters.
				//
				// TODO various flags from from ARDOUR::ParameterDescriptor
				// to Evoral::ParameterDescriptor

				value -= src_desc.lower;  // translate to 0-relative
				value /= (src_desc.upper - src_desc.lower);  // normalize range
				value *= (_desc.upper - _desc.lower);  // scale to our range
				value += _desc.lower;  // translate to our offset
				if (_desc.toggled) {
					value = (value < 0.5) ? 0.0 : 1.0;
				}
				/* catch possible rounding errors */
				value = std::min ((double)_desc.upper, std::max ((double)_desc.lower, value));
			}

			timepos_t adj_pos;

			if (_time_domain == (*i)->when.time_domain()) {
				adj_pos = (*i)->when + pos;
			} else {
				if (_time_domain == AudioTime) {
					adj_pos = timepos_t (((*i)->when + pos).samples());
				} else {
					adj_pos = timepos_t (((*i)->when + pos).beats());
				}
			}

			_events.insert (where, new ControlEvent (adj_pos, value));
			end = (*i)->when + pos;
		}


		/* move all  points after the insertion along the timeline by
		   the correct amount.
		*/

		while (where != _events.end()) {
			iterator tmp;
			if ((*where)->when <= end) {
				tmp = where;
				++tmp;
				_events.erase(where);
				where = tmp;

			} else {
				break;
			}
		}

		unlocked_invalidate_insert_iterator ();
		mark_dirty ();
	}
	maybe_signal_changed ();
	return true;
}

/** Move automation around according to a list of region movements.
 *  @param return true if anything was changed, otherwise false (ie nothing needed changing)
 */
bool
ControlList::move_ranges (const list< RangeMove> & movements)
{
	typedef list<RangeMove> RangeMoveList;

	{
		Glib::Threads::RWLock::WriterLock lm (_lock);

		/* a copy of the events list before we started moving stuff around */
		EventList old_events = _events;

		/* clear the source and destination ranges in the new list */
		bool things_erased = false;
		for (RangeMoveList::const_iterator i = movements.begin (); i != movements.end (); ++i) {

			timepos_t start = i->from;
			timepos_t end = i->from + i->length;

			if (erase_range_internal (start, end, _events)) {
				things_erased = true;
			}

			start = i->to;
			end = i->to + i->length;

			if (erase_range_internal (start, end, _events)) {
				things_erased = true;
			}
		}

		/* if nothing was erased, there is nothing to do */
		if (!things_erased) {
			return false;
		}

		/* copy the events into the new list */
		for (RangeMoveList::const_iterator i = movements.begin (); i != movements.end (); ++i) {
			iterator j = old_events.begin ();

			const timepos_t limit = i->from + i->length;
			const timecnt_t dx = i->from.distance (i->to);

			while (j != old_events.end ()) {

				timepos_t jtime;

				switch (_time_domain) {
				case AudioTime:
					jtime = (*j)->when;
					break;
				case BeatTime:
					jtime = (*j)->when;
					break;
				default:
					/*NOTREACHED*/
					return false;
				}

				if (jtime > limit) {
					break;
				}

				if (jtime >= i->from) {
					ControlEvent* ev = new ControlEvent (**j);

					switch (_time_domain) {
					case AudioTime:
						ev->when += dx;
						break;
					case BeatTime:
						ev->when += dx;
						break;
					default:
						/*NOTREACHED*/
						return false;
					}

					_events.push_back (ev);
				}

				++j;
			}
		}

		if (!_frozen) {
			_events.sort (event_time_less_than);
			unlocked_remove_duplicates ();
			unlocked_invalidate_insert_iterator ();
		} else {
			_sort_pending = true;
		}

		mark_dirty ();
	}
	maybe_signal_changed ();
	return true;
}

bool
ControlList::set_interpolation (InterpolationStyle s)
{
	if (_interpolation == s) {
		return true;
	}

	switch (s) {
		case Logarithmic:
			if (_desc.lower * _desc.upper <= 0 || _desc.upper <= _desc.lower) {
				return false;
			}
			break;
		case Exponential:
			if (_desc.lower != 0 || _desc.upper <= _desc.lower) {
				return false;
			}
		default:
			break;
	}

	_interpolation = s;
	InterpolationChanged (s); /* EMIT SIGNAL */
	return true;
}

bool
ControlList::operator!= (ControlList const & other) const
{
	if (_events.size() != other._events.size()) {
		return true;
	}

	EventList::const_iterator i = _events.begin ();
	EventList::const_iterator j = other._events.begin ();

	while (i != _events.end() && (*i)->when == (*j)->when && (*i)->value == (*j)->value) {
	        ++i;
		++j;
	}

	if (i != _events.end ()) {
		return true;
	}

	return (
		_parameter != other._parameter ||
		_interpolation != other._interpolation ||
		_desc.lower != other._desc.lower ||
		_desc.upper != other._desc.upper ||
		_desc.normal != other._desc.normal
		);
}

bool
ControlList::is_sorted () const
{
	Glib::Threads::RWLock::ReaderLock lm (_lock);
	if (_events.size () == 0) {
		return true;
	}
	const_iterator i = _events.begin();
	const_iterator n = i;
	while (++n != _events.end ()) {
		if (event_time_less_than(*n,*i)) {
			return false;
		}
		++i;
	}
	return true;
}

void
ControlList::dump (ostream& o)
{
	/* NOT LOCKED ... for debugging only */

	for (EventList::iterator x = _events.begin(); x != _events.end(); ++x) {
		o << (*x)->value << " @ " << (*x)->when << endl;
	}
}

void
ControlList::set_time_domain (Temporal::TimeDomain td)
{
	assert (_events.empty());
	_time_domain = td;
	/* XXX: TODO: apply to all points */
}

void
ControlList::set_time_domain_empty (Temporal::TimeDomain td)
{
	/* the event list may or may not be empty, but we act as if it is. This
	   is used in e.g. ::set_state(), since we do not need to modify the
	   event time domains there.
	*/
	_time_domain = td;
}

} // namespace Evoral