CSE2410 Fall 2014 Bounce

// Copyright 2008 the V8 project authors. All rights reserved.

// Copyright 1996 John Maloney and Mario Wolczko.

// 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., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA

// This implementation of the DeltaBlue benchmark is derived

// from the Smalltalk implementation by John Maloney and Mario

// Wolczko. Some parts have been translated directly, whereas

// others have been modified more aggresively to make it feel

// more like a JavaScript program.

var DeltaBlue = new BenchmarkSuite('DeltaBlue', 66118, [

  new Benchmark('DeltaBlue', deltaBlue)

]);

/**

 * A JavaScript implementation of the DeltaBlue constraint-solving

 * algorithm, as described in:

 *

 * "The DeltaBlue Algorithm: An Incremental Constraint Hierarchy Solver"

 *   Bjorn N. Freeman-Benson and John Maloney

 *   January 1990 Communications of the ACM,

 *   also available as University of Washington TR 89-08-06.

 *

 * Beware: this benchmark is written in a grotesque style where

 * the constraint model is built by side-effects from constructors.

 * I've kept it this way to avoid deviating too much from the original

 * implementation.

 */

/* --- O b j e c t   M o d e l --- */

Object.prototype.inheritsFrom = function (shuper) {

  function Inheriter() { }

  Inheriter.prototype = shuper.prototype;

  this.prototype = new Inheriter();

  this.superConstructor = shuper;

}

function OrderedCollection() {

  this.elms = new Array();

}

OrderedCollection.prototype.add = function (elm) {

  this.elms.push(elm);

}

OrderedCollection.prototype.at = function (index) {

  return this.elms[index];

}

OrderedCollection.prototype.size = function () {

  return this.elms.length;

}

OrderedCollection.prototype.removeFirst = function () {

  return this.elms.pop();

}

OrderedCollection.prototype.remove = function (elm) {

  var index = 0, skipped = 0;

  for (var i = 0; i < this.elms.length; i++) {

    var value = this.elms[i];

    if (value != elm) {

      this.elms[index] = value;

      index++;

    } else {

      skipped++;

    }

  }

  for (var i = 0; i < skipped; i++)

    this.elms.pop();

}

/* --- *

 * S t r e n g t h

 * --- */

/**

 * Strengths are used to measure the relative importance of constraints.

 * New strengths may be inserted in the strength hierarchy without

 * disrupting current constraints.  Strengths cannot be created outside

 * this class, so pointer comparison can be used for value comparison.

 */

function Strength(strengthValue, name) {

  this.strengthValue = strengthValue;

  this.name = name;

}

Strength.stronger = function (s1, s2) {

  return s1.strengthValue < s2.strengthValue;

}

Strength.weaker = function (s1, s2) {

  return s1.strengthValue > s2.strengthValue;

}

Strength.weakestOf = function (s1, s2) {

  return this.weaker(s1, s2) ? s1 : s2;

}

Strength.strongest = function (s1, s2) {

  return this.stronger(s1, s2) ? s1 : s2;

}

Strength.prototype.nextWeaker = function () {

  switch (this.strengthValue) {

    case 0: return Strength.STRONG_PREFERRED;

    case 1: return Strength.PREFERRED;

    case 2: return Strength.STRONG_DEFAULT;

    case 3: return Strength.NORMAL;

    case 4: return Strength.WEAK_DEFAULT;

    case 5: return Strength.WEAKEST;

  }

}

// Strength constants.

Strength.REQUIRED         = new Strength(0, "required");

Strength.STRONG_PREFERRED = new Strength(1, "strongPreferred");

Strength.PREFERRED        = new Strength(2, "preferred");

Strength.STRONG_DEFAULT   = new Strength(3, "strongDefault");

Strength.NORMAL           = new Strength(4, "normal");

Strength.WEAK_DEFAULT     = new Strength(5, "weakDefault");

Strength.WEAKEST          = new Strength(6, "weakest");

/* --- *

 * C o n s t r a i n t

 * --- */

/**

 * An abstract class representing a system-maintainable relationship

 * (or "constraint") between a set of variables. A constraint supplies

 * a strength instance variable; concrete subclasses provide a means

 * of storing the constrained variables and other information required

 * to represent a constraint.

 */

function Constraint(strength) {

  this.strength = strength;

}

/**

 * Activate this constraint and attempt to satisfy it.

 */

Constraint.prototype.addConstraint = function () {

  this.addToGraph();

  planner.incrementalAdd(this);

}

/**

 * Attempt to find a way to enforce this constraint. If successful,

 * record the solution, perhaps modifying the current dataflow

 * graph. Answer the constraint that this constraint overrides, if

 * there is one, or nil, if there isn't.

 * Assume: I am not already satisfied.

 */

Constraint.prototype.satisfy = function (mark) {

  this.chooseMethod(mark);

  if (!this.isSatisfied()) {

    if (this.strength == Strength.REQUIRED)

      alert("Could not satisfy a required constraint!");

    return null;

  }

  this.markInputs(mark);

  var out = this.output();

  var overridden = out.determinedBy;

  if (overridden != null) overridden.markUnsatisfied();

  out.determinedBy = this;

  if (!planner.addPropagate(this, mark))

    alert("Cycle encountered");

  out.mark = mark;

  return overridden;

}

Constraint.prototype.destroyConstraint = function () {

  if (this.isSatisfied()) planner.incrementalRemove(this);

  else this.removeFromGraph();

}

/**

 * Normal constraints are not input constraints.  An input constraint

 * is one that depends on external state, such as the mouse, the

 * keybord, a clock, or some arbitraty piece of imperative code.

 */

Constraint.prototype.isInput = function () {

  return false;

}

/* --- *

 * U n a r y   C o n s t r a i n t

 * --- */

/**

 * Abstract superclass for constraints having a single possible output

 * variable.

 */

function UnaryConstraint(v, strength) {

  UnaryConstraint.superConstructor.call(this, strength);

  this.myOutput = v;

  this.satisfied = false;

  this.addConstraint();

}

UnaryConstraint.inheritsFrom(Constraint);

/**

 * Adds this constraint to the constraint graph

 */

UnaryConstraint.prototype.addToGraph = function () {

  this.myOutput.addConstraint(this);

  this.satisfied = false;

}

/**

 * Decides if this constraint can be satisfied and records that

 * decision.

 */

UnaryConstraint.prototype.chooseMethod = function (mark) {

  this.satisfied = (this.myOutput.mark != mark)

    && Strength.stronger(this.strength, this.myOutput.walkStrength);

}

/**

 * Returns true if this constraint is satisfied in the current solution.

 */

UnaryConstraint.prototype.isSatisfied = function () {

  return this.satisfied;

}

UnaryConstraint.prototype.markInputs = function (mark) {

  // has no inputs

}

/**

 * Returns the current output variable.

 */

UnaryConstraint.prototype.output = function () {

  return this.myOutput;

}

/**

 * Calculate the walkabout strength, the stay flag, and, if it is

 * 'stay', the value for the current output of this constraint. Assume

 * this constraint is satisfied.

 */

UnaryConstraint.prototype.recalculate = function () {

  this.myOutput.walkStrength = this.strength;

  this.myOutput.stay = !this.isInput();

  if (this.myOutput.stay) this.execute(); // Stay optimization

}

/**

 * Records that this constraint is unsatisfied

 */

UnaryConstraint.prototype.markUnsatisfied = function () {

  this.satisfied = false;

}

UnaryConstraint.prototype.inputsKnown = function () {

  return true;

}

UnaryConstraint.prototype.removeFromGraph = function () {

  if (this.myOutput != null) this.myOutput.removeConstraint(this);

  this.satisfied = false;

}

/* --- *

 * S t a y   C o n s t r a i n t

 * --- */

/**

 * Variables that should, with some level of preference, stay the same.

 * Planners may exploit the fact that instances, if satisfied, will not

 * change their output during plan execution.  This is called "stay

 * optimization".

 */

function StayConstraint(v, str) {

  StayConstraint.superConstructor.call(this, v, str);

}

StayConstraint.inheritsFrom(UnaryConstraint);

StayConstraint.prototype.execute = function () {

  // Stay constraints do nothing

}

/* --- *

 * E d i t   C o n s t r a i n t

 * --- */

/**

 * A unary input constraint used to mark a variable that the client

 * wishes to change.

 */

function EditConstraint(v, str) {

  EditConstraint.superConstructor.call(this, v, str);

}

EditConstraint.inheritsFrom(UnaryConstraint);

/**

 * Edits indicate that a variable is to be changed by imperative code.

 */

EditConstraint.prototype.isInput = function () {

  return true;

}

EditConstraint.prototype.execute = function () {

  // Edit constraints do nothing

}

/* --- *

 * B i n a r y   C o n s t r a i n t

 * --- */

var Direction = new Object();

Direction.NONE     = 0;

Direction.FORWARD  = 1;

Direction.BACKWARD = -1;

/**

 * Abstract superclass for constraints having two possible output

 * variables.

 */

function BinaryConstraint(var1, var2, strength) {

  BinaryConstraint.superConstructor.call(this, strength);

  this.v1 = var1;

  this.v2 = var2;

  this.direction = Direction.NONE;

  this.addConstraint();

}

BinaryConstraint.inheritsFrom(Constraint);

/**

 * Decides if this constraint can be satisfied and which way it

 * should flow based on the relative strength of the variables related,

 * and record that decision.

 */

BinaryConstraint.prototype.chooseMethod = function (mark) {

  if (this.v1.mark == mark) {

    this.direction = (this.v2.mark != mark && Strength.stronger(this.strength, this.v2.walkStrength))

      ? Direction.FORWARD

      : Direction.NONE;

  }

  if (this.v2.mark == mark) {

    this.direction = (this.v1.mark != mark && Strength.stronger(this.strength, this.v1.walkStrength))

      ? Direction.BACKWARD

      : Direction.NONE;

  }

  if (Strength.weaker(this.v1.walkStrength, this.v2.walkStrength)) {

    this.direction = Strength.stronger(this.strength, this.v1.walkStrength)

      ? Direction.BACKWARD

      : Direction.NONE;

  } else {

    this.direction = Strength.stronger(this.strength, this.v2.walkStrength)

      ? Direction.FORWARD

      : Direction.BACKWARD

  }

}

/**

 * Add this constraint to the constraint graph

 */

BinaryConstraint.prototype.addToGraph = function () {

  this.v1.addConstraint(this);

  this.v2.addConstraint(this);

  this.direction = Direction.NONE;

}

/**

 * Answer true if this constraint is satisfied in the current solution.

 */

BinaryConstraint.prototype.isSatisfied = function () {

  return this.direction != Direction.NONE;

}

/**

 * Mark the input variable with the given mark.

 */

BinaryConstraint.prototype.markInputs = function (mark) {

  this.input().mark = mark;

}

/**

 * Returns the current input variable

 */

BinaryConstraint.prototype.input = function () {

  return (this.direction == Direction.FORWARD) ? this.v1 : this.v2;

}

/**

 * Returns the current output variable

 */

BinaryConstraint.prototype.output = function () {

  return (this.direction == Direction.FORWARD) ? this.v2 : this.v1;

}

/**

 * Calculate the walkabout strength, the stay flag, and, if it is

 * 'stay', the value for the current output of this

 * constraint. Assume this constraint is satisfied.

 */

BinaryConstraint.prototype.recalculate = function () {

  var ihn = this.input(), out = this.output();

  out.walkStrength = Strength.weakestOf(this.strength, ihn.walkStrength);

  out.stay = ihn.stay;

  if (out.stay) this.execute();

}

/**

 * Record the fact that this constraint is unsatisfied.

 */

BinaryConstraint.prototype.markUnsatisfied = function () {

  this.direction = Direction.NONE;

}

BinaryConstraint.prototype.inputsKnown = function (mark) {

  var i = this.input();

  return i.mark == mark || i.stay || i.determinedBy == null;

}

BinaryConstraint.prototype.removeFromGraph = function () {

  if (this.v1 != null) this.v1.removeConstraint(this);

  if (this.v2 != null) this.v2.removeConstraint(this);

  this.direction = Direction.NONE;

}

/* --- *

 * S c a l e   C o n s t r a i n t

 * --- */

/**

 * Relates two variables by the linear scaling relationship: "v2 =

 * (v1 * scale) + offset". Either v1 or v2 may be changed to maintain

 * this relationship but the scale factor and offset are considered

 * read-only.

 */

function ScaleConstraint(src, scale, offset, dest, strength) {

  this.direction = Direction.NONE;

  this.scale = scale;

  this.offset = offset;

  ScaleConstraint.superConstructor.call(this, src, dest, strength);

}

ScaleConstraint.inheritsFrom(BinaryConstraint);

/**

 * Adds this constraint to the constraint graph.

 */

ScaleConstraint.prototype.addToGraph = function () {

  ScaleConstraint.superConstructor.prototype.addToGraph.call(this);

  this.scale.addConstraint(this);

  this.offset.addConstraint(this);

}

ScaleConstraint.prototype.removeFromGraph = function () {

  ScaleConstraint.superConstructor.prototype.removeFromGraph.call(this);

  if (this.scale != null) this.scale.removeConstraint(this);

  if (this.offset != null) this.offset.removeConstraint(this);

}

ScaleConstraint.prototype.markInputs = function (mark) {

  ScaleConstraint.superConstructor.prototype.markInputs.call(this, mark);

  this.scale.mark = this.offset.mark = mark;

}

/**

 * Enforce this constraint. Assume that it is satisfied.

 */

ScaleConstraint.prototype.execute = function () {

  if (this.direction == Direction.FORWARD) {

    this.v2.value = this.v1.value * this.scale.value + this.offset.value;

  } else {

    this.v1.value = (this.v2.value - this.offset.value) / this.scale.value;

  }

}

/**

 * Calculate the walkabout strength, the stay flag, and, if it is

 * 'stay', the value for the current output of this constraint. Assume

 * this constraint is satisfied.

 */

ScaleConstraint.prototype.recalculate = function () {

  var ihn = this.input(), out = this.output();

  out.walkStrength = Strength.weakestOf(this.strength, ihn.walkStrength);

  out.stay = ihn.stay && this.scale.stay && this.offset.stay;

  if (out.stay) this.execute();

}

/* --- *

 * E q u a l i t  y   C o n s t r a i n t

 * --- */

/**

 * Constrains two variables to have the same value.

 */

function EqualityConstraint(var1, var2, strength) {

  EqualityConstraint.superConstructor.call(this, var1, var2, strength);

}

EqualityConstraint.inheritsFrom(BinaryConstraint);

/**

 * Enforce this constraint. Assume that it is satisfied.

 */

EqualityConstraint.prototype.execute = function () {

  this.output().value = this.input().value;

}

/* --- *

 * V a r i a b l e

 * --- */

/**

 * A constrained variable. In addition to its value, it maintain the

 * structure of the constraint graph, the current dataflow graph, and

 * various parameters of interest to the DeltaBlue incremental

 * constraint solver.

 **/

function Variable(name, initialValue) {

  this.value = initialValue || 0;

  this.constraints = new OrderedCollection();

  this.determinedBy = null;

  this.mark = 0;

  this.walkStrength = Strength.WEAKEST;

  this.stay = true;

  this.name = name;

}

/**

 * Add the given constraint to the set of all constraints that refer

 * this variable.

 */

Variable.prototype.addConstraint = function (c) {

  this.constraints.add(c);

}

/**

 * Removes all traces of c from this variable.

 */

Variable.prototype.removeConstraint = function (c) {

  this.constraints.remove(c);

  if (this.determinedBy == c) this.determinedBy = null;

}

/* --- *

 * P l a n n e r

 * --- */

/**

 * The DeltaBlue planner

 */

function Planner() {

  this.currentMark = 0;

}

/**

 * Attempt to satisfy the given constraint and, if successful,

 * incrementally update the dataflow graph.  Details: If satifying

 * the constraint is successful, it may override a weaker constraint

 * on its output. The algorithm attempts to resatisfy that

 * constraint using some other method. This process is repeated

 * until either a) it reaches a variable that was not previously

 * determined by any constraint or b) it reaches a constraint that

 * is too weak to be satisfied using any of its methods. The

 * variables of constraints that have been processed are marked with

 * a unique mark value so that we know where we've been. This allows

 * the algorithm to avoid getting into an infinite loop even if the

 * constraint graph has an inadvertent cycle.

 */

Planner.prototype.incrementalAdd = function (c) {

  var mark = this.newMark();

  var overridden = c.satisfy(mark);

  while (overridden != null)

    overridden = overridden.satisfy(mark);

}

/**

 * Entry point for retracting a constraint. Remove the given

 * constraint and incrementally update the dataflow graph.

 * Details: Retracting the given constraint may allow some currently

 * unsatisfiable downstream constraint to be satisfied. We therefore collect

 * a list of unsatisfied downstream constraints and attempt to

 * satisfy each one in turn. This list is traversed by constraint

 * strength, strongest first, as a heuristic for avoiding

 * unnecessarily adding and then overriding weak constraints.

 * Assume: c is satisfied.

 */

Planner.prototype.incrementalRemove = function (c) {

  var out = c.output();

  c.markUnsatisfied();

  c.removeFromGraph();

  var unsatisfied = this.removePropagateFrom(out);

  var strength = Strength.REQUIRED;

  do {

    for (var i = 0; i < unsatisfied.size(); i++) {

      var u = unsatisfied.at(i);

      if (u.strength == strength)

        this.incrementalAdd(u);

    }

    strength = strength.nextWeaker();

  } while (strength != Strength.WEAKEST);

}

/**

 * Select a previously unused mark value.

 */

Planner.prototype.newMark = function () {

  return ++this.currentMark;

}

/**

 * Extract a plan for resatisfaction starting from the given source

 * constraints, usually a set of input constraints. This method

 * assumes that stay optimization is desired; the plan will contain

 * only constraints whose output variables are not stay. Constraints

 * that do no computation, such as stay and edit constraints, are

 * not included in the plan.

 * Details: The outputs of a constraint are marked when it is added

 * to the plan under construction. A constraint may be appended to

 * the plan when all its input variables are known. A variable is

 * known if either a) the variable is marked (indicating that has

 * been computed by a constraint appearing earlier in the plan), b)

 * the variable is 'stay' (i.e. it is a constant at plan execution

 * time), or c) the variable is not determined by any

 * constraint. The last provision is for past states of history

 * variables, which are not stay but which are also not computed by

 * any constraint.

 * Assume: sources are all satisfied.

 */

Planner.prototype.makePlan = function (sources) {

  var mark = this.newMark();

  var plan = new Plan();

  var todo = sources;

  while (todo.size() > 0) {

    var c = todo.removeFirst();

    if (c.output().mark != mark && c.inputsKnown(mark)) {

      plan.addConstraint(c);

      c.output().mark = mark;

      this.addConstraintsConsumingTo(c.output(), todo);

    }

  }

  return plan;

}

/**

 * Extract a plan for resatisfying starting from the output of the

 * given constraints, usually a set of input constraints.

 */

Planner.prototype.extractPlanFromConstraints = function (constraints) {

  var sources = new OrderedCollection();

  for (var i = 0; i < constraints.size(); i++) {

    var c = constraints.at(i);

    if (c.isInput() && c.isSatisfied())

      // not in plan already and eligible for inclusion

      sources.add(c);

  }

  return this.makePlan(sources);

}

/**

 * Recompute the walkabout strengths and stay flags of all variables

 * downstream of the given constraint and recompute the actual

 * values of all variables whose stay flag is true. If a cycle is

 * detected, remove the given constraint and answer

 * false. Otherwise, answer true.

 * Details: Cycles are detected when a marked variable is

 * encountered downstream of the given constraint. The sender is

 * assumed to have marked the inputs of the given constraint with

 * the given mark. Thus, encountering a marked node downstream of

 * the output constraint means that there is a path from the

 * constraint's output to one of its inputs.

 */

Planner.prototype.addPropagate = function (c, mark) {

  var todo = new OrderedCollection();

  todo.add(c);

  while (todo.size() > 0) {

    var d = todo.removeFirst();

    if (d.output().mark == mark) {

      this.incrementalRemove(c);

      return false;

    }

    d.recalculate();

    this.addConstraintsConsumingTo(d.output(), todo);

  }

  return true;

}

/**

 * Update the walkabout strengths and stay flags of all variables

 * downstream of the given constraint. Answer a collection of

 * unsatisfied constraints sorted in order of decreasing strength.

 */

Planner.prototype.removePropagateFrom = function (out) {

  out.determinedBy = null;

  out.walkStrength = Strength.WEAKEST;

  out.stay = true;

  var unsatisfied = new OrderedCollection();

  var todo = new OrderedCollection();

  todo.add(out);

  while (todo.size() > 0) {

    var v = todo.removeFirst();

    for (var i = 0; i < v.constraints.size(); i++) {

      var c = v.constraints.at(i);

      if (!c.isSatisfied())

        unsatisfied.add(c);

    }

    var determining = v.determinedBy;

    for (var i = 0; i < v.constraints.size(); i++) {

      var next = v.constraints.at(i);

      if (next != determining && next.isSatisfied()) {

        next.recalculate();

        todo.add(next.output());

      }

    }

  }

  return unsatisfied;

}

Planner.prototype.addConstraintsConsumingTo = function (v, coll) {

  var determining = v.determinedBy;

  var cc = v.constraints;

  for (var i = 0; i < cc.size(); i++) {

    var c = cc.at(i);

    if (c != determining && c.isSatisfied())

      coll.add(c);

  }

}

/* --- *

 * P l a n

 * --- */

/**

 * A Plan is an ordered list of constraints to be executed in sequence

 * to resatisfy all currently satisfiable constraints in the face of

 * one or more changing inputs.

 */

function Plan() {

  this.v = new OrderedCollection();

}

Plan.prototype.addConstraint = function (c) {

  this.v.add(c);

}

Plan.prototype.size = function () {

  return this.v.size();

}

Plan.prototype.constraintAt = function (index) {

  return this.v.at(index);

}

Plan.prototype.execute = function () {

  for (var i = 0; i < this.size(); i++) {

    var c = this.constraintAt(i);

    c.execute();

  }

}

/* --- *

 * M a i n

 * --- */

/**

 * This is the standard DeltaBlue benchmark. A long chain of equality

 * constraints is constructed with a stay constraint on one end. An

 * edit constraint is then added to the opposite end and the time is

 * measured for adding and removing this constraint, and extracting

 * and executing a constraint satisfaction plan. There are two cases.

 * In case 1, the added constraint is stronger than the stay

 * constraint and values must propagate down the entire length of the

 * chain. In case 2, the added constraint is weaker than the stay

 * constraint so it cannot be accomodated. The cost in this case is,

 * of course, very low. Typical situations lie somewhere between these

 * two extremes.

 */

function chainTest(n) {

  planner = new Planner();

  var prev = null, first = null, last = null;

  // Build chain of n equality constraints

  for (var i = 0; i <= n; i++) {

    var name = "v" + i;

    var v = new Variable(name);

    if (prev != null)

      new EqualityConstraint(prev, v, Strength.REQUIRED);

    if (i == 0) first = v;

    if (i == n) last = v;

    prev = v;

  }

  new StayConstraint(last, Strength.STRONG_DEFAULT);

  var edit = new EditConstraint(first, Strength.PREFERRED);

  var edits = new OrderedCollection();

  edits.add(edit);

  var plan = planner.extractPlanFromConstraints(edits);

  for (var i = 0; i < 100; i++) {

    first.value = i;

    plan.execute();

    if (last.value != i)

      alert("Chain test failed.");

  }

}

/**

 * This test constructs a two sets of variables related to each

 * other by a simple linear transformation (scale and offset). The

 * time is measured to change a variable on either side of the

 * mapping and to change the scale and offset factors.

 */

function projectionTest(n) {

  planner = new Planner();

  var scale = new Variable("scale", 10);

  var offset = new Variable("offset", 1000);

  var src = null, dst = null;

  var dests = new OrderedCollection();

  for (var i = 0; i < n; i++) {

    src = new Variable("src" + i, i);

    dst = new Variable("dst" + i, i);

    dests.add(dst);

    new StayConstraint(src, Strength.NORMAL);

    new ScaleConstraint(src, scale, offset, dst, Strength.REQUIRED);

  }

  change(src, 17);

  if (dst.value != 1170) alert("Projection 1 failed");

  change(dst, 1050);

  if (src.value != 5) alert("Projection 2 failed");

  change(scale, 5);

  for (var i = 0; i < n - 1; i++) {

    if (dests.at(i).value != i * 5 + 1000)

      alert("Projection 3 failed");

  }

  change(offset, 2000);

  for (var i = 0; i < n - 1; i++) {

    if (dests.at(i).value != i * 5 + 2000)

      alert("Projection 4 failed");

  }

}

function change(v, newValue) {

  var edit = new EditConstraint(v, Strength.PREFERRED);

  var edits = new OrderedCollection();

  edits.add(edit);

  var plan = planner.extractPlanFromConstraints(edits);

  for (var i = 0; i < 10; i++) {

    v.value = newValue;

    plan.execute();

  }

  edit.destroyConstraint();

}

// Global variable holding the current planner.

var planner = null;

function deltaBlue() {

  chainTest(100);

  projectionTest(100);

}