Merge pull request #29 from abarth/basic_structure

Start building the repository structure

.travis.yml

+language: dart
+sudo: false
+dart:
+  - stable
+before_script:
+  - ./travis/setup.sh
+script:
+  - ./travis/test.sh

packages/cassowary/lib/cassowary.dart

+// Copyright (c) 2015 The Chromium Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style license that can be
+// found in the LICENSE file.
+
+library cassowary;
+
+import 'dart:math';
+
+part 'constraint.dart';
+part 'expression.dart';
+part 'term.dart';
+part 'variable.dart';
+part 'equation_member.dart';
+part 'constant_member.dart';
+part 'solver.dart';
+part 'symbol.dart';
+part 'row.dart';
+part 'utils.dart';
+part 'result.dart';
+part 'parser_exception.dart';
+part 'param.dart';
+part 'priority.dart';

packages/cassowary/lib/constant_member.dart

+// Copyright (c) 2015 The Chromium Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style license that can be
+// found in the LICENSE file.
+
+part of cassowary;
+
+class ConstantMember extends _EquationMember {
+  final double value;
+
+  bool get isConstant => true;
+
+  ConstantMember(this.value);
+
+  Expression asExpression() => new Expression([], this.value);
+}
+
+ConstantMember cm(double value) {
+  return new ConstantMember(value);
+}

packages/cassowary/lib/constraint.dart

+// Copyright (c) 2015 The Chromium Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style license that can be
+// found in the LICENSE file.
+
+part of cassowary;
+
+enum Relation { equalTo, lessThanOrEqualTo, greaterThanOrEqualTo, }
+
+class Constraint {
+  final Relation relation;
+  final Expression expression;
+  double priority = Priority.required;
+
+  Constraint(this.expression, this.relation);
+
+  Constraint operator |(double p) => this..priority = p;
+
+  String toString() {
+    StringBuffer buffer = new StringBuffer();
+    buffer.write(expression.toString());
+
+    switch (relation) {
+      case Relation.equalTo:
+        buffer.write(" == 0 ");
+        break;
+      case Relation.greaterThanOrEqualTo:
+        buffer.write(" >= 0 ");
+        break;
+      case Relation.lessThanOrEqualTo:
+        buffer.write(" <= 0 ");
+        break;
+    }
+
+    buffer.write(" | priority = ${priority}");
+
+    if (priority == Priority.required) {
+      buffer.write(" (required)");
+    }
+
+    return buffer.toString();
+  }
+}

packages/cassowary/lib/equation_member.dart

+// Copyright (c) 2015 The Chromium Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style license that can be
+// found in the LICENSE file.
+
+part of cassowary;
+
+abstract class _EquationMember {
+  Expression asExpression();
+
+  bool get isConstant;
+
+  double get value;
+
+  Constraint operator >=(_EquationMember m) => asExpression() >= m;
+
+  Constraint operator <=(_EquationMember m) => asExpression() <= m;
+
+  operator ==(_EquationMember m) => asExpression() == m;
+
+  Expression operator +(_EquationMember m) => asExpression() + m;
+
+  Expression operator -(_EquationMember m) => asExpression() - m;
+
+  Expression operator *(_EquationMember m) => asExpression() * m;
+
+  Expression operator /(_EquationMember m) => asExpression() / m;
+
+  int get hashCode =>
+      throw "An equation member is not comparable and cannot be added to collections";
+}

packages/cassowary/lib/expression.dart

+// Copyright (c) 2015 The Chromium Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style license that can be
+// found in the LICENSE file.
+
+part of cassowary;
+
+class Expression extends _EquationMember {
+  final List<Term> terms;
+
+  final double constant;
+
+  bool get isConstant => terms.length == 0;
+
+  double get value => terms.fold(constant, (value, term) => value + term.value);
+
+  Expression(this.terms, this.constant);
+  Expression.fromExpression(Expression expr)
+      : this.terms = new List<Term>.from(expr.terms),
+        this.constant = expr.constant;
+
+  Expression asExpression() => this;
+
+  Constraint _createConstraint(
+      _EquationMember /* rhs */ value, Relation relation) {
+    if (value is ConstantMember) {
+      return new Constraint(
+          new Expression(new List.from(terms), constant - value.value),
+          relation);
+    }
+
+    if (value is Param) {
+      var newTerms = new List<Term>.from(terms)
+        ..add(new Term(value.variable, -1.0));
+      return new Constraint(new Expression(newTerms, constant), relation);
+    }
+
+    if (value is Term) {
+      var newTerms = new List<Term>.from(terms)
+        ..add(new Term(value.variable, -value.coefficient));
+      return new Constraint(new Expression(newTerms, constant), relation);
+    }
+
+    if (value is Expression) {
+      var newTerms = value.terms.fold(new List<Term>.from(terms),
+          (list, t) => list..add(new Term(t.variable, -t.coefficient)));
+      return new Constraint(
+          new Expression(newTerms, constant - value.constant), relation);
+    }
+
+    assert(false);
+    return null;
+  }
+
+  Constraint operator >=(_EquationMember value) =>
+      _createConstraint(value, Relation.greaterThanOrEqualTo);
+
+  Constraint operator <=(_EquationMember value) =>
+      _createConstraint(value, Relation.lessThanOrEqualTo);
+
+  operator ==(_EquationMember value) =>
+      _createConstraint(value, Relation.equalTo);
+
+  Expression operator +(_EquationMember m) {
+    if (m is ConstantMember) {
+      return new Expression(new List.from(terms), constant + m.value);
+    }
+
+    if (m is Param) {
+      return new Expression(
+          new List.from(terms)..add(new Term(m.variable, 1.0)), constant);
+    }
+
+    if (m is Term) {
+      return new Expression(new List.from(terms)..add(m), constant);
+    }
+
+    if (m is Expression) {
+      return new Expression(
+          new List.from(terms)..addAll(m.terms), constant + m.constant);
+    }
+
+    assert(false);
+    return null;
+  }
+
+  Expression operator -(_EquationMember m) {
+    if (m is ConstantMember) {
+      return new Expression(new List.from(terms), constant - m.value);
+    }
+
+    if (m is Param) {
+      return new Expression(
+          new List.from(terms)..add(new Term(m.variable, -1.0)), constant);
+    }
+
+    if (m is Term) {
+      return new Expression(new List.from(terms)
+        ..add(new Term(m.variable, -m.coefficient)), constant);
+    }
+
+    if (m is Expression) {
+      var copiedTerms = new List<Term>.from(terms);
+      m.terms.forEach(
+          (t) => copiedTerms.add(new Term(t.variable, -t.coefficient)));
+      return new Expression(copiedTerms, constant - m.constant);
+    }
+
+    assert(false);
+    return null;
+  }
+
+  _EquationMember _applyMultiplicand(double m) {
+    var newTerms = terms.fold(new List<Term>(), (list, term) => list
+      ..add(new Term(term.variable, term.coefficient * m)));
+    return new Expression(newTerms, constant * m);
+  }
+
+  _Pair<Expression, double> _findMulitplierAndMultiplicand(_EquationMember m) {
+    // At least on of the the two members must be constant for the resulting
+    // expression to be linear
+
+    if (!this.isConstant && !m.isConstant) {
+      return null;
+    }
+
+    if (this.isConstant) {
+      return new _Pair(m.asExpression(), this.value);
+    }
+
+    if (m.isConstant) {
+      return new _Pair(this.asExpression(), m.value);
+    }
+
+    assert(false);
+    return null;
+  }
+
+  _EquationMember operator *(_EquationMember m) {
+    _Pair<Expression, double> args = _findMulitplierAndMultiplicand(m);
+
+    if (args == null) {
+      throw new ParserException(
+          "Could not find constant multiplicand or multiplier", [this, m]);
+      return null;
+    }
+
+    return args.first._applyMultiplicand(args.second);
+  }
+
+  _EquationMember operator /(_EquationMember m) {
+    if (!m.isConstant) {
+      throw new ParserException(
+          "The divisor was not a constant expression", [this, m]);
+      return null;
+    }
+
+    return this._applyMultiplicand(1.0 / m.value);
+  }
+
+  String toString() {
+    StringBuffer buffer = new StringBuffer();
+
+    terms.forEach((t) => buffer.write("${t}"));
+
+    if (constant != 0.0) {
+      buffer.write(constant.sign > 0.0 ? "+" : "-");
+      buffer.write(constant.abs());
+    }
+
+    return buffer.toString();
+  }
+}

packages/cassowary/lib/param.dart

+// Copyright (c) 2015 The Chromium Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style license that can be
+// found in the LICENSE file.
+
+part of cassowary;
+
+class Param extends _EquationMember {
+  final Variable variable;
+  dynamic context;
+
+  Param([double value = 0.0]) : variable = new Variable(value) {
+    variable._owner = this;
+  }
+
+  Param.withContext(ctx, [double value = 0.0])
+      : variable = new Variable(value),
+        context = ctx {
+    variable._owner = this;
+  }
+
+  bool get isConstant => false;
+
+  double get value => variable.value;
+
+  String get name => variable.name;
+  set name(String name) => variable.name = name;
+
+  Expression asExpression() => new Expression([new Term(variable, 1.0)], 0.0);
+}

packages/cassowary/lib/parser_exception.dart

+// Copyright (c) 2015 The Chromium Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style license that can be
+// found in the LICENSE file.
+
+part of cassowary;
+
+class ParserException implements Exception {
+  final String message;
+  List<_EquationMember> members;
+  ParserException(this.message, this.members);
+
+  String toString() {
+    if (message == null) return "Error while parsing constraint or expression";
+    return "Error: '$message' while trying to parse constraint or expression";
+  }
+}

packages/cassowary/lib/priority.dart

+// Copyright (c) 2015 The Chromium Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style license that can be
+// found in the LICENSE file.
+
+part of cassowary;
+
+class Priority {
+  static final double required = create(1e3, 1e3, 1e3);
+  static final double strong = create(1.0, 0.0, 0.0);
+  static final double medium = create(0.0, 1.0, 0.0);
+  static final double weak = create(0.0, 0.0, 1.0);
+
+  static double create(double a, double b, double c) {
+    double result = 0.0;
+    result += max(0.0, min(1e3, a)) * 1e6;
+    result += max(0.0, min(1e3, b)) * 1e3;
+    result += max(0.0, min(1e3, c));
+    return result;
+  }
+
+  static double clamp(double value) {
+    return max(0.0, min(required, value));
+  }
+}

packages/cassowary/lib/result.dart

+// Copyright (c) 2015 The Chromium Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style license that can be
+// found in the LICENSE file.
+
+part of cassowary;
+
+class Result {
+  final String message;
+  final bool error;
+
+  const Result(this.message, { bool isError: true }) : error = isError;
+
+  static final Result success = const Result("Success", isError: false);
+  static final Result unimplemented = const Result("Unimplemented");
+  static final Result duplicateConstraint =
+      const Result("Duplicate Constraint");
+  static final Result unsatisfiableConstraint =
+      const Result("Unsatisfiable Constraint");
+  static final Result unknownConstraint =
+      const Result("Unknown Constraint");
+  static final Result duplicateEditVariable =
+      const Result("Duplicate Edit Variable");
+  static final Result badRequiredStrength =
+      const Result("Bad Required Strength");
+  static final Result unknownEditVariable =
+      const Result("Unknown Edit Variable");
+  static final Result internalSolverError =
+      const Result("Internal Solver Error");
+}

packages/cassowary/lib/row.dart

+// Copyright (c) 2015 The Chromium Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style license that can be
+// found in the LICENSE file.
+
+part of cassowary;
+
+class _Row {
+  final Map<_Symbol, double> cells;
+  double constant = 0.0;
+
+  _Row(this.constant) : this.cells = new Map<_Symbol, double>();
+  _Row.fromRow(_Row row)
+      : this.cells = new Map<_Symbol, double>.from(row.cells),
+        this.constant = row.constant;
+
+  double add(double value) => constant += value;
+
+  void insertSymbol(_Symbol symbol, [double coefficient = 1.0]) {
+    double val = _elvis(cells[symbol], 0.0);
+
+    if (_nearZero(val + coefficient)) {
+      cells.remove(symbol);
+    } else {
+      cells[symbol] = val + coefficient;
+    }
+  }
+
+  void insertRow(_Row other, [double coefficient = 1.0]) {
+    constant += other.constant * coefficient;
+    other.cells.forEach((s, v) => insertSymbol(s, v * coefficient));
+  }
+
+  void removeSymbol(_Symbol symbol) {
+    cells.remove(symbol);
+  }
+
+  void reverseSign() {
+    constant = -constant;
+    cells.forEach((s, v) => cells[s] = -v);
+  }
+
+  void solveForSymbol(_Symbol symbol) {
+    assert(cells.containsKey(symbol));
+    double coefficient = -1.0 / cells[symbol];
+    cells.remove(symbol);
+    constant *= coefficient;
+    cells.forEach((s, v) => cells[s] = v * coefficient);
+  }
+
+  void solveForSymbols(_Symbol lhs, _Symbol rhs) {
+    insertSymbol(lhs, -1.0);
+    solveForSymbol(rhs);
+  }
+
+  double coefficientForSymbol(_Symbol symbol) => _elvis(cells[symbol], 0.0);
+
+  void substitute(_Symbol symbol, _Row row) {
+    double coefficient = cells[symbol];
+
+    if (coefficient == null) {
+      return;
+    }
+
+    cells.remove(symbol);
+    insertRow(row, coefficient);
+  }
+
+  String toString() {
+    StringBuffer buffer = new StringBuffer();
+
+    buffer.write(constant);
+
+    cells.forEach((symbol, value) =>
+        buffer.write(" + " + value.toString() + " * " + symbol.toString()));
+
+    return buffer.toString();
+  }
+}

packages/cassowary/lib/solver.dart

+// Copyright (c) 2015 The Chromium Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style license that can be
+// found in the LICENSE file.
+
+part of cassowary;
+
+class Solver {
+  final Map<Constraint, _Tag> _constraints = new Map<Constraint, _Tag>();
+  final Map<_Symbol, _Row> _rows = new Map<_Symbol, _Row>();
+  final Map<Variable, _Symbol> _vars = new Map<Variable, _Symbol>();
+  final Map<Variable, _EditInfo> _edits = new Map<Variable, _EditInfo>();
+  final List<_Symbol> _infeasibleRows = new List<_Symbol>();
+  final _Row _objective = new _Row(0.0);
+  _Row _artificial = new _Row(0.0);
+  int tick = 1;
+
+  /// Attempts to add the constraints in the list to the solver. If it cannot
+  /// add any for some reason, a cleanup is attempted so that either all
+  /// constraints will be added or none.
+  Result addConstraints(List<Constraint> constraints) {
+    _SolverBulkUpdate applier = (Constraint c) => addConstraint(c);
+    _SolverBulkUpdate undoer = (Constraint c) => removeConstraint(c);
+
+    return _bulkEdit(constraints, applier, undoer);
+  }
+
+  Result addConstraint(Constraint constraint) {
+    if (_constraints.containsKey(constraint)) {
+      return Result.duplicateConstraint;
+    }
+
+    _Tag tag = new _Tag(new _Symbol(_SymbolType.invalid, 0),
+        new _Symbol(_SymbolType.invalid, 0));
+
+    _Row row = _createRow(constraint, tag);
+
+    _Symbol subject = _chooseSubjectForRow(row, tag);
+
+    if (subject.type == _SymbolType.invalid && _allDummiesInRow(row)) {
+      if (!_nearZero(row.constant)) {
+        return Result.unsatisfiableConstraint;
+      } else {
+        subject = tag.marker;
+      }
+    }
+
+    if (subject.type == _SymbolType.invalid) {
+      if (!_addWithArtificialVariableOnRow(row)) {
+        return Result.unsatisfiableConstraint;
+      }
+    } else {
+      row.solveForSymbol(subject);
+      _substitute(subject, row);
+      _rows[subject] = row;
+    }
+
+    _constraints[constraint] = tag;
+
+    return _optimizeObjectiveRow(_objective);
+  }
+
+  Result removeConstraints(List<Constraint> constraints) {
+    _SolverBulkUpdate applier = (Constraint c) => removeConstraint(c);
+    _SolverBulkUpdate undoer = (Constraint c) => addConstraint(c);
+
+    return _bulkEdit(constraints, applier, undoer);
+  }
+
+  Result removeConstraint(Constraint constraint) {
+    _Tag tag = _constraints[constraint];
+    if (tag == null) {
+      return Result.unknownConstraint;
+    }
+
+    tag = new _Tag.fromTag(tag);
+    _constraints.remove(constraint);
+
+    _removeConstraintEffects(constraint, tag);
+
+    _Row row = _rows[tag.marker];
+    if (row != null) {
+      _rows.remove(tag.marker);
+    } else {
+      _Pair<_Symbol, _Row> rowPair = _leavingRowPairForMarkerSymbol(tag.marker);
+
+      if (rowPair == null) {
+        return Result.internalSolverError;
+      }
+
+      _Symbol leaving = rowPair.first;
+      row = rowPair.second;
+      var removed = _rows.remove(rowPair.first);
+      assert(removed != null);
+      row.solveForSymbols(leaving, tag.marker);
+      _substitute(tag.marker, row);
+    }
+
+    return _optimizeObjectiveRow(_objective);
+  }
+
+  bool hasConstraint(Constraint constraint) {
+    return _constraints.containsKey(constraint);
+  }
+
+  Result addEditVariables(List<Variable> variables, double priority) {
+    _SolverBulkUpdate applier = (Variable v) => addEditVariable(v, priority);
+    _SolverBulkUpdate undoer = (Variable v) => removeEditVariable(v);
+
+    return _bulkEdit(variables, applier, undoer);
+  }
+
+  Result addEditVariable(Variable variable, double priority) {
+    if (_edits.containsKey(variable)) {
+      return Result.duplicateEditVariable;
+    }
+
+    if (!_isValidNonRequiredPriority(priority)) {
+      return Result.badRequiredStrength;
+    }
+
+    Constraint constraint = new Constraint(
+        new Expression([new Term(variable, 1.0)], 0.0), Relation.equalTo);
+    constraint.priority = priority;
+
+    if (addConstraint(constraint) != Result.success) {
+      return Result.internalSolverError;
+    }
+
+    _EditInfo info = new _EditInfo();
+    info.tag = _constraints[constraint];
+    info.constraint = constraint;
+    info.constant = 0.0;
+
+    _edits[variable] = info;
+
+    return Result.success;
+  }
+
+  Result removeEditVariables(List<Variable> variables) {
+    _SolverBulkUpdate applier = (Variable v) => removeEditVariable(v);
+    _SolverBulkUpdate undoer = (Variable v) =>
+        addEditVariable(v, _edits[v].constraint.priority);
+
+    return _bulkEdit(variables, applier, undoer);
+  }
+
+  Result removeEditVariable(Variable variable) {
+    _EditInfo info = _edits[variable];
+    if (info == null) {
+      return Result.unknownEditVariable;
+    }
+
+    if (removeConstraint(info.constraint) != Result.success) {
+      return Result.internalSolverError;
+    }
+
+    _edits.remove(variable);
+    return Result.success;
+  }
+
+  bool hasEditVariable(Variable variable) {
+    return _edits.containsKey(variable);
+  }
+
+  Result suggestValueForVariable(Variable variable, double value) {
+    if (!_edits.containsKey(variable)) {
+      return Result.unknownEditVariable;
+    }
+
+    _suggestValueForEditInfoWithoutDualOptimization(_edits[variable], value);
+
+    return _dualOptimize();
+  }
+
+  Set flushUpdates() {
+    Set updates = new Set();
+
+    for (Variable variable in _vars.keys) {
+      _Symbol symbol = _vars[variable];
+      _Row row = _rows[symbol];
+
+      double updatedValue = row == null ? 0.0 : row.constant;
+
+      if (variable._applyUpdate(updatedValue) && variable._owner != null) {
+        dynamic context = variable._owner.context;
+
+        if (context != null) {
+          updates.add(context);
+        }
+      }
+    }
+
+    return updates;
+  }
+
+  Result _bulkEdit(Iterable items,
+                   _SolverBulkUpdate applier,
+                   _SolverBulkUpdate undoer) {
+    List applied = new List();
+    bool needsCleanup = false;
+
+    Result result = Result.success;
+
+    for (dynamic item in items) {
+      result = applier(item);
+      if (result == Result.success) {
+        applied.add(item);
+      } else {
+        needsCleanup = true;
+        break;
+      }
+    }
+
+    if (needsCleanup) {
+      for (dynamic item in applied.reversed) {
+        undoer(item);
+      }
+    }
+
+    return result;
+  }
+
+  _Symbol _symbolForVariable(Variable variable) {
+    _Symbol symbol = _vars[variable];
+
+    if (symbol != null) {
+      return symbol;
+    }
+
+    symbol = new _Symbol(_SymbolType.external, tick++);
+    _vars[variable] = symbol;
+
+    return symbol;
+  }
+
+  _Row _createRow(Constraint constraint, _Tag tag) {
+    Expression expr = new Expression.fromExpression(constraint.expression);
+    _Row row = new _Row(expr.constant);
+
+    expr.terms.forEach((term) {
+      if (!_nearZero(term.coefficient)) {
+        _Symbol symbol = _symbolForVariable(term.variable);
+
+        _Row foundRow = _rows[symbol];
+
+        if (foundRow != null) {
+          row.insertRow(foundRow, term.coefficient);
+        } else {
+          row.insertSymbol(symbol, term.coefficient);
+        }
+      }
+    });
+
+    switch (constraint.relation) {
+      case Relation.lessThanOrEqualTo:
+      case Relation.greaterThanOrEqualTo:
+        {
+          double coefficient =
+              constraint.relation == Relation.lessThanOrEqualTo ? 1.0 : -1.0;
+
+          _Symbol slack = new _Symbol(_SymbolType.slack, tick++);
+          tag.marker = slack;
+          row.insertSymbol(slack, coefficient);
+
+          if (constraint.priority < Priority.required) {
+            _Symbol error = new _Symbol(_SymbolType.error, tick++);
+            tag.other = error;
+            row.insertSymbol(error, -coefficient);
+            _objective.insertSymbol(error, constraint.priority);
+          }
+        }
+        break;
+      case Relation.equalTo:
+        if (constraint.priority < Priority.required) {
+          _Symbol errPlus = new _Symbol(_SymbolType.error, tick++);
+          _Symbol errMinus = new _Symbol(_SymbolType.error, tick++);
+          tag.marker = errPlus;
+          tag.other = errMinus;
+          row.insertSymbol(errPlus, -1.0);
+          row.insertSymbol(errMinus, 1.0);
+          _objective.insertSymbol(errPlus, constraint.priority);
+          _objective.insertSymbol(errMinus, constraint.priority);
+        } else {
+          _Symbol dummy = new _Symbol(_SymbolType.dummy, tick++);
+          tag.marker = dummy;
+          row.insertSymbol(dummy);
+        }
+        break;
+    }
+
+    if (row.constant < 0.0) {
+      row.reverseSign();
+    }
+
+    return row;
+  }
+
+  _Symbol _chooseSubjectForRow(_Row row, _Tag tag) {
+    for (_Symbol symbol in row.cells.keys) {
+      if (symbol.type == _SymbolType.external) {
+        return symbol;
+      }
+    }
+
+    if (tag.marker.type == _SymbolType.slack ||
+        tag.marker.type == _SymbolType.error) {
+      if (row.coefficientForSymbol(tag.marker) < 0.0) {
+        return tag.marker;
+      }
+    }
+
+    if (tag.other.type == _SymbolType.slack ||
+        tag.other.type == _SymbolType.error) {
+      if (row.coefficientForSymbol(tag.other) < 0.0) {
+        return tag.other;
+      }
+    }
+
+    return new _Symbol(_SymbolType.invalid, 0);
+  }
+
+  bool _allDummiesInRow(_Row row) {
+    for (_Symbol symbol in row.cells.keys) {
+      if (symbol.type != _SymbolType.dummy) {
+        return false;
+      }
+    }
+    return true;
+  }
+
+  bool _addWithArtificialVariableOnRow(_Row row) {
+    _Symbol artificial = new _Symbol(_SymbolType.slack, tick++);
+    _rows[artificial] = new _Row.fromRow(row);
+    _artificial = new _Row.fromRow(row);
+
+    Result result = _optimizeObjectiveRow(_artificial);
+
+    if (result.error) {
+      // FIXME(csg): Propagate this up!
+      return false;
+    }
+
+    bool success = _nearZero(_artificial.constant);
+    _artificial = new _Row(0.0);
+
+    _Row foundRow = _rows[artificial];
+    if (foundRow != null) {
+      _rows.remove(artificial);
+      if (foundRow.cells.isEmpty) {
+        return success;
+      }
+
+      _Symbol entering = _anyPivotableSymbol(foundRow);
+      if (entering.type == _SymbolType.invalid) {
+        return false;
+      }
+
+      foundRow.solveForSymbols(artificial, entering);
+      _substitute(entering, foundRow);
+      _rows[entering] = foundRow;
+    }
+
+    for (_Row row in _rows.values) {
+      row.removeSymbol(artificial);
+    }
+    _objective.removeSymbol(artificial);
+    return success;
+  }
+
+  Result _optimizeObjectiveRow(_Row objective) {
+    while (true) {
+      _Symbol entering = _enteringSymbolForObjectiveRow(objective);
+      if (entering.type == _SymbolType.invalid) {
+        return Result.success;
+      }
+
+      _Pair<_Symbol, _Row> leavingPair = _leavingRowForEnteringSymbol(entering);
+
+      if (leavingPair == null) {
+        return Result.internalSolverError;
+      }
+
+      _Symbol leaving = leavingPair.first;
+      _Row row = leavingPair.second;
+      _rows.remove(leavingPair.first);
+      row.solveForSymbols(leaving, entering);
+      _substitute(entering, row);
+      _rows[entering] = row;
+    }
+  }
+
+  _Symbol _enteringSymbolForObjectiveRow(_Row objective) {
+    Map<_Symbol, double> cells = objective.cells;
+
+    for (_Symbol symbol in cells.keys) {
+      if (symbol.type != _SymbolType.dummy && cells[symbol] < 0.0) {
+        return symbol;
+      }
+    }
+
+    return new _Symbol(_SymbolType.invalid, 0);
+  }
+
+  _Pair<_Symbol, _Row> _leavingRowForEnteringSymbol(_Symbol entering) {
+    double ratio = double.MAX_FINITE;
+    _Pair<_Symbol, _Row> result = new _Pair(null, null);
+
+    _rows.forEach((symbol, row) {
+      if (symbol.type != _SymbolType.external) {
+        double temp = row.coefficientForSymbol(entering);
+
+        if (temp < 0.0) {
+          double temp_ratio = -row.constant / temp;
+
+          if (temp_ratio < ratio) {
+            ratio = temp_ratio;
+            result.first = symbol;
+            result.second = row;
+          }
+        }
+      }
+    });
+
+    if (result.first == null || result.second == null) {
+      return null;
+    }
+
+    return result;
+  }
+
+  void _substitute(_Symbol symbol, _Row row) {
+    _rows.forEach((first, second) {
+      second.substitute(symbol, row);
+      if (first.type != _SymbolType.external && second.constant < 0.0) {
+        _infeasibleRows.add(first);
+      }
+    });
+
+    _objective.substitute(symbol, row);
+    if (_artificial != null) {
+      _artificial.substitute(symbol, row);
+    }
+  }
+
+  _Symbol _anyPivotableSymbol(_Row row) {
+    for (_Symbol symbol in row.cells.keys) {
+      if (symbol.type == _SymbolType.slack ||
+          symbol.type == _SymbolType.error) {
+        return symbol;
+      }
+    }
+    return new _Symbol(_SymbolType.invalid, 0);
+  }
+
+  void _removeConstraintEffects(Constraint cn, _Tag tag) {
+    if (tag.marker.type == _SymbolType.error) {
+      _removeMarkerEffects(tag.marker, cn.priority);
+    }
+    if (tag.other.type == _SymbolType.error) {
+      _removeMarkerEffects(tag.other, cn.priority);
+    }
+  }
+
+  void _removeMarkerEffects(_Symbol marker, double strength) {
+    _Row row = _rows[marker];
+    if (row != null) {
+      _objective.insertRow(row, -strength);
+    } else {
+      _objective.insertSymbol(marker, -strength);
+    }
+  }
+
+  _Pair<_Symbol, _Row> _leavingRowPairForMarkerSymbol(_Symbol marker) {
+    double r1 = double.MAX_FINITE;
+    double r2 = double.MAX_FINITE;
+
+    _Pair<_Symbol, _Row> first, second, third;
+
+    _rows.forEach((symbol, row) {
+      double c = row.coefficientForSymbol(marker);
+
+      if (c == 0.0) {
+        return;
+      }
+
+      if (symbol.type == _SymbolType.external) {
+        third = new _Pair(symbol, row);
+      } else if (c < 0.0) {
+        double r = -row.constant / c;
+        if (r < r1) {
+          r1 = r;
+          first = new _Pair(symbol, row);
+        }
+      } else {
+        double r = row.constant / c;
+        if (r < r2) {
+          r2 = r;
+          second = new _Pair(symbol, row);
+        }
+      }
+    });
+
+    if (first != null) {
+      return first;
+    }
+    if (second != null) {
+      return second;
+    }
+    return third;
+  }
+
+  void _suggestValueForEditInfoWithoutDualOptimization(
+      _EditInfo info, double value) {
+    double delta = value - info.constant;
+    info.constant = value;
+
+    {
+      _Symbol symbol = info.tag.marker;
+      _Row row = _rows[info.tag.marker];
+
+      if (row != null) {
+        if (row.add(-delta) < 0.0) {
+          _infeasibleRows.add(symbol);
+        }
+        return;
+      }
+
+      symbol = info.tag.other;
+      row = _rows[info.tag.other];
+
+      if (row != null) {
+        if (row.add(delta) < 0.0) {
+          _infeasibleRows.add(symbol);
+        }
+        return;
+      }
+    }
+
+    for (_Symbol symbol in _rows.keys) {
+      _Row row = _rows[symbol];
+      double coeff = row.coefficientForSymbol(info.tag.marker);
+      if (coeff != 0.0 &&
+          row.add(delta * coeff) < 0.0 &&
+          symbol.type != _SymbolType.external) {
+        _infeasibleRows.add(symbol);
+      }
+    }
+  }
+
+  Result _dualOptimize() {
+    while (_infeasibleRows.length != 0) {
+      _Symbol leaving = _infeasibleRows.removeLast();
+      _Row row = _rows[leaving];
+
+      if (row != null && row.constant < 0.0) {
+        _Symbol entering = _dualEnteringSymbolForRow(row);
+
+        if (entering.type == _SymbolType.invalid) {
+          return Result.internalSolverError;
+        }
+
+        _rows.remove(leaving);
+
+        row.solveForSymbols(leaving, entering);
+        _substitute(entering, row);
+        _rows[entering] = row;
+      }
+    }
+    return Result.success;
+  }
+
+  _Symbol _dualEnteringSymbolForRow(_Row row) {
+    _Symbol entering;
+
+    double ratio = double.MAX_FINITE;
+
+    Map<_Symbol, double> rowCells = row.cells;
+
+    for (_Symbol symbol in rowCells.keys) {
+      double value = rowCells[symbol];
+
+      if (value > 0.0 && symbol.type != _SymbolType.dummy) {
+        double coeff = _objective.coefficientForSymbol(symbol);
+        double r = coeff / value;
+        if (r < ratio) {
+          ratio = r;
+          entering = symbol;
+        }
+      }
+    }
+
+    return _elvis(entering, new _Symbol(_SymbolType.invalid, 0));
+  }
+
+  String toString() {
+    StringBuffer buffer = new StringBuffer();
+    String separator = "\n~~~~~~~~~";
+
+    // Objective
+    buffer.writeln(separator + " Objective");
+    buffer.writeln(_objective.toString());
+
+    // Tableau
+    buffer.writeln(separator + " Tableau");
+    _rows.forEach((symbol, row) {
+      buffer.write(symbol.toString());
+      buffer.write(" | ");
+      buffer.writeln(row.toString());
+    });
+
+    // Infeasible
+    buffer.writeln(separator + " Infeasible");
+    _infeasibleRows.forEach((symbol) => buffer.writeln(symbol.toString()));
+
+    // Variables
+    buffer.writeln(separator + " Variables");
+    _vars.forEach((variable, symbol) =>
+        buffer.writeln("${variable.toString()} = ${symbol.toString()}"));
+
+    // Edit Variables
+    buffer.writeln(separator + " Edit Variables");
+    _edits.forEach((variable, editinfo) => buffer.writeln(variable));
+
+    // Constraints
+    buffer.writeln(separator + " Constraints");
+    _constraints.forEach((constraint, _) => buffer.writeln(constraint));
+
+    return buffer.toString();
+  }
+}
+
+class _Tag {
+  _Symbol marker;
+  _Symbol other;
+
+  _Tag(this.marker, this.other);
+  _Tag.fromTag(_Tag tag)
+      : this.marker = tag.marker,
+        this.other = tag.other;
+}
+
+class _EditInfo {
+  _Tag tag;
+  Constraint constraint;
+  double constant;
+}
+
+bool _isValidNonRequiredPriority(double priority) {
+  return (priority >= 0.0 && priority < Priority.required);
+}
+
+typedef Result _SolverBulkUpdate(dynamic item);

packages/cassowary/lib/symbol.dart

+// Copyright (c) 2015 The Chromium Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style license that can be
+// found in the LICENSE file.
+
+part of cassowary;
+
+enum _SymbolType { invalid, external, slack, error, dummy, }
+
+class _Symbol {
+  final _SymbolType type;
+  final int tick;
+
+  _Symbol(this.type, this.tick);
+
+  String toString() {
+    String typeString = "unknown";
+    switch (type) {
+      case _SymbolType.invalid:
+        typeString = "i";
+        break;
+      case _SymbolType.external:
+        typeString = "v";
+        break;
+      case _SymbolType.slack:
+        typeString = "s";
+        break;
+      case _SymbolType.error:
+        typeString = "e";
+        break;
+      case _SymbolType.dummy:
+        typeString = "d";
+        break;
+    }
+    return "${typeString}${tick}";
+  }
+}

packages/cassowary/lib/term.dart

+// Copyright (c) 2015 The Chromium Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style license that can be
+// found in the LICENSE file.
+
+part of cassowary;
+
+class Term extends _EquationMember {
+  final Variable variable;
+  final double coefficient;
+
+  bool get isConstant => false;
+
+  double get value => coefficient * variable.value;
+
+  Term(this.variable, this.coefficient);
+
+  Expression asExpression() =>
+      new Expression([new Term(this.variable, this.coefficient)], 0.0);
+
+  String toString() {
+    StringBuffer buffer = new StringBuffer();
+
+    buffer.write(coefficient.sign > 0.0 ? "+" : "-");
+
+    if (coefficient.abs() != 1.0) {
+      buffer.write(coefficient.abs());
+      buffer.write("*");
+    }
+
+    buffer.write(variable);
+
+    return buffer.toString();
+  }
+}

packages/cassowary/lib/utils.dart

+// Copyright (c) 2015 The Chromium Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style license that can be
+// found in the LICENSE file.
+
+part of cassowary;
+
+bool _nearZero(double value) {
+  const double epsilon = 1.0e-8;
+  return value < 0.0 ? -value < epsilon : value < epsilon;
+}
+
+// Workaround for the lack of a null coalescing operator. Uses a ternary
+// instead. Sadly, due the lack of generic types on functions, we have to use
+// dynamic instead.
+_elvis(a, b) => a != null ? a : b;
+
+class _Pair<X, Y> {
+  X first;
+  Y second;
+  _Pair(this.first, this.second);
+}

packages/cassowary/lib/variable.dart

+// Copyright (c) 2015 The Chromium Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style license that can be
+// found in the LICENSE file.
+
+part of cassowary;
+
+class Variable {
+  double value;
+  String name;
+
+  Param _owner;
+
+  final int _tick;
+  static int _total = 0;
+
+  Variable(this.value) : _tick = _total++;
+
+  bool _applyUpdate(double updated) {
+    bool res = updated != value;
+    value = updated;
+    return res;
+  }
+
+  String get debugName => _elvis(name, "variable${_tick}");
+
+  String toString() => debugName;
+}

packages/cassowary/pubspec.yaml

+name: cassowary
+description: Cassowary Constraint Solving Toolkit
+version: 0.1.7
+author: Flutter Authors <flutter-dev@googlegroups.com>
+homepage: https://github.com/flutter/flutter/tree/master/packages/cassowary
+environment:
+  sdk: '>=1.0.0 <2.0.0'
+dev_dependencies:
+  test: '>=0.12.0 <0.13.0'
+  test_runner: '<=0.2.16'
+  dart_coveralls: '<=0.3.0'

packages/cassowary/test/cassowary_test.dart

+// Copyright (c) 2015 The Chromium Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style license that can be
+// found in the LICENSE file.
+
+library cassowary.test;
+
+import 'package:test/test.dart';
+
+import 'package:cassowary/cassowary.dart';
+
+void main() {
+  test('variable', () {
+    var v = new Param(22.0);
+    expect(v.value, 22);
+  });
+
+  test('variable1', () {
+    var v = new Param(22.0);
+    expect((v + cm(22.0)).value, 44.0);
+    expect((v - cm(20.0)).value, 2.0);
+  });
+
+  test('term', () {
+    var t = new Term(new Variable(22.0), 2.0);
+    expect(t.value, 44);
+  });
+
+  test('expression', () {
+    var terms = [
+      new Term(new Variable(22.0), 2.0),
+      new Term(new Variable(1.0), 1.0),
+    ];
+    var e = new Expression(terms, 40.0);
+    expect(e.value, 85.0);
+  });
+
+  test('expression1', () {
+    var v1 = new Param(10.0);
+    var v2 = new Param(10.0);
+    var v3 = new Param(22.0);
+
+    expect(v1 is Param, true);
+    expect(v1 + cm(20.0) is Expression, true);
+    expect(v1 + v2 is Expression, true);
+
+    expect((v1 + v2).value, 20.0);
+    expect((v1 - v2).value, 0.0);
+
+    expect((v1 + v2 + v3) is Expression, true);
+    expect((v1 + v2 + v3).value, 42.0);
+  });
+
+  test('expression2', () {
+    var e = new Param(10.0) + cm(5.0);
+    expect(e.value, 15.0);
+    expect(e is Expression, true);
+
+    // Constant
+    expect((e + cm(2.0)) is Expression, true);
+    expect((e + cm(2.0)).value, 17.0);
+    expect((e - cm(2.0)) is Expression, true);
+    expect((e - cm(2.0)).value, 13.0);
+
+    expect(e.value, 15.0);
+
+    // Param
+    var v = new Param(2.0);
+    expect((e + v) is Expression, true);
+    expect((e + v).value, 17.0);
+    expect((e - v) is Expression, true);
+    expect((e - v).value, 13.0);
+
+    expect(e.value, 15.0);
+
+    // Term
+    var t = new Term(v.variable, 2.0);
+    expect((e + t) is Expression, true);
+    expect((e + t).value, 19.0);
+    expect((e - t) is Expression, true);
+    expect((e - t).value, 11.0);
+
+    expect(e.value, 15.0);
+
+    // Expression
+    var e2 = new Param(7.0) + new Param(3.0);
+    expect((e + e2) is Expression, true);
+    expect((e + e2).value, 25.0);
+    expect((e - e2) is Expression, true);
+    expect((e - e2).value, 5.0);
+
+    expect(e.value, 15.0);
+  });
+
+  test('term2', () {
+    var t = new Term(new Variable(12.0), 1.0);
+
+    // Constant
+    var c = cm(2.0);
+    expect((t + c) is Expression, true);
+    expect((t + c).value, 14.0);
+    expect((t - c) is Expression, true);
+    expect((t - c).value, 10.0);
+
+    // Variable
+    var v = new Param(2.0);
+    expect((t + v) is Expression, true);
+    expect((t + v).value, 14.0);
+    expect((t - v) is Expression, true);
+    expect((t - v).value, 10.0);
+
+    // Term
+    var t2 = new Term(new Variable(1.0), 2.0);
+    expect((t + t2) is Expression, true);
+    expect((t + t2).value, 14.0);
+    expect((t - t2) is Expression, true);
+    expect((t - t2).value, 10.0);
+
+    // Expression
+    var exp = new Param(1.0) + cm(1.0);
+    expect((t + exp) is Expression, true);
+    expect((t + exp).value, 14.0);
+    expect((t - exp) is Expression, true);
+    expect((t - exp).value, 10.0);
+  });
+
+  test('variable3', () {
+    var v = new Param(3.0);
+
+    // Constant
+    var c = cm(2.0);
+    expect((v + c) is Expression, true);
+    expect((v + c).value, 5.0);
+    expect((v - c) is Expression, true);
+    expect((v - c).value, 1.0);
+
+    // Variable
+    var v2 = new Param(2.0);
+    expect((v + v2) is Expression, true);
+    expect((v + v2).value, 5.0);
+    expect((v - v2) is Expression, true);
+    expect((v - v2).value, 1.0);
+
+    // Term
+    var t2 = new Term(new Variable(1.0), 2.0);
+    expect((v + t2) is Expression, true);
+    expect((v + t2).value, 5.0);
+    expect((v - t2) is Expression, true);
+    expect((v - t2).value, 1.0);
+
+    // Expression
+    var exp = new Param(1.0) + cm(1.0);
+    expect(exp.terms.length, 1);
+
+    expect((v + exp) is Expression, true);
+    expect((v + exp).value, 5.0);
+    expect((v - exp) is Expression, true);
+    expect((v - exp).value, 1.0);
+  });
+
+  test('constantmember', () {
+    var c = cm(3.0);
+
+    // Constant
+    var c2 = cm(2.0);
+    expect((c + c2) is Expression, true);
+    expect((c + c2).value, 5.0);
+    expect((c - c2) is Expression, true);
+    expect((c - c2).value, 1.0);
+
+    // Variable
+    var v2 = new Param(2.0);
+    expect((c + v2) is Expression, true);
+    expect((c + v2).value, 5.0);
+    expect((c - v2) is Expression, true);
+    expect((c - v2).value, 1.0);
+
+    // Term
+    var t2 = new Term(new Variable(1.0), 2.0);
+    expect((c + t2) is Expression, true);
+    expect((c + t2).value, 5.0);
+    expect((c - t2) is Expression, true);
+    expect((c - t2).value, 1.0);
+
+    // Expression
+    var exp = new Param(1.0) + cm(1.0);
+
+    expect((c + exp) is Expression, true);
+    expect((c + exp).value, 5.0);
+    expect((c - exp) is Expression, true);
+    expect((c - exp).value, 1.0);
+  });
+
+  test('constraint2', () {
+    var left = new Param(10.0);
+    var right = new Param(100.0);
+
+    var c = right - left >= cm(25.0);
+    expect(c is Constraint, true);
+  });
+
+  test('simple_multiplication', () {
+    // Constant
+    var c = cm(20.0);
+    expect((c * cm(2.0)).value, 40.0);
+
+    // Variable
+    var v = new Param(20.0);
+    expect((v * cm(2.0)).value, 40.0);
+
+    // Term
+    var t = new Term(v.variable, 1.0);
+    expect((t * cm(2.0)).value, 40.0);
+
+    // Expression
+    var e = new Expression([t], 0.0);
+    expect((e * cm(2.0)).value, 40.0);
+  });
+
+  test('simple_division', () {
+    // Constant
+    var c = cm(20.0);
+    expect((c / cm(2.0)).value, 10.0);
+
+    // Variable
+    var v = new Param(20.0);
+    expect((v / cm(2.0)).value, 10.0);
+
+    // Term
+    var t = new Term(v.variable, 1.0);
+    expect((t / cm(2.0)).value, 10.0);
+
+    // Expression
+    var e = new Expression([t], 0.0);
+    expect((e / cm(2.0)).value, 10.0);
+  });
+
+  test('full_constraints_setup', () {
+    var left = new Param(2.0);
+    var right = new Param(10.0);
+
+    var c1 = right - left >= cm(20.0);
+    expect(c1 is Constraint, true);
+    expect(c1.expression.constant, -20.0);
+    expect(c1.relation, Relation.greaterThanOrEqualTo);
+
+    var c2 = (right - left == cm(30.0)) as Constraint;
+    expect(c2 is Constraint, true);
+    expect(c2.expression.constant, -30.0);
+    expect(c2.relation, Relation.equalTo);
+
+    var c3 = right - left <= cm(30.0);
+    expect(c3 is Constraint, true);
+    expect(c3.expression.constant, -30.0);
+    expect(c3.relation, Relation.lessThanOrEqualTo);
+  });
+
+  test('constraint_strength_update', () {
+    var left = new Param(2.0);
+    var right = new Param(10.0);
+
+    var c = (right - left >= cm(200.0)) | 750.0;
+    expect(c is Constraint, true);
+    expect(c.expression.terms.length, 2);
+    expect(c.expression.constant, -200.0);
+    expect(c.priority, 750.0);
+  });
+
+  test('solver', () {
+    var s = new Solver();
+
+    var left = new Param(2.0);
+    var right = new Param(100.0);
+
+    var c1 = right - left >= cm(200.0);
+
+    expect((right >= left) is Constraint, true);
+
+    expect(s.addConstraint(c1), Result.success);
+  });
+
+  test('constraint_complex', () {
+    var e = new Param(200.0) - new Param(100.0);
+
+    // Constant
+    var c1 = e >= cm(50.0);
+    expect(c1 is Constraint, true);
+    expect(c1.expression.terms.length, 2);
+    expect(c1.expression.constant, -50.0);
+
+    // Variable
+    var c2 = e >= new Param(2.0);
+    expect(c2 is Constraint, true);
+    expect(c2.expression.terms.length, 3);
+    expect(c2.expression.constant, 0.0);
+
+    // Term
+    var c3 = e >= new Term(new Variable(2.0), 1.0);
+    expect(c3 is Constraint, true);
+    expect(c3.expression.terms.length, 3);
+    expect(c3.expression.constant, 0.0);
+
+    // Expression
+    var c4 = e >= new Expression([new Term(new Variable(2.0), 1.0)], 20.0);
+    expect(c4 is Constraint, true);
+    expect(c4.expression.terms.length, 3);
+    expect(c4.expression.constant, -20.0);
+  });
+
+  test('constraint_complex_non_exprs', () {
+    // Constant
+    var c1 = cm(100.0) >= cm(50.0);
+    expect(c1 is Constraint, true);
+    expect(c1.expression.terms.length, 0);
+    expect(c1.expression.constant, 50.0);
+
+    // Variable
+    var c2 = new Param(100.0) >= new Param(2.0);
+    expect(c2 is Constraint, true);
+    expect(c2.expression.terms.length, 2);
+    expect(c2.expression.constant, 0.0);
+
+    // Term
+    var t = new Term(new Variable(100.0), 1.0);
+    var c3 = t >= new Term(new Variable(2.0), 1.0);
+    expect(c3 is Constraint, true);
+    expect(c3.expression.terms.length, 2);
+    expect(c3.expression.constant, 0.0);
+
+    // Expression
+    var e = new Expression([t], 0.0);
+    var c4 = e >= new Expression([new Term(new Variable(2.0), 1.0)], 20.0);
+    expect(c4 is Constraint, true);
+    expect(c4.expression.terms.length, 2);
+    expect(c4.expression.constant, -20.0);
+  });
+
+  test('constraint_update_in_solver', () {
+    var s = new Solver();
+
+    var left = new Param(2.0);
+    var right = new Param(100.0);
+
+    var c1 = right - left >= cm(200.0);
+    var c2 = right >= right;
+
+    expect(s.addConstraint(c1), Result.success);
+    expect(s.addConstraint(c1), Result.duplicateConstraint);
+    expect(s.removeConstraint(c2), Result.unknownConstraint);
+    expect(s.removeConstraint(c1), Result.success);
+    expect(s.removeConstraint(c1), Result.unknownConstraint);
+  });
+
+  test('test_multiplication_division_override', () {
+    var c = cm(10.0);
+    var v = new Param(c.value);
+    var t = new Term(v.variable, 1.0);
+    var e = new Expression([t], 0.0);
+
+    // Constant
+    expect((c * cm(10.0)).value, 100);
+
+    // Variable
+    expect((v * cm(10.0)).value, 100);
+
+    // Term
+    expect((t * cm(10.0)).value, 100);
+
+    // Expression
+    expect((e * cm(10.0)).value, 100);
+
+    // Constant
+    expect((c / cm(10.0)).value, 1);
+
+    // Variable
+    expect((v / cm(10.0)).value, 1);
+
+    // Term
+    expect((t / cm(10.0)).value, 1);
+
+    // Expression
+    expect((e / cm(10.0)).value, 1);
+  });
+
+  test('test_multiplication_division_exceptions', () {
+    var c = cm(10.0);
+    var v = new Param(c.value);
+    var t = new Term(v.variable, 1.0);
+    var e = new Expression([t], 0.0);
+
+    expect((c * c).value, 100);
+    expect(() => v * v, throwsA(new isInstanceOf<ParserException>()));
+    expect(() => v / v, throwsA(new isInstanceOf<ParserException>()));
+    expect(() => v * t, throwsA(new isInstanceOf<ParserException>()));
+    expect(() => v / t, throwsA(new isInstanceOf<ParserException>()));
+    expect(() => v * e, throwsA(new isInstanceOf<ParserException>()));
+    expect(() => v / e, throwsA(new isInstanceOf<ParserException>()));
+    expect(() => v * c, returnsNormally);
+    expect(() => v / c, returnsNormally);
+  });
+
+  test('edit_updates', () {
+    Solver s = new Solver();
+
+    var left = new Param(0.0);
+    var right = new Param(100.0);
+    var mid = new Param(0.0);
+
+    Constraint c = left + right >= cm(2.0) * mid;
+    expect(s.addConstraint(c), Result.success);
+
+    expect(s.addEditVariable(mid.variable, 999.0), Result.success);
+    expect(
+        s.addEditVariable(mid.variable, 999.0), Result.duplicateEditVariable);
+    expect(s.removeEditVariable(mid.variable), Result.success);
+    expect(s.removeEditVariable(mid.variable), Result.unknownEditVariable);
+  });
+
+  test('bug1', () {
+    var left = new Param(0.0);
+    var right = new Param(100.0);
+    var mid = new Param(0.0);
+
+    expect(((left + right) >= (cm(2.0) * mid)) is Constraint, true);
+  });
+
+  test('single_item', () {
+    var left = new Param(-20.0);
+    Solver s = new Solver();
+    s.addConstraint(left >= cm(0.0));
+    s.flushUpdates();
+    expect(left.value, 0.0);
+  });
+
+  test('midpoints', () {
+    var left = new Param(0.0)..name = "left";
+    var right = new Param(0.0)..name = "right";
+    var mid = new Param(0.0)..name = "mid";
+
+    Solver s = new Solver();
+
+    expect(s.addConstraint((right + left == mid * cm(2.0)) as Constraint),
+        Result.success);
+    expect(s.addConstraint(right - left >= cm(100.0)), Result.success);
+    expect(s.addConstraint(left >= cm(0.0)), Result.success);
+
+    s.flushUpdates();
+
+    expect(left.value, 0.0);
+    expect(mid.value, 50.0);
+    expect(right.value, 100.0);
+  });
+
+  test('addition_of_multiple', () {
+    var left = new Param(0.0);
+    var right = new Param(0.0);
+    var mid = new Param(0.0);
+
+    Solver s = new Solver();
+
+    var c = (left >= cm(0.0));
+
+    expect(s.addConstraints([
+      (left + right == cm(2.0) * mid) as Constraint,
+      (right - left >= cm(100.0)),
+      c
+    ]), Result.success);
+
+    expect(s.addConstraints([(right >= cm(-20.0)), c]),
+        Result.duplicateConstraint);
+  });
+
+  test('edit_constraints', () {
+    var left = new Param(0.0)..name = "left";
+    var right = new Param(0.0)..name = "right";
+    var mid = new Param(0.0)..name = "mid";
+
+    Solver s = new Solver();
+
+    expect(s.addConstraint((right + left == mid * cm(2.0)) as Constraint),
+        Result.success);
+    expect(s.addConstraint(right - left >= cm(100.0)), Result.success);
+    expect(s.addConstraint(left >= cm(0.0)), Result.success);
+
+    expect(s.addEditVariable(mid.variable, Priority.strong), Result.success);
+    expect(s.suggestValueForVariable(mid.variable, 300.0), Result.success);
+
+    s.flushUpdates();
+
+    expect(left.value, 0.0);
+    expect(mid.value, 300.0);
+    expect(right.value, 600.0);
+  });
+
+  test('test_description', () {
+    var left = new Param(0.0);
+    var right = new Param(100.0);
+    var c1 = right >= left;
+    var c2 = right <= left;
+    var c3 = (right == left) as Constraint;
+
+    Solver s = new Solver();
+    expect(s.addConstraint(c1), Result.success);
+    expect(s.addConstraint(c2), Result.success);
+    expect(s.addConstraint(c3), Result.success);
+
+    expect(s.toString() != null, true);
+  });
+
+  test('solution_with_optimize', () {
+    Param p1 = new Param();
+    Param p2 = new Param();
+    Param p3 = new Param();
+
+    Param container = new Param();
+
+    Solver solver = new Solver();
+
+    solver.addEditVariable(container.variable, Priority.strong);
+    solver.suggestValueForVariable(container.variable, 100.0);
+
+    solver.addConstraint((p1 >= cm(30.0)) | Priority.strong);
+    solver.addConstraint(((p1 == p3) as Constraint) | Priority.medium);
+    solver.addConstraint((p2 == cm(2.0) * p1) as Constraint);
+    solver.addConstraint((container == (p1 + p2 + p3)) as Constraint);
+
+    solver.flushUpdates();
+
+    expect(container.value, 100.0);
+
+    expect(p1.value, 30.0);
+    expect(p2.value, 60.0);
+    expect(p3.value, 10.0);
+  });
+
+  test('test_updates_collection', () {
+    Param left = new Param.withContext("left");
+    Param mid = new Param.withContext("mid");
+    Param right = new Param.withContext("right");
+
+    Solver s = new Solver();
+
+    expect(s.addEditVariable(mid.variable, Priority.strong), Result.success);
+
+    expect(s.addConstraint((mid * cm(2.0) == left + right) as Constraint),
+        Result.success);
+    expect(s.addConstraint(left >= cm(0.0)), Result.success);
+
+    expect(s.suggestValueForVariable(mid.variable, 50.0), Result.success);
+
+    var updates = s.flushUpdates();
+
+    expect(updates.length, 2);
+
+    expect(left.value, 0.0);
+    expect(mid.value, 50.0);
+    expect(right.value, 100.0);
+  });
+
+  test('test_updates_collection_is_set', () {
+    Param left = new Param.withContext("a");
+    Param mid = new Param.withContext("a");
+    Param right = new Param.withContext("a");
+
+    Solver s = new Solver();
+
+    expect(s.addEditVariable(mid.variable, Priority.strong), Result.success);
+
+    expect(s.addConstraint((mid * cm(2.0) == left + right) as Constraint),
+        Result.success);
+    expect(s.addConstraint(left >= cm(10.0)), Result.success);
+
+    expect(s.suggestValueForVariable(mid.variable, 50.0), Result.success);
+
+    var updates = s.flushUpdates();
+
+    expect(updates.length, 1);
+
+    expect(left.value, 10.0);
+    expect(mid.value, 50.0);
+    expect(right.value, 90.0);
+  });
+
+  test('param_context_non_final', () {
+    var p = new Param.withContext("a");
+    p.context = "b";
+    expect(p.context, "b");
+  });
+
+  test('check_type_of_eq_result', () {
+    Param left = new Param();
+    Param right = new Param();
+
+    expect((left == right).runtimeType, Constraint);
+  });
+
+  test('bulk_add_edit_variables', () {
+    Solver s = new Solver();
+
+    var left = new Param(0.0);
+    var right = new Param(100.0);
+    var mid = new Param(0.0);
+
+    expect(s.addEditVariables(
+         [left.variable, right.variable, mid.variable], 999.0), Result.success);
+  });
+
+  test('bulk_remove_constraints_and_variables', () {
+    Solver s = new Solver();
+
+    var left = new Param(0.0);
+    var right = new Param(100.0);
+    var mid = new Param(0.0);
+
+    expect(s.addEditVariables(
+         [left.variable, right.variable, mid.variable], 999.0), Result.success);
+
+    var c1 = left <= mid;
+    var c2 = mid <= right;
+
+    expect(s.addConstraints([c1, c2]), Result.success);
+
+    expect(s.removeConstraints([c1, c2]), Result.success);
+
+    expect(s.removeEditVariables(
+                [left.variable, right.variable, mid.variable]), Result.success);
+  });
+}

packages/newton/README.md

+# Newton
+[![Build Status](https://travis-ci.org/flutter/newton.svg?branch=master)](https://travis-ci.org/flutter/newton)
+[![Coverage Status](https://coveralls.io/repos/domokit/newton/badge.svg?branch=master)](https://coveralls.io/r/domokit/newton?branch=master)
+
+Simple Physics Simulations for Dart. Springs, friction, gravity, etc.
+
+To run the tests:
+pub get
+dart test/newton_test.dart

packages/newton/lib/newton.dart

+// Copyright (c) 2015 The Chromium Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style license that can be
+// found in the LICENSE file.
+
+library newton;
+
+import 'dart:math' as math;
+
+part 'src/simulation.dart';
+part 'src/simulation_group.dart';
+part 'src/tolerance.dart';
+part 'src/utils.dart';
+
+part 'src/friction_simulation.dart';
+part 'src/gravity_simulation.dart';
+part 'src/scroll_simulation.dart';
+part 'src/spring_simulation.dart';
+part 'src/spring_solution.dart';

packages/newton/lib/src/friction_simulation.dart

+// Copyright (c) 2015 The Chromium Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style license that can be
+// found in the LICENSE file.
+
+part of newton;
+
+class FrictionSimulation extends Simulation {
+  final double _drag;
+  final double _dragLog;
+  final double _x;
+  final double _v;
+
+  FrictionSimulation(double drag, double position, double velocity)
+      : _drag = drag,
+        _dragLog = math.log(drag),
+        _x = position,
+        _v = velocity;
+
+  // Return the drag value for a FrictionSimulation whose x() and dx() values pass
+  // through the specified start and end position/velocity values.
+  //
+  // Total time to reach endVelocity is just: (log(endVelocity) / log(startVelocity)) / log(_drag)
+  // or (log(v1) - log(v0)) / log(D), given v = v0 * D^t per the dx() function below.
+  // Solving for D given x(time) is trickier. Algebra courtesy of Wolfram Alpha:
+  // x1 = x0 + (v0 * D^((log(v1) - log(v0)) / log(D))) / log(D) - v0 / log(D), find D
+  static double _dragFor(double startPosition, double endPosition, double startVelocity, double endVelocity) {
+    return math.pow(math.E, (startVelocity - endVelocity) / (startPosition - endPosition));
+  }
+
+  // A friction simulation that starts and ends at the specified positions
+  // and velocities.
+  factory FrictionSimulation.through(double startPosition, double endPosition, double startVelocity, double endVelocity) {
+    return new FrictionSimulation(
+      _dragFor(startPosition, endPosition, startVelocity, endVelocity),
+      startPosition,
+      startVelocity)
+      .. tolerance = new Tolerance(velocity: endVelocity.abs());
+  }
+
+  double x(double time) => _x + _v * math.pow(_drag, time) / _dragLog - _v / _dragLog;
+
+  double dx(double time) => _v * math.pow(_drag, time);
+
+  @override
+  bool isDone(double time) => dx(time).abs() < this.tolerance.velocity;
+}
+
+class BoundedFrictionSimulation extends FrictionSimulation {
+  BoundedFrictionSimulation(
+    double drag,
+    double position,
+    double velocity,
+    double this._minX,
+    double this._maxX) : super(drag, position, velocity);
+
+  final double _minX;
+  final double _maxX;
+
+  double x(double time) {
+    return super.x(time).clamp(_minX, _maxX);
+  }
+
+  bool isDone(double time) {
+    return super.isDone(time) ||
+      (x(time) - _minX).abs() < tolerance.distance ||
+      (x(time) - _maxX).abs() < tolerance.distance;
+  }
+}

packages/newton/lib/src/gravity_simulation.dart

+// Copyright (c) 2015 The Chromium Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style license that can be
+// found in the LICENSE file.
+
+part of newton;
+
+class GravitySimulation extends Simulation {
+  final double _x;
+  final double _v;
+  final double _a;
+  final double _end;
+
+  GravitySimulation(
+      double acceleration, double distance, double endDistance, double velocity)
+      : _a = acceleration,
+        _x = distance,
+        _v = velocity,
+        _end = endDistance;
+
+  double x(double time) => _x + _v * time + 0.5 * _a * time * time;
+
+  double dx(double time) => _v + time * _a;
+
+  @override
+  bool isDone(double time) => x(time).abs() >= _end;
+}

packages/newton/lib/src/scroll_simulation.dart

+// Copyright (c) 2015 The Chromium Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style license that can be
+// found in the LICENSE file.
+
+part of newton;
+
+/// Simulates kinetic scrolling behavior between a leading and trailing
+/// boundary. Friction is applied within the extends and a spring action applied
+/// at the boundaries. This simulation can only step forward.
+class ScrollSimulation extends SimulationGroup {
+  ScrollSimulation(
+    double position,
+    double velocity,
+    this._leadingExtent,
+    this._trailingExtent,
+    this._spring,
+    this._drag) {
+    _chooseSimulation(position, velocity, 0.0);
+  }
+
+  final double _leadingExtent;
+  final double _trailingExtent;
+  final SpringDescription _spring;
+  final double _drag;
+
+  bool _isSpringing = false;
+  Simulation _currentSimulation;
+  double _offset = 0.0;
+
+  @override
+  bool step(double time) => _chooseSimulation(
+      _currentSimulation.x(time - _offset),
+      _currentSimulation.dx(time - _offset), time);
+
+  @override
+  Simulation get currentSimulation => _currentSimulation;
+
+  @override
+  double get currentIntervalOffset => _offset;
+
+  bool _chooseSimulation(double position, double velocity, double intervalOffset) {
+    if (_spring == null && (position > _trailingExtent || position < _leadingExtent))
+      return false;
+
+    /// This simulation can only step forward.
+    if (!_isSpringing) {
+      if (position > _trailingExtent) {
+        _isSpringing = true;
+        _offset = intervalOffset;
+        _currentSimulation = new ScrollSpringSimulation(_spring, position, _trailingExtent, velocity);
+        return true;
+      } else if (position < _leadingExtent) {
+        _isSpringing = true;
+        _offset = intervalOffset;
+        _currentSimulation = new ScrollSpringSimulation(_spring, position, _leadingExtent, velocity);
+        return true;
+      }
+    }
+
+    if (_currentSimulation == null) {
+      _currentSimulation = new FrictionSimulation(_drag, position, velocity);
+      return true;
+    }
+
+    return false;
+  }
+}

packages/newton/lib/src/simulation.dart

+// Copyright (c) 2015 The Chromium Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style license that can be
+// found in the LICENSE file.
+
+part of newton;
+
+abstract class Simulatable {
+  /// The current position of the object in the simulation
+  double x(double time);
+
+  /// The current velocity of the object in the simulation
+  double dx(double time);
+}
+
+/// The base class for all simulations. The user is meant to instantiate an
+/// instance of a simulation and query the same for the position and velocity
+/// of the body at a given interval.
+abstract class Simulation implements Simulatable {
+  Tolerance tolerance = toleranceDefault;
+
+  /// Returns if the simulation is done at a given time
+  bool isDone(double time);
+}

packages/newton/lib/src/simulation_group.dart

+// Copyright (c) 2015 The Chromium Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style license that can be
+// found in the LICENSE file.
+
+part of newton;
+
+/// The abstract base class for all composite simulations. Concrete subclasses
+/// must implement the appropriate methods to select the appropriate simulation
+/// at a given time interval. The simulation group takes care to call the `step`
+/// method at appropriate intervals. If more fine grained control over the the
+/// step is necessary, subclasses may override `Simulatable` methods.
+abstract class SimulationGroup extends Simulation {
+
+  /// The currently active simulation
+  Simulation get currentSimulation;
+
+  /// The time offset applied to the currently active simulation;
+  double get currentIntervalOffset;
+
+  /// Called when a significant change in the interval is detected. Subclasses
+  /// must decide if the the current simulation must be switched (or updated).
+  /// The result is whether the simulation was switched in this step.
+  bool step(double time);
+
+  double x(double time) {
+    _stepIfNecessary(time);
+    return currentSimulation.x(time - currentIntervalOffset);
+  }
+
+  double dx(double time) {
+    _stepIfNecessary(time);
+    return currentSimulation.dx(time - currentIntervalOffset);
+  }
+
+  @override
+  void set tolerance(Tolerance t) {
+    this.currentSimulation.tolerance = t;
+    super.tolerance = t;
+  }
+
+  @override
+  bool isDone(double time) {
+    _stepIfNecessary(time);
+    return currentSimulation.isDone(time - currentIntervalOffset);
+  }
+
+  double _lastStep = -1.0;
+  void _stepIfNecessary(double time) {
+    if (_nearEqual(_lastStep, time, toleranceDefault.time)) {
+      return;
+    }
+
+    _lastStep = time;
+    if (step(time)) {
+      this.currentSimulation.tolerance = this.tolerance;
+    }
+  }
+}

packages/newton/lib/src/spring_simulation.dart

+// Copyright (c) 2015 The Chromium Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style license that can be
+// found in the LICENSE file.
+
+part of newton;
+
+class SpringDescription {
+  /// The mass of the spring (m)
+  final double mass;
+
+  /// The spring constant (k)
+  final double springConstant;
+
+  /// The damping coefficient.
+  /// Note: Not to be confused with the damping ratio. Use the separate
+  ///       constructor provided for this purpose
+  final double damping;
+
+  SpringDescription(
+      {double this.mass, double this.springConstant, double this.damping}) {
+    assert(mass != null);
+    assert(springConstant != null);
+    assert(damping != null);
+  }
+
+  /// Create a spring given the mass, spring constant and the damping ratio. The
+  /// damping ratio is especially useful trying to determing the type of spring
+  /// to create. A ratio of 1.0 creates a critically damped spring, > 1.0
+  /// creates an overdamped spring and < 1.0 an underdamped one.
+  SpringDescription.withDampingRatio(
+      {double mass, double springConstant, double ratio: 1.0})
+      : mass = mass,
+        springConstant = springConstant,
+        damping = ratio * 2.0 * math.sqrt(mass * springConstant);
+}
+
+enum SpringType { unknown, criticallyDamped, underDamped, overDamped, }
+
+/// Creates a spring simulation. Depending on the spring description, a
+/// critically, under or overdamped spring will be created.
+class SpringSimulation extends Simulation {
+  final double _endPosition;
+
+  final _SpringSolution _solution;
+
+  /// A spring description with the provided spring description, start distance,
+  /// end distance and velocity.
+  SpringSimulation(
+      SpringDescription desc, double start, double end, double velocity)
+      : this._endPosition = end,
+        _solution = new _SpringSolution(desc, start - end, velocity);
+
+  SpringType get type => _solution.type;
+
+  double x(double time) => _endPosition + _solution.x(time);
+
+  double dx(double time) => _solution.dx(time);
+
+  @override
+  bool isDone(double time) =>
+      _nearEqual(x(time), _endPosition, this.tolerance.distance) &&
+          _nearZero(dx(time), this.tolerance.velocity);
+}
+
+/// A SpringSimulation where the value of x() is guaranteed to have exactly the
+/// end value when the simulation isDone().
+class ScrollSpringSimulation extends SpringSimulation {
+  ScrollSpringSimulation(SpringDescription desc, double start, double end, double velocity)
+    : super(desc, start, end, velocity);
+
+  bool _isDone(double position, double velocity) {
+    return _nearEqual(position, _endPosition, tolerance.distance) && _nearZero(velocity, tolerance.velocity);
+  }
+
+  @override
+  double x(double time) {
+    double xAtTime = super.x(time);
+    return _isDone(xAtTime, dx(time)) ? _endPosition : xAtTime;
+  }
+
+  @override
+  bool isDone(double time) => _isDone(x(time), dx(time));
+}

packages/newton/lib/src/spring_solution.dart

+// Copyright (c) 2015 The Chromium Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style license that can be
+// found in the LICENSE file.
+
+part of newton;
+
+abstract class _SpringSolution implements Simulatable {
+  factory _SpringSolution(
+      SpringDescription desc, double initialPosition, double initialVelocity) {
+    double cmk =
+        desc.damping * desc.damping - 4 * desc.mass * desc.springConstant;
+
+    if (cmk == 0.0) {
+      return new _CriticalSolution(desc, initialPosition, initialVelocity);
+    } else if (cmk > 0.0) {
+      return new _OverdampedSolution(desc, initialPosition, initialVelocity);
+    } else {
+      return new _UnderdampedSolution(desc, initialPosition, initialVelocity);
+    }
+
+    return null;
+  }
+
+  SpringType get type;
+}
+
+class _CriticalSolution implements _SpringSolution {
+  final double _r, _c1, _c2;
+
+  factory _CriticalSolution(
+      SpringDescription desc, double distance, double velocity) {
+    final double r = -desc.damping / (2.0 * desc.mass);
+    final double c1 = distance;
+    final double c2 = velocity / (r * distance);
+    return new _CriticalSolution.withArgs(r, c1, c2);
+  }
+
+  SpringType get type => SpringType.criticallyDamped;
+
+  _CriticalSolution.withArgs(double r, double c1, double c2)
+      : _r = r,
+        _c1 = c1,
+        _c2 = c2;
+
+  double x(double time) => (_c1 + _c2 * time) * math.pow(math.E, _r * time);
+
+  double dx(double time) {
+    final double power = math.pow(math.E, _r * time);
+    return _r * (_c1 + _c2 * time) * power + _c2 * power;
+  }
+}
+
+class _OverdampedSolution implements _SpringSolution {
+  final double _r1, _r2, _c1, _c2;
+
+  factory _OverdampedSolution(
+      SpringDescription desc, double distance, double velocity) {
+    final double cmk =
+        desc.damping * desc.damping - 4 * desc.mass * desc.springConstant;
+
+    final double r1 = (-desc.damping - math.sqrt(cmk)) / (2.0 * desc.mass);
+    final double r2 = (-desc.damping + math.sqrt(cmk)) / (2.0 * desc.mass);
+    final double c2 = (velocity - r1 * distance) / (r2 - r1);
+    final double c1 = distance - c2;
+
+    return new _OverdampedSolution.withArgs(r1, r2, c1, c2);
+  }
+
+  _OverdampedSolution.withArgs(double r1, double r2, double c1, double c2)
+      : _r1 = r1,
+        _r2 = r2,
+        _c1 = c1,
+        _c2 = c2;
+
+  SpringType get type => SpringType.overDamped;
+
+  double x(double time) =>
+      (_c1 * math.pow(math.E, _r1 * time) + _c2 * math.pow(math.E, _r2 * time));
+
+  double dx(double time) => (_c1 * _r1 * math.pow(math.E, _r1 * time) +
+      _c2 * _r2 * math.pow(math.E, _r2 * time));
+}
+
+class _UnderdampedSolution implements _SpringSolution {
+  final double _w, _r, _c1, _c2;
+
+  factory _UnderdampedSolution(
+      SpringDescription desc, double distance, double velocity) {
+    final double w = math.sqrt(4.0 * desc.mass * desc.springConstant -
+            desc.damping * desc.damping) /
+        (2.0 * desc.mass);
+    final double r = -(desc.damping / 2.0 * desc.mass);
+    final double c1 = distance;
+    final double c2 = (velocity - r * distance) / w;
+
+    return new _UnderdampedSolution.withArgs(w, r, c1, c2);
+  }
+
+  _UnderdampedSolution.withArgs(double w, double r, double c1, double c2)
+      : _w = w,
+        _r = r,
+        _c1 = c1,
+        _c2 = c2;
+
+  SpringType get type => SpringType.underDamped;
+
+  double x(double time) => math.pow(math.E, _r * time) *
+      (_c1 * math.cos(_w * time) + _c2 * math.sin(_w * time));
+
+  double dx(double time) {
+    final double power = math.pow(math.E, _r * time);
+    final double cosine = math.cos(_w * time);
+    final double sine = math.sin(_w * time);
+
+    return power * (_c2 * _w * cosine - _c1 * _w * sine) +
+        _r * power * (_c2 * sine + _c1 * cosine);
+  }
+}

packages/newton/lib/src/tolerance.dart

+// Copyright (c) 2015 The Chromium Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style license that can be
+// found in the LICENSE file.
+
+part of newton;
+
+class Tolerance {
+  final double distance;
+  final double time;
+  final double velocity;
+
+  const Tolerance({this.distance: epsilonDefault, this.time: epsilonDefault,
+      this.velocity: epsilonDefault});
+}
+
+const double epsilonDefault = 1e-3;
+const Tolerance toleranceDefault = const Tolerance();

packages/newton/lib/src/utils.dart

+// Copyright (c) 2015 The Chromium Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style license that can be
+// found in the LICENSE file.
+
+part of newton;
+
+bool _nearEqual(double a, double b, double epsilon) =>
+    (a > (b - epsilon)) && (a < (b + epsilon));
+
+bool _nearZero(double a, double epsilon) => _nearEqual(a, 0.0, epsilon);

packages/newton/pubspec.yaml

+name: newton
+description: Simple Physics Simulations for Dart
+version: 0.1.5
+author: Flutter Authors <flutter-dev@googlegroups.com>
+homepage: https://github.com/flutter/flutter/tree/master/packages/newton
+environment:
+  sdk: '>=1.0.0 <2.0.0'
+dev_dependencies:
+  test: '>=0.12.0 <0.13.0'
+  test_runner: '<=0.2.16'
+  dart_coveralls: '<=0.3.0'

packages/newton/test/newton_test.dart

+// Copyright (c) 2015 The Chromium Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style license that can be
+// found in the LICENSE file.
+
+library simple_physics.test;
+
+import 'package:test/test.dart';
+
+import 'package:newton/newton.dart';
+
+void main() {
+  test('test_friction', () {
+    var friction = new FrictionSimulation(0.3, 100.0, 400.0);
+
+    friction.tolerance = const Tolerance(velocity: 1.0);
+
+    expect(friction.isDone(0.0), false);
+    expect(friction.x(0.0), 100);
+    expect(friction.dx(0.0), 400.0);
+
+    expect(friction.x(1.0) > 330 && friction.x(1.0) < 335, true);
+
+    expect(friction.dx(1.0), 120.0);
+    expect(friction.dx(2.0), 36.0);
+    expect(friction.dx(3.0), 10.8);
+    expect(friction.dx(4.0) < 3.5, true);
+
+    expect(friction.isDone(5.0), true);
+    expect(friction.x(5.0) > 431 && friction.x(5.0) < 432, true);
+  });
+
+  test('test_friction_through', () {
+    // Use a normal FrictionSimulation to generate start and end
+    // velocity and positions with drag = 0.025.
+    var startPosition = 10.0;
+    var startVelocity = 600.0;
+    var f = new FrictionSimulation(0.025, startPosition, startVelocity);
+    var endPosition = f.x(1.0);
+    var endVelocity = f.dx(1.0);
+    expect(endPosition, greaterThan(startPosition));
+    expect(endVelocity, lessThan(startVelocity));
+
+    // Verify that that the "through" FrictionSimulation ends up at
+    // endPosition and endVelocity; implies that it computed the right
+    // value for _drag.
+    var friction = new FrictionSimulation.through(
+        startPosition, endPosition, startVelocity, endVelocity);
+    expect(friction.isDone(0.0), false);
+    expect(friction.x(0.0), 10.0);
+    expect(friction.dx(0.0), 600.0);
+
+    double epsilon = 1e-4;
+    expect(friction.isDone(1.0 + epsilon), true);
+    expect(friction.x(1.0), closeTo(endPosition, epsilon));
+    expect(friction.dx(1.0), closeTo(endVelocity, epsilon));
+
+    // Same scenario as above except that the velocities are
+    // are negative.
+    startPosition = 1000.0;
+    startVelocity = -500.0;
+    f = new FrictionSimulation(0.025, 1000.0, -500.0);
+    endPosition = f.x(1.0);
+    endVelocity = f.dx(1.0);
+    expect(endPosition, lessThan(startPosition));
+    expect(endVelocity, greaterThan(startVelocity));
+
+    friction = new FrictionSimulation.through(
+        startPosition, endPosition, startVelocity, endVelocity);
+    expect(friction.isDone(1.0 + epsilon), true);
+    expect(friction.x(1.0), closeTo(endPosition, epsilon));
+    expect(friction.dx(1.0), closeTo(endVelocity, epsilon));
+  });
+
+  test('test_gravity', () {
+    var gravity = new GravitySimulation(200.0, 100.0, 600.0, 0.0);
+
+    expect(gravity.isDone(0.0), false);
+    expect(gravity.x(0.0), 100.0);
+    expect(gravity.dx(0.0), 0.0);
+
+    // Starts at 100
+    expect(gravity.x(0.25), 106.25);
+    expect(gravity.x(0.50), 125);
+    expect(gravity.x(0.75), 156.25);
+    expect(gravity.x(1.00), 200);
+    expect(gravity.x(1.25), 256.25);
+    expect(gravity.x(1.50), 325);
+    expect(gravity.x(1.75), 406.25);
+
+    // Starts at 0.0
+    expect(gravity.dx(0.25), 50.0);
+    expect(gravity.dx(0.50), 100);
+    expect(gravity.dx(0.75), 150.00);
+    expect(gravity.dx(1.00), 200.0);
+    expect(gravity.dx(1.25), 250.0);
+    expect(gravity.dx(1.50), 300);
+    expect(gravity.dx(1.75), 350);
+
+    expect(gravity.isDone(2.5), true);
+    expect(gravity.x(2.5), 725);
+    expect(gravity.dx(2.5), 500.0);
+  });
+
+  test('spring_types', () {
+    var crit = new SpringSimulation(new SpringDescription.withDampingRatio(
+        mass: 1.0, springConstant: 100.0), 0.0, 300.0, 0.0);
+    expect(crit.type, SpringType.criticallyDamped);
+
+    crit = new SpringSimulation(new SpringDescription.withDampingRatio(
+        mass: 1.0, springConstant: 100.0, ratio: 1.0), 0.0, 300.0, 0.0);
+    expect(crit.type, SpringType.criticallyDamped);
+
+    var under = new SpringSimulation(new SpringDescription.withDampingRatio(
+        mass: 1.0, springConstant: 100.0, ratio: 0.75), 0.0, 300.0, 0.0);
+    expect(under.type, SpringType.underDamped);
+
+    var over = new SpringSimulation(new SpringDescription.withDampingRatio(
+        mass: 1.0, springConstant: 100.0, ratio: 1.25), 0.0, 300.0, 0.0);
+    expect(over.type, SpringType.overDamped);
+
+    // Just so we don't forget how to create a desc without the ratio.
+    var other = new SpringSimulation(
+        new SpringDescription(mass: 1.0, springConstant: 100.0, damping: 20.0),
+        0.0, 20.0, 20.0);
+    expect(other.type, SpringType.criticallyDamped);
+  });
+
+  test('crit_spring', () {
+    var crit = new SpringSimulation(new SpringDescription.withDampingRatio(
+        mass: 1.0, springConstant: 100.0, ratio: 1.0), 0.0, 500.0, 0.0);
+
+    crit.tolerance = const Tolerance(distance: 0.01, velocity: 0.01);
+
+    expect(crit.type, SpringType.criticallyDamped);
+
+    expect(crit.isDone(0.0), false);
+    expect(crit.x(0.0), 0.0);
+    expect(crit.dx(0.0), 5000.0);
+
+    expect(crit.x(0.25).floor(), 458.0);
+    expect(crit.x(0.50).floor(), 496.0);
+    expect(crit.x(0.75).floor(), 499.0);
+
+    expect(crit.dx(0.25).floor(), 410);
+    expect(crit.dx(0.50).floor(), 33);
+    expect(crit.dx(0.75).floor(), 2);
+
+    expect(crit.isDone(1.50), true);
+    expect(crit.x(1.5) > 499.0 && crit.x(1.5) < 501.0, true);
+    expect(crit.dx(1.5) < 0.1, true /* basically within tolerance */);
+  });
+
+  test('overdamped_spring', () {
+    var over = new SpringSimulation(new SpringDescription.withDampingRatio(
+        mass: 1.0, springConstant: 100.0, ratio: 1.25), 0.0, 500.0, 0.0);
+
+    over.tolerance = const Tolerance(distance: 0.01, velocity: 0.01);
+
+    expect(over.type, SpringType.overDamped);
+
+    expect(over.isDone(0.0), false);
+    expect(over.x(0.0), 0.0);
+
+    expect(over.x(0.5).floor(), 445.0);
+    expect(over.x(1.0).floor(), 495.0);
+    expect(over.x(1.5).floor(), 499.0);
+
+    expect(over.dx(0.5).floor(), 273.0);
+    expect(over.dx(1.0).floor(), 22.0);
+    expect(over.dx(1.5).floor(), 1.0);
+
+    expect(over.isDone(3.0), true);
+  });
+
+  test('underdamped_spring', () {
+    var under = new SpringSimulation(new SpringDescription.withDampingRatio(
+        mass: 1.0, springConstant: 100.0, ratio: 0.25), 0.0, 300.0, 0.0);
+    expect(under.type, SpringType.underDamped);
+
+    expect(under.isDone(0.0), false);
+
+    // Overshot with negative velocity
+    expect(under.x(1.0).floor(), 325);
+    expect(under.dx(1.0).floor(), -65);
+
+    expect(under.dx(6.0).floor(), 0.0);
+    expect(under.x(6.0).floor(), 299);
+
+    expect(under.isDone(6.0), true);
+  });
+
+  test('test_kinetic_scroll', () {
+    var spring = new SpringDescription.withDampingRatio(
+        mass: 1.0, springConstant: 50.0, ratio: 0.5);
+
+    var scroll = new ScrollSimulation(100.0, 800.0, 0.0, 300.0, spring, 0.3);
+    scroll.tolerance = const Tolerance(velocity: 0.5, distance: 0.1);
+    expect(scroll.isDone(0.0), false);
+    expect(scroll.isDone(0.5), false); // switch from friction to spring
+    expect(scroll.isDone(3.5), true);
+
+    var scroll2 = new ScrollSimulation(100.0, -800.0, 0.0, 300.0, spring, 0.3);
+    scroll2.tolerance = const Tolerance(velocity: 0.5, distance: 0.1);
+    expect(scroll2.isDone(0.0), false);
+    expect(scroll2.isDone(0.5), false); // switch from friction to spring
+    expect(scroll2.isDone(3.5), true);
+  });
+
+  test('scroll_with_inf_edge_ends', () {
+    var spring = new SpringDescription.withDampingRatio(
+        mass: 1.0, springConstant: 50.0, ratio: 0.5);
+
+    var scroll =
+        new ScrollSimulation(100.0, 400.0, 0.0, double.INFINITY, spring, 0.3);
+    scroll.tolerance = const Tolerance(velocity: 1.0);
+
+    expect(scroll.isDone(0.0), false);
+    expect(scroll.x(0.0), 100);
+    expect(scroll.dx(0.0), 400.0);
+
+    expect(scroll.x(1.0) > 330 && scroll.x(1.0) < 335, true);
+
+    expect(scroll.dx(1.0), 120.0);
+    expect(scroll.dx(2.0), 36.0);
+    expect(scroll.dx(3.0), 10.8);
+    expect(scroll.dx(4.0) < 3.5, true);
+
+    expect(scroll.isDone(5.0), true);
+    expect(scroll.x(5.0) > 431 && scroll.x(5.0) < 432, true);
+
+    // We should never switch
+    expect(scroll.currentIntervalOffset, 0.0);
+  });
+
+  test('over/under scroll spring', () {
+    var spring = new SpringDescription.withDampingRatio(mass: 1.0, springConstant: 170.0, ratio: 1.1);
+    var scroll = new ScrollSimulation(500.0, -7500.0, 0.0, 1000.0, spring, 0.025);
+    scroll.tolerance = new Tolerance(velocity: 45.0, distance: 1.5);
+
+    expect(scroll.isDone(0.0), false);
+    expect(scroll.x(0.0), closeTo(500.0, .0001));
+    expect(scroll.dx(0.0), closeTo(-7500.0, .0001));
+
+    expect(scroll.isDone(0.025), false);
+    expect(scroll.x(0.025), closeTo(320.0, 1.0));
+    expect(scroll.dx(0.25), closeTo(-2982, 1.0));
+
+    expect(scroll.isDone(2.0), true);
+    expect(scroll.x(2.0), 0.0);
+    expect(scroll.dx(2.0), closeTo(0.0, 45.0));
+  });
+}

travis/setup.sh

+#!/bin/bash
+set -ex
+
+(cd packages/cassowary; pub get)
+(cd packages/newton; pub get)
+
+pub global activate tuneup

travis/test.sh

+#!/bin/bash
+set -ex
+
+(cd packages/cassowary; pub global run tuneup check; pub run test -j1)
+(cd packages/newton; pub global run tuneup check; pub run test -j1)