public LinearConstraintSystem/*!*/ Widen(LinearConstraintSystem/*!*/ lcs) {
Contract.Requires(lcs != null);
Contract.Ensures(Contract.Result<LinearConstraintSystem>() != null);
#endif
if (this.IsBottom()) {
return cce.NonNull(lcs.Clone());
} else if (lcs.IsBottom()) {
return cce.NonNull(this.Clone());
} else if (this.IsTop() || lcs.IsTop()) {
return new LinearConstraintSystem(new ArrayList /*LinearConstraint*/ ());
}
// create new LCS, we will add only verified constraints to this...
ArrayList /*LinearConstraint*/ newConstraints = new ArrayList /*LinearConstraint*/ ();
Contract.Assume(this.Constraints != null);
foreach (LinearConstraint/*!*/ ccX in this.Constraints) {
Contract.Assert(ccX != null);
LinearConstraint cc = ccX;
#if DEBUG_PRINT
Console.WriteLine("Widen checking: Starting to check constraint: {0}", cc);
#endif
if (cc.IsConstant()) {
// (Can this ever occur in the stable state of a LinearConstraintSystem? --KRML)
// constraint is unaffected by the frame components
#if DEBUG_PRINT
Console.WriteLine("Widen checking: --Adding it!");
#endif
newConstraints.Add(cc);
continue;
}
// PHASE I: verify constraints against all frame vertices...
foreach (FrameElement/*!*/ vertex in cce.NonNull(lcs.FrameVertices)) {
Contract.Assert(vertex != null);
Rational lhs = cc.EvaluateLhs(vertex);
if (lhs > cc.rhs) {
// the vertex does not satisfy the inequality <=
if (cc.Relation == LinearConstraint.ConstraintRelation.LE) {
#if DEBUG_PRINT
Console.WriteLine("Widen checking: throwing out because of vertex: {0}", vertex);
#endif
goto CHECK_NEXT_CONSTRAINT;
} else {
// ... but it does satisfy the inequality >=
#if DEBUG_PRINT
Console.WriteLine("Widen checking: throwing out <= because of vertex: {0}", vertex);
#endif
cc = cc.ChangeRelationToAtLeast();
#if DEBUG_PRINT
Console.WriteLine("Widen checking: left with constraint: {0}", cc);
#endif
}
} else if (cc.Relation == LinearConstraint.ConstraintRelation.EQ && lhs < cc.rhs) {
// the vertex does not satisfy the inequality >=, and the constraint is an equality constraint
#if DEBUG_PRINT
Console.WriteLine("Widen checking: throwing out >= because of vertex: {0}", vertex);
#endif
cc = cc.ChangeRelation(LinearConstraint.ConstraintRelation.LE);
#if DEBUG_PRINT
Console.WriteLine("Widen checking: left with contraint: {0}", cc);
#endif
}
}
// PHASE II: verify constraints against all frame rays...
foreach (FrameElement/*!*/ ray in cce.NonNull(lcs.FrameRays)) {
Contract.Assert(ray != null);
// The following assumes the constraint to have some dimension with a non-zero coefficient
Rational lhs = cc.EvaluateLhs(ray);
if (lhs.IsPositive) {
// the ray does not satisfy the inequality <=
if (cc.Relation == LinearConstraint.ConstraintRelation.LE) {
#if DEBUG_PRINT
Console.WriteLine("Widen checking: throwing out because of ray: {0}", ray);
#endif
goto CHECK_NEXT_CONSTRAINT;
} else {
// ... but it does satisfy the inequality >=
#if DEBUG_PRINT
Console.WriteLine("Widen checking: throwing out <= because of ray: {0}", ray);
#endif
cc = cc.ChangeRelationToAtLeast();
#if DEBUG_PRINT
Console.WriteLine("Widen checking: left with contraint: {0}", cc);
#endif
}
} else if (cc.Relation == LinearConstraint.ConstraintRelation.EQ && lhs.IsNegative) {
// the ray does not satisfy the inequality >=, and the constraint is an equality constraint
#if DEBUG_PRINT
Console.WriteLine("Widen checking: throwing out >= because of ray: {0}", ray);
#endif
cc = cc.ChangeRelation(LinearConstraint.ConstraintRelation.LE);
#if DEBUG_PRINT
Console.WriteLine("Widen checking: left with constraint: {0}", cc);
#endif
}
}
// PHASE III: verify constraints against all frame lines...
foreach (FrameElement/*!*/ line in cce.NonNull(lcs.FrameLines)) {
Contract.Assert(line != null);
// The following assumes the constraint to have some dimension with a non-zero coefficient
Rational lhs = cc.EvaluateLhs(line);
if (!lhs.IsZero) {
// The line satisfies neither the inequality <= nor the equality ==
#if DEBUG_PRINT
Console.WriteLine("Widen checking: throwing out because of line: {0}", line);
#endif
goto CHECK_NEXT_CONSTRAINT;
}
}
// constraint has been verified, so add to new constraint system
#if DEBUG_PRINT
Console.WriteLine("Widen checking: --Adding it!");
#endif
newConstraints.Add(cc);
CHECK_NEXT_CONSTRAINT: {
}
#if DEBUG_PRINT
Console.WriteLine("Widen checking: done with that constraint");
#endif
}
return new LinearConstraintSystem(newConstraints);
}
/* IsSubset(): determines if 'lcs' is a subset of 'this'
* -- See Cousot/Halbwachs 1978, section
*/
public bool IsSubset(LinearConstraintSystem/*!*/ lcs) {
Contract.Requires(lcs != null);
if (lcs.IsBottom()) {
return true;
} else if (this.IsBottom()) {
return false;
#if DEBUG
#else
} else if (this.IsTop()) { // optimization -- this case not needed for correctness
return true;
} else if (lcs.IsTop()) { // optimization -- this case not needed for correctness
return false;
#endif
} else {
// phase 0: check if frame dimensions are a superset of the constraint dimensions
ISet /*IVariable!*//*!*/ frameDims = lcs.GetDefinedDimensions();
Contract.Assert(frameDims != null);
#if DEBUG_PRINT
Console.WriteLine("DEBUG: IsSubset:");
Console.WriteLine(" --- this:");
this.Dump();
Console.WriteLine(" --- lcs:");
lcs.Dump();
Console.WriteLine(" ---");
#endif
foreach (LinearConstraint/*!*/ cc in cce.NonNull(this.Constraints)) {
Contract.Assert(cc != null);
#if DEBUG_PRINT
Console.WriteLine(" cc: {0}", cc);
Console.WriteLine(" cc.GetDefinedDimensions(): {0}", cc.GetDefinedDimensions());
#endif
if (!Contract.ForAll(cc.GetDefinedDimensionsGeneric(), var => frameDims.Contains(var))) {
#if DEBUG_PRINT
Console.WriteLine(" ---> phase 0 subset violated, return false from IsSubset");
#endif
return false;
}
}
}
// phase 1: check frame vertices against each constraint...
foreach (FrameElement/*!*/ v in cce.NonNull(lcs.FrameVertices)) {
Contract.Assert(v != null);
foreach (LinearConstraint/*!*/ cc in this.Constraints) {
Contract.Assert(cc != null);
Rational q = cc.EvaluateLhs(v);
if (cc.Relation == LinearConstraint.ConstraintRelation.LE) {
if (!(q <= cc.rhs)) {
#if DEBUG_PRINT
Console.WriteLine(" ---> phase 1a subset violated, return false from IsSubset");
#endif
return false;
}
} else {
if (!(q == cc.rhs)) {
#if DEBUG_PRINT
Console.WriteLine(" ---> phase 1b subset violated, return false from IsSubset");
#endif
return false;
}
}
}
}
// phase 2: check frame rays against each constraint...
// To check if a ray "r" falls within a constraint "cc", we add the vector "r" to
// any point "p" on the side of the half-space or plane described by constraint, and
// then check if the resulting point satisfies the constraint. That is, we check (for
// an inequality constraint with coefficients a1,a2,...,an and right-hand side
// constant C):
// a1*(r1+p1) + a2*(r2+p2) + ... + an*(rn+pn) <= C
// Equivalently:
// a1*r1 + a2*r2 + ... + an*rn + a1*p1 + a2*p2 + ... + an*pn <= C
// To find a point "p", we can pick out a coordinate, call it 1, with a non-zero
// coefficient in the constraint, and then choose "p" as the point that has the
// value C/a1 in coordinate 1 and has 0 in all other coordinates. We then check:
// a1*r1 + a2*r2 + ... + an*rn + a1*(C/a1) + a2*0 + ... + an*0 <= C
// which simplifies to:
// a1*r1 + a2*r2 + ... + an*rn + C <= C
// which in turn simplifies to:
// a1*r1 + a2*r2 + ... + an*rn <= 0
// If the constraint is an equality constraint, we simply replace "<=" with "=="
// above.
foreach (FrameElement/*!*/ r in cce.NonNull(lcs.FrameRays)) {
Contract.Assert(r != null);
System.Diagnostics.Debug.Assert(r != null, "encountered a null ray...");
foreach (LinearConstraint/*!*/ cc in this.Constraints) {
Contract.Assert(cc != null);
System.Diagnostics.Debug.Assert(cc != null, "encountered an null constraint...");
Rational q = cc.EvaluateLhs(r);
if (cc.Relation == LinearConstraint.ConstraintRelation.LE) {
if (q.IsPositive) {
#if DEBUG_PRINT
Console.WriteLine(" ---> phase 2a subset violated, return false from IsSubset");
#endif
return false;
}
} else {
if (q.IsNonZero) {
#if DEBUG_PRINT
Console.WriteLine(" ---> phase 2b subset violated, return false from IsSubset");
#endif
return false;
}
}
}
}
// phase 3: check frame lines against each constraint...
// To check if a line "L" falls within a constraint "cc", we check if both the
// vector "L" and "-L", interpreted as rays, fall within the constraint. From
// the discussion above, this means we check the following two properties:
// a1*L1 + a2*L2 + ... + an*Ln <= 0 (*)
// a1*(-L1) + a2*(-L2) + ... + an*(-Ln) <= 0
// The second of these lines can be rewritten as:
// - a1*L1 - a2*L2 - ... - an*Ln <= 0
// which is equivalent to:
// -1 * (a1*L1 + a2*L2 + ... + an*Ln) <= 0
// Multiplying both sides by -1 and flipping the direction of the inequality,
// we have:
// a1*L1 + a2*L2 + ... + an*Ln >= 0 (**)
// Putting (*) and (**) together, we conclude that we need to check:
// a1*L1 + a2*L2 + ... + an*Ln == 0
// If the constraint is an equality constraint, we end up with the same equation.
foreach (FrameElement/*!*/ line in cce.NonNull(lcs.FrameLines)) {
Contract.Assert(line != null);
System.Diagnostics.Debug.Assert(line != null, "encountered a null line...");
foreach (LinearConstraint/*!*/ cc in this.Constraints) {
Contract.Assert(cc != null);
System.Diagnostics.Debug.Assert(cc != null, "encountered an null constraint...");
Rational q = cc.EvaluateLhs(line);
if (q.IsNonZero) {
#if DEBUG_PRINT
Console.WriteLine(" ---> phase 3 subset violated, return false from IsSubset");
#endif
return false;
}
}
}
#if DEBUG_PRINT
Console.WriteLine(" ---> IsSubset returns true");
#endif
return true;
}
public LinearConstraintSystem/*!*/ Join(LinearConstraintSystem/*!*/ lcs) {
Contract.Requires(lcs != null);
Contract.Ensures(Contract.Result<LinearConstraintSystem>() != null);
#endif
if (this.IsBottom()) {
return cce.NonNull(lcs.Clone());
} else if (lcs.IsBottom()) {
return cce.NonNull(this.Clone());
} else if (this.IsTop() || lcs.IsTop()) {
return new LinearConstraintSystem(new ArrayList /*LinearConstraint*/ ());
} else {
LinearConstraintSystem/*!*/ z;
// Start from the "larger" of the two frames (this is just a heuristic measure intended
// to save work).
Contract.Assume(this.FrameVertices != null);
Contract.Assume(this.FrameRays != null);
Contract.Assume(this.FrameLines != null);
Contract.Assume(lcs.FrameVertices != null);
Contract.Assume(lcs.FrameRays != null);
Contract.Assume(lcs.FrameLines != null);
if (this.FrameVertices.Count + this.FrameRays.Count + this.FrameLines.Count - this.FrameDimensions.Count <
lcs.FrameVertices.Count + lcs.FrameRays.Count + lcs.FrameLines.Count - lcs.FrameDimensions.Count) {
z = cce.NonNull(lcs.Clone());
lcs = this;
} else {
z = cce.NonNull(this.Clone());
}
#if DEBUG_PRINT
Console.WriteLine("DEBUG: LinearConstraintSystem.Join ---------------");
Console.WriteLine("z:");
z.Dump();
Console.WriteLine("lcs:");
lcs.Dump();
#endif
// Start by explicating the implicit lines of z for the dimensions dims(lcs)-dims(z).
foreach (IVariable/*!*/ dim in lcs.FrameDimensions) {
Contract.Assert(dim != null);
if (!z.FrameDimensions.Contains(dim)) {
z.FrameDimensions.Add(dim);
FrameElement line = new FrameElement();
line.AddCoordinate(dim, Rational.ONE);
// Note: AddLine is not called (because the line already exists in z--it's just that
// it was represented implicitly). Instead, just tack the explicit representation onto
// FrameLines.
Contract.Assume(z.FrameLines != null);
z.FrameLines.Add(line);
#if DEBUG_PRINT
Console.WriteLine("Join: After explicating line: {0}", line);
z.Dump();
#endif
}
}
// Now, the vertices, rays, and lines can be added.
foreach (FrameElement/*!*/ v in lcs.FrameVertices) {
Contract.Assert(v != null);
z.AddVertex(v);
#if DEBUG_PRINT
Console.WriteLine("Join: After adding vertex: {0}", v);
z.Dump();
#endif
}
foreach (FrameElement/*!*/ r in lcs.FrameRays) {
Contract.Assert(r != null);
z.AddRay(r);
#if DEBUG_PRINT
Console.WriteLine("Join: After adding ray: {0}", r);
z.Dump();
#endif
}
foreach (FrameElement/*!*/ l in lcs.FrameLines) {
Contract.Assert(l != null);
z.AddLine(l);
#if DEBUG_PRINT
Console.WriteLine("Join: After adding line: {0}", l);
z.Dump();
#endif
}
// also add to z the implicit lines of lcs
foreach (IVariable/*!*/ dim in z.FrameDimensions) {
Contract.Assert(dim != null);
if (!lcs.FrameDimensions.Contains(dim)) {
// "dim" is a dimension that's explicit in "z" but implicit in "lcs"
FrameElement line = new FrameElement();
line.AddCoordinate(dim, Rational.ONE);
z.AddLine(line);
#if DEBUG_PRINT
Console.WriteLine("Join: After adding lcs's implicit line: {0}", line);
z.Dump();
#endif
}
}
z.SimplifyFrame();
z.SimplifyConstraints();
z.CheckInvariant();
#if DEBUG_PRINT
Console.WriteLine("Join: Returning z:");
z.Dump();
Console.WriteLine("----------------------------------------");
#endif
return z;
}
}
public override Answer CheckVariableDisequality(Element/*!*/ e, IVariable/*!*/ var1, IVariable/*!*/ var2) {
//Contract.Requires(var2 != null);
//Contract.Requires(var1 != null);
//Contract.Requires(e != null);
PolyhedraLatticeElement/*!*/ ple = (PolyhedraLatticeElement)cce.NonNull(e);
Contract.Assume(ple.lcs.Constraints != null);
ArrayList /*LinearConstraint!*//*!*/ clist = (ArrayList /*LinearConstraint!*/)cce.NonNull(ple.lcs.Constraints.Clone());
LinearConstraint/*!*/ lc = new LinearConstraint(LinearConstraint.ConstraintRelation.EQ);
Contract.Assert(lc != null);
lc.SetCoefficient(var1, Rational.ONE);
lc.SetCoefficient(var2, Rational.MINUS_ONE);
clist.Add(lc);
LinearConstraintSystem newLcs = new LinearConstraintSystem(clist);
if (newLcs.IsBottom()) {
return Answer.Yes;
} else {
return Answer.Maybe;
}
}