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 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);
}
public static void RunValidationA() {
IVariable/*!*/ dim1 = new TestVariable("X");
IVariable/*!*/ dim2 = new TestVariable("Y");
IVariable/*!*/ dim3 = new TestVariable("Z");
Contract.Assert(dim1 != null);
Contract.Assert(dim2 != null);
Contract.Assert(dim3 != null);
FrameElement s1 = new FrameElement();
s1.AddCoordinate(dim1, Rational.ONE);
s1.AddCoordinate(dim2, Rational.MINUS_ONE);
s1.AddCoordinate(dim3, Rational.ZERO);
FrameElement s2 = new FrameElement();
s2.AddCoordinate(dim1, Rational.MINUS_ONE);
s2.AddCoordinate(dim2, Rational.ONE);
s2.AddCoordinate(dim3, Rational.ZERO);
FrameElement r1 = new FrameElement();
r1.AddCoordinate(dim1, Rational.ZERO);
r1.AddCoordinate(dim2, Rational.ZERO);
r1.AddCoordinate(dim3, Rational.ONE);
FrameElement d1 = new FrameElement();
d1.AddCoordinate(dim1, Rational.ONE);
d1.AddCoordinate(dim2, Rational.ONE);
d1.AddCoordinate(dim3, Rational.ZERO);
// create lcs from frame -- cf. Cousot/Halbwachs 1978, section 3.3.1.1
LinearConstraintSystem lcs = new LinearConstraintSystem(s1);
lcs.Dump();
lcs.AddVertex(s2);
lcs.Dump();
lcs.AddRay(r1);
lcs.Dump();
lcs.AddLine(d1);
lcs.Dump();
lcs.SimplifyConstraints();
lcs.Dump();
#if LATER
lcs.GenerateFrameFromConstraints(); // should give us back the original frame...
#endif
Console.WriteLine("IsSubset? {0}", lcs.IsSubset(lcs.Clone()));
lcs.Dump();
}
