/// <summary>
/// We only add less equals
/// </summary>
public NonRelationalValueAbstraction <Variable, Expression> AssumeInformationFrom <Exp>(INumericalAbstractDomainQuery <Variable, Exp> oracle)
{
var result = this;
if (this.IsNormal())
{
#region Update <
if (this.StrictUpperBounds.IsNormal())
{
var newConstraints = new Set <Variable>(this.StrictUpperBounds.Values);
foreach (var x in this.StrictUpperBounds.Values)
{
// Add S such that x <= S
var newBounds = oracle.UpperBoundsFor(x, true).ApplyToAll(oracle.ToVariable);
Contract.Assert(newBounds != null);
newConstraints.AddRange(newBounds);
}
result = result.Update(ADomains.StrictUpperBounds, new SetOfConstraints <Variable>(newConstraints, false));
}
#endregion
#region Update <=
if (this.WeakUpperBounds.IsNormal())
{
var newConstraints = new Set <Variable>(this.WeakUpperBounds.Values);
foreach (var x in this.WeakUpperBounds.Values)
{
// Add S such that x <= S
var newBounds = oracle.UpperBoundsFor(x, false).ApplyToAll(oracle.ToVariable);
Contract.Assert(newBounds != null);
newConstraints.AddRange(newBounds);
}
result = result.Update(ADomains.WeakUpperBounds, new SetOfConstraints <Variable>(newConstraints, false));
}
#endregion
}
return(result);
}
private void Helper_Match_kY(
Expression x, INumericalAbstractDomainQuery <Variable, Expression> oracleDomain, List <Expression> result, Expression y)
{
Contract.Requires(result != null);
Expression ltExp;
if (oracleDomain.BoundsFor(y).LowerBound >= 1)
{
ltExp = expManager.Encoder.CompoundExpressionFor(ExpressionType.Bool, ExpressionOperator.LessThan, y, x);
result.Add(ltExp);
result.AddRange(UpperBounds(y, oracleDomain.UpperBoundsFor(x, false)));
}
}
public override Set <Expression> VisitShiftRight(Expression left, Expression right, Expression original, INumericalAbstractDomainQuery <Variable, Expression> data)
{
if (this.AreInfinities(left, right))
{
return(new Set <Expression>());
}
var bounds = data.BoundsFor(right).AsInterval;
int val;
Polynomial <Variable, Expression> pol;
if (bounds.IsFiniteAndInt32Singleton(out val) && val > 0 &&
Polynomial <Variable, Expression> .TryToPolynomialForm(left, this.Decoder, out pol) &&
pol.IsLinear && !pol.Relation.HasValue && pol.Left.Length <= (1 << val))
{
var ub = null as IEnumerable <Expression>;
foreach (var m in pol.Left)
{
Variable v;
if (m.IsVariable(out v) && data.BoundsFor(v).LowerBound >= 0)
{
var upperbounds = data.UpperBoundsFor(v, true);
ub = ub == null ? upperbounds : ub.Intersect(upperbounds);
if (ub.Any())
{
continue;
}
}
return(new Set <Expression>());
}
// If we reach this point, we have meaningful constraints
return(new Set <Expression>(ub.ApplyToAll(exp => expManager.Encoder.CompoundExpressionFor(ExpressionType.Bool, ExpressionOperator.LessThan, x, exp))));
}
return(new Set <Expression>());
}
//[SuppressMessage("Microsoft.Contracts", "Ensures-106-407")]
public List <Expression> InferConstraints(Expression x, Expression exp, INumericalAbstractDomainQuery <Variable, Expression> adom)
{
Contract.Assert(adom != null);
var xExp = new Pair <Expression, Expression>(x, exp);
var result = new List <Expression>();
Polynomial <Variable, Expression> expAsPol;
var decoder = expManager.Decoder;
var encoder = expManager.Encoder;
if (Polynomial <Variable, Expression> .TryToPolynomialForm(exp, decoder, out expAsPol))
{
if (expAsPol.IsLinear)
{
#region The cases
Expression leqExp;
Variable y;
Rational k;
// If it is in the form y - k, with k constant, then we add the constraint " x <= y "
if (expAsPol.TryMatch_YMinusK(out y, out k))
{
var yExp = encoder.VariableFor(y);
leqExp = encoder.CompoundExpressionFor(ExpressionType.Bool, ExpressionOperator.LessEqualThan, x, yExp);
Contract.Assert(leqExp != null);
result.Add(leqExp); // add the constraint x <= y
}
// If it is in the form y + k, with k constant, we add the constraint "y <= x"
else if (expAsPol.TryMatch_YPlusK(out y, out k))
{
var yExp = encoder.VariableFor(y);
leqExp = encoder.CompoundExpressionFor(ExpressionType.Bool, ExpressionOperator.LessEqualThan, yExp, x);
Contract.Assert(leqExp != null);
result.Add(leqExp); // As we know x, this is a clever encoding for the constraint y <= x
// x = y + 1 then if y < z => x <= z
if (k == 1)
{
result.AddRange(UpperBoundsNonStrict(x, adom.UpperBoundsFor(y, true)));
}
}
// If it is in the form k * y then it add the constaints "y <= x" or "x <= y"
else if (expAsPol.TryMatch_kY(out y, out k))
{
var yExp = encoder.VariableFor(y);
Contract.Assert(yExp != null);
if (TryHelperFor_MatchkY(x, adom, yExp, k, out leqExp))
{
// F: this should be some bug, it is not taking into account the postcondition
Contract.Assume(leqExp != null);
result.Add(leqExp);
}
}
#endregion
}
}
var nonPolynomial = new TreatNonPolynomialCases(x, expManager).Visit(exp, adom);
Contract.Assert(nonPolynomial != null);
result.AddRange(nonPolynomial);
Contract.Assume(Contract.ForAll(result, e => e != null));
return(result);
}
public List <Expression> InferConstraints(Expression x, Expression exp, INumericalAbstractDomainQuery <Variable, Expression> oracleDomain)
{
Polynomial <Variable, Expression> expAsPol;
Expression ltExp;
var result = new List <Expression>();
var xExp = new Pair <Expression, Expression>(x, exp);
#region 0. Fetch the cache
Cache_Entry <Expression> cached;
if (cache.TryGetValue(xExp, out cached))
{
switch (cached.Match_case)
{
case Cache_Entry.MatchCase.YMinusK:
result.Add(cached.ResultExpression);
result.AddRange(UpperBounds(cached.X, oracleDomain.UpperBoundsFor(cached.Y, false)));
break;
case Cache_Entry.MatchCase.YPlusK:
result.Add(cached.ResultExpression);
result.AddRange(UpperBounds(cached.Y, oracleDomain.UpperBoundsFor(cached.X, false)));
break;
case Cache_Entry.MatchCase.kY:
Helper_Match_kY(cached.X, oracleDomain, result, cached.Y);
break;
case Cache_Entry.MatchCase.NotLinear:
// do nothing: this case essentially avoids the computation in the other branchs that we know to be unfruitfull
break;
default:
// error?
break;
}
}
#endregion
#region 1. If failed, Try to put the r-exp in a polynomial (with simplifications, etc.)
else if (Polynomial <Variable, Expression> .TryToPolynomialForm(exp, expManager.Decoder, out expAsPol))
{
if (expAsPol.IsLinear)
{
// If it is in the form y - k, with k constant, then we add the constraint
Variable y;
Rational k;
if (expAsPol.TryMatch_YMinusK(out y, out k) && !x.Equals(y))
{
var yExp = expManager.Encoder.VariableFor(y);
ltExp = expManager.Encoder.CompoundExpressionFor(ExpressionType.Bool, ExpressionOperator.LessThan, x, yExp);
result.Add(ltExp);
result.AddRange(UpperBounds(x, oracleDomain.UpperBoundsFor(y, false)));
// update the cache
cache.Add(xExp, Cache_Entry.For(Cache_Entry.MatchCase.YMinusK, x, yExp, k, ltExp));
}
// If it is in the form y + k, with k constant, we add the constraint "y < x" to the back constraits
else if (expAsPol.TryMatch_YPlusK(out y, out k) && !x.Equals(y))
{
var yExp = expManager.Encoder.VariableFor(y);
ltExp = expManager.Encoder.CompoundExpressionFor(ExpressionType.Bool, ExpressionOperator.LessThan, yExp, x);
result.Add(ltExp);
result.AddRange(UpperBounds(yExp, oracleDomain.UpperBoundsFor(x, false)));
// update the cache
cache.Add(xExp, Cache_Entry.For(Cache_Entry.MatchCase.YPlusK, x, yExp, k, ltExp));
}
// If it is in the form k*y, with k constant, if k > 1 we add the constraint "x > y"
else if (expAsPol.TryMatch_kY(out y, out k) && !x.Equals(y))
{
var yExp = expManager.Encoder.VariableFor(y);
if (k > 1)
{
Helper_Match_kY(x, oracleDomain, result, yExp);
cache.Add(xExp, Cache_Entry.For(Cache_Entry.MatchCase.kY, x, yExp, k, default(Expression)));
}
else
{
cache.Add(xExp, Cache_Entry.ForNonLinear <Expression>());
}
}
}
}
#endregion
#region 2. Special treatment for reminder and non polynomial expressions
result.AddRange(new TreatNonPolynomialCases(x, expManager).Visit(exp, oracleDomain));
#endregion
return(result);
}
