static public List <Pair <Variable, IType> > InferConstraints_Leq <Variable, Expression, IType>(
bool isSignedComparison,
Expression left, Expression right,
IExpressionDecoder <Variable, Expression> decoder,
ISetOfNumbersAbstraction <Variable, Expression, Rational, IType> iquery,
out bool isBottom)
where IType : IntervalBase <IType, Rational>
{
Contract.Requires(iquery != null);
Contract.Ensures(Contract.Result <List <Pair <Variable, IType> > >() != null);
isBottom = false; // false, unless someine proves the contrary
var result = new List <Pair <Variable, IType> >();
if (IsFloat(left, decoder) || IsFloat(right, decoder))
{
return(result);
}
var kLeft = iquery.Eval(left);
var kRight = iquery.Eval(right);
// We have to take into account the polymorphism of constants
if (!isSignedComparison)
{
kLeft = kLeft.ToUnsigned();
kRight = kRight.ToUnsigned();
}
//AssumeKLessEqualThanRight(kLeft, this.Decoder.UnderlyingVariable(right))
IType refinedIntv;
var rightVar = decoder.UnderlyingVariable(right);
if (IntervalInference.TryRefine_KLessEqualThanRight(isSignedComparison, kLeft, rightVar, iquery, out refinedIntv))
{
// If it is an unsigned comparison, and it is a constant, then we should avoid generating the constraint
// Example: left <={un} right, with right == -1 then we do not want to generate the constraint right == 2^{32}-1 which is wrong!
// unsigned ==> right is not a constant
if (isSignedComparison || !kRight.IsSingleton)
{
result.Add(rightVar, refinedIntv);
}
}
//AssumeLeftLessEqualThanK(this.Decoder.UnderlyingVariable(left), kRight);
var leftVar = decoder.UnderlyingVariable(left);
if (IntervalInference.TryRefine_LeftLessEqualThanK(isSignedComparison, leftVar, kRight, iquery, out refinedIntv))
{
// unsigned ==> left is not a constant
if (isSignedComparison || !kLeft.IsSingleton)
{
result.Add(leftVar, refinedIntv);
}
}
if (isSignedComparison)
{
Polynomial <Variable, Expression> guardInCanonicalForm;
if (Polynomial <Variable, Expression> .TryToPolynomialForm(ExpressionOperator.LessEqualThan, left, right, decoder, out guardInCanonicalForm) &&
guardInCanonicalForm.IsLinear)
{
// We consider only the case when there is at MOST one variable on the left, i.e. a * x \leq b, or TWO, i.e. a*x +b*y <= c
if (guardInCanonicalForm.Left.Length == 1)
{
return(HelperFortestTrueLessEqualThan_AxLeqK(guardInCanonicalForm, iquery, result, out isBottom));
}
else if (guardInCanonicalForm.Left.Length == 2)
{
return(HelperFortestTrueLessEqualThan_AxByLtK(guardInCanonicalForm, iquery, result, out isBottom));
}
}
}
return(result);
}
