// Division
public static IntervalElement /*!*/ operator %(IntervalElement /*!*/ a, IntervalElement /*!*/ b)
{
Contract.Requires(b != null);
Contract.Requires(a != null);
Contract.Ensures(Contract.Result <IntervalElement>() != null);
if (b.inf.IsZero && b.sup.IsZero) // Check division by zero
{
return(IntervalElement.Top);
}
ExtendedInt /*!*/ infinf = a.inf % b.inf;
Contract.Assert(infinf != null);
ExtendedInt /*!*/ infsup = a.inf % b.sup;
Contract.Assert(infsup != null);
ExtendedInt /*!*/ supinf = a.sup % b.inf;
Contract.Assert(supinf != null);
ExtendedInt /*!*/ supsup = a.sup % b.sup;
Contract.Assert(supsup != null);
ExtendedInt inf = ExtendedInt.Inf(infinf, infsup, supinf, supsup);
ExtendedInt sup = ExtendedInt.Sup(infinf, infsup, supinf, supsup);
return(Factory(inf, sup));
}
// Multiplication
public static IntervalElement /*!*/ operator *(IntervalElement /*!*/ a, IntervalElement /*!*/ b)
{
Contract.Requires(b != null);
Contract.Requires(a != null);
Contract.Ensures(Contract.Result <IntervalElement>() != null);
ExtendedInt /*!*/ infinf = a.inf * b.inf;
Contract.Assert(infinf != null);
ExtendedInt /*!*/ infsup = a.inf * b.sup;
Contract.Assert(infsup != null);
ExtendedInt /*!*/ supinf = a.sup * b.inf;
Contract.Assert(supinf != null);
ExtendedInt /*!*/ supsup = a.sup * b.sup;
Contract.Assert(supsup != null);
ExtendedInt /*!*/ inf = ExtendedInt.Inf(infinf, infsup, supinf, supsup);
Contract.Assert(inf != null);
ExtendedInt /*!*/ sup = ExtendedInt.Sup(infinf, infsup, supinf, supsup);
Contract.Assert(sup != null);
return(Factory(inf, sup));
}
protected IntervalElement(ExtendedInt /*!*/ inf, ExtendedInt /*!*/ sup)
{
Contract.Requires(sup != null);
Contract.Requires(inf != null);
this.inf = inf;
this.sup = sup;
// base();
}
public static IntervalElement /*!*/ Factory(BigNum inf, BigNum sup)
{
Contract.Ensures(Contract.Result <IntervalElement>() != null);
ExtendedInt /*!*/ i = ExtendedInt.Factory(inf);
ExtendedInt /*!*/ s = ExtendedInt.Factory(sup);
return(Factory(i, s));
}
public override int CompareTo(ExtendedInt /*!*/ that)
{
//Contract.Requires(that != null);
if (that is MinusInfinity)
{
return(0);
}
else
{
return(-1);
}
}
/// <summary>
/// The classic, pointwise, meet of intervals
/// </summary>
public override Element /*!*/ NontrivialMeet(Element /*!*/ left, Element /*!*/ right)
{
//Contract.Requires(right != null);
//Contract.Requires(left != null);
Contract.Ensures(Contract.Result <Element>() != null);
IntervalElement /*!*/ leftInterval = (IntervalElement /*!*/)cce.NonNull(left);
IntervalElement /*!*/ rightInterval = (IntervalElement /*!*/)cce.NonNull(right);
ExtendedInt inf = ExtendedInt.Sup(leftInterval.Inf, rightInterval.Inf);
ExtendedInt sup = ExtendedInt.Inf(leftInterval.Sup, rightInterval.Sup);
return(IntervalElement.Factory(inf, sup));
}
// Addition
public static IntervalElement /*!*/ operator +(IntervalElement /*!*/ a, IntervalElement /*!*/ b)
{
Contract.Requires(b != null);
Contract.Requires(a != null);
Contract.Ensures(Contract.Result <IntervalElement>() != null);
ExtendedInt /*!*/ inf = a.inf + b.inf;
Contract.Assert(inf != null);
ExtendedInt /*!*/ sup = a.sup + b.sup;
Contract.Assert(sup != null);
return(Factory(inf, sup));
}
public static ExtendedInt /*!*/ Sup(ExtendedInt /*!*/ inf, ExtendedInt /*!*/ sup)
{
Contract.Requires(sup != null);
Contract.Requires(inf != null);
Contract.Ensures(Contract.Result <ExtendedInt>() != null);
if (inf > sup)
{
return(inf);
}
else
{
return(sup);
}
}
/// <summary>
/// The very simple widening of intervals, to be improved with thresholds
/// left is the PREVIOUS value in the iterations and right is the NEW one
/// </summary>
public override Element /*!*/ Widen(Element /*!*/ left, Element /*!*/ right)
{
//Contract.Requires(right != null);
//Contract.Requires(left != null);
Contract.Ensures(Contract.Result <Element>() != null);
IntervalElement /*!*/ prevInterval = (IntervalElement /*!*/)cce.NonNull(left);
IntervalElement /*!*/ nextInterval = (IntervalElement /*!*/)cce.NonNull(right);
ExtendedInt inf = nextInterval.Inf < prevInterval.Inf ? ExtendedInt.MinusInfinity : prevInterval.Inf;
ExtendedInt sup = nextInterval.Sup > prevInterval.Sup ? ExtendedInt.PlusInfinity : prevInterval.Sup;
IntervalElement widening = IntervalElement.Factory(inf, sup);
return(widening);
}
// Construct an Interval
public static IntervalElement /*!*/ Factory(ExtendedInt /*!*/ inf, ExtendedInt /*!*/ sup)
{
Contract.Requires((sup != null));
Contract.Requires((inf != null));
Contract.Ensures(Contract.Result <IntervalElement>() != null);
if (inf is MinusInfinity && sup is PlusInfinity)
{
return(Top);
}
if (inf > sup)
{
return(Bottom);
}
// otherwise...
return(new IntervalElement(inf, sup));
}
public static ExtendedInt /*!*/ Sup(ExtendedInt /*!*/ a, ExtendedInt /*!*/ b, ExtendedInt /*!*/ c, ExtendedInt /*!*/ d)
{
Contract.Requires(d != null);
Contract.Requires(c != null);
Contract.Requires(b != null);
Contract.Requires(a != null);
Contract.Ensures(Contract.Result <ExtendedInt>() != null);
ExtendedInt /*!*/ supab = Sup(a, b);
Contract.Assert(supab != null);
ExtendedInt /*!*/ supcd = Sup(c, d);
Contract.Assert(supcd != null);
return(Sup(supab, supcd));
}
public override int CompareTo(ExtendedInt /*!*/ that)
{
//Contract.Requires(that != null);
if (that is PlusInfinity)
{
return(-1);
}
else if (that is PureInteger)
{
return(this.Value.CompareTo(that.Value));
}
else // then that is a MinusInfinity
{
return(1);
}
}
public static ExtendedInt /*!*/ Inf(ExtendedInt /*!*/ a, ExtendedInt /*!*/ b, ExtendedInt /*!*/ c, ExtendedInt /*!*/ d)
{
Contract.Requires(d != null);
Contract.Requires(c != null);
Contract.Requires(b != null);
Contract.Requires(a != null);
Contract.Ensures(Contract.Result <ExtendedInt>() != null);
ExtendedInt /*!*/ infab = Inf(a, b);
Contract.Assert(infab != null);
ExtendedInt /*!*/ infcd = Inf(c, d);
Contract.Assert(infcd != null);
return(Inf(infab, infcd));
}
// Unary minus
public static ExtendedInt /*!*/ UnaryMinus(ExtendedInt /*!*/ a)
{
Contract.Requires(a != null);
Contract.Ensures(Contract.Result <ExtendedInt>() != null);
if (a is PlusInfinity)
{
return(cachedMinusInf);
}
if (a is MinusInfinity)
{
return(cachedPlusInf);
}
else // a is a PureInteger
{
return(new PureInteger(-a.Value));
}
}
// Subtraction
public static ExtendedInt /*!*/ operator -(ExtendedInt /*!*/ a, ExtendedInt /*!*/ b)
{
Contract.Requires(b != null);
Contract.Requires(a != null);
Contract.Ensures(Contract.Result <ExtendedInt>() != null);
if (a is InfinitaryInt)
{
return(a);
}
else if (b is InfinitaryInt)
{
return(UnaryMinus(b));
}
else
{
return(ExtendedInt.Factory(a.Value - b.Value));
}
}
// Modulo
public static ExtendedInt /*!*/ operator %(ExtendedInt /*!*/ a, ExtendedInt /*!*/ b)
{
Contract.Requires(b != null);
Contract.Requires(a != null);
Contract.Ensures(Contract.Result <ExtendedInt>() != null);
if (b.IsZero)
{
return(a.IsPositive ? (ExtendedInt)cachedPlusInf : cachedMinusInf);
}
if (a is InfinitaryInt)
{
return(a);
}
else if (b is InfinitaryInt)
{
return(b);
}
else
{
return(ExtendedInt.Factory(a.Value % b.Value));
}
}
public abstract int CompareTo(ExtendedInt/*!*/ that);
// Unary minus
public static ExtendedInt/*!*/ UnaryMinus(ExtendedInt/*!*/ a) {
Contract.Requires(a != null);
Contract.Ensures(Contract.Result<ExtendedInt>() != null);
if (a is PlusInfinity)
return cachedMinusInf;
if (a is MinusInfinity)
return cachedPlusInf;
else // a is a PureInteger
return new PureInteger(-a.Value);
}
// Construct an Interval
public static IntervalElement/*!*/ Factory(ExtendedInt/*!*/ inf, ExtendedInt/*!*/ sup) {
Contract.Requires((sup != null));
Contract.Requires((inf != null));
Contract.Ensures(Contract.Result<IntervalElement>() != null);
if (inf is MinusInfinity && sup is PlusInfinity)
return Top;
if (inf > sup)
return Bottom;
// otherwise...
return new IntervalElement(inf, sup);
}
protected IntervalElement(ExtendedInt/*!*/ inf, ExtendedInt/*!*/ sup) {
Contract.Requires(sup != null);
Contract.Requires(inf != null);
this.inf = inf;
this.sup = sup;
// base();
}
public override int CompareTo(ExtendedInt/*!*/ that) {
//Contract.Requires(that != null);
if (that is PlusInfinity)
return -1;
else if (that is PureInteger)
return this.Value.CompareTo(that.Value);
else // then that is a MinusInfinity
return 1;
}
public static ExtendedInt/*!*/ Sup(ExtendedInt/*!*/ a, ExtendedInt/*!*/ b, ExtendedInt/*!*/ c, ExtendedInt/*!*/ d) {
Contract.Requires(d != null);
Contract.Requires(c != null);
Contract.Requires(b != null);
Contract.Requires(a != null);
Contract.Ensures(Contract.Result<ExtendedInt>() != null);
ExtendedInt/*!*/ supab = Sup(a, b);
Contract.Assert(supab != null);
ExtendedInt/*!*/ supcd = Sup(c, d);
Contract.Assert(supcd != null);
return Sup(supab, supcd);
}
public override int CompareTo(ExtendedInt that)
{
Contract.Requires(that != null);
throw new NotImplementedException();
}
// Construct the interval [inf, sup]
protected IntervalElement(BigNum infInt, BigNum supInt)
{
this.inf = ExtendedInt.Factory(infInt);
this.sup = ExtendedInt.Factory(supInt);
// base(); // to please the compiler...
}
public abstract int CompareTo(ExtendedInt /*!*/ that);
public static ExtendedInt/*!*/ Inf(ExtendedInt/*!*/ a, ExtendedInt/*!*/ b, ExtendedInt/*!*/ c, ExtendedInt/*!*/ d) {
Contract.Requires(d != null);
Contract.Requires(c != null);
Contract.Requires(b != null);
Contract.Requires(a != null);
Contract.Ensures(Contract.Result<ExtendedInt>() != null);
ExtendedInt/*!*/ infab = Inf(a, b);
Contract.Assert(infab != null);
ExtendedInt/*!*/ infcd = Inf(c, d);
Contract.Assert(infcd != null);
return Inf(infab, infcd);
}
public static ExtendedInt/*!*/ Sup(ExtendedInt/*!*/ inf, ExtendedInt/*!*/ sup) {
Contract.Requires(sup != null);
Contract.Requires(inf != null);
Contract.Ensures(Contract.Result<ExtendedInt>() != null);
if (inf > sup)
return inf;
else
return sup;
}
// Construct the inteval [val, val]
protected IntervalElement(BigNum val)
{
this.inf = this.sup = ExtendedInt.Factory(val);
// base();
}
public override int CompareTo(ExtendedInt that) {
Contract.Requires(that != null);
throw new NotImplementedException();
}
// Construct the inteval [val, val]
protected IntervalElement(BigNum val) {
this.inf = this.sup = ExtendedInt.Factory(val);
// base();
}
public override int CompareTo(ExtendedInt/*!*/ that) {
//Contract.Requires(that != null);
if (that is MinusInfinity)
return 0;
else
return -1;
}
// Construct the interval [inf, sup]
protected IntervalElement(BigNum infInt, BigNum supInt) {
this.inf = ExtendedInt.Factory(infInt);
this.sup = ExtendedInt.Factory(supInt);
// base(); // to please the compiler...
}