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//
// Interval.cs
//
// Authors:
// Alexander Chebaturkin (chebaturkin@gmail.com)
//
// Copyright (C) 2012 Alexander Chebaturkin
//
// Permission is hereby granted, free of charge, to any person obtaining
// a copy of this software and associated documentation files (the
// "Software"), to deal in the Software without restriction, including
// without limitation the rights to use, copy, modify, merge, publish,
// distribute, sublicense, and/or sell copies of the Software, and to
// permit persons to whom the Software is furnished to do so, subject to
// the following conditions:
//
// The above copyright notice and this permission notice shall be
// included in all copies or substantial portions of the Software.
//
// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
// EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
// MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
// NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE
// LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION
// OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION
// WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
//
using System;
using System.Collections.Generic;
using System.IO;
using System.Linq;
using Mono.CodeContracts.Static.AST;
using Mono.CodeContracts.Static.DataStructures;
using Mono.CodeContracts.Static.Lattices;
using Mono.CodeContracts.Static.Providers;
namespace Mono.CodeContracts.Static.Analysis.Numerical {
/// <summary>
/// Represents a closed interval of <see cref="Rational"/> values.
/// </summary>
public class Interval : IntervalBase<Interval, Rational>, IEquatable<Interval> {
static Interval cached_top_value;
static Interval cached_bottom_value;
readonly bool is_bottom;
readonly bool is_top;
Interval (Rational lowerBound, Rational upperBound)
: base (lowerBound, upperBound)
{
if (lowerBound.IsMinusInfinity && upperBound.IsPlusInfinity ||
lowerBound.IsMinusInfinity && upperBound.IsMinusInfinity ||
lowerBound.IsPlusInfinity && upperBound.IsPlusInfinity) {
LowerBound = Rational.MinusInfinity;
UpperBound = Rational.PlusInfinity;
is_top = true;
}
is_bottom = LowerBound > UpperBound;
}
public static Interval TopValue
{
get
{
if (ReferenceEquals (cached_top_value, null))
cached_top_value = new Interval (Rational.MinusInfinity, Rational.PlusInfinity);
return cached_top_value;
}
}
public static Interval BottomValue
{
get
{
if (ReferenceEquals (cached_bottom_value, null))
cached_bottom_value = new Interval (Rational.PlusInfinity,
Rational.MinusInfinity);
return cached_bottom_value;
}
}
public override Interval Top { get { return TopValue; } }
public override Interval Bottom { get { return BottomValue; } }
public override bool IsTop { get { return is_top; } }
public override bool IsBottom { get { return is_bottom; } }
public override bool LessEqual (Interval that)
{
bool result;
if (this.TryTrivialLessEqual (that, out result))
return result;
//less equal <==> is included in
return LowerBound >= that.LowerBound && UpperBound <= that.UpperBound;
}
public bool LessEqual (IEnumerable<Interval> right)
{
return right.Any (LessEqual);
}
public override Interval Join (Interval that, bool widening, out bool weaker)
{
weaker = false;
return widening ? Widen (that) : Join (that);
}
public override Interval Join (Interval that)
{
Interval result;
if (this.TryTrivialJoin (that, out result))
return result;
return For (Rational.Min (LowerBound, that.LowerBound),
Rational.Max (UpperBound, that.UpperBound));
}
public override Interval Widen (Interval that)
{
Interval result;
if (this.TryTrivialJoin (that, out result))
return result;
return For (LowerBound < that.LowerBound
? ThresholdDB.GetPrevious (LowerBound)
: that.LowerBound,
UpperBound > that.UpperBound
? ThresholdDB.GetNext (UpperBound)
: that.UpperBound);
}
public override Interval Meet (Interval that)
{
Interval result;
if (this.TryTrivialMeet (that, out result))
return result;
return For (
Rational.Max (LowerBound, that.LowerBound),
Rational.Min (UpperBound, that.UpperBound));
}
public static Interval For (Rational lowerBound, Rational upperBound)
{
return new Interval (lowerBound, upperBound);
}
public static Interval For (Rational lowerBound, long upperBound)
{
return For (lowerBound, Rational.For (upperBound));
}
public static Interval For (long lowerBound, long upperBound)
{
return For (Rational.For (lowerBound), Rational.For (upperBound));
}
public static Interval For (long lower, Rational upperBound)
{
return For (Rational.For (lower), upperBound);
}
public static Interval For (Rational value)
{
return For (value, value);
}
public static Interval For (long value)
{
return For (Rational.For (value));
}
public static Interval operator + (Interval l, Interval r)
{
if (l.IsBottom || r.IsBottom)
return BottomValue;
Rational lower, upper;
if (l.IsTop || r.IsTop
|| !Rational.TryAdd (l.LowerBound, r.LowerBound, out lower)
|| !Rational.TryAdd (l.UpperBound, r.UpperBound, out upper))
return TopValue;
return For (lower, upper);
}
public static Interval operator - (Interval l, Interval r)
{
if (l.IsBottom || r.IsBottom)
return BottomValue;
Rational lower, upper;
if (l.IsTop || r.IsTop
|| !Rational.TrySubtract (l.LowerBound, r.UpperBound, out lower)
|| !Rational.TrySubtract (l.UpperBound, r.LowerBound, out upper))
return TopValue;
return For (lower, upper);
}
public static Interval operator / (Interval l, Interval r)
{
if (l.IsBottom || r.IsBottom)
return BottomValue;
Rational a, b, c, d;
if (l.IsTop || r.IsTop || r.Includes (0)
|| !Rational.TryDivide (l.LowerBound, r.UpperBound, out a)
|| !Rational.TryDivide (l.LowerBound, r.LowerBound, out b)
|| !Rational.TryDivide (l.UpperBound, r.UpperBound, out c)
|| !Rational.TryDivide (l.UpperBound, r.LowerBound, out d))
return TopValue;
var lower = Rational.Min (Rational.Min (a, b), Rational.Min (c, d));
var upper = Rational.Max (Rational.Max (a, b), Rational.Max (c, d));
return For (lower, upper);
}
public static Interval operator * (Interval l, Interval r)
{
if (l.IsBottom || r.IsBottom)
return BottomValue;
Rational lower, upper;
if (l.IsTop || r.IsTop
|| !Rational.TryMultiply (l.LowerBound, r.LowerBound, out lower)
|| !Rational.TryMultiply (l.UpperBound, r.UpperBound, out upper))
return TopValue;
return For (lower, upper);
}
public static Interval operator - (Interval l)
{
if (!l.IsNormal ())
return l;
Rational lower;
Rational upper;
if (!Rational.TryUnaryMinus (l.UpperBound, out lower) ||
!Rational.TryUnaryMinus (l.LowerBound, out upper))
return TopValue;
return For (lower, upper);
}
public static bool AreConsecutiveIntegers (Interval prev, Interval next)
{
if (!prev.IsNormal () || !next.IsNormal () ||
!prev.UpperBound.IsInteger || !next.LowerBound.IsInteger)
return false;
return prev.UpperBound + Rational.One == next.LowerBound;
}
public static Interval ApplyConversion (ExpressionOperator conv, Interval intv)
{
if (intv.is_bottom)
return intv;
switch (conv) {
case ExpressionOperator.ConvertToInt32:
return intv.RefineWithTypeRanges (int.MinValue, int.MaxValue);
default:
return intv;
}
}
public bool TryGetSingletonFiniteInt32 (out int value)
{
int lower;
int upper;
if (IsFiniteAndInt32 (out lower, out upper) && lower == upper)
return true.With (lower, out value);
return false.Without (out value);
}
public bool Includes (long x)
{
return this.IsNormal () && LowerBound <= x && x <= UpperBound;
}
public bool Includes (int x)
{
return this.IsNormal () && LowerBound <= x && x <= UpperBound;
}
public bool OverlapsWith (Interval that)
{
return !Meet (that).IsBottom;
}
public bool OnTheLeftOf (Interval that)
{
if (!this.IsNormal () || !that.IsNormal ())
return false;
return UpperBound <= that.LowerBound;
}
public override Interval ImmutableVersion ()
{
return this;
}
public override Interval Clone ()
{
return this;
}
public override bool Equals (object obj)
{
if (ReferenceEquals (null, obj))
return false;
if (ReferenceEquals (this, obj))
return true;
return Equals ((Interval) obj);
}
public bool Equals (Interval that)
{
if (ReferenceEquals (this, that))
return true;
if (ReferenceEquals (that, null))
return false;
return LowerBound == that.LowerBound && UpperBound == that.UpperBound;
}
public override int GetHashCode ()
{
return (LowerBound.GetHashCode () * 397) ^ UpperBound.GetHashCode ();
}
public override void Dump (TextWriter tw)
{
tw.WriteLine (ToString ());
}
protected override bool IsFiniteBound (Rational n)
{
return n.IsInteger;
}
bool IsFiniteAndInt32 (out int lower, out int upper)
{
if (IsFinite && LowerBound.IsInt32 && UpperBound.IsInt32) {
try {
lower = (int) LowerBound;
upper = (int) UpperBound;
return true;
}
catch (ArithmeticException) {
}
}
return false.With (0, out lower).
With (0, out upper);
}
Interval RefineWithTypeRanges (int min, int max)
{
var lower = LowerBound.IsInfinity || !LowerBound.IsInRange (min, max)
? Rational.MinusInfinity
: LowerBound.PreviousInt32;
var upper = UpperBound.IsInfinity || !UpperBound.IsInRange (min, max)
? Rational.PlusInfinity
: UpperBound.NextInt32;
return For (lower, upper);
}
internal static class Ranges {
static Interval int8Range;
static Interval int32Range;
static Interval int64Range;
public static Interval Int8Range { get { return int8Range ?? (int8Range = For (sbyte.MinValue, sbyte.MaxValue)); } }
public static Interval Int32Range { get { return int32Range ?? (int32Range = For (int.MinValue, int.MaxValue)); } }
public static Interval Int64Range { get { return int64Range ?? (int64Range = For (int.MinValue, int.MaxValue)); } }
public static Interval GetIntervalForType (TypeNode type, IMetaDataProvider provider)
{
if (provider.Equal (provider.System_Int8, type))
return Int8Range;
if (provider.Equal (provider.System_Int32, type))
return Int32Range;
if (provider.Equal (provider.System_Int64, type))
return Int64Range;
return TopValue;
}
}
}
}
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