1 files changed, 248 insertions, 248 deletions
diff --git a/Source/Basetypes/Rational.cs b/Source/Basetypes/Rational.cs
index cd0eddce..ef59cf4f 100644
--- a/Source/Basetypes/Rational.cs
+++ b/Source/Basetypes/Rational.cs
@@ -1,248 +1,248 @@
-//-----------------------------------------------------------------------------
-//
-// Copyright (C) Microsoft Corporation.  All Rights Reserved.
-//
-//-----------------------------------------------------------------------------
-using System;
-using System.Diagnostics.Contracts;
-
-namespace Microsoft.Basetypes {
-  /// <summary>
-  /// The representation of a rational number.
-  /// </summary>
-  public struct Rational {
-    public static readonly Rational ZERO = Rational.FromInts(0, 1);
-    public static readonly Rational ONE = Rational.FromInts(1, 1);
-    public static readonly Rational MINUS_ONE = Rational.FromInts(-1, 1);
-
-    private BigNum numerator, denominator;
-
-    //    int numerator;
-    //    int denominator;
-
-
-    // invariant: 0 < denominator || (numerator == 0 && denominator == 0);
-    // invariant: numerator != 0 ==> gcd(abs(numerator),denominator) == 1;
-    // invariant: numerator == 0 ==> denominator == 1 || denominator == 0;
-
-    public static Rational FromInt(int x) {
-      return FromBignum(BigNum.FromInt(x));
-    }
-
-    public static Rational FromBignum(BigNum n)       
-    {
-      return new Rational(n, BigNum.ONE);
-    }
-
-    private Rational(BigNum num, BigNum den)
-    {
-      Contract.Assert(den.Signum > 0);
-      Contract.Assert(num == BigNum.ZERO || num.Gcd(den) == BigNum.ONE);
-      numerator = num;
-      denominator = den;
-    }
-
-    public static Rational FromBignums(BigNum num, BigNum den) {
-      Contract.Assert(!den.IsZero);
-      if (num == BigNum.ZERO)
-        return ZERO;
-      if (den.Signum < 0) {
-        den = -den;
-        num = -num;
-      }
-      if (den == BigNum.ONE)
-        return new Rational(num, den);
-      var gcd = num.Gcd(den);
-      if (gcd == BigNum.ONE)
-        return new Rational(num, den);
-      return new Rational(num / gcd, den / gcd);
-    }
-
-    public static Rational FromInts(int num, int den) {
-      return FromBignums(BigNum.FromInt(num), BigNum.FromInt(den));
-    }
-
-    /// <summary>
-    /// Returns the absolute value of the rational.
-    /// </summary>
-    public Rational Abs() {
-      Contract.Ensures(Contract.Result<Rational>().IsNonNegative);
-      if (IsNonNegative) {
-        return this;
-      } else {
-        return -this;
-      }
-    }
-
-    /// <summary>
-    /// Returns a rational whose numerator and denominator, resepctively, are the Gcd
-    /// of the numerators and denominators of r and s.  If one of r and s is 0, the absolute
-    /// value of the other is returned.  If both are 0, 1 is returned.
-    /// </summary>
-    public static Rational Gcd(Rational r, Rational s) {
-      Contract.Ensures(Contract.Result<Rational>().IsPositive);
-      if (r.IsZero) {
-        if (s.IsZero) {
-          return ONE;
-        } else {
-          return s.Abs();
-        }
-      } else if (s.IsZero) {
-        return r.Abs();
-      } else {
-        return new Rational(r.Numerator.Gcd(s.Numerator),
-                             r.Denominator.Gcd(s.Denominator));
-      }
-    }
-
-    public BigNum Numerator { get { return numerator; } }
-    public BigNum Denominator { get { return denominator == BigNum.ZERO ? BigNum.ONE : denominator; } }
-
-    public override string/*!*/ ToString() {
-      Contract.Ensures(Contract.Result<string>() != null);
-      return String.Format("{0}/{1}", Numerator, Denominator);
-    }
-
-
-    public static bool operator ==(Rational r, Rational s) {
-      return r.Numerator == s.Numerator && r.Denominator == s.Denominator;
-    }
-
-    public static bool operator !=(Rational r, Rational s) {
-      return !(r == s);
-    }
-
-    public override bool Equals(object obj) {
-      if (obj == null)
-        return false;
-      return obj is Rational && (Rational)obj == this;
-    }
-
-    public override int GetHashCode() {
-      return this.Numerator.GetHashCode() * 13 + this.Denominator.GetHashCode();
-    }
-
-    public int Signum {
-      get {
-        return this.Numerator.Signum;
-      }
-    }
-
-    public bool IsZero {
-      get {
-        return Signum == 0;
-      }
-    }
-
-    public bool IsNonZero {
-      get {
-        return Signum != 0;
-      }
-    }
-
-    public bool IsIntegral {
-      get {
-        return Denominator == BigNum.ONE;
-      }
-    }
-
-
-    [Pure]
-    [Reads(ReadsAttribute.Reads.Nothing)]
-    public bool HasValue(int n) {
-      return this == FromInt(n);
-    }
-
-    /// <summary>
-    /// Returns the rational as an integer.  Requires the rational to be integral.
-    /// </summary>
-    public int AsInteger {
-      get {
-        Contract.Assert(this.IsIntegral);
-        return Numerator.ToIntSafe;
-      }
-    }
-
-    public BigNum AsBigNum {
-      get {
-        Contract.Assert(this.IsIntegral);
-        return Numerator;
-      }
-    }
-
-    public double AsDouble {
-      [Pure]
-      get {
-        if (this.IsZero) {
-          return 0.0;
-        } else {
-          return (double)Numerator.ToIntSafe / (double)Denominator.ToIntSafe;
-        }
-      }
-    }
-
-    public bool IsNegative {
-      [Pure]
-      get {
-        return Signum < 0;
-      }
-    }
-
-    public bool IsPositive {
-      [Pure]
-      get {
-        return 0 < Signum;
-      }
-    }
-
-    public bool IsNonNegative {
-      [Pure]
-      get {
-        return 0 <= Signum;
-      }
-    }
-
-    public static Rational operator -(Rational r)
-    {
-      return new Rational(-r.Numerator, r.Denominator);
-    }
-
-    public static Rational operator /(Rational r, Rational s)
-    {
-      return FromBignums(r.Numerator * s.Denominator, r.Denominator * s.Numerator);
-    }
-
-    public static Rational operator -(Rational r, Rational s)
-    {
-      return r + (-s);
-    }
-
-    public static Rational operator +(Rational r, Rational s)
-    {
-      return FromBignums(r.Numerator * s.Denominator + s.Numerator * r.Denominator, r.Denominator * s.Denominator);
-    }
-
-    public static Rational operator *(Rational r, Rational s)
-    {
-      return FromBignums(r.Numerator * s.Numerator, r.Denominator * s.Denominator);
-    }
-
-    public static bool operator <(Rational r, Rational s)
-    {
-      return (r - s).Signum < 0;
-    }
-
-    public static bool operator <=(Rational r, Rational s)
-    {
-      return !(r > s);
-    }
-
-    public static bool operator >=(Rational r, Rational s) {
-      return !(r < s);
-    }
-
-    public static bool operator >(Rational r, Rational s) {
-      return s < r;
-    }
-  }
-}
+//-----------------------------------------------------------------------------
+//
+// Copyright (C) Microsoft Corporation.  All Rights Reserved.
+//
+//-----------------------------------------------------------------------------
+using System;
+using System.Diagnostics.Contracts;
+
+namespace Microsoft.Basetypes {
+  /// <summary>
+  /// The representation of a rational number.
+  /// </summary>
+  public struct Rational {
+    public static readonly Rational ZERO = Rational.FromInts(0, 1);
+    public static readonly Rational ONE = Rational.FromInts(1, 1);
+    public static readonly Rational MINUS_ONE = Rational.FromInts(-1, 1);
+
+    private BigNum numerator, denominator;
+
+    //    int numerator;
+    //    int denominator;
+
+
+    // invariant: 0 < denominator || (numerator == 0 && denominator == 0);
+    // invariant: numerator != 0 ==> gcd(abs(numerator),denominator) == 1;
+    // invariant: numerator == 0 ==> denominator == 1 || denominator == 0;
+
+    public static Rational FromInt(int x) {
+      return FromBignum(BigNum.FromInt(x));
+    }
+
+    public static Rational FromBignum(BigNum n)       
+    {
+      return new Rational(n, BigNum.ONE);
+    }
+
+    private Rational(BigNum num, BigNum den)
+    {
+      Contract.Assert(den.Signum > 0);
+      Contract.Assert(num == BigNum.ZERO || num.Gcd(den) == BigNum.ONE);
+      numerator = num;
+      denominator = den;
+    }
+
+    public static Rational FromBignums(BigNum num, BigNum den) {
+      Contract.Assert(!den.IsZero);
+      if (num == BigNum.ZERO)
+        return ZERO;
+      if (den.Signum < 0) {
+        den = -den;
+        num = -num;
+      }
+      if (den == BigNum.ONE)
+        return new Rational(num, den);
+      var gcd = num.Gcd(den);
+      if (gcd == BigNum.ONE)
+        return new Rational(num, den);
+      return new Rational(num / gcd, den / gcd);
+    }
+
+    public static Rational FromInts(int num, int den) {
+      return FromBignums(BigNum.FromInt(num), BigNum.FromInt(den));
+    }
+
+    /// <summary>
+    /// Returns the absolute value of the rational.
+    /// </summary>
+    public Rational Abs() {
+      Contract.Ensures(Contract.Result<Rational>().IsNonNegative);
+      if (IsNonNegative) {
+        return this;
+      } else {
+        return -this;
+      }
+    }
+
+    /// <summary>
+    /// Returns a rational whose numerator and denominator, resepctively, are the Gcd
+    /// of the numerators and denominators of r and s.  If one of r and s is 0, the absolute
+    /// value of the other is returned.  If both are 0, 1 is returned.
+    /// </summary>
+    public static Rational Gcd(Rational r, Rational s) {
+      Contract.Ensures(Contract.Result<Rational>().IsPositive);
+      if (r.IsZero) {
+        if (s.IsZero) {
+          return ONE;
+        } else {
+          return s.Abs();
+        }
+      } else if (s.IsZero) {
+        return r.Abs();
+      } else {
+        return new Rational(r.Numerator.Gcd(s.Numerator),
+                             r.Denominator.Gcd(s.Denominator));
+      }
+    }
+
+    public BigNum Numerator { get { return numerator; } }
+    public BigNum Denominator { get { return denominator == BigNum.ZERO ? BigNum.ONE : denominator; } }
+
+    public override string/*!*/ ToString() {
+      Contract.Ensures(Contract.Result<string>() != null);
+      return String.Format("{0}/{1}", Numerator, Denominator);
+    }
+
+
+    public static bool operator ==(Rational r, Rational s) {
+      return r.Numerator == s.Numerator && r.Denominator == s.Denominator;
+    }
+
+    public static bool operator !=(Rational r, Rational s) {
+      return !(r == s);
+    }
+
+    public override bool Equals(object obj) {
+      if (obj == null)
+        return false;
+      return obj is Rational && (Rational)obj == this;
+    }
+
+    public override int GetHashCode() {
+      return this.Numerator.GetHashCode() * 13 + this.Denominator.GetHashCode();
+    }
+
+    public int Signum {
+      get {
+        return this.Numerator.Signum;
+      }
+    }
+
+    public bool IsZero {
+      get {
+        return Signum == 0;
+      }
+    }
+
+    public bool IsNonZero {
+      get {
+        return Signum != 0;
+      }
+    }
+
+    public bool IsIntegral {
+      get {
+        return Denominator == BigNum.ONE;
+      }
+    }
+
+
+    [Pure]
+    [Reads(ReadsAttribute.Reads.Nothing)]
+    public bool HasValue(int n) {
+      return this == FromInt(n);
+    }
+
+    /// <summary>
+    /// Returns the rational as an integer.  Requires the rational to be integral.
+    /// </summary>
+    public int AsInteger {
+      get {
+        Contract.Assert(this.IsIntegral);
+        return Numerator.ToIntSafe;
+      }
+    }
+
+    public BigNum AsBigNum {
+      get {
+        Contract.Assert(this.IsIntegral);
+        return Numerator;
+      }
+    }
+
+    public double AsDouble {
+      [Pure]
+      get {
+        if (this.IsZero) {
+          return 0.0;
+        } else {
+          return (double)Numerator.ToIntSafe / (double)Denominator.ToIntSafe;
+        }
+      }
+    }
+
+    public bool IsNegative {
+      [Pure]
+      get {
+        return Signum < 0;
+      }
+    }
+
+    public bool IsPositive {
+      [Pure]
+      get {
+        return 0 < Signum;
+      }
+    }
+
+    public bool IsNonNegative {
+      [Pure]
+      get {
+        return 0 <= Signum;
+      }
+    }
+
+    public static Rational operator -(Rational r)
+    {
+      return new Rational(-r.Numerator, r.Denominator);
+    }
+
+    public static Rational operator /(Rational r, Rational s)
+    {
+      return FromBignums(r.Numerator * s.Denominator, r.Denominator * s.Numerator);
+    }
+
+    public static Rational operator -(Rational r, Rational s)
+    {
+      return r + (-s);
+    }
+
+    public static Rational operator +(Rational r, Rational s)
+    {
+      return FromBignums(r.Numerator * s.Denominator + s.Numerator * r.Denominator, r.Denominator * s.Denominator);
+    }
+
+    public static Rational operator *(Rational r, Rational s)
+    {
+      return FromBignums(r.Numerator * s.Numerator, r.Denominator * s.Denominator);
+    }
+
+    public static bool operator <(Rational r, Rational s)
+    {
+      return (r - s).Signum < 0;
+    }
+
+    public static bool operator <=(Rational r, Rational s)
+    {
+      return !(r > s);
+    }
+
+    public static bool operator >=(Rational r, Rational s) {
+      return !(r < s);
+    }
+
+    public static bool operator >(Rational r, Rational s) {
+      return s < r;
+    }
+  }
+}