815 lines
33 KiB
C#
815 lines
33 KiB
C#
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//
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// Rational.cs
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//
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// Authors:
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// Alexander Chebaturkin (chebaturkin@gmail.com)
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//
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// Copyright (C) 2012 Alexander Chebaturkin
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//
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// Permission is hereby granted, free of charge, to any person obtaining
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// a copy of this software and associated documentation files (the
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// "Software"), to deal in the Software without restriction, including
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// without limitation the rights to use, copy, modify, merge, publish,
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// distribute, sublicense, and/or sell copies of the Software, and to
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// permit persons to whom the Software is furnished to do so, subject to
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// the following conditions:
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//
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// The above copyright notice and this permission notice shall be
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// included in all copies or substantial portions of the Software.
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//
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// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
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// EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
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// MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
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// NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE
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// LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION
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// OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION
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// WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
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//
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using System;
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using Mono.CodeContracts.Static.DataStructures;
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namespace Mono.CodeContracts.Static.Analysis.Numerical {
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/// <summary>
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/// Represents a rational number.
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/// </summary>
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public struct Rational : IEquatable<Rational> {
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public static readonly Rational Zero = new Rational (0L);
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public static readonly Rational One = new Rational (1L);
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public static readonly Rational MinusOne = new Rational (-1L);
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public static Rational PlusInfinity = new Rational (Kind.PlusInfinity);
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public static Rational MinusInfinity = new Rational (Kind.MinusInfinity);
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public static Rational MaxValue = new Rational (long.MaxValue);
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public static Rational MinValue = new Rational (long.MinValue);
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readonly long down;
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readonly Kind kind;
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readonly long up;
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Rational (Kind kind)
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{
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if (kind == Kind.Normal)
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throw new ArgumentException (
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"Kind should be equal to Kind.PlusInfinity or Kind.MinusInfinity", "kind");
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this.kind = kind;
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this.up = 0L;
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this.down = 0L;
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}
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Rational (long number)
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: this (number, 1L)
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{
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}
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Rational (long nominator, long denominator)
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{
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if (denominator == 0L)
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throw new ArgumentException ("Denominator should not be equal to 0");
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if (nominator == 0L) {
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this.kind = Kind.Normal;
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this.up = 0L;
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this.down = 1L;
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return;
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}
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this.kind = Kind.Normal;
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int sign = System.Math.Sign (nominator) * System.Math.Sign (denominator);
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if (nominator == long.MinValue)
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nominator = sign >= 0 ? long.MaxValue : long.MinValue;
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else
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nominator = sign * System.Math.Abs (nominator);
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if (denominator == long.MinValue)
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denominator = long.MaxValue;
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else
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denominator = System.Math.Abs (denominator);
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if (nominator % denominator == 0) {
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this.up = nominator / denominator;
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this.down = 1L;
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return;
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}
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long gcd = (nominator == 0L || nominator == long.MaxValue ||
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denominator == 0L || denominator == long.MaxValue)
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? 1L
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: GCD (System.Math.Abs (nominator), System.Math.Abs (denominator));
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this.up = nominator / gcd;
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this.down = denominator / gcd;
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}
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public bool IsInteger { get { return !this.IsInfinity && (this.up % this.down == 0L); } }
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public bool IsInt32 { get { return this.IsInteger && this.up >= int.MinValue && this.up <= int.MaxValue; } }
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public bool IsInfinity { get { return this.kind == Kind.PlusInfinity || this.kind == Kind.MinusInfinity; } }
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public bool IsPlusInfinity { get { return this.kind == Kind.PlusInfinity; } }
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public bool IsMinusInfinity { get { return this.kind == Kind.MinusInfinity; } }
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public bool IsZero { get { return this.kind == Kind.Normal && this.up == 0L; } }
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public bool IsMaxValue { get { return this.kind == Kind.Normal && this.up == long.MaxValue && this.down == 1L; } }
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public bool IsMinValue { get { return this.kind == Kind.Normal && this.up == -long.MaxValue && this.down == 1L; } }
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public int Sign { get { return GetSign (this); } }
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public Rational NextInt32
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{
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get
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{
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if (this.IsInfinity)
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return this;
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var next = (long) System.Math.Ceiling ((double) this);
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return For (next >= int.MaxValue ? int.MaxValue : next);
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}
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}
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public Rational PreviousInt32
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{
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get
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{
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if (this.IsInfinity)
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return this;
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var prev = (long) System.Math.Floor ((double) this);
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return For (prev <= int.MinValue ? int.MinValue : prev);
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}
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}
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public Rational NextInt64
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{
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get
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{
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if (this.IsInfinity)
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return this;
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double next = System.Math.Ceiling ((double) this);
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return For (next >= (double) long.MaxValue ? long.MaxValue : (long) System.Math.Truncate (next));
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}
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}
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public long Up { get { return up; } }
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public long Down { get { return down; } }
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public bool IsInRange (long min, long max)
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{
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return min <= this && this <= max;
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}
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public static Rational For (long number)
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{
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return new Rational (number);
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}
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public static Rational For (long nominator, long denominator)
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{
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switch (denominator) {
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case 0L:
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return new Rational (nominator >= 0 ? Kind.PlusInfinity : Kind.MinusInfinity);
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default:
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return new Rational (nominator, denominator);
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}
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}
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public static bool operator == (Rational l, Rational r)
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{
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if (l.kind != r.kind)
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return false;
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if (l.kind != Kind.Normal)
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return true;
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return l.up == r.up && l.down == r.down;
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}
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public static bool operator != (Rational l, Rational r)
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{
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return !(l == r);
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}
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public static bool operator < (Rational l, Rational r)
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{
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if (l.IsMinusInfinity && !r.IsMinusInfinity
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|| r.IsPlusInfinity && !l.IsPlusInfinity)
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return true;
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if (l.IsPlusInfinity || r.IsMinusInfinity)
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return false;
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if (l.down == r.down)
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return l.up < r.up;
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if (l.up <= 0L && r.up > 0L)
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return true;
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if (l.up < 0L && r.up == 0L)
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return true;
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try {
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return checked(l.up * r.down) < checked(r.up * l.down);
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}
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catch (ArithmeticException) {
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return (decimal) l.up / l.down < (decimal) r.up / r.down;
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}
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}
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public static bool operator <= (Rational l, Rational r)
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{
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if (l.IsMinusInfinity || r.IsPlusInfinity)
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return true;
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if (l.IsPlusInfinity || r.IsMinusInfinity)
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return false;
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if (l.down == r.down)
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return l.up <= r.up;
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try {
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return checked(l.up * r.down) <= checked(r.up * l.down);
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}
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catch (ArithmeticException) {
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return (decimal) l.up / l.down <= (decimal) r.up / r.down;
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}
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}
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public static bool operator >= (Rational l, Rational r)
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{
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return r <= l;
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}
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public static bool operator <= (Rational l, long r)
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{
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switch (l.kind) {
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case Kind.PlusInfinity:
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return false;
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case Kind.MinusInfinity:
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return true;
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default:
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try {
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return l.up <= checked(l.down * r);
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}
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catch (ArithmeticException) {
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return (decimal) l.up / l.down <= r;
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}
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}
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}
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public static bool operator <= (long l, Rational r)
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{
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switch (r.kind) {
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case Kind.PlusInfinity:
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return true;
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case Kind.MinusInfinity:
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return false;
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default:
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try {
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return r.up >= checked(r.down * l);
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}
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catch (ArithmeticException) {
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return (decimal) r.up / r.down >= l;
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}
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}
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}
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public static bool operator >= (long l, Rational r)
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{
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return r <= l;
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}
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public static bool operator >= (Rational l, long r)
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{
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return r <= l;
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}
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public static bool operator > (Rational l, Rational r)
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{
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return r < l;
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}
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public static bool operator < (Rational l, long r)
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{
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switch (l.kind) {
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case Kind.PlusInfinity:
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return false;
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case Kind.MinusInfinity:
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return true;
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default:
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try {
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return l.up < checked(r * l.down);
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}
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catch {
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return (decimal) l.up / l.down < r;
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}
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}
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}
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public static bool operator > (Rational l, long r)
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{
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return r < l;
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}
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public static bool operator < (long l, Rational r)
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{
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switch (r.kind) {
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case Kind.PlusInfinity:
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return true;
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case Kind.MinusInfinity:
|
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return false;
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default:
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try {
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return checked(l * r.down) < r.up;
|
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}
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catch {
|
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return l < (decimal) r.up / r.down;
|
|||
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}
|
|||
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}
|
|||
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}
|
|||
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|
|||
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public static bool operator > (long l, Rational r)
|
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{
|
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return r < l;
|
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}
|
|||
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public static Rational operator + (Rational l, Rational r)
|
|||
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{
|
|||
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Rational result;
|
|||
|
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if (TryAdd (l, r, out result))
|
|||
|
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return result;
|
|||
|
|
|
|||
|
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throw new ArithmeticException ();
|
|||
|
|
}
|
|||
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|
|
|||
|
|
public static Rational operator - (Rational l, Rational r)
|
|||
|
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{
|
|||
|
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Rational result;
|
|||
|
|
if (TrySubtract (l, r, out result))
|
|||
|
|
return result;
|
|||
|
|
|
|||
|
|
throw new ArithmeticException ();
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
public static Rational operator * (Rational l, Rational r)
|
|||
|
|
{
|
|||
|
|
Rational result;
|
|||
|
|
if (TryMultiply (l, r, out result))
|
|||
|
|
return result;
|
|||
|
|
|
|||
|
|
throw new ArithmeticException ();
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
public static Rational operator / (Rational l, Rational r)
|
|||
|
|
{
|
|||
|
|
Rational result;
|
|||
|
|
if (TryDivide (l, r, out result))
|
|||
|
|
return result;
|
|||
|
|
|
|||
|
|
throw new ArithmeticException ();
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
public static Rational operator - (Rational l, long i)
|
|||
|
|
{
|
|||
|
|
if (l.kind == Kind.Normal && l.down == 1L)
|
|||
|
|
try {
|
|||
|
|
return For (checked(l.up - i));
|
|||
|
|
}
|
|||
|
|
catch (ArithmeticException) {
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
return l - For (i);
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
public static Rational operator + (Rational l, long i)
|
|||
|
|
{
|
|||
|
|
if (l.kind == Kind.Normal && l.down == 1L)
|
|||
|
|
try {
|
|||
|
|
return For (checked(l.up + i));
|
|||
|
|
}
|
|||
|
|
catch (ArithmeticException) {
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
return l + For (i);
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
public static Rational operator - (Rational value)
|
|||
|
|
{
|
|||
|
|
Rational result;
|
|||
|
|
if (TryUnaryMinus (value, out result))
|
|||
|
|
return result;
|
|||
|
|
|
|||
|
|
throw new ArithmeticException ();
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
public static explicit operator double (Rational r)
|
|||
|
|
{
|
|||
|
|
switch (r.kind) {
|
|||
|
|
case Kind.PlusInfinity:
|
|||
|
|
return double.PositiveInfinity;
|
|||
|
|
case Kind.MinusInfinity:
|
|||
|
|
return double.NegativeInfinity;
|
|||
|
|
default:
|
|||
|
|
return (double) r.up / r.down;
|
|||
|
|
}
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
public static explicit operator long (Rational r)
|
|||
|
|
{
|
|||
|
|
if (r.down == 0L)
|
|||
|
|
return r.up >= 0L ? long.MaxValue : long.MinValue;
|
|||
|
|
|
|||
|
|
if (!r.IsInteger)
|
|||
|
|
return (long) System.Math.Round ((double) r.up / r.down);
|
|||
|
|
|
|||
|
|
return r.up;
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
public static explicit operator int (Rational r)
|
|||
|
|
{
|
|||
|
|
if (r.down != 0L)
|
|||
|
|
return (int) System.Math.Round ((double) r.up / r.down);
|
|||
|
|
|
|||
|
|
return r.up >= 0L ? int.MaxValue : int.MinValue;
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
public static implicit operator Rational (long l)
|
|||
|
|
{
|
|||
|
|
return For (l);
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
public static Rational Abs (Rational a)
|
|||
|
|
{
|
|||
|
|
switch (a.kind) {
|
|||
|
|
case Kind.PlusInfinity:
|
|||
|
|
case Kind.MinusInfinity:
|
|||
|
|
return PlusInfinity;
|
|||
|
|
default:
|
|||
|
|
return a.IsZero || a > 0L ? a : -a;
|
|||
|
|
}
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
public static Rational Max (Rational a, Rational b)
|
|||
|
|
{
|
|||
|
|
return a < b ? b : a;
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
public static Rational Min (Rational a, Rational b)
|
|||
|
|
{
|
|||
|
|
return a < b ? a : b;
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
public static bool TryAdd (Rational l, Rational r, out Rational result)
|
|||
|
|
{
|
|||
|
|
if (l.IsZero)
|
|||
|
|
return true.With (r, out result);
|
|||
|
|
|
|||
|
|
if (r.IsZero || l.IsInfinity)
|
|||
|
|
return true.With (l, out result);
|
|||
|
|
|
|||
|
|
if (r.IsInfinity)
|
|||
|
|
return true.With (r, out result);
|
|||
|
|
|
|||
|
|
if (l.IsMaxValue && r > 0L || r.IsMaxValue && l > 0L)
|
|||
|
|
return true.With (PlusInfinity, out result);
|
|||
|
|
|
|||
|
|
long nom;
|
|||
|
|
long denom;
|
|||
|
|
try {
|
|||
|
|
if (l.down == r.down) {
|
|||
|
|
if (l.up == r.up && (r.down & 1L) == 0L) {
|
|||
|
|
nom = l.up;
|
|||
|
|
denom = l.down >> 1;
|
|||
|
|
}
|
|||
|
|
else {
|
|||
|
|
nom = checked (l.up + r.up);
|
|||
|
|
denom = l.down;
|
|||
|
|
}
|
|||
|
|
}
|
|||
|
|
else {
|
|||
|
|
nom = checked (l.up * r.down + r.up * l.down);
|
|||
|
|
denom = checked (l.down * r.down);
|
|||
|
|
}
|
|||
|
|
}
|
|||
|
|
catch (ArithmeticException) {
|
|||
|
|
try {
|
|||
|
|
long gcd = GCD (l.down, r.down);
|
|||
|
|
nom =
|
|||
|
|
checked (
|
|||
|
|
l.up * unchecked (r.down / gcd) +
|
|||
|
|
r.up * unchecked (l.down / gcd));
|
|||
|
|
denom = checked ((l.down / gcd) * r.down);
|
|||
|
|
}
|
|||
|
|
catch (ArithmeticException) {
|
|||
|
|
return false.Without (out result);
|
|||
|
|
}
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
return true.With (denom == 1L ? For (nom) : For (nom, denom), out result);
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
public static bool TrySubtract (Rational l, Rational r, out Rational result)
|
|||
|
|
{
|
|||
|
|
if (r.IsZero)
|
|||
|
|
return true.With (l, out result);
|
|||
|
|
|
|||
|
|
if (l.IsZero)
|
|||
|
|
return true.With (-r, out result);
|
|||
|
|
|
|||
|
|
if (l == r)
|
|||
|
|
return true.With (Zero, out result);
|
|||
|
|
|
|||
|
|
if (r < 0L && !r.IsMinValue)
|
|||
|
|
return TryAdd (l, Abs (r), out result);
|
|||
|
|
|
|||
|
|
if (l.IsInfinity)
|
|||
|
|
return true.With (l, out result);
|
|||
|
|
|
|||
|
|
if (r.IsInfinity)
|
|||
|
|
return true.With (-r, out result);
|
|||
|
|
|
|||
|
|
if (l.IsMinValue && r > 0L)
|
|||
|
|
return true.With (MinusInfinity, out result);
|
|||
|
|
|
|||
|
|
long nom;
|
|||
|
|
long denom;
|
|||
|
|
try {
|
|||
|
|
if (l.down == r.down) {
|
|||
|
|
nom = checked (l.up - r.up);
|
|||
|
|
denom = l.down;
|
|||
|
|
}
|
|||
|
|
else {
|
|||
|
|
nom = checked (l.up * r.down - r.up * l.down);
|
|||
|
|
denom = checked (l.down * r.down);
|
|||
|
|
}
|
|||
|
|
}
|
|||
|
|
catch (ArithmeticException) {
|
|||
|
|
return false.Without (out result);
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
return true.With (For (nom, denom), out result);
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
public static bool TryDivide (Rational l, Rational r, out Rational result)
|
|||
|
|
{
|
|||
|
|
if (r == One)
|
|||
|
|
return true.With (l, out result);
|
|||
|
|
|
|||
|
|
if (r.IsZero)
|
|||
|
|
return false.Without (out result);
|
|||
|
|
|
|||
|
|
if (l.IsZero || r.IsInfinity)
|
|||
|
|
return true.With (Zero, out result);
|
|||
|
|
|
|||
|
|
if (l.IsPlusInfinity)
|
|||
|
|
return true.With (r.Sign > 0 ? PlusInfinity : MinusInfinity, out result);
|
|||
|
|
|
|||
|
|
if (l.IsMinusInfinity)
|
|||
|
|
return true.With (r.Sign > 0 ? MinusInfinity : PlusInfinity, out result);
|
|||
|
|
|
|||
|
|
long nom;
|
|||
|
|
long denom;
|
|||
|
|
|
|||
|
|
if (l.up == r.up) {
|
|||
|
|
// (a/b)/(a/c) = (c/b)
|
|||
|
|
|
|||
|
|
nom = r.down;
|
|||
|
|
denom = l.down;
|
|||
|
|
}
|
|||
|
|
else if (l.down == r.down) {
|
|||
|
|
// (a/c)/(b/c) = (a/b)
|
|||
|
|
|
|||
|
|
nom = l.up;
|
|||
|
|
denom = r.up;
|
|||
|
|
}
|
|||
|
|
else {
|
|||
|
|
// (x/y) / (e/f) == (x/e) * (f/y)
|
|||
|
|
|
|||
|
|
Rational a = For (l.up, r.up);
|
|||
|
|
Rational b = For (r.down, l.down);
|
|||
|
|
|
|||
|
|
try {
|
|||
|
|
return TryMultiply (a, b, out result);
|
|||
|
|
}
|
|||
|
|
catch (ArithmeticException) {
|
|||
|
|
return false.Without (out result);
|
|||
|
|
}
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
return true.With (For (nom, denom), out result);
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
public static bool TryMultiply (Rational l, Rational r, out Rational result)
|
|||
|
|
{
|
|||
|
|
if (l.IsZero || r.IsZero)
|
|||
|
|
return true.With (Zero, out result);
|
|||
|
|
|
|||
|
|
if (l == One)
|
|||
|
|
return true.With (r, out result);
|
|||
|
|
if (r == One)
|
|||
|
|
return true.With (l, out result);
|
|||
|
|
|
|||
|
|
if (l.IsPlusInfinity) {
|
|||
|
|
if (r.IsPlusInfinity)
|
|||
|
|
result = PlusInfinity;
|
|||
|
|
else if (r.IsMinusInfinity)
|
|||
|
|
result = MinusInfinity;
|
|||
|
|
else if (r.IsZero)
|
|||
|
|
result = Zero;
|
|||
|
|
else
|
|||
|
|
result = r.Sign > 0 ? PlusInfinity : MinusInfinity;
|
|||
|
|
|
|||
|
|
return true;
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
if (l.IsMinusInfinity) {
|
|||
|
|
if (r.IsPlusInfinity)
|
|||
|
|
result = MinusInfinity;
|
|||
|
|
else if (r.IsMinusInfinity)
|
|||
|
|
result = PlusInfinity;
|
|||
|
|
else if (r.IsZero)
|
|||
|
|
result = Zero;
|
|||
|
|
else
|
|||
|
|
result = r.Sign > 0 ? MinusInfinity : PlusInfinity;
|
|||
|
|
|
|||
|
|
return true;
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
if (r.IsPlusInfinity) {
|
|||
|
|
if (l.IsZero)
|
|||
|
|
result = Zero;
|
|||
|
|
else
|
|||
|
|
result = l.Sign > 0 ? PlusInfinity : MinusInfinity;
|
|||
|
|
|
|||
|
|
return true;
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
if (r.IsMinusInfinity) {
|
|||
|
|
if (l.IsZero)
|
|||
|
|
result = Zero;
|
|||
|
|
else
|
|||
|
|
result = l.Sign > 0 ? MinusInfinity : PlusInfinity;
|
|||
|
|
|
|||
|
|
return true;
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
long nom;
|
|||
|
|
long denom;
|
|||
|
|
|
|||
|
|
try {
|
|||
|
|
Rational a = For (l.up, r.down);
|
|||
|
|
Rational b = For (r.up, l.down);
|
|||
|
|
|
|||
|
|
nom = checked(a.up * b.up);
|
|||
|
|
denom = checked(a.down * b.down);
|
|||
|
|
}
|
|||
|
|
catch (ArithmeticException) {
|
|||
|
|
return false.Without (out result);
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
return true.With (For (nom, denom), out result);
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
public static bool TryUnaryMinus (Rational value, out Rational result)
|
|||
|
|
{
|
|||
|
|
if (value.IsZero)
|
|||
|
|
return true.With (value, out result);
|
|||
|
|
|
|||
|
|
switch (value.kind) {
|
|||
|
|
case Kind.PlusInfinity:
|
|||
|
|
return true.With (MinusInfinity, out result);
|
|||
|
|
case Kind.MinusInfinity:
|
|||
|
|
return true.With (PlusInfinity, out result);
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
if (value.IsMinValue)
|
|||
|
|
return true.With (MaxValue, out result);
|
|||
|
|
if (value.IsMaxValue)
|
|||
|
|
return true.With (MinValue, out result);
|
|||
|
|
|
|||
|
|
return true.With (For (-value.up, value.down), out result);
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
static int GetSign (Rational r)
|
|||
|
|
{
|
|||
|
|
switch (r.kind) {
|
|||
|
|
case Kind.PlusInfinity:
|
|||
|
|
return 1;
|
|||
|
|
case Kind.MinusInfinity:
|
|||
|
|
return -1;
|
|||
|
|
default:
|
|||
|
|
return System.Math.Sign (r.up) * System.Math.Sign (r.down);
|
|||
|
|
}
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
static long GCD (long a, long b)
|
|||
|
|
{
|
|||
|
|
var aa = (ulong) a;
|
|||
|
|
var bb = (ulong) b;
|
|||
|
|
|
|||
|
|
int pow = 0;
|
|||
|
|
|
|||
|
|
while (((aa | bb) & 1L) == 0L) //while both divide by 2
|
|||
|
|
{
|
|||
|
|
aa >>= 1;
|
|||
|
|
bb >>= 1;
|
|||
|
|
++pow;
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
while ((aa & 1L) == 0L) //get rid of other 2's factors
|
|||
|
|
aa >>= 1;
|
|||
|
|
|
|||
|
|
do {
|
|||
|
|
while ((bb & 1L) == 0L)
|
|||
|
|
bb >>= 1;
|
|||
|
|
|
|||
|
|
ulong cc;
|
|||
|
|
if (aa < bb)
|
|||
|
|
cc = bb - aa;
|
|||
|
|
else {
|
|||
|
|
ulong tmp = aa - bb;
|
|||
|
|
aa = bb;
|
|||
|
|
cc = tmp;
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
bb = cc >> 1;
|
|||
|
|
} while (bb != 0L);
|
|||
|
|
|
|||
|
|
return (long) aa << pow;
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
public override bool Equals (object obj)
|
|||
|
|
{
|
|||
|
|
if (ReferenceEquals (null, obj))
|
|||
|
|
return false;
|
|||
|
|
if (ReferenceEquals (this, obj))
|
|||
|
|
return true;
|
|||
|
|
return obj is Rational && this.Equals ((Rational) obj);
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
public bool Equals (Rational other)
|
|||
|
|
{
|
|||
|
|
return this == other;
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
public override int GetHashCode ()
|
|||
|
|
{
|
|||
|
|
unchecked {
|
|||
|
|
int hashCode = this.kind.GetHashCode ();
|
|||
|
|
hashCode = (hashCode * 397) ^ this.up.GetHashCode ();
|
|||
|
|
hashCode = (hashCode * 1001) ^ this.down.GetHashCode ();
|
|||
|
|
return hashCode;
|
|||
|
|
}
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
public override string ToString ()
|
|||
|
|
{
|
|||
|
|
switch (this.kind) {
|
|||
|
|
case Kind.MinusInfinity:
|
|||
|
|
return "-oo" +
|
|||
|
|
(this.up == -1L || this.down == 0L
|
|||
|
|
? ""
|
|||
|
|
: string.Format ("({0} / {1})", this.up, this.down));
|
|||
|
|
case Kind.PlusInfinity:
|
|||
|
|
return "+oo" +
|
|||
|
|
(this.up == 1L || this.down == 0L
|
|||
|
|
? ""
|
|||
|
|
: string.Format ("({0} / {1})", this.up, this.down));
|
|||
|
|
default:
|
|||
|
|
return this.IsInteger
|
|||
|
|
? this.up.ToString ()
|
|||
|
|
: string.Format ("({0} / {1})", this.up, this.down);
|
|||
|
|
}
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
enum Kind {
|
|||
|
|
Normal,
|
|||
|
|
PlusInfinity,
|
|||
|
|
MinusInfinity,
|
|||
|
|
}
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
static class RationalExtensions {
|
|||
|
|
public static TExpr ToExpression<TVar, TExpr>(this Rational value, IExpressionEncoder<TVar, TExpr> encoder )
|
|||
|
|
{
|
|||
|
|
if (value.IsInteger)
|
|||
|
|
return encoder.ConstantFor ((long) value);
|
|||
|
|
if (value.IsPlusInfinity)
|
|||
|
|
return encoder.CompoundFor (ExpressionType.Int32, ExpressionOperator.Div,
|
|||
|
|
encoder.ConstantFor (1L), encoder.ConstantFor (0L));
|
|||
|
|
if (value.IsMinusInfinity)
|
|||
|
|
return encoder.CompoundFor (ExpressionType.Int32, ExpressionOperator.Div,
|
|||
|
|
encoder.ConstantFor (-1L), encoder.ConstantFor (0L));
|
|||
|
|
|
|||
|
|
TExpr l = encoder.ConstantFor (value.Up);
|
|||
|
|
TExpr r = encoder.ConstantFor (value.Down);
|
|||
|
|
|
|||
|
|
return encoder.CompoundFor (ExpressionType.Int32, ExpressionOperator.Div, l, r);
|
|||
|
|
}
|
|||
|
|
}
|
|||
|
|
}
|