/*
 * Bernoulli Compiler
 * Copyright (c) Cornell University
 * Department of Computer Science
 * 
 * Kamen Yotov (kamen@yotov.org)
 * 
 * $Source: C:/CVS/kyotov/kyotov/Research/BC/ILP/Math/Element.cs,v $
 * $Revision: 1.3 $
 * $Date: 2003/03/24 22:26:42 $
 */

using System;

namespace ILP
{
	namespace Math
	{
		public class Element
		{
			private int v;

			public Element (int v)
			{
				this.v = v;
			}

			public static implicit operator int (Element i)
			{
				return i.v;
			}

			public static implicit operator Element (int i)
			{
				return new Element(i);
			}

			public static Element operator + (Element i1, Element i2)
			{
				checked
				{
					return i1.v + i2.v;
				}
			}

			public static Element operator * (Element i1, Element i2)
			{
				checked
				{
					return i1.v * i2.v;
				}
			}

			public static Element operator - (Element i)
			{
				checked
				{
					return -i.v;
				}
			}
		
			public static Element operator - (Element i1, Element i2)
			{
				checked
				{
					return i1 + (-i2);
				}
			}

			public static Element operator / (Element i1, Element i2)
			{
				checked
				{
					return i1.v / i2.v;
				}
			}

			public static bool operator == (Element i1, Element i2)
			{
				return i1.v == i2.v;
			}

			public static bool operator != (Element i1, Element i2)
			{
				return !(i1 == i2);
			}

			public static bool operator < (Element i1, Element i2)
			{
				return i1.v < i2.v;
			}

			public static bool operator > (Element i1, Element i2)
			{
				return i2.v < i1.v;
			}

			public static bool operator <= (Element i1, Element i2)
			{
				return !(i1 > i2);
			}

			public static bool operator >= (Element i1, Element i2)
			{
				return !(i1 < i2);
			}

			public override bool Equals (object o)
			{
				return o is Element && this == (Element)o;
			}

			public override int GetHashCode ()
			{
				return base.GetHashCode();
			}

			public override string ToString ()
			{
				return v.ToString();
			}

			public int Sign
			{
				get
				{
					return System.Math.Sign(this);
				}
			}

			public Element Abs
			{
				get
				{
					return new Element(System.Math.Abs(v));
				}
			}

			protected static void gcd (Element u, Element d, Element nu, Element nd, out Element ou, out Element od)
			{
				if (nd == 0)
				{
					ou = u;
					od = d;
				}
				else
					gcd(nu, nd, u - d / nd * nu, d % nd, out ou, out od);
			}

			public static Element gcd (Element a, Element b, out Element u, out Element v)
			{
				Element d;

				int sa = a.Sign;
				int sb = b.Sign;

				a = a.Abs;
				b = b.Abs;

				gcd(1, a, 0, b, out u, out d);

				if (d == a * u)
					v = 0;
				else
					v = (d - a * u) / b;

				if (a != 0)
				{
					u += v / a * b;
					v -= v / a * a;
				}

				u *= sa;
				v *= sb;

				return d;
			}

			public static Element gcd (Element x, Element y)
			{
				Element u;
				Element v;

				return gcd(x, y, out u, out v);
			}

			public static Element lcm (Element x, Element y)
			{
				return x / gcd(x, y) * y;
			}
		}
	}
}