//******************************************************************************************************//  Euclidean.cs - Gbtc////  Copyright © 2013, Grid Protection Alliance.  All Rights Reserved.////  Licensed to the Grid Protection Alliance (GPA) under one or more contributor license agreements. See//  the NOTICE file distributed with this work for additional information regarding copyright ownership.//  The GPA licenses this file to you under the MIT License (MIT), the "License"; you may//  not use this file except in compliance with the License. You may obtain a copy of the License at:////      http://www.opensource.org/licenses/MIT////  Unless agreed to in writing, the subject software distributed under the License is distributed on an//  "AS-IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. Refer to the//  License for the specific language governing permissions and limitations.////  Code Modification History://  ----------------------------------------------------------------------------------------------------//  12/30/2013 - Stephen C. Wills//       Generated original version of source code.////****************************************************************************************************** using System;using System.Collections.Generic;using System.Linq; namespace GSF.NumericalAnalysis{    /// <summary>    /// Contains an implementation of greatest common denominator    /// and least common multiple using the Euclidean algorithm.    /// </summary>    public static class Euclidean    {        /// <summary>        /// Implementation of the modulo operator using Euclidean division.        /// </summary>        /// <param name="numerator">The number to be divided.</param>        /// <param name="denominator">The number to divide by.</param>        /// <returns></returns>        public static double Mod(double numerator, double denominator)        {            double quotient = Math.Floor(numerator / denominator);            return numerator - quotient * denominator;        }         /// <summary>        /// Wraps a value to a range of values defined        /// by the given minimum value and range.        /// </summary>        /// <param name="value">The value to be wrapped.</param>        /// <param name="minimum">The minimum value of the range.</param>        /// <param name="range">The size of the range.</param>        /// <returns>The given value wrapped to the given range.</returns>        /// <remarks>        /// This method wraps the given value based on the assumption that        /// for every pair of values x and y where x-y=range, the values are        /// equivalent. This is probably most widely understood in terms of        /// angles, where 0, 360, 720, etc. are all equivalent angles. If        /// you wanted to wrap an angle such that it is between 120 and 480,        /// for instance, you could call Euclidean.Wrap(angle, 120, 360).        /// </remarks>        public static double Wrap(double value, double minimum, double range)        {            double transform = value - minimum;            double remainder = Mod(transform, range);            return remainder + minimum;        }         /// <summary>        /// Gets the greatest common denominator of all the integers in the source collection.        /// </summary>        /// <param name="source">The collection of integers.</param>        /// <returns>The greatest common denominator.</returns>        public static int GreatestCommonDenominator(this IEnumerable<int> source)        {            if ((object)source == null)                throw new ArgumentNullException(nameof(source), "source is null");             return source.Aggregate(GreatestCommonDenominator);        }         /// <summary>        /// Gets the greatest common denominator of all the integers in the source collection.        /// </summary>        /// <param name="source">The collection of integers.</param>        /// <returns>The greatest common denominator.</returns>        public static int GreatestCommonDenominator(params int[] source)        {            if ((object)source == null)                throw new ArgumentNullException(nameof(source), "source is null");             return source.Aggregate(GreatestCommonDenominator);        }         /// <summary>        /// Gets the greatest common denominator of the given integers.        /// </summary>        /// <param name="a">The first of the given integers.</param>        /// <param name="b">The second of the given integers.</param>        /// <returns>The greatest common denominator.</returns>        public static int GreatestCommonDenominator(int a, int b)        {            return (b != 0) ? GreatestCommonDenominator(b, a % b) : a;        }         /// <summary>        /// Gets the greatest common denominator of all the integers in the source collection.        /// </summary>        /// <param name="source">The collection of integers.</param>        /// <returns>The greatest common denominator.</returns>        public static long GreatestCommonDenominator(this IEnumerable<long> source)        {            if ((object)source == null)                throw new ArgumentNullException(nameof(source), "source is null");             return source.Aggregate(GreatestCommonDenominator);        }         /// <summary>        /// Gets the greatest common denominator of all the integers in the source collection.        /// </summary>        /// <param name="source">The collection of integers.</param>        /// <returns>The greatest common denominator.</returns>        public static long GreatestCommonDenominator(params long[] source)        {            if ((object)source == null)                throw new ArgumentNullException(nameof(source), "source is null");             return source.Aggregate(GreatestCommonDenominator);        }         /// <summary>        /// Gets the greatest common denominator of the given integers.        /// </summary>        /// <param name="a">The first of the given integers.</param>        /// <param name="b">The second of the given integers.</param>        /// <returns>The greatest common denominator.</returns>        public static long GreatestCommonDenominator(long a, long b)        {            return (b != 0) ? GreatestCommonDenominator(b, a % b) : a;        }         /// <summary>        /// Gets the least common multiple of all the integers in the source collection.        /// </summary>        /// <param name="source">The collection of integers.</param>        /// <returns>The least common multiple.</returns>        public static int LeastCommonMultiple(this IEnumerable<int> source)        {            if ((object)source == null)                throw new ArgumentNullException(nameof(source), "source is null");             return source.Aggregate(LeastCommonMultiple);        }         /// <summary>        /// Gets the least common multiple of all the integers in the source collection.        /// </summary>        /// <param name="source">The collection of integers.</param>        /// <returns>The least common multiple.</returns>        public static int LeastCommonMultiple(params int[] source)        {            if ((object)source == null)                throw new ArgumentNullException(nameof(source), "source is null");             return source.Aggregate(LeastCommonMultiple);        }         /// <summary>        /// Gets the least common multiple of the given integers.        /// </summary>        /// <param name="a">The first of the given integers.</param>        /// <param name="b">The second of the given integers.</param>        /// <returns>The least common multiple.</returns>        public static int LeastCommonMultiple(int a, int b)        {            return a * (b / GreatestCommonDenominator(a, b));        }         /// <summary>        /// Gets the least common multiple of all the integers in the source collection.        /// </summary>        /// <param name="source">The collection of integers.</param>        /// <returns>The least common multiple.</returns>        public static long LeastCommonMultiple(this IEnumerable<long> source)        {            if ((object)source == null)                throw new ArgumentNullException(nameof(source), "source is null");             return source.Aggregate(LeastCommonMultiple);        }         /// <summary>        /// Gets the least common multiple of all the integers in the source collection.        /// </summary>        /// <param name="source">The collection of integers.</param>        /// <returns>The least common multiple.</returns>        public static long LeastCommonMultiple(params long[] source)        {            if ((object)source == null)                throw new ArgumentNullException(nameof(source), "source is null");             return source.Aggregate(LeastCommonMultiple);        }         /// <summary>        /// Gets the least common multiple of the given integers.        /// </summary>        /// <param name="a">The first of the given integers.</param>        /// <param name="b">The second of the given integers.</param>        /// <returns>The least common multiple.</returns>        public static long LeastCommonMultiple(long a, long b)        {            return a * (b / GreatestCommonDenominator(a, b));        }    }}