Elementary Functions QuickStart Sample (C#)

Illustrates how to use additional elementary functions in C#.

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using System;

namespace Extreme.Mathematics.QuickStart.CSharp
{
	// We use many classes from the Extreme.Mathematics namespace.
	using Extreme.Mathematics;

	/// <summary>
	/// Illustrates the use of the elementary functions implemented
	/// by the Elementary class in the Extreme.Mathematics.Curve namespace of 
	/// the Extreme Optimization Mathematics Library for .NET.
	/// </summary>
	class ElementaryFunctionsSample
	{
		/// <summary>
		/// The main entry point for the application.
		/// </summary>
		[STAThread]
		static void Main(string[] args)
		{
			// This QuickStart sample deals with elementary 
			// functions, implemented in the Elementary class.

			//
			// Elementary functions
			//

			// Evaluating Log(1+x) directly causes significant
			// round-off error when x is close to 0. The
			// Log1PlusX function allows high precision evaluation
			// of this expression for values of x close to 0:
			Console.WriteLine("Logarithm of 1+1e-12");
			Console.WriteLine("  Math.Log: {0}", 
				Math.Log(1+1e-12));
			Console.WriteLine("  Log1PlusX: {0}", 
				Elementary.Log1PlusX(1e-12));

			// In a similar way, Exp(x) - 1 has a variant, 
			// ExpXMinus1, for values of x close to 0:
			Console.WriteLine("Exponential of 1e-12 minus 1.");
			Console.WriteLine("  Math.Exp: {0}", 
				Math.Exp(1e-12) - 1);
			Console.WriteLine("  ExpMinus1: {0}", 
				Elementary.ExpMinus1(1e-12));

			// The hypotenuse of two numbers that are very large
			// may cause an overflow when not evaluated properly:
			Console.WriteLine("Hypotenuse:");
			double a = 3e200;
			double b = 4e200;
			Console.Write("  Simple method: ");
			try
			{
				double sumOfSquares = a*a + b*b;
				Console.WriteLine(Math.Sqrt(sumOfSquares));
			}
			catch (OverflowException)
			{
				Console.WriteLine("Overflow!");
			}
			Console.WriteLine("  Elementary.Hypot: {0}",
				Elementary.Hypot(a, b));

			// Raising numbers to integer powers is much faster
			// than raising numbers to real numbers. The
			// overloaded Pow method implements this:
			Console.WriteLine("2.5^19 = {0}", Elementary.Pow(2.5, 19));
			// You can raise numbers to negative integer powers
			// as well:
			Console.WriteLine("2.5^-19 = {0}", Elementary.Pow(2.5,-19));

			Console.Write("Press Enter key to exit...");
			Console.ReadLine();
		}
	}
}