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QuickStart Samples

Elementary Functions QuickStart Sample (C#)

Illustrates how to use additional elementary functions in C#.

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using System;

namespace Extreme.Numerics.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>
        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}", 
            Console.WriteLine("  Log1PlusX: {0}", 

            // 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}", 

            // The hypotenuse of two numbers that are very large
            // may cause an overflow when not evaluated properly:
            double a = 3e200;
            double b = 4e200;
            Console.Write("  Simple method: ");
                double sumOfSquares = a*a + b*b;
            catch (OverflowException)
            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...");