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QuickStart Samples

# Elementary Functions QuickStart Sample (C#)

Illustrates how to use additional elementary functions in C#.

```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}",
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...");