Elementary Functions QuickStart Sample (F#)

// 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.

#light

open System

// We use many classes from the Extreme.Mathematics namespace.
open Extreme.Mathematics

// 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:
printfn "Logarithm of 1+1e-12"
printfn "  Math.Log: %A" (Math.Log(1.0 + 1e-12))
printfn "  Log1PlusX: %A" (Elementary.Log1PlusX(1e-12))

// In a similar way, Exp(x) - 1 has a variant, 
// ExpXMinus1, for values of x close to 0:
printfn "Exponential of 1e-12 minus 1."
printfn "  Math.Exp: %A" (Math.Exp(1e-12) - 1.0)
printfn "  ExpMinus1: %A" (Elementary.ExpMinus1(1e-12))

// The hypotenuse of two numbers that are very large
// may cause an overflow when not evaluated properly:
printfn "Hypotenuse:"
let a = 3e200
let b = 4e200
printf "  Simple method: "
try
    let sumOfSquares = a*a + b*b
    printfn "%A" (Math.Sqrt(sumOfSquares))
with
| :? OverflowException -> printfn "Overflow!"

printfn "  Elementary.Hypot: %A" (Elementary.Hypot(a, b))

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

printf "Press Enter key to exit..."
Console.ReadLine() |> ignore