Fraction.txt

using System;
using System.Collections.Generic;
using System.Diagnostics;
using System.Numerics;
using System.Text;

namespace Fractions {
    public static class FractionExtensions
    {

        /// <summary>
        /// Returns the square root of a fraction. Use <paramref name="numberOFDecimalPlaceAccuracy"/> to set the accuracy.
        /// </summary>
        /// <param name="numberOFDecimalPlaceAccuracy"></param>
        public static Fraction Sqrt(this Fraction x, int numberOFDecimalPlaceAccuracy = 30) {
            //Babylonian Method of computing square roots

            if (x < 0) {
                throw new OverflowException("Cannot calculate square root from a negative number");
            }


            Fraction oldGuess;
            var newGuess = Fraction.Zero;
            var tolerance = new Fraction(BigInteger.One, BigInteger.Pow(new BigInteger(10), numberOFDecimalPlaceAccuracy));


            //Using Math.Sqrt to get a good starting guess
            var guessDouble = Math.Sqrt((double)x);
            if (double.IsInfinity(guessDouble)) {
                oldGuess = x / 2;
            } else {
                oldGuess = (Fraction)guessDouble;
            }


            while ((oldGuess - newGuess).Abs() > tolerance) {
                //Babylonian Method
                newGuess = (oldGuess + (x / oldGuess)) / 2;
                oldGuess = newGuess;
            }

            return newGuess;
        }

        //calculates the value of e to the power of x, where e is the base of the natural logarithm
        public static Fraction Exp(this Fraction x, int accuracy = 100) {

            var sum = Fraction.One;

           // var tolerance = new Fraction(BigInteger.One, BigInteger.Pow(new BigInteger(10), numberOFDecimalPlaceAccuracy));

            for (int i = accuracy - 1; i > 0; i--) {

                sum = 1 + x * sum / i;
            }

            return sum;
       
        }

        public static Fraction Ln(this Fraction x, int numberOFDecimalPlaceAccuracy = 30) {

            Fraction oldGuess;
            var newGuess = Fraction.Zero;
            var tolerance = new Fraction(BigInteger.One, BigInteger.Pow(new BigInteger(10), numberOFDecimalPlaceAccuracy));


            //Using Math.Sqrt to get a good starting guess
            var guessDouble = Math.Log((double)x);
            if (double.IsInfinity(guessDouble)) {
                oldGuess = x / 2;
            } else {
                oldGuess = (Fraction)guessDouble;
            }


            while ((oldGuess - newGuess).Abs() > tolerance) {
                newGuess = oldGuess + 2 * (((x - oldGuess.Exp()) / (x + oldGuess.Exp())));
                oldGuess = newGuess;
            }

            return oldGuess;

        }
		
		public static Fraction Pow(this Fraction x,decimal power, int numberOFDecimalPlaceAccuracy = 30) {

            // fx 2.1^3.37
			//--> 3.37 * Ln(2.1)
			
			var fraction test = x.Ln(numberOFDecimalPlaceAccuracy) * (fraction)power;
			
			return test.exp(numberOFDecimalPlaceAccuracy);
			

        }




    }
}