RAMKillerZ/NewtonsMethod.java at master · therocram/RAMKillerZ · GitHub

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package test;
//Finding a root or an exponent of a BigDecimal using Newton's Method

import java.math.*;

public class NewtonsMethod{

	//---------------------------------------------------------------VARIANTS OF BDexp----------------------------------------------------------------------------------------------------

	public static BigDecimal BDexp(BigDecimal base, BigDecimal expD) {
		BigDecimal num = base;
		BigInteger expI = new BigInteger((expD.toBigInteger()).toString()); //Converts expD to integer (Drops the decimal) then changes it to a string so expI can have the integer value

		for(BigInteger i = new BigInteger("1"); i.compareTo(expI) == -1; i = i.add(BigInteger.ONE)) {
			num = num.multiply(base);
			System.out.println(num); //<-for debuging purposes
		}

		//preparing numbers for the root portion of the calculation
		BigInteger rootB = //got from StackOverflow   this takes the decimal part of expD
                expD.remainder(BigDecimal.ONE).movePointRight(expD.scale()).abs().toBigInteger();
		long scale = 10^expD.scale();
		long root = rootB.intValue();
		BigDecimal rootBD = new BigDecimal(rootB.toString());


		//Math derived from x^(a/b) = xroot(x,b) * x^a
		if(root!=0) {
			num = (BDexp(num, root)).multiply(BDroot(num, scale, num.divide(rootBD,MathContext.DECIMAL128)));
		}

		return num;
	}


	public static  BigDecimal BDexp(BigDecimal base, long exp) {//is equivilant to bd.pow(long) (long instead of int)

		BigDecimal num = base;

		for(long i = 1; i < exp; i++) {
			num = num.multiply(base);
		}

		return num;
	}


	public static  BigDecimal BDexp(BigDecimal base, int exp) {//is equivilant to bd.pow(int)

		BigDecimal num = base;

		for(int i = 1; i < exp; i++) {
			num = num.multiply(base);
		}

		return num;
	}


	//--------------------------------------------------------------------VARIANTS OF BDroot-------------------------------------------------------------------------------------------


	public static BigDecimal BDroot(BigDecimal base, int root, BigDecimal guess){

		BigDecimal rootBD = new BigDecimal(String.valueOf(root));
		BigDecimal num = BigDecimal.ONE;
		int count = 0;
		//MathContext round = new MathContext(20,RoundingMode.HALF_DOWN);


		num = guess.subtract((BDexp(guess,root).subtract(base, MathContext.DECIMAL128)).divide(rootBD.multiply(guess.pow(root-1), MathContext.DECIMAL128), MathContext.DECIMAL128), MathContext.DECIMAL128);
		//divide has DECIMAL64 (precision 16) and subtract has DECIMAL32 (precision 7)
		// (above) num = guess - (guess^root - start)/(root * guess^(root-1))

		do {

			num = num.subtract((num.pow(root).subtract(base, MathContext.DECIMAL128)).divide(rootBD.multiply(guess.pow(root-1), MathContext.DECIMAL128), MathContext.DECIMAL128), MathContext.DECIMAL128);

			count++;

		}while(count < 100);

		return num;
	}


	public static BigDecimal BDroot(BigDecimal base, long root, BigDecimal guess){

		BigDecimal rootBD = new BigDecimal(String.valueOf(root));
		BigDecimal num = BigDecimal.ONE;
		int count = 0;
		//MathContext round = new MathContext(20,RoundingMode.HALF_DOWN);


		num = guess.subtract((BDexp(guess,root).subtract(base, MathContext.DECIMAL128)).divide(rootBD.multiply(BDexp(guess,(root-1)), MathContext.DECIMAL128), MathContext.DECIMAL128), MathContext.DECIMAL128);
		//divide has DECIMAL64 (precision 16) and subtract has DECIMAL32 (precision 7)
		// (above) num = guess - (guess^root - start)/(root * guess^(root-1))

		do {

			num = num.subtract((BDexp(guess,root).subtract(base, MathContext.DECIMAL128)).divide(rootBD.multiply(BDexp(guess,(root-1)), MathContext.DECIMAL128), MathContext.DECIMAL128), MathContext.DECIMAL128);

			count++;

		}while(count < 100);

		return num;
	}

}