Java BigDecimal Square Root sqrtProcedure(MathContext mc, int digits, BigDecimal numberToBeSquareRooted, BigDecimal iteration1, BigDecimal iteration2, BigDecimal temp1, BigDecimal temp2)

Here you can find the source of sqrtProcedure(MathContext mc, int digits, BigDecimal numberToBeSquareRooted, BigDecimal iteration1, BigDecimal iteration2, BigDecimal temp1, BigDecimal temp2)

Description

Square root by coupled Newton iteration, sqrtProcedure() is the iteration part I adopted the Algorithm from the book "Pi-unleashed", so now it looks more natural I give sparse math comments from the book, it assumes argument mc precision >= 1

License

Open Source License

Parameter

Parameter	Description
mc	a parameter
digits	a parameter
numberToBeSquareRooted	a parameter
iteration1	a parameter
iteration2	a parameter
temp1	a parameter
temp2	a parameter

Declaration

private static BigDecimal sqrtProcedure(MathContext mc, int digits, BigDecimal numberToBeSquareRooted,
        BigDecimal iteration1, BigDecimal iteration2, BigDecimal temp1, BigDecimal temp2)

Method Source Code


//package com.java2s;
//License from project: Open Source License 

import java.math.BigDecimal;

import java.math.MathContext;

public class Main {
    public static final BigDecimal TWO = BigDecimal.valueOf(2);

    /**// w w  w.  j  av  a  2s.  co m
    * Square root by coupled Newton iteration, sqrtProcedure() is the iteration part I adopted the Algorithm from the
    * book "Pi-unleashed", so now it looks more natural I give sparse math comments from the book, it assumes argument
    * mc precision >= 1
    *
    * @param mc
    * @param digits
    * @param numberToBeSquareRooted
    * @param iteration1
    * @param iteration2
    * @param temp1
    * @param temp2
    * @return
    */
    private static BigDecimal sqrtProcedure(MathContext mc, int digits, BigDecimal numberToBeSquareRooted,
            BigDecimal iteration1, BigDecimal iteration2, BigDecimal temp1, BigDecimal temp2) {
        // next v                                         // g = 1 - 2*x*v
        temp1 = BigDecimal.ONE.subtract(TWO.multiply(iteration1, mc).multiply(iteration2, mc), mc);
        iteration2 = iteration2.add(temp1.multiply(iteration2, mc), mc); // v += g*v        ~ 1/2/sqrt(d)

        // next x
        temp2 = numberToBeSquareRooted.subtract(iteration1.multiply(iteration1, mc), mc); // e = d - x^2
        iteration1 = iteration1.add(temp2.multiply(iteration2, mc), mc); // x += e*v        ~ sqrt(d)

        // increase precision
        int m = mc.getPrecision();
        if (m < 2)
            m++;
        else
            m = m * 2 - 1; // next Newton iteration supplies so many exact digits

        if (m < 2 * digits) // digits limit not yet reached?
        {
            mc = new MathContext(m, mc.getRoundingMode()); // apply new precision
            sqrtProcedure(mc, digits, numberToBeSquareRooted, iteration1, iteration2, temp1, temp2); // next iteration
        }

        return iteration1; // returns the iterated square roots
    }
}