Package de.tilman_neumann.jml.roots

Class RootsReal

java.lang.Object

de.tilman_neumann.jml.roots.RootsReal

public class RootsReal
extends Object

i.th root of floating point numbers. The current state-of-the-art is a Heron-style algorithm with a good initial guess derived from double computations. The Heron-style algorithm realizes the iteration formula x(k+1) = 1/n * ( (n-1) * x(k) + N/(x(k)^(n-1)) ), see {@link "https://en.wikipedia.org/wiki/Nth_root_algorithm"}.

Author:

Tilman Neumann

Constructor Summary

Constructors

Constructor	Description
RootsReal()

Method Summary

Modifier and Type	Method	Description
static BigDecimal	ithRoot(BigDecimal x, int i, Scale resultScale)	Compute i.th root of x.
static BigDecimal	ithRoot(BigDecimal x, int i, BigDecimal guess, Scale resultScale)	Compute the i.th root with initial guess.
static void	main(String[] argv)	Test.

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Constructor Detail

RootsReal

public RootsReal()

Method Detail

ithRoot

public static BigDecimal ithRoot(BigDecimal x,
                                 int i,
                                 Scale resultScale)

Compute i.th root of x.

Parameters:

x - argument

i - the degree of the root

resultScale - desired precision in after-comma digits

Returns:

i.th root(x) with error < 0.5*10^-resultScale, i.e. resultScale decimal digits are rounded correctly

ithRoot

public static BigDecimal ithRoot(BigDecimal x,
                                 int i,
                                 BigDecimal guess,
                                 Scale resultScale)

Compute the i.th root with initial guess.

Parameters:

x - argument

i - degree of the root

guess - initial guess of i.th root(x)

resultScale - desired precision in after-comma digits

Returns:

i.th root(x) with error < 0.5*10^-resultScale, i.e. resultScale decimal digits are rounded correctly

main

public static void main(String[] argv)

Test.

Parameters:

argv - command line arguments