kcl.waterloo.math

Class fp

java.lang.Object

kcl.waterloo.math.fp

public class fp
extends java.lang.Object

Provides static methods for double arithmetic with corrections for loss of precision. See:

Fast and Accurate Computation of Sum and Dot Product

or

Accurate Computation of Sum and Dot Product [NOTE TYPO IN THE TWOSUM ALGORITHM IN THIS ONE]

Method Summary

Methods

Modifier and Type	Method and Description
static double[]	cusum(double[] in) Returns the cumulative sum of the elements of the input using Knuth's correction to accumulate the error.
static double[]	cusumi(double[] in) Returns the cumulative sum of the elements of the input using Knuth's correction to accumulate the error (in-place).
static double	dot(double[] a, double[] b) Returns the dot product.
static double[]	split(double val) Splits a double value into two double values where the sum of the two is the input.
static double	sum(double[] in) Returns the sum of in using Knuth's correction to accumulate the error.
static double	sum(double[] in, int idx0, int idx1) Returns the sum between two indices (inclusive).
static boolean	tolEquals(double a, double b, double tol)
static double[]	twoProduct(double a, double b) Returns the product of two double values and a correction for loss of precision in the multiplication.
static double[]	twoSum(double a, double b) Returns the sum of two double values and a correction for loss of precision in the summation.

Methods inherited from class java.lang.Object

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

Method Detail

split

public static double[] split(double val)

Splits a double value into two double values where the sum of the two is the input. See T. J. Dekker, A floating-point technique for extending the available precision, Numer. Math., 18 (1971), pp. 224-242.

Parameters:

val - a double input

Returns:

a double[2] array - where the sum of values==the input.

twoProduct

public static double[] twoProduct(double a,
                  double b)

Returns the product of two double values and a correction for loss of precision in the multiplication.

Parameters:

a - a double value.

b - a double value.

Returns:

a double[2] array containing in [0]: the product, and in [1]: the required correction.

twoSum

public static double[] twoSum(double a,
              double b)

Returns the sum of two double values and a correction for loss of precision in the summation.

Parameters:

a - a double value.

b - a double value.

Returns:

a double[2] array containing in [0]: the sum, and in [1]: the required correction.

sum

public static double sum(double[] in)

Returns the sum of in using Knuth's correction to accumulate the error. The accumulated error is added to the output.

Parameters:

in -

Returns:

the sum

sum

public static double sum(double[] in,
         int idx0,
         int idx1)

Returns the sum between two indices (inclusive).

Parameters:

in - input array

idx0 - start index

idx1 - end index

Returns:

the sum of in[idx0] thtough in[idx1]

cusum

public static double[] cusum(double[] in)

Returns the cumulative sum of the elements of the input using Knuth's correction to accumulate the error. The accumulated error for each element is added to the output.

Parameters:

in -

Returns:

a double[]

cusumi

public static double[] cusumi(double[] in)

Returns the cumulative sum of the elements of the input using Knuth's correction to accumulate the error (in-place). The accumulated error for each element is added to the output.

Parameters:

in -

Returns:

a double[]

dot

public static double dot(double[] a,
         double[] b)

Returns the dot product.

Parameters:

a - double[] input a

b - double[] input b

Returns:

the sum of a[k]*b[k] for k = 0 .. length(a)-1

tolEquals

public static boolean tolEquals(double a,
                double b,
                double tol)