edu.northwestern.at.utils.math
Class ArithUtils

java.lang.Object
  edu.northwestern.at.utils.math.ArithUtils

public class ArithUtils
extends java.lang.Object

Basic numeric operations not included in standard Java run-time library.

The binomial methods are modified from those in the Colt library.

The following methods for trigonometric functions come from the Sfun class written by Visual Numerics.

• acosh
• asinh
• atanh
• cot
• cosh
• sinh
• tanh

These methods are covered by the following license.

------------------------------------------------------------------------- $Id: Sfun.java,v 1.1.1.1 1999/03/05 21:43:39 brophy Exp $ ------------------------------------------------------------------------- Copyright (c) 1997 - 1998 by Visual Numerics, Inc. All rights reserved. Permission to use, copy, modify, and distribute this software is freely granted by Visual Numerics, Inc., provided that the copyright notice above and the following warranty disclaimer are preserved in human readable form. Because this software is licenses free of charge, it is provided "AS IS", with NO WARRANTY. TO THE EXTENT PERMITTED BY LAW, VNI DISCLAIMS ALL WARRANTIES, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO ITS PERFORMANCE, MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE. VNI WILL NOT BE LIABLE FOR ANY DAMAGES WHATSOEVER ARISING OUT OF THE USE OF OR INABILITY TO USE THIS SOFTWARE, INCLUDING BUT NOT LIMITED TO DIRECT, INDIRECT, SPECIAL, CONSEQUENTIAL, PUNITIVE, AND EXEMPLARY DAMAGES, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGES. -------------------------------------------------------------------------

Field Summary

static double	EPSILON_LARGE The largest relative spacing for doubles.
static double	EPSILON_SMALL The smallest relative spacing for doubles.

Constructor Summary

protected

ArithUtils()

Method Summary

static double	acosh(double x) Return the inverse (arc) hyperbolic cosine of a double.
static boolean	areEqual(double a, double b) Check if two doubles are equal to machine precision.
static boolean	areEqual(double a, double b, double tolerance) Check if two doubles are equal to specified tolerance.
static double	asinh(double x) Return the inverse (arc) hyperbolic sine of a double.
static double	atanh(double x) Returns the inverse (arc) hyperbolic tangent of a double.
static double	binomial(double n, long k) Efficiently returns the binomial coefficient, often also referred to as "n over k" or "n choose k".
static double	binomial(long n, long k) Efficiently returns the binomial coefficient, often also referred to as "n over k" or "n choose k".
static double	cosh(double x) Return the hyperbolic cosine of a double.
static double	cot(double x) Return the contangent of a double.
static int	fuzzyCompare(double a, double b, double tolerance) Perform fuzzy comparison of two doubles with specified tolerance.
static double	hypot(double a, double b) Safely calculate hypotenuse value.
static boolean	isNegativeZero(double x) Check if number is negative zero.
static double	log10(double x) Get log base 10 of a double.
static double	log2(double x) Get log base 2 of a double.
static double	round(double x, int n) Round double to specified number of decimal places.
static double	safeLog(double x) Return natural log of a double.
static int	sign(double d) Return sign of a double.
static double	sign(double x, double y) Return the value of a double with the sign of another double.
static int	sign(int n) Return sign of an integer.
static double	sinh(double x) Compute hyperbolic sine of a double.
static double	tanh(double x) Return the hyperbolic tangent of a double.
static double	trunc(double x) Return the integer portion of a double as a double.

Methods inherited from class java.lang.Object

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

Field Detail

EPSILON_SMALL

public static final double EPSILON_SMALL

The smallest relative spacing for doubles.

EPSILON_LARGE

public static final double EPSILON_LARGE

The largest relative spacing for doubles.

Constructor Detail

ArithUtils

protected ArithUtils()

Method Detail

acosh

public static double acosh(double x)

Return the inverse (arc) hyperbolic cosine of a double.

Parameters:

x - Double whose inverse hyperbolic cosine is desired.

Returns:

The inverse hyperbolic cosine of x.

If x is NaN or less than one, the result is NaN.

This method is a modified version of the one in the Visual Numerics Sfun class.

areEqual

public static boolean areEqual(double a,
                               double b)

Check if two doubles are equal to machine precision.

Parameters:

a - First double.

b - Second double.

Returns:

True if a and b are equal to machine precision.

areEqual

public static boolean areEqual(double a,
                               double b,
                               double tolerance)

Check if two doubles are equal to specified tolerance.

Parameters:

a - First double.

b - Second double.

tolerance - Tolerance.

Returns:

True if a and b are equal to specified tolerance.

asinh

public static double asinh(double x)

Return the inverse (arc) hyperbolic sine of a double.

Parameters:

x - The value whose inverse hyperbolic sine is desired.

Returns:

The inverse hyperbolic sine of x.

If x is NaN, the result is NaN.

This method is a modified version of the one in the Visual Numerics Sfun class.

atanh

public static double atanh(double x)

Returns the inverse (arc) hyperbolic tangent of a double.

Parameters:

x - The value whose inverse hyperbolic tangent is desired.

Returns:

The arc hyperbolic tangent of x.

If x is NaN or |x|>1, the result is NaN.

This method is a modified version of the one in the Visual Numerics Sfun class.

binomial

public static double binomial(double n,
                              long k)

Efficiently returns the binomial coefficient, often also referred to as "n over k" or "n choose k".

The binomial coefficient is defined as (n * n-1 * ... * n-k+1 ) / ( 1 * 2 * ... * k ).

• k<0: 0.
• k==0: 1.
• k==1: n.
• else: (n * n-1 * ... * n-k+1 ) / ( 1 * 2 * ... * k ).

Returns:

The binomial coefficient.

binomial

public static double binomial(long n,
                              long k)

Efficiently returns the binomial coefficient, often also referred to as "n over k" or "n choose k".

The binomial coefficient is defined as

• k<0: 0.
• k==0 || k==n: 1.
• k==1 || k==n-1: n.
• else: (n * n-1 * ... * n-k+1 ) / ( 1 * 2 * ... * k ).

Returns:

The binomial coefficient.

cosh

public static double cosh(double x)

Return the hyperbolic cosine of a double.

Parameters:

x - The value whose hyperbolic cosine is desired.

Returns:

The hyperbolic cosine of x.

If x is NaN, the result is NaN.

This method is a modified version of the one in the Visual Numerics Sfun class.

cot

public static double cot(double x)

Return the contangent of a double.

Parameters:

x - The number whose cotangent is desired.

Returns:

The cotangent.

This method is a modified version of the one in the Visual Numerics Sfun class.

fuzzyCompare

public static int fuzzyCompare(double a,
                               double b,
                               double tolerance)

Perform fuzzy comparison of two doubles with specified tolerance.

Parameters:

a - First double.

b - Second double.

tolerance - Tolerance value.

Returns:

1 if a > b. 0 if a ~= b. -1 if a < b.

This is an implementation of an algorithm suggested by Donald E. Knuth in Section 4.2.2 of Seminumerical Algorithms (3rd edition).

hypot

public static double hypot(double a,
                           double b)

Safely calculate hypotenuse value.

Parameters:

a - One leg of triangle.

b - Second leg of triangle.

Returns:

Hypotenuse value.

The hypotenuse value is given mathematically as the sqrt( a^2 + b^2 ). The method implemented here reduces the chances of cancellation and roundoff error. If the |a| > |b|, we compute the hypotenuse as:

hypotenuse = |a| * sqrt( 1 + (b/a) * (b/a) )

Otherwise b != 0 compute the hypotenuse as:

hypotenuse = |b| * sqrt( 1 + (a/b) * (a/b) )

If b is zero, the hypotenuse is zero.

isNegativeZero

public static boolean isNegativeZero(double x)

Check if number is negative zero.

Parameters:

x - The number to check.

Returns:

true if x is negative zero, false otherwise.

log2

public static double log2(double x)

Get log base 2 of a double.

Parameters:

x - The number whose log base 2 value is desired.

Returns:

The log base 2 of x. If x is <= 0, 0 is returned.

Example: log2( 32 ) is 5.0D .

log10

public static double log10(double x)

Get log base 10 of a double.

Parameters:

x - The number whose log base 10 value is desired.

Returns:

The log base 10 of x. If x is <= 0, 0 is returned.

Example: log10( 100.0D ) is 2.0D .

round

public static double round(double x,
                           int n)

Round double to specified number of decimal places.

Parameters:

x - The double to round.

n - The number of decimal places to round to.

Returns:

x rounded to n decimal places.

safeLog

public static double safeLog(double x)

Return natural log of a double.

Parameters:

x - The number whose natural log is desired.

Returns:

The natural log of x. If x is zero, returns 0.

sign

public static int sign(int n)

Return sign of an integer.

Parameters:

n - Number whose sign is desired.

Returns:

-1 if n < 0, 0 if n isn 0, 1 if n > 0.

sign

public static int sign(double d)

Return sign of a double.

Parameters:

d - double whose sign is desired.

Returns:

-1 if d < 0, 0 if d is 0, 1 if d > 0.

sign

public static double sign(double x,
                          double y)

Return the value of a double with the sign of another double.

Parameters:

x - First double.

y - Second double.

Returns:

x with the sign of y.

sinh

public static double sinh(double x)

Compute hyperbolic sine of a double.

Parameters:

x - The number whose hyperbolic sine is desired.

Returns:

The hyperbolic sine of x.

This method is a modified version of the one in the Visual Numerics Sfun class.

trunc

public static double trunc(double x)

Return the integer portion of a double as a double.

Parameters:

x - The double whose integer portion is to be found.

Returns:

The integer portion of x.

Example: trunc( 30.12345D ) is 30.0D .

tanh

public static double tanh(double x)

Return the hyperbolic tangent of a double.

Parameters:

x - The value whose hyperbolic tangent is desired.

Returns:

The hyperbolic tangent of x.

This method is a modified version of the one in the Visual Numerics Sfun class.