Package org.apache.commons.numbers.core

Class Precision

java.lang.Object

org.apache.commons.numbers.core.Precision

public final class Precision
extends Object

Utilities for comparing numbers.

Nested Class Summary

Nested Classes

Modifier and Type	Class	Description
static interface	Precision.DoubleEquivalence	Interface containing comparison operations for doubles that allow values to be considered equal even if they are not exactly equal.

Field Summary

Fields

Modifier and Type	Field	Description
static double	EPSILON	Largest double-precision floating-point number such that 1 + EPSILON is numerically equal to 1.
static double	SAFE_MIN	Safe minimum, such that 1 / SAFE_MIN does not overflow.

Method Summary

Modifier and Type	Method	Description
static int	compareTo(double x, double y, double eps)	Compares two numbers given some amount of allowed error.
static int	compareTo(double x, double y, int maxUlps)	Compares two numbers given some amount of allowed error.
static Precision.DoubleEquivalence	doubleEquivalenceOfEpsilon(double eps)	Creates a Precision.DoubleEquivalence instance that uses the given epsilon value for determining equality.
static boolean	equals(double x, double y)	Returns true iff they are equal as defined by equals(x, y, 1).
static boolean	equals(double x, double y, double eps)	Returns true if there is no double value strictly between the arguments or the difference between them is within the range of allowed error (inclusive).
static boolean	equals(double x, double y, int maxUlps)	Returns true if the arguments are equal or within the range of allowed error (inclusive).
static boolean	equals(float x, float y)	Returns true iff they are equal as defined by equals(x, y, 1).
static boolean	equals(float x, float y, float eps)	Returns true if there is no float value strictly between the arguments or the difference between them is within the range of allowed error (inclusive).
static boolean	equals(float x, float y, int maxUlps)	Returns true if the arguments are equal or within the range of allowed error (inclusive).
static boolean	equalsIncludingNaN(double x, double y)	Returns true if the arguments are both NaN or they are equal as defined by equals(x, y, 1).
static boolean	equalsIncludingNaN(double x, double y, double eps)	Returns true if the arguments are both NaN, there are no double value strictly between the arguments or the difference between them is within the range of allowed error (inclusive).
static boolean	equalsIncludingNaN(double x, double y, int maxUlps)	Returns true if both arguments are NaN or if they are equal as defined by equals(x, y, maxUlps).
static boolean	equalsIncludingNaN(float x, float y)	Returns true if both arguments are NaN or they are equal as defined by equals(x, y, 1).
static boolean	equalsIncludingNaN(float x, float y, float eps)	Returns true if the arguments are both NaN, there are no float value strictly between the arguments or the difference between them is within the range of allowed error (inclusive).
static boolean	equalsIncludingNaN(float x, float y, int maxUlps)	Returns true if both arguments are NaN or if they are equal as defined by equals(x, y, maxUlps).
static boolean	equalsWithRelativeTolerance(double x, double y, double eps)	Returns true if there is no double value strictly between the arguments or the relative difference between them is less than or equal to the given tolerance.
static double	representableDelta(double x, double delta)	Computes a number close to delta with the property that (x + delta - x) is exactly machine-representable.
static double	round(double x, int scale)	Rounds the given value to the specified number of decimal places.
static double	round(double x, int scale, RoundingMode roundingMethod)	Rounds the given value to the specified number of decimal places.

Methods inherited from class java.lang.Object

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

Field Detail

EPSILON

public static final double EPSILON

Largest double-precision floating-point number such that 1 + EPSILON is numerically equal to 1. This value is an upper bound on the relative error due to rounding real numbers to double precision floating-point numbers.

In IEEE 754 arithmetic, this is 2^-53.

See Also:

Machine epsilon

SAFE_MIN

public static final double SAFE_MIN

Safe minimum, such that 1 / SAFE_MIN does not overflow. In IEEE 754 arithmetic, this is also the smallest normalized number 2^-1022.

Method Detail

compareTo

public static int compareTo(double x,
                            double y,
                            double eps)

Compares two numbers given some amount of allowed error. The returned value is

• 0 if equals(x, y, eps),
• negative if !equals(x, y, eps) and x < y,
• positive if !equals(x, y, eps) and x > y or either argument is NaN.

Parameters:

x - First value.

y - Second value.

eps - Allowed error when checking for equality.

Returns:

0 if the value are considered equal, -1 if the first is smaller than the second, 1 is the first is larger than the second.

compareTo

public static int compareTo(double x,
                            double y,
                            int maxUlps)

Compares two numbers given some amount of allowed error. Two float numbers are considered equal if there are (maxUlps - 1) (or fewer) floating point numbers between them, i.e. two adjacent floating point numbers are considered equal. Adapted from Bruce Dawson. Returns false if either of the arguments is NaN. The returned value is

• zero if equals(x, y, maxUlps),
• negative if !equals(x, y, maxUlps) and x < y,
• positive if !equals(x, y, maxUlps) and x > y or either argument is NaN.

Parameters:

x - First value.

y - Second value.

maxUlps - (maxUlps - 1) is the number of floating point values between x and y.

Returns:

0 if the value are considered equal, -1 if the first is smaller than the second, 1 is the first is larger than the second.

equals

public static boolean equals(float x,
                             float y)

Returns true iff they are equal as defined by equals(x, y, 1).

Parameters:

x - first value

y - second value

Returns:

true if the values are equal.

equalsIncludingNaN

public static boolean equalsIncludingNaN(float x,
                                         float y)

Returns true if both arguments are NaN or they are equal as defined by equals(x, y, 1).

Parameters:

x - first value

y - second value

Returns:

true if the values are equal or both are NaN.

equals

public static boolean equals(float x,
                             float y,
                             float eps)

Returns true if there is no float value strictly between the arguments or the difference between them is within the range of allowed error (inclusive). Returns false if either of the arguments is NaN.

Parameters:

x - first value

y - second value

eps - the amount of absolute error to allow.

Returns:

true if the values are equal or within range of each other.

equalsIncludingNaN

public static boolean equalsIncludingNaN(float x,
                                         float y,
                                         float eps)

Returns true if the arguments are both NaN, there are no float value strictly between the arguments or the difference between them is within the range of allowed error (inclusive).

Parameters:

x - first value

y - second value

eps - the amount of absolute error to allow.

Returns:

true if the values are equal or within range of each other, or both are NaN.

equals

public static boolean equals(float x,
                             float y,
                             int maxUlps)

Returns true if the arguments are equal or within the range of allowed error (inclusive). Returns false if either of the arguments is NaN.

Two double numbers are considered equal if there are (maxUlps - 1) (or fewer) floating point numbers between them, i.e. two adjacent floating point numbers are considered equal.

Adapted from Bruce Dawson.

Parameters:

x - first value

y - second value

maxUlps - (maxUlps - 1) is the number of floating point values between x and y.

Returns:

true if there are fewer than maxUlps floating point values between x and y.

equalsIncludingNaN

public static boolean equalsIncludingNaN(float x,
                                         float y,
                                         int maxUlps)

Returns true if both arguments are NaN or if they are equal as defined by equals(x, y, maxUlps).

Parameters:

x - first value

y - second value

maxUlps - (maxUlps - 1) is the number of floating point values between x and y.

Returns:

true if both arguments are NaN or if there are less than maxUlps floating point values between x and y.

equals

public static boolean equals(double x,
                             double y)

Returns true iff they are equal as defined by equals(x, y, 1).

Parameters:

x - first value

y - second value

Returns:

true if the values are equal.

equalsIncludingNaN

public static boolean equalsIncludingNaN(double x,
                                         double y)

Returns true if the arguments are both NaN or they are equal as defined by equals(x, y, 1).

Parameters:

x - first value

y - second value

Returns:

true if the values are equal or both are NaN.

equals

public static boolean equals(double x,
                             double y,
                             double eps)

Returns true if there is no double value strictly between the arguments or the difference between them is within the range of allowed error (inclusive). Returns false if either of the arguments is NaN.

Parameters:

x - First value.

y - Second value.

eps - Amount of allowed absolute error.

Returns:

true if the values are equal or within range of each other.

equalsWithRelativeTolerance

public static boolean equalsWithRelativeTolerance(double x,
                                                  double y,
                                                  double eps)

Returns true if there is no double value strictly between the arguments or the relative difference between them is less than or equal to the given tolerance. Returns false if either of the arguments is NaN.

Parameters:

x - First value.

y - Second value.

eps - Amount of allowed relative error.

Returns:

true if the values are two adjacent floating point numbers or they are within range of each other.

equalsIncludingNaN

public static boolean equalsIncludingNaN(double x,
                                         double y,
                                         double eps)

Returns true if the arguments are both NaN, there are no double value strictly between the arguments or the difference between them is within the range of allowed error (inclusive).

Parameters:

x - first value

y - second value

eps - the amount of absolute error to allow.

Returns:

true if the values are equal or within range of each other, or both are NaN.

equals

public static boolean equals(double x,
                             double y,
                             int maxUlps)

Returns true if the arguments are equal or within the range of allowed error (inclusive). Returns false if either of the arguments is NaN.

Two float numbers are considered equal if there are (maxUlps - 1) (or fewer) floating point numbers between them, i.e. two adjacent floating point numbers are considered equal.

Adapted from Bruce Dawson.

Parameters:

x - first value

y - second value

maxUlps - (maxUlps - 1) is the number of floating point values between x and y.

Returns:

true if there are fewer than maxUlps floating point values between x and y.

equalsIncludingNaN

public static boolean equalsIncludingNaN(double x,
                                         double y,
                                         int maxUlps)

Returns true if both arguments are NaN or if they are equal as defined by equals(x, y, maxUlps).

Parameters:

x - first value

y - second value

maxUlps - (maxUlps - 1) is the number of floating point values between x and y.

Returns:

true if both arguments are NaN or if there are less than maxUlps floating point values between x and y.

round

public static double round(double x,
                           int scale)

Rounds the given value to the specified number of decimal places. The value is rounded using the RoundingMode.HALF_UP method.

Parameters:

x - Value to round.

scale - Number of digits to the right of the decimal point.

Returns:

the rounded value.

round

public static double round(double x,
                           int scale,
                           RoundingMode roundingMethod)

Rounds the given value to the specified number of decimal places. The value is rounded using the given method which is any method defined in BigDecimal. If x is infinite or NaN, then the value of x is returned unchanged, regardless of the other parameters.

Parameters:

x - Value to round.

scale - Number of digits to the right of the decimal point.

roundingMethod - Rounding method as defined in BigDecimal.

Returns:

the rounded value.

Throws:

ArithmeticException - if roundingMethod is RoundingMode.UNNECESSARY and the specified scaling operation would require rounding.

representableDelta

public static double representableDelta(double x,
                                        double delta)

Computes a number close to delta with the property that (x + delta - x) is exactly machine-representable. This is useful when computing numerical derivatives, in order to reduce roundoff errors.

Parameters:

x - Value.

delta - Offset value.

Returns:

the machine-representable floating number closest to the difference between x + delta and x.

doubleEquivalenceOfEpsilon

public static Precision.DoubleEquivalence doubleEquivalenceOfEpsilon(double eps)

Creates a Precision.DoubleEquivalence instance that uses the given epsilon value for determining equality.

Parameters:

eps - Value to use for determining equality.

Returns:

a new instance.