org.hipparchus.util

Class Precision

java.lang.Object

org.hipparchus.util.Precision

public class Precision
extends Object

Utilities for comparing numbers.

Field Summary

Fields

Modifier and Type	Field and 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 and 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 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 the arguments are equal or 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, are equal or are 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, are equal, or are within the range of allowed error (inclusive).
static boolean	equalsIncludingNaN(float x, float y, int maxUlps) Returns true if the arguments are both 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 originalDelta) Computes a number delta close to originalDelta with the property that
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, int roundingMethod) Rounds the given value to the specified number of decimal places.
static float	round(float x, int scale) Rounds the given value to the specified number of decimal places.
static float	round(float x, int scale, int 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.

Parameters:

x - the first number

y - the second number

eps - the amount of error to allow when checking for equality

Returns:

• 0 if equals(x, y, eps)
• < 0 if !equals(x, y, eps) && x < y
• > 0 if !equals(x, y, eps) && x > y or either argument is NaN

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.

Parameters:

x - first value

y - second value

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

Returns:

• 0 if equals(x, y, maxUlps)
• < 0 if !equals(x, y, maxUlps) && x < y
• > 0 if !equals(x, y, maxUlps) && x > y or either argument is NaN

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 the arguments are equal or 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, are equal, or are 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). 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.

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 the arguments are both 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 two adjacent floating point numbers or they are 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, are equal or are 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).

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.

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 BigDecimal.ROUND_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,
                           int 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 == ROUND_UNNECESSARY and the specified scaling operation would require rounding.

IllegalArgumentException - if roundingMethod does not represent a valid rounding mode.

round

public static float round(float x,
                          int scale)

Rounds the given value to the specified number of decimal places. The value is rounded using the BigDecimal.ROUND_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 float round(float x,
                          int scale,
                          int roundingMethod)
                   throws MathRuntimeException,
                          MathIllegalArgumentException

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.

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:

MathRuntimeException - if an exact operation is required but result is not exact

MathIllegalArgumentException - if roundingMethod is not a valid rounding method.

representableDelta

public static double representableDelta(double x,
                                        double originalDelta)

Computes a number delta close to originalDelta 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.

originalDelta - Offset value.

Returns:

a number delta so that x + delta and x differ by a representable floating number.