fr.cnes.sirius.patrius.math.util

Class Precision

java.lang.Object

fr.cnes.sirius.patrius.math.util.Precision

public final class Precision
extends Object

Utilities for comparing numbers.

Since:

3.0

Version:

$Id: Precision.java 18108 2017-10-04 06:45:27Z bignon $

Field Summary

Fields

Modifier and Type	Field and Description
static double	DOUBLE_COMPARISON_EPSILON Epsilon used for doubles relative comparison.
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 both arguments are equal or within the range of allowed error (inclusive).
static boolean	equals(float x, float y) Returns true if they are equal as defined by equals(x, y, 1).
static boolean	equals(float x, float y, float eps) Returns true if both arguments are equal or within the range of allowed error (inclusive).
static boolean	equals(float x, float y, int maxUlps) Returns true if both arguments are equal or within the range of allowed error (inclusive).
static boolean	equalsIncludingNaN(double x, double y) Returns true if both arguments are NaN or neither is NaN and they are equal as defined by equals(x, y, 1).
static boolean	equalsIncludingNaN(double x, double y, double eps) Returns true if both arguments are NaN or are equal or 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 neither is NaN and they are equal as defined by equals(x, y, 1).
static boolean	equalsIncludingNaN(float x, float y, float eps) Returns true if both arguments are NaN or are equal or 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	equalsWithAbsoluteAndRelativeTolerances(double x, double y, double relThreshold, double absThreshold) Returns true if there is no double value strictly between the arguments or the relative difference between them is smaller or equal to the given tolerance AND 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	equalsWithAbsoluteOrRelativeTolerances(double x, double y, double relThreshold, double absThreshold) Returns true if there is no double value strictly between the arguments or the relative difference between them is smaller or equal to the given tolerance OR 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	equalsWithRelativeTolerance(double x, double y) Returns true if both arguments are found equal with a relative comparison using a default epsilon.
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 smaller or equal to the given tolerance.
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.
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

DOUBLE_COMPARISON_EPSILON

public static final double DOUBLE_COMPARISON_EPSILON

Epsilon used for doubles relative comparison. Value is 1.0E-14.

See Also:

Constant Field Values

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

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

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

equals

public static boolean equals(float x,
                             float y)

Returns true if 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 neither is NaN and 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.

Since:

2.2

equals

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

Returns true if both arguments are equal or 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.

Since:

2.2

equalsIncludingNaN

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

Returns true if both arguments are NaN or are equal or 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.

Since:

2.2

equals

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

Returns true if both 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

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.

Since:

2.2

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.

Since:

2.2

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 both arguments are NaN or neither is NaN and 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.

Since:

2.2

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).

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 smaller or equal to the given tolerance.

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.

Since:

3.1

equalsIncludingNaN

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

Returns true if both arguments are NaN or are equal or 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.

Since:

2.2

equals

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

Returns true if both 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

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.

Since:

2.2

equalsWithRelativeTolerance

public static boolean equalsWithRelativeTolerance(double x,
                                                  double y)

Returns true if both arguments are found equal with a relative comparison using a default epsilon.

Parameters:

x - first double to be compared

y - second double to be compared

Returns:

a boolean : "true" if the doubles are found equals.

The value "Nan" as input always imply the return "false"

equalsWithAbsoluteAndRelativeTolerances

public static boolean equalsWithAbsoluteAndRelativeTolerances(double x,
                                                              double y,
                                                              double relThreshold,
                                                              double absThreshold)

Returns true if there is no double value strictly between the arguments or the relative difference between them is smaller or equal to the given tolerance AND if there is 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.

relThreshold - Amount of allowed relative error.

absThreshold - Amount of allowed absolute error.

Returns:

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

Since:

4.5

See Also:

Precision#equals(double, double, double)} and {@link Precision#equalsWithRelativeTolerance(double, double, double)}

equalsWithAbsoluteOrRelativeTolerances

public static boolean equalsWithAbsoluteOrRelativeTolerances(double x,
                                                             double y,
                                                             double relThreshold,
                                                             double absThreshold)

Returns true if there is no double value strictly between the arguments or the relative difference between them is smaller or equal to the given tolerance OR if there is 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.

relThreshold - Amount of allowed relative error.

absThreshold - Amount of allowed absolute error.

Returns:

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

Since:

4.5

See Also:

Precision#equals(double, double, double)} and {@link Precision#equalsWithRelativeTolerance(double, double, double)}

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.

Since:

1.1 (previously in MathUtils, moved as of version 3.0)

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.

Since:

1.1 (previously in MathUtils, moved as of version 3.0)

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.

Since:

1.1 (previously in MathUtils, moved as of version 3.0)

round

public static float round(float 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.

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:

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

MathIllegalArgumentException - if roundingMethod is not a valid rounding method.

Since:

1.1 (previously in MathUtils, moved as of version 3.0)

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.