Precision (patrimoine de base SIRIUS 4.15 API)

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

All Methods Static Methods Concrete Methods
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.
`static double`	`twoProductError(double a, double b, double aDotB)` Compute the exact round-off error of a floating point multiplication operation according to the Veltkamp and Dekker algorithm.
`static double`	`twoSumError(double a, double b, double aPlusB)` Compute the exact round-off error of a floating point addition operation according to the Møller-Knuth TwoSum algorithm.

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:
    
    equals(double, double, double), 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:
    
    equals(double, double, double), 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.
  - twoSumError
```
public static double twoSumError(double a,
                                 double b,
                                 double aPlusB)
```
    Compute the exact round-off error of a floating point addition operation according to the Møller-Knuth TwoSum algorithm.
    See, for example, the 2005 paper Accurate Sum and Dot Product by Takeshi Ogita, Siegfried M. Rump, and Shin'ichi Oishi published in SIAM J. Sci. Comput.
    
    Parameters:
    
    a - First element of the sum
    
    b - Second element of the sum
    
    aPlusB - The floating sum of the first and second element. Note: could be internally recomputed, but is in argument to minimize computation.
    
    Returns:
    
    the error e so that aPlusB + e = a+b, i.e. the floating point error of aPlusB
  - twoProductError
```
public static double twoProductError(double a,
                                     double b,
                                     double aDotB)
```
    Compute the exact round-off error of a floating point multiplication operation according to the Veltkamp and Dekker algorithm.
    See, for example, the 2005 paper Accurate Sum and Dot Product by Takeshi Ogita, Siegfried M. Rump, and Shin'ichi Oishi published in SIAM J. Sci. Comput.
    
    Parameters:
    
    a - First element of the product
    
    b - Second element of the product
    
    aDotB - The floating product of the first and second element. Note: could be internally recomputed, but is in argument to minimize computation.
    
    Returns:
    
    the error e so that aDotB + e = a*b, i.e. the floating point error of aDotB

Class Precision

Field Summary

Method Summary

Methods inherited from class java.lang.Object

Field Detail

EPSILON

DOUBLE_COMPARISON_EPSILON

SAFE_MIN

Method Detail

compareTo

compareTo

equals

equalsIncludingNaN

equals

equalsIncludingNaN

equals

equalsIncludingNaN

equals

equalsIncludingNaN

equals

equalsWithRelativeTolerance

equalsIncludingNaN

equals

equalsIncludingNaN

equalsWithRelativeTolerance

equalsWithAbsoluteAndRelativeTolerances

equalsWithAbsoluteOrRelativeTolerances

round

round

round

round

representableDelta

twoSumError

twoProductError