public final class DD extends Object implements Serializable, Comparable, Cloneable
A DoubleDouble uses a representation containing two double-precision values. A number x is represented as a pair of doubles, x.hi and x.lo, such that the number represented by x is x.hi + x.lo, where
|x.lo| <= 0.5*ulp(x.hi)and ulp(y) means "unit in the last place of y". The basic arithmetic operations are implemented using convenient properties of IEEE-754 floating-point arithmetic.
The range of values which can be represented is the same as in IEEE-754. The precision of the representable numbers is twice as great as IEEE-754 double precision.
The correctness of the arithmetic algorithms relies on operations being performed with standard IEEE-754 double precision and rounding. This is the Java standard arithmetic model, but for performance reasons Java implementations are not constrained to using this standard by default. Some processors (notably the Intel Pentium architecture) perform floating point operations in (non-IEEE-754-standard) extended-precision. A JVM implementation may choose to use the non-standard extended-precision as its default arithmetic mode. To prevent this from happening, this code uses the Java strictfp modifier, which forces all operations to take place in the standard IEEE-754 rounding model.
The API provides both a set of value-oriented operations and a set of mutating operations. Value-oriented operations treat DoubleDouble values as immutable; operations on them return new objects carrying the result of the operation. This provides a simple and safe semantics for writing DoubleDouble expressions. However, there is a performance penalty for the object allocations required. The mutable interface updates object values in-place. It provides optimum memory performance, but requires care to ensure that aliasing errors are not created and constant values are not changed.
For example, the following code example constructs three DD instances: two to hold the input values and one to hold the result of the addition.
DD a = new DD(2.0); DD b = new DD(3.0); DD c = a.add(b);In contrast, the following approach uses only one object:
DD a = new DD(2.0); a.selfAdd(3.0);
This implementation uses algorithms originally designed variously by Knuth, Kahan, Dekker, and Linnainmaa. Douglas Priest developed the first C implementation of these techniques. Other more recent C++ implementation are due to Keith M. Briggs and David Bailey et al.
Modifier and Type | Field and Description |
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static DD |
E
The value nearest to the constant e (the natural logarithm base).
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static double |
EPS
The smallest representable relative difference between two {link @ DoubleDouble} values
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static DD |
NaN
A value representing the result of an operation which does not return a valid number.
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static DD |
PI
The value nearest to the constant Pi.
|
static DD |
PI_2
The value nearest to the constant Pi / 2.
|
static DD |
TWO_PI
The value nearest to the constant 2 * Pi.
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Constructor and Description |
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DD()
Creates a new DoubleDouble with value 0.0.
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DD(DD dd)
Creates a new DoubleDouble with value equal to the argument.
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DD(double x)
Creates a new DoubleDouble with value x.
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DD(double hi,
double lo)
Creates a new DoubleDouble with value (hi, lo).
|
DD(String str)
Creates a new DoubleDouble with value equal to the argument.
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Modifier and Type | Method and Description |
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DD |
abs()
Returns the absolute value of this value.
|
DD |
add(DD y)
Returns a new DoubleDouble whose value is (this + y).
|
DD |
add(double y)
Returns a new DoubleDouble whose value is (this + y).
|
DD |
ceil()
Returns the smallest (closest to negative infinity) value
that is not less than the argument and is equal to a mathematical integer.
|
Object |
clone()
Creates and returns a copy of this value.
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int |
compareTo(Object o)
Compares two DoubleDouble objects numerically.
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static DD |
copy(DD dd)
Creates a new DoubleDouble with the value of the argument.
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static DD |
determinant(DD x1,
DD y1,
DD x2,
DD y2)
Computes the determinant of the 2x2 matrix with the given entries.
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static DD |
determinant(double x1,
double y1,
double x2,
double y2)
Computes the determinant of the 2x2 matrix with the given entries.
|
DD |
divide(DD y)
Computes a new DoubleDouble whose value is (this / y).
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DD |
divide(double y)
Computes a new DoubleDouble whose value is (this / y).
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double |
doubleValue()
Converts this value to the nearest double-precision number.
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String |
dump()
Dumps the components of this number to a string.
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boolean |
equals(DD y)
Tests whether this value is equal to another DoubleDouble value.
|
DD |
floor()
Returns the largest (closest to positive infinity)
value that is not greater than the argument
and is equal to a mathematical integer.
|
boolean |
ge(DD y)
Tests whether this value is greater than or equals to another DoubleDouble value.
|
boolean |
gt(DD y)
Tests whether this value is greater than another DoubleDouble value.
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int |
intValue()
Converts this value to the nearest integer.
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boolean |
isNaN()
Tests whether this value is NaN.
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boolean |
isNegative()
Tests whether this value is less than 0.
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boolean |
isPositive()
Tests whether this value is greater than 0.
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boolean |
isZero()
Tests whether this value is equal to 0.
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boolean |
le(DD y)
Tests whether this value is less than or equal to another DoubleDouble value.
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boolean |
lt(DD y)
Tests whether this value is less than another DoubleDouble value.
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DD |
max(DD x)
Computes the maximum of this and another DD number.
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DD |
min(DD x)
Computes the minimum of this and another DD number.
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DD |
multiply(DD y)
Returns a new DoubleDouble whose value is (this * y).
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DD |
multiply(double y)
Returns a new DoubleDouble whose value is (this * y).
|
DD |
negate()
Returns a new DoubleDouble whose value is -this.
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static DD |
parse(String str)
Converts a string representation of a real number into a DoubleDouble value.
|
DD |
pow(int exp)
Computes the value of this number raised to an integral power.
|
DD |
reciprocal()
Returns a DoubleDouble whose value is 1 / this.
|
DD |
rint()
Rounds this value to the nearest integer.
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DD |
selfAdd(DD y)
Adds the argument to the value of this.
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DD |
selfAdd(double y)
Adds the argument to the value of this.
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DD |
selfDivide(DD y)
Divides this object by the argument, returning this.
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DD |
selfDivide(double y)
Divides this object by the argument, returning this.
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DD |
selfMultiply(DD y)
Multiplies this object by the argument, returning this.
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DD |
selfMultiply(double y)
Multiplies this object by the argument, returning this.
|
DD |
selfSqr()
Squares this object.
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DD |
selfSubtract(DD y)
Subtracts the argument from the value of this.
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DD |
selfSubtract(double y)
Subtracts the argument from the value of this.
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DD |
setValue(DD value)
Set the value for the DD object.
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DD |
setValue(double value)
Set the value for the DD object.
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int |
signum()
Returns an integer indicating the sign of this value.
|
DD |
sqr()
Computes the square of this value.
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static DD |
sqr(double x)
Computes the square of this value.
|
DD |
sqrt()
Computes the positive square root of this value.
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static DD |
sqrt(double x) |
DD |
subtract(DD y)
Computes a new DoubleDouble object whose value is (this - y).
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DD |
subtract(double y)
Computes a new DoubleDouble object whose value is (this - y).
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String |
toSciNotation()
Returns the string representation of this value in scientific notation.
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String |
toStandardNotation()
Returns the string representation of this value in standard notation.
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String |
toString()
Returns a string representation of this number, in either standard or scientific notation.
|
DD |
trunc()
Returns the integer which is largest in absolute value and not further
from zero than this value.
|
static DD |
valueOf(double x)
Converts the double argument to a DoubleDouble number.
|
static DD |
valueOf(String str)
Converts the string argument to a DoubleDouble number.
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public static final DD PI
public static final DD TWO_PI
public static final DD PI_2
public static final DD E
public static final DD NaN
public static final double EPS
public DD()
public DD(double x)
x
- the value to initializepublic DD(double hi, double lo)
hi
- the high-order componentlo
- the high-order componentpublic DD(DD dd)
dd
- the value to initializepublic DD(String str) throws NumberFormatException
str
- the value to initialize byNumberFormatException
- if str is not a valid representation of a numberpublic static DD valueOf(String str) throws NumberFormatException
str
- a string containing a representation of a numeric valueNumberFormatException
- if s is not a valid representation of a numberpublic static DD valueOf(double x)
x
- a numeric valuepublic static DD copy(DD dd)
dd
- the DoubleDouble value to copypublic Object clone()
public DD setValue(DD value)
value
- a DD instance supplying an extended-precision value.public DD setValue(double value)
value
- a floating point value to be stored in the instance.public final DD add(DD y)
y
- the addendpublic final DD add(double y)
y
- the addendpublic final DD selfAdd(DD y)
y
- the addendpublic final DD selfAdd(double y)
y
- the addendpublic final DD subtract(DD y)
y
- the subtrahendpublic final DD subtract(double y)
y
- the subtrahendpublic final DD selfSubtract(DD y)
y
- the addendpublic final DD selfSubtract(double y)
y
- the addendpublic final DD negate()
public final DD multiply(DD y)
y
- the multiplicandpublic final DD multiply(double y)
y
- the multiplicandpublic final DD selfMultiply(DD y)
y
- the value to multiply bypublic final DD selfMultiply(double y)
y
- the value to multiply bypublic final DD divide(DD y)
y
- the divisorpublic final DD divide(double y)
y
- the divisorpublic final DD selfDivide(DD y)
y
- the value to divide bypublic final DD selfDivide(double y)
y
- the value to divide bypublic final DD reciprocal()
public DD floor()
public DD ceil()
public int signum()
public DD rint()
public DD trunc()
public DD abs()
public DD sqr()
public DD selfSqr()
public static DD sqr(double x)
public DD sqrt()
public static DD sqrt(double x)
public DD pow(int exp)
exp
- the integer exponentpublic static DD determinant(double x1, double y1, double x2, double y2)
x1
- a double valuey1
- a double valuex2
- a double valuey2
- a double valuepublic static DD determinant(DD x1, DD y1, DD x2, DD y2)
x1
- a matrix entryy1
- a matrix entryx2
- a matrix entryy2
- a matrix entrypublic DD min(DD x)
x
- a DD numberpublic DD max(DD x)
x
- a DD numberpublic double doubleValue()
public int intValue()
public boolean isZero()
public boolean isNegative()
public boolean isPositive()
public boolean isNaN()
public boolean equals(DD y)
y
- a DoubleDouble valuepublic boolean gt(DD y)
y
- a DoubleDouble valuepublic boolean ge(DD y)
y
- a DoubleDouble valuepublic boolean lt(DD y)
y
- a DoubleDouble valuepublic boolean le(DD y)
y
- a DoubleDouble valuepublic int compareTo(Object o)
compareTo
in interface Comparable
public String dump()
public String toString()
public String toStandardNotation()
public String toSciNotation()
public static DD parse(String str) throws NumberFormatException
[+|-] {digit} [ . {digit} ] [ ( e | E ) [+|-] {digit}+
str
- the string to parseNumberFormatException
- if str is not a valid representation of a numberCopyright © 2024. All rights reserved.