Class DD
- java.lang.Object
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- org.locationtech.jts.math.DD
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- All Implemented Interfaces:
java.io.Serializable
,java.lang.Cloneable
,java.lang.Comparable
public final class DD extends java.lang.Object implements java.io.Serializable, java.lang.Comparable, java.lang.Cloneable
Implements extended-precision floating-point numbers which maintain 106 bits (approximately 30 decimal digits) of precision.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.
References
- Priest, D., Algorithms for Arbitrary Precision Floating Point Arithmetic, in P. Kornerup and D. Matula, Eds., Proc. 10th Symposium on Computer Arithmetic, IEEE Computer Society Press, Los Alamitos, Calif., 1991.
- Yozo Hida, Xiaoye S. Li and David H. Bailey, Quad-Double Arithmetic: Algorithms, Implementation, and Application, manuscript, Oct 2000; Lawrence Berkeley National Laboratory Report BNL-46996.
- David Bailey, High Precision Software Directory; http://crd.lbl.gov/~dhbailey/mpdist/index.html
- See Also:
- Serialized Form
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Field Summary
Fields Modifier and Type Field Description static DD
E
The value nearest to the constant e (the natural logarithm base).static double
EPS
The smallest representable relative difference between two {link @ DoubleDouble} valuesprivate double
hi
The high-order component of the double-double precision value.private double
lo
The low-order component of the double-double precision value.private static int
MAX_PRINT_DIGITS
static DD
NaN
A value representing the result of an operation which does not return a valid number.private static DD
ONE
static DD
PI
The value nearest to the constant Pi.static DD
PI_2
The value nearest to the constant Pi / 2.private static java.lang.String
SCI_NOT_EXPONENT_CHAR
private static java.lang.String
SCI_NOT_ZERO
private static double
SPLIT
The value to split a double-precision value on during multiplicationprivate static DD
TEN
static DD
TWO_PI
The value nearest to the constant 2 * Pi.
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Constructor Summary
Constructors Constructor Description DD()
Creates a new DoubleDouble with value 0.0.DD(double x)
Creates a new DoubleDouble with value x.DD(double hi, double lo)
Creates a new DoubleDouble with value (hi, lo).DD(java.lang.String str)
Creates a new DoubleDouble with value equal to the argument.DD(DD dd)
Creates a new DoubleDouble with value equal to the argument.
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Method Summary
All Methods Static Methods Instance Methods Concrete Methods Modifier and Type Method Description DD
abs()
Returns the absolute value of this value.DD
add(double y)
Returns a new DoubleDouble whose value is (this + y).DD
add(DD 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.java.lang.Object
clone()
Creates and returns a copy of this value.int
compareTo(java.lang.Object o)
Compares two DoubleDouble objects numerically.static DD
copy(DD dd)
Creates a new DoubleDouble with the value of the argument.private static DD
createNaN()
DD
divide(double y)
Computes a new DoubleDouble whose value is (this / y).DD
divide(DD y)
Computes a new DoubleDouble whose value is (this / y).double
doubleValue()
Converts this value to the nearest double-precision number.java.lang.String
dump()
Dumps the components of this number to a string.boolean
equals(DD y)
Tests whether this value is equal to another DoubleDouble value.private java.lang.String
extractSignificantDigits(boolean insertDecimalPoint, int[] magnitude)
Extracts the significant digits in the decimal representation of the argument.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.private java.lang.String
getSpecialNumberString()
Returns the string for this value if it has a known representation.boolean
gt(DD y)
Tests whether this value is greater than another DoubleDouble value.private void
init(double x)
private void
init(double hi, double lo)
private void
init(DD dd)
int
intValue()
Converts this value to the nearest integer.boolean
isNaN()
Tests whether this value is NaN.boolean
isNegative()
Tests whether this value is less than 0.boolean
isPositive()
Tests whether this value is greater than 0.boolean
isZero()
Tests whether this value is equal to 0.boolean
le(DD y)
Tests whether this value is less than or equal to another DoubleDouble value.boolean
lt(DD y)
Tests whether this value is less than another DoubleDouble value.private static int
magnitude(double x)
Determines the decimal magnitude of a number.DD
max(DD x)
Computes the maximum of this and another DD number.DD
min(DD x)
Computes the minimum of this and another DD number.DD
multiply(double y)
Returns a new DoubleDouble whose value is (this * y).DD
multiply(DD y)
Returns a new DoubleDouble whose value is (this * y).DD
negate()
Returns a new DoubleDouble whose value is -this.static DD
parse(java.lang.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.DD
selfAdd(double y)
Adds the argument to the value of this.private DD
selfAdd(double yhi, double ylo)
DD
selfAdd(DD y)
Adds the argument to the value of this.DD
selfDivide(double y)
Divides this object by the argument, returning this.private DD
selfDivide(double yhi, double ylo)
DD
selfDivide(DD y)
Divides this object by the argument, returning this.DD
selfMultiply(double y)
Multiplies this object by the argument, returning this.private DD
selfMultiply(double yhi, double ylo)
DD
selfMultiply(DD y)
Multiplies this object by the argument, returning this.DD
selfSqr()
Squares this object.DD
selfSubtract(double y)
Subtracts the argument from the value of this.DD
selfSubtract(DD y)
Subtracts the argument from the value of this.DD
setValue(double value)
Set the value for the DD object.DD
setValue(DD value)
Set the value for the DD object.int
signum()
Returns an integer indicating the sign of this value.DD
sqr()
Computes the square of this value.static DD
sqr(double x)
Computes the square of this value.DD
sqrt()
Computes the positive square root of this value.static DD
sqrt(double x)
private static java.lang.String
stringOfChar(char ch, int len)
Creates a string of a given length containing the given characterDD
subtract(double y)
Computes a new DoubleDouble object whose value is (this - y).DD
subtract(DD y)
Computes a new DoubleDouble object whose value is (this - y).java.lang.String
toSciNotation()
Returns the string representation of this value in scientific notation.java.lang.String
toStandardNotation()
Returns the string representation of this value in standard notation.java.lang.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(java.lang.String str)
Converts the string argument to a DoubleDouble number.
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Field Detail
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PI
public static final DD PI
The value nearest to the constant Pi.
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TWO_PI
public static final DD TWO_PI
The value nearest to the constant 2 * Pi.
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PI_2
public static final DD PI_2
The value nearest to the constant Pi / 2.
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E
public static final DD E
The value nearest to the constant e (the natural logarithm base).
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NaN
public static final DD NaN
A value representing the result of an operation which does not return a valid number.
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EPS
public static final double EPS
The smallest representable relative difference between two {link @ DoubleDouble} values- See Also:
- Constant Field Values
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SPLIT
private static final double SPLIT
The value to split a double-precision value on during multiplication- See Also:
- Constant Field Values
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hi
private double hi
The high-order component of the double-double precision value.
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lo
private double lo
The low-order component of the double-double precision value.
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MAX_PRINT_DIGITS
private static final int MAX_PRINT_DIGITS
- See Also:
- Constant Field Values
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TEN
private static final DD TEN
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ONE
private static final DD ONE
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SCI_NOT_EXPONENT_CHAR
private static final java.lang.String SCI_NOT_EXPONENT_CHAR
- See Also:
- Constant Field Values
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SCI_NOT_ZERO
private static final java.lang.String SCI_NOT_ZERO
- See Also:
- Constant Field Values
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Constructor Detail
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DD
public DD()
Creates a new DoubleDouble with value 0.0.
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DD
public DD(double x)
Creates a new DoubleDouble with value x.- Parameters:
x
- the value to initialize
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DD
public DD(double hi, double lo)
Creates a new DoubleDouble with value (hi, lo).- Parameters:
hi
- the high-order componentlo
- the high-order component
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DD
public DD(DD dd)
Creates a new DoubleDouble with value equal to the argument.- Parameters:
dd
- the value to initialize
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DD
public DD(java.lang.String str) throws java.lang.NumberFormatException
Creates a new DoubleDouble with value equal to the argument.- Parameters:
str
- the value to initialize by- Throws:
java.lang.NumberFormatException
- if str is not a valid representation of a number
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Method Detail
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createNaN
private static DD createNaN()
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valueOf
public static DD valueOf(java.lang.String str) throws java.lang.NumberFormatException
Converts the string argument to a DoubleDouble number.- Parameters:
str
- a string containing a representation of a numeric value- Returns:
- the extended precision version of the value
- Throws:
java.lang.NumberFormatException
- if s is not a valid representation of a number
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valueOf
public static DD valueOf(double x)
Converts the double argument to a DoubleDouble number.- Parameters:
x
- a numeric value- Returns:
- the extended precision version of the value
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copy
public static DD copy(DD dd)
Creates a new DoubleDouble with the value of the argument.- Parameters:
dd
- the DoubleDouble value to copy- Returns:
- a copy of the input value
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clone
public java.lang.Object clone()
Creates and returns a copy of this value.- Overrides:
clone
in classjava.lang.Object
- Returns:
- a copy of this value
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init
private final void init(double x)
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init
private final void init(double hi, double lo)
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init
private final void init(DD dd)
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setValue
public DD setValue(DD value)
Set the value for the DD object. This method supports the mutating operations concept described in the class documentation (see above).- Parameters:
value
- a DD instance supplying an extended-precision value.- Returns:
- a self-reference to the DD instance.
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setValue
public DD setValue(double value)
Set the value for the DD object. This method supports the mutating operations concept described in the class documentation (see above).- Parameters:
value
- a floating point value to be stored in the instance.- Returns:
- a self-reference to the DD instance.
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add
public final DD add(DD y)
Returns a new DoubleDouble whose value is (this + y).- Parameters:
y
- the addend- Returns:
- (this + y)
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add
public final DD add(double y)
Returns a new DoubleDouble whose value is (this + y).- Parameters:
y
- the addend- Returns:
- (this + y)
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selfAdd
public final DD selfAdd(DD y)
Adds the argument to the value of this. To prevent altering constants, this method must only be used on values known to be newly created.- Parameters:
y
- the addend- Returns:
- this object, increased by y
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selfAdd
public final DD selfAdd(double y)
Adds the argument to the value of this. To prevent altering constants, this method must only be used on values known to be newly created.- Parameters:
y
- the addend- Returns:
- this object, increased by y
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selfAdd
private final DD selfAdd(double yhi, double ylo)
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subtract
public final DD subtract(DD y)
Computes a new DoubleDouble object whose value is (this - y).- Parameters:
y
- the subtrahend- Returns:
- (this - y)
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subtract
public final DD subtract(double y)
Computes a new DoubleDouble object whose value is (this - y).- Parameters:
y
- the subtrahend- Returns:
- (this - y)
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selfSubtract
public final DD selfSubtract(DD y)
Subtracts the argument from the value of this. To prevent altering constants, this method must only be used on values known to be newly created.- Parameters:
y
- the addend- Returns:
- this object, decreased by y
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selfSubtract
public final DD selfSubtract(double y)
Subtracts the argument from the value of this. To prevent altering constants, this method must only be used on values known to be newly created.- Parameters:
y
- the addend- Returns:
- this object, decreased by y
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negate
public final DD negate()
Returns a new DoubleDouble whose value is -this.- Returns:
- -this
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multiply
public final DD multiply(DD y)
Returns a new DoubleDouble whose value is (this * y).- Parameters:
y
- the multiplicand- Returns:
- (this * y)
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multiply
public final DD multiply(double y)
Returns a new DoubleDouble whose value is (this * y).- Parameters:
y
- the multiplicand- Returns:
- (this * y)
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selfMultiply
public final DD selfMultiply(DD y)
Multiplies this object by the argument, returning this. To prevent altering constants, this method must only be used on values known to be newly created.- Parameters:
y
- the value to multiply by- Returns:
- this object, multiplied by y
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selfMultiply
public final DD selfMultiply(double y)
Multiplies this object by the argument, returning this. To prevent altering constants, this method must only be used on values known to be newly created.- Parameters:
y
- the value to multiply by- Returns:
- this object, multiplied by y
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selfMultiply
private final DD selfMultiply(double yhi, double ylo)
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divide
public final DD divide(DD y)
Computes a new DoubleDouble whose value is (this / y).- Parameters:
y
- the divisor- Returns:
- a new object with the value (this / y)
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divide
public final DD divide(double y)
Computes a new DoubleDouble whose value is (this / y).- Parameters:
y
- the divisor- Returns:
- a new object with the value (this / y)
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selfDivide
public final DD selfDivide(DD y)
Divides this object by the argument, returning this. To prevent altering constants, this method must only be used on values known to be newly created.- Parameters:
y
- the value to divide by- Returns:
- this object, divided by y
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selfDivide
public final DD selfDivide(double y)
Divides this object by the argument, returning this. To prevent altering constants, this method must only be used on values known to be newly created.- Parameters:
y
- the value to divide by- Returns:
- this object, divided by y
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selfDivide
private final DD selfDivide(double yhi, double ylo)
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reciprocal
public final DD reciprocal()
Returns a DoubleDouble whose value is 1 / this.- Returns:
- the reciprocal of this value
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floor
public DD floor()
Returns the largest (closest to positive infinity) value that is not greater than the argument and is equal to a mathematical integer. Special cases:- If this value is NaN, returns NaN.
- Returns:
- the largest (closest to positive infinity) value that is not greater than the argument and is equal to a mathematical integer.
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ceil
public DD ceil()
Returns the smallest (closest to negative infinity) value that is not less than the argument and is equal to a mathematical integer. Special cases:- If this value is NaN, returns NaN.
- Returns:
- the smallest (closest to negative infinity) value that is not less than the argument and is equal to a mathematical integer.
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signum
public int signum()
Returns an integer indicating the sign of this value.- if this value is > 0, returns 1
- if this value is < 0, returns -1
- if this value is = 0, returns 0
- if this value is NaN, returns 0
- Returns:
- an integer indicating the sign of this value
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rint
public DD rint()
Rounds this value to the nearest integer. The value is rounded to an integer by adding 1/2 and taking the floor of the result. Special cases:- If this value is NaN, returns NaN.
- Returns:
- this value rounded to the nearest integer
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trunc
public DD trunc()
Returns the integer which is largest in absolute value and not further from zero than this value. Special cases:- If this value is NaN, returns NaN.
- Returns:
- the integer which is largest in absolute value and not further from zero than this value
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abs
public DD abs()
Returns the absolute value of this value. Special cases:- If this value is NaN, it is returned.
- Returns:
- the absolute value of this value
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sqr
public DD sqr()
Computes the square of this value.- Returns:
- the square of this value.
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selfSqr
public DD selfSqr()
Squares this object. To prevent altering constants, this method must only be used on values known to be newly created.- Returns:
- the square of this value.
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sqr
public static DD sqr(double x)
Computes the square of this value.- Returns:
- the square of this value.
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sqrt
public DD sqrt()
Computes the positive square root of this value. If the number is NaN or negative, NaN is returned.- Returns:
- the positive square root of this number. If the argument is NaN or less than zero, the result is NaN.
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sqrt
public static DD sqrt(double x)
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pow
public DD pow(int exp)
Computes the value of this number raised to an integral power. Follows semantics of Java Math.pow as closely as possible.- Parameters:
exp
- the integer exponent- Returns:
- x raised to the integral power exp
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min
public DD min(DD x)
Computes the minimum of this and another DD number.- Parameters:
x
- a DD number- Returns:
- the minimum of the two numbers
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max
public DD max(DD x)
Computes the maximum of this and another DD number.- Parameters:
x
- a DD number- Returns:
- the maximum of the two numbers
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doubleValue
public double doubleValue()
Converts this value to the nearest double-precision number.- Returns:
- the nearest double-precision number to this value
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intValue
public int intValue()
Converts this value to the nearest integer.- Returns:
- the nearest integer to this value
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isZero
public boolean isZero()
Tests whether this value is equal to 0.- Returns:
- true if this value is equal to 0
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isNegative
public boolean isNegative()
Tests whether this value is less than 0.- Returns:
- true if this value is less than 0
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isPositive
public boolean isPositive()
Tests whether this value is greater than 0.- Returns:
- true if this value is greater than 0
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isNaN
public boolean isNaN()
Tests whether this value is NaN.- Returns:
- true if this value is NaN
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equals
public boolean equals(DD y)
Tests whether this value is equal to another DoubleDouble value.- Parameters:
y
- a DoubleDouble value- Returns:
- true if this value = y
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gt
public boolean gt(DD y)
Tests whether this value is greater than another DoubleDouble value.- Parameters:
y
- a DoubleDouble value- Returns:
- true if this value > y
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ge
public boolean ge(DD y)
Tests whether this value is greater than or equals to another DoubleDouble value.- Parameters:
y
- a DoubleDouble value- Returns:
- true if this value >= y
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lt
public boolean lt(DD y)
Tests whether this value is less than another DoubleDouble value.- Parameters:
y
- a DoubleDouble value- Returns:
- true if this value < y
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le
public boolean le(DD y)
Tests whether this value is less than or equal to another DoubleDouble value.- Parameters:
y
- a DoubleDouble value- Returns:
- true if this value <= y
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compareTo
public int compareTo(java.lang.Object o)
Compares two DoubleDouble objects numerically.- Specified by:
compareTo
in interfacejava.lang.Comparable
- Returns:
- -1,0 or 1 depending on whether this value is less than, equal to or greater than the value of o
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dump
public java.lang.String dump()
Dumps the components of this number to a string.- Returns:
- a string showing the components of the number
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toString
public java.lang.String toString()
Returns a string representation of this number, in either standard or scientific notation. If the magnitude of the number is in the range [ 10-3, 108 ] standard notation will be used. Otherwise, scientific notation will be used.- Overrides:
toString
in classjava.lang.Object
- Returns:
- a string representation of this number
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toStandardNotation
public java.lang.String toStandardNotation()
Returns the string representation of this value in standard notation.- Returns:
- the string representation in standard notation
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toSciNotation
public java.lang.String toSciNotation()
Returns the string representation of this value in scientific notation.- Returns:
- the string representation in scientific notation
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extractSignificantDigits
private java.lang.String extractSignificantDigits(boolean insertDecimalPoint, int[] magnitude)
Extracts the significant digits in the decimal representation of the argument. A decimal point may be optionally inserted in the string of digits (as long as its position lies within the extracted digits - if not, the caller must prepend or append the appropriate zeroes and decimal point).- Parameters:
y
- the number to extract ( >= 0)decimalPointPos
- the position in which to insert a decimal point- Returns:
- the string containing the significant digits and possibly a decimal point
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stringOfChar
private static java.lang.String stringOfChar(char ch, int len)
Creates a string of a given length containing the given character- Parameters:
ch
- the character to be repeatedlen
- the len of the desired string- Returns:
- the string
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getSpecialNumberString
private java.lang.String getSpecialNumberString()
Returns the string for this value if it has a known representation. (E.g. NaN or 0.0)- Returns:
- the string for this special number or null if the number is not a special number
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magnitude
private static int magnitude(double x)
Determines the decimal magnitude of a number. The magnitude is the exponent of the greatest power of 10 which is less than or equal to the number.- Parameters:
x
- the number to find the magnitude of- Returns:
- the decimal magnitude of x
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parse
public static DD parse(java.lang.String str) throws java.lang.NumberFormatException
Converts a string representation of a real number into a DoubleDouble value. The format accepted is similar to the standard Java real number syntax. It is defined by the following regular expression:[+|-] {digit} [ . {digit} ] [ ( e | E ) [+|-] {digit}+
- Parameters:
str
- the string to parse- Returns:
- the value of the parsed number
- Throws:
java.lang.NumberFormatException
- if str is not a valid representation of a number
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