# Class Double

All Implemented Interfaces:
`Serializable`, `Comparable<Double>`, `Constable`, `ConstantDesc`

public final class Double extends Number implements Comparable<Double>, Constable, ConstantDesc
The `Double` class wraps a value of the primitive type `double` in an object. An object of type `Double` contains a single field whose type is `double`.

In addition, this class provides several methods for converting a `double` to a `String` and a `String` to a `double`, as well as other constants and methods useful when dealing with a `double`.

This is a value-based class; programmers should treat instances that are equal as interchangeable and should not use instances for synchronization, or unpredictable behavior may occur. For example, in a future release, synchronization may fail.

## Floating-point Equality, Equivalence, and Comparison

IEEE 754 floating-point values include finite nonzero values, signed zeros (`+0.0` and `-0.0`), signed infinities (positive infinity and negative infinity), and NaN (not-a-number).

An equivalence relation on a set of values is a boolean relation on pairs of values that is reflexive, symmetric, and transitive. For more discussion of equivalence relations and object equality, see the `Object.equals` specification. An equivalence relation partitions the values it operates over into sets called equivalence classes. All the members of the equivalence class are equal to each other under the relation. An equivalence class may contain only a single member. At least for some purposes, all the members of an equivalence class are substitutable for each other. In particular, in a numeric expression equivalent values can be substituted for one another without changing the result of the expression, meaning changing the equivalence class of the result of the expression.

Notably, the built-in `==` operation on floating-point values is not an equivalence relation. Despite not defining an equivalence relation, the semantics of the IEEE 754 `==` operator were deliberately designed to meet other needs of numerical computation. There are two exceptions where the properties of an equivalence relation are not satisfied by ``` ==``` on floating-point values:

• If `v1` and `v2` are both NaN, then ```v1 == v2``` has the value `false`. Therefore, for two NaN arguments the reflexive property of an equivalence relation is not satisfied by the `==` operator.
• If `v1` represents `+0.0` while `v2` represents `-0.0`, or vice versa, then `v1 == v2` has the value `true` even though `+0.0` and `-0.0` are distinguishable under various floating-point operations. For example, `1.0/+0.0` evaluates to positive infinity while `1.0/-0.0` evaluates to negative infinity and positive infinity and negative infinity are neither equal to each other nor equivalent to each other. Thus, while a signed zero input most commonly determines the sign of a zero result, because of dividing by zero, `+0.0` and `-0.0` may not be substituted for each other in general. The sign of a zero input also has a non-substitutable effect on the result of some math library methods.

For ordered comparisons using the built-in comparison operators (`<`, `<=`, etc.), NaN values have another anomalous situation: a NaN is neither less than, nor greater than, nor equal to any value, including itself. This means the trichotomy of comparison does not hold.

To provide the appropriate semantics for `equals` and `compareTo` methods, those methods cannot simply be wrappers around `==` or ordered comparison operations. Instead, `equals` uses representation equivalence, defining NaN arguments to be equal to each other, restoring reflexivity, and defining `+0.0` to not be equal to `-0.0`. For comparisons, `compareTo` defines a total order where `-0.0` is less than `+0.0` and where a NaN is equal to itself and considered greater than positive infinity.

The operational semantics of `equals` and ``` compareTo``` are expressed in terms of bit-wise converting the floating-point values to integral values.

The natural ordering implemented by `compareTo` is consistent with equals. That is, two objects are reported as equal by `equals` if and only if `compareTo` on those objects returns zero.

The adjusted behaviors defined for `equals` and ``` compareTo``` allow instances of wrapper classes to work properly with conventional data structures. For example, defining NaN values to be `equals` to one another allows NaN to be used as an element of a `HashSet` or as the key of a `HashMap`. Similarly, defining ``` compareTo``` as a total ordering, including `+0.0`, ``` -0.0```, and NaN, allows instances of wrapper classes to be used as elements of a `SortedSet` or as keys of a `SortedMap`.

Comparing numerical equality to various useful equivalence relations that can be defined over floating-point values:

numerical equality (`==` operator): (Not an equivalence relation)
Two floating-point values represent the same extended real number. The extended real numbers are the real numbers augmented with positive infinity and negative infinity. Under numerical equality, `+0.0` and `-0.0` are equal since they both map to the same real value, 0. A NaN does not map to any real number and is not equal to any value, including itself.
bit-wise equivalence:
The bits of the two floating-point values are the same. This equivalence relation for `double` values `a` and ``` b``` is implemented by the expression
`Double.doubleTo``Raw``LongBits(a) == Double.doubleTo``Raw``LongBits(b)`
Under this relation, `+0.0` and `-0.0` are distinguished from each other and every bit pattern encoding a NaN is distinguished from every other bit pattern encoding a NaN.
representation equivalence:
The two floating-point values represent the same IEEE 754 datum. In particular, for finite values, the sign, exponent, and significand components of the floating-point values are the same. Under this relation:
• `+0.0` and `-0.0` are distinguished from each other.
• every bit pattern encoding a NaN is considered equivalent to each other
• positive infinity is equivalent to positive infinity; negative infinity is equivalent to negative infinity.
Expressions implementing this equivalence relation include:
• `Double.doubleToLongBits(a) == Double.doubleToLongBits(b)`
• `Double.valueOf(a).equals(Double.valueOf(b))`
• `Double.compare(a, b) == 0`
Note that representation equivalence is often an appropriate notion of equivalence to test the behavior of math libraries.
For two binary floating-point values `a` and `b`, if neither of `a` and `b` is zero or NaN, then the three relations numerical equality, bit-wise equivalence, and representation equivalence of `a` and `b` have the same `true`/`false` value. In other words, for binary floating-point values, the three relations only differ if at least one argument is zero or NaN.

## Decimal ↔ Binary Conversion Issues

Many surprising results of binary floating-point arithmetic trace back to aspects of decimal to binary conversion and binary to decimal conversion. While integer values can be exactly represented in any base, which fractional values can be exactly represented in a base is a function of the base. For example, in base 10, 1/3 is a repeating fraction (0.33333....); but in base 3, 1/3 is exactly 0.1(3), that is 1 × 3-1. Similarly, in base 10, 1/10 is exactly representable as 0.1 (1 × 10-1), but in base 2, it is a repeating fraction (0.0001100110011...(2)).

Values of the `float` type have 24 bits of precision and values of the `double` type have 53 bits of precision. Therefore, since 0.1 is a repeating fraction in base 2 with a four-bit repeat, ``` 0.1f``` != `0.1d`. In more detail, including hexadecimal floating-point literals:

• The exact numerical value of `0.1f` (`0x1.99999a0000000p-4f`) is 0.100000001490116119384765625.
• The exact numerical value of `0.1d` (`0x1.999999999999ap-4d`) is 0.1000000000000000055511151231257827021181583404541015625.
These are the closest `float` and `double` values, respectively, to the numerical value of 0.1. These results are consistent with a `float` value having the equivalent of 6 to 9 digits of decimal precision and a `double` value having the equivalent of 15 to 17 digits of decimal precision. (The equivalent precision varies according to the different relative densities of binary and decimal values at different points along the real number line.)

This representation hazard of decimal fractions is one reason to use caution when storing monetary values as `float` or ``` double```. Alternatives include:

• using `BigDecimal` to store decimal fractional values exactly
• scaling up so the monetary value is an integer — for example, multiplying by 100 if the value is denominated in cents or multiplying by 1000 if the value is denominated in mills — and then storing that scaled value in an integer type

For each finite floating-point value and a given floating-point type, there is a contiguous region of the real number line which maps to that value. Under the default round to nearest rounding policy (JLS 15.4), this contiguous region for a value is typically one ulp (unit in the last place) wide and centered around the exactly representable value. (At exponent boundaries, the region is asymmetrical and larger on the side with the larger exponent.) For example, for `0.1f`, the region can be computed as follows:
// Numeric values listed are exact values
oneTenthApproxAsFloat = 0.100000001490116119384765625;
ulpOfoneTenthApproxAsFloat = Math.ulp(0.1f) = 7.450580596923828125E-9;
// Numeric range that is converted to the float closest to 0.1, _excludes_ endpoints
(oneTenthApproxAsFloat - ½ulpOfoneTenthApproxAsFloat, oneTenthApproxAsFloat + ½ulpOfoneTenthApproxAsFloat) =
(0.0999999977648258209228515625, 0.1000000052154064178466796875)

In particular, a correctly rounded decimal to binary conversion of any string representing a number in this range, say by `Float.parseFloat(String)`, will be converted to the same value:

``````Float.parseFloat("0.0999999977648258209228515625000001"); // rounds up to oneTenthApproxAsFloat
Float.parseFloat("0.099999998");                          // rounds up to oneTenthApproxAsFloat
Float.parseFloat("0.1");                                  // rounds up to oneTenthApproxAsFloat
Float.parseFloat("0.100000001490116119384765625");        // exact conversion
Float.parseFloat("0.100000005215406417846679687");        // rounds down to oneTenthApproxAsFloat
Float.parseFloat("0.100000005215406417846679687499999");  // rounds down to oneTenthApproxAsFloat
``````

Similarly, an analogous range can be constructed for the ``` double``` type based on the exact value of `double` approximation to `0.1d` and the numerical value of ``` Math.ulp(0.1d)``` and likewise for other particular numerical values in the `float` and `double` types.

As seen in the above conversions, compared to the exact numerical value the operation would have without rounding, the same floating-point value as a result can be:

• greater than the exact result
• equal to the exact result
• less than the exact result
A floating-point value doesn't "know" whether it was the result of rounding up, or rounding down, or an exact operation; it contains no history of how it was computed. Consequently, the sum of
``````0.1f + 0.1f + 0.1f + 0.1f + 0.1f + 0.1f + 0.1f + 0.1f + 0.1f + 0.1f;
// Numerical value of computed sum: 1.00000011920928955078125,
// the next floating-point value larger than 1.0f, equal to Math.nextUp(1.0f).
``````
or
``````0.1d + 0.1d + 0.1d + 0.1d + 0.1d + 0.1d + 0.1d + 0.1d + 0.1d + 0.1d;
// Numerical value of computed sum: 0.99999999999999988897769753748434595763683319091796875,
// the next floating-point value smaller than 1.0d, equal to Math.nextDown(1.0d).
``````
should not be expected to be exactly equal to 1.0, but only to be close to 1.0. Consequently, the following code is an infinite loop:
``````double d = 0.0;
while (d != 1.0) { // Surprising infinite loop
d += 0.1; // Sum never _exactly_ equals 1.0
}
``````
Instead, use an integer loop count for counted loops:
``````double d = 0.0;
for (int i = 0; i < 10; i++) {
d += 0.1;
} // Value of d is equal to Math.nextDown(1.0).
``````
or test against a floating-point limit using ordered comparisons (`<`, `<=`, `>`, `>=`):
``````double d = 0.0;
while (d <= 1.0) {
d += 0.1;
} // Value of d approximately 1.0999999999999999
``````
While floating-point arithmetic may have surprising results, IEEE 754 floating-point arithmetic follows a principled design and its behavior is predictable on the Java platform.
See Java Language Specification:
4.2.3 Floating-Point Types, Formats, and Values
4.2.4. Floating-Point Operations
15.21.1 Numerical Equality Operators == and !=
15.20.1 Numerical Comparison Operators `<`, `<=`, `>`, and `>=`
Since:
1.0
• ## Field Summary

Fields
Modifier and Type
Field
Description
`static final int`
`BYTES`
The number of bytes used to represent a `double` value, 8.
`static final int`
`MAX_EXPONENT`
Maximum exponent a finite `double` variable may have, 1023.
`static final double`
`MAX_VALUE`
A constant holding the largest positive finite value of type `double`, (2-2-52)·21023.
`static final int`
`MIN_EXPONENT`
Minimum exponent a normalized `double` variable may have, -1022.
`static final double`
`MIN_NORMAL`
A constant holding the smallest positive normal value of type `double`, 2-1022.
`static final double`
`MIN_VALUE`
A constant holding the smallest positive nonzero value of type `double`, 2-1074.
`static final double`
`NaN`
A constant holding a Not-a-Number (NaN) value of type `double`.
`static final double`
`NEGATIVE_INFINITY`
A constant holding the negative infinity of type `double`.
`static final double`
`POSITIVE_INFINITY`
A constant holding the positive infinity of type `double`.
`static final int`
`PRECISION`
The number of bits in the significand of a `double` value, 53.
`static final int`
`SIZE`
The number of bits used to represent a `double` value, 64.
`static final Class<Double>`
`TYPE`
The `Class` instance representing the primitive type `double`.
• ## Constructor Summary

Constructors
Constructor
Description
`Double(double value)`
Deprecated, for removal: This API element is subject to removal in a future version.
It is rarely appropriate to use this constructor.
`Double(String s)`
Deprecated, for removal: This API element is subject to removal in a future version.
It is rarely appropriate to use this constructor.
• ## Method Summary

Modifier and Type
Method
Description
`byte`
`byteValue()`
Returns the value of this `Double` as a `byte` after a narrowing primitive conversion.
`static int`
```compare(double d1, double d2)```
Compares the two specified `double` values.
`int`
`compareTo(Double anotherDouble)`
Compares two `Double` objects numerically.
`Optional<Double>`
`describeConstable()`
Returns an `Optional` containing the nominal descriptor for this instance, which is the instance itself.
`static long`
`doubleToLongBits(double value)`
Returns a representation of the specified floating-point value according to the IEEE 754 floating-point "double format" bit layout.
`static long`
`doubleToRawLongBits(double value)`
Returns a representation of the specified floating-point value according to the IEEE 754 floating-point "double format" bit layout, preserving Not-a-Number (NaN) values.
`double`
`doubleValue()`
Returns the `double` value of this `Double` object.
`boolean`
`equals(Object obj)`
Compares this object against the specified object.
`float`
`floatValue()`
Returns the value of this `Double` as a `float` after a narrowing primitive conversion.
`int`
`hashCode()`
Returns a hash code for this `Double` object.
`static int`
`hashCode(double value)`
Returns a hash code for a `double` value; compatible with `Double.hashCode()`.
`int`
`intValue()`
Returns the value of this `Double` as an `int` after a narrowing primitive conversion.
`static boolean`
`isFinite(double d)`
Returns `true` if the argument is a finite floating-point value; returns `false` otherwise (for NaN and infinity arguments).
`boolean`
`isInfinite()`
Returns `true` if this `Double` value is infinitely large in magnitude, `false` otherwise.
`static boolean`
`isInfinite(double v)`
Returns `true` if the specified number is infinitely large in magnitude, `false` otherwise.
`boolean`
`isNaN()`
Returns `true` if this `Double` value is a Not-a-Number (NaN), `false` otherwise.
`static boolean`
`isNaN(double v)`
Returns `true` if the specified number is a Not-a-Number (NaN) value, `false` otherwise.
`static double`
`longBitsToDouble(long bits)`
Returns the `double` value corresponding to a given bit representation.
`long`
`longValue()`
Returns the value of this `Double` as a `long` after a narrowing primitive conversion.
`static double`
```max(double a, double b)```
Returns the greater of two `double` values as if by calling `Math.max`.
`static double`
```min(double a, double b)```
Returns the smaller of two `double` values as if by calling `Math.min`.
`static double`
`parseDouble(String s)`
Returns a new `double` initialized to the value represented by the specified `String`, as performed by the `valueOf` method of class `Double`.
`Double`
`resolveConstantDesc(MethodHandles.Lookup lookup)`
Resolves this instance as a `ConstantDesc`, the result of which is the instance itself.
`short`
`shortValue()`
Returns the value of this `Double` as a `short` after a narrowing primitive conversion.
`static double`
```sum(double a, double b)```
Adds two `double` values together as per the + operator.
`static String`
`toHexString(double d)`
Returns a hexadecimal string representation of the `double` argument.
`String`
`toString()`
Returns a string representation of this `Double` object.
`static String`
`toString(double d)`
Returns a string representation of the `double` argument.
`static Double`
`valueOf(double d)`
Returns a `Double` instance representing the specified `double` value.
`static Double`
`valueOf(String s)`
Returns a `Double` object holding the `double` value represented by the argument string `s`.

### Methods declared in class java.lang.Object

`clone, finalize, getClass, notify, notifyAll, wait, wait, wait`
• ## Field Details

• ### POSITIVE_INFINITY

public static final double POSITIVE_INFINITY
A constant holding the positive infinity of type `double`. It is equal to the value returned by `Double.longBitsToDouble(0x7ff0000000000000L)`.
• ### NEGATIVE_INFINITY

public static final double NEGATIVE_INFINITY
A constant holding the negative infinity of type `double`. It is equal to the value returned by `Double.longBitsToDouble(0xfff0000000000000L)`.
• ### NaN

public static final double NaN
A constant holding a Not-a-Number (NaN) value of type `double`. It is equivalent to the value returned by `Double.longBitsToDouble(0x7ff8000000000000L)`.
• ### MAX_VALUE

public static final double MAX_VALUE
A constant holding the largest positive finite value of type `double`, (2-2-52)·21023. It is equal to the hexadecimal floating-point literal `0x1.fffffffffffffP+1023` and also equal to `Double.longBitsToDouble(0x7fefffffffffffffL)`.
• ### MIN_NORMAL

public static final double MIN_NORMAL
A constant holding the smallest positive normal value of type `double`, 2-1022. It is equal to the hexadecimal floating-point literal `0x1.0p-1022` and also equal to `Double.longBitsToDouble(0x0010000000000000L)`.
Since:
1.6
• ### MIN_VALUE

public static final double MIN_VALUE
A constant holding the smallest positive nonzero value of type `double`, 2-1074. It is equal to the hexadecimal floating-point literal `0x0.0000000000001P-1022` and also equal to `Double.longBitsToDouble(0x1L)`.
• ### SIZE

public static final int SIZE
The number of bits used to represent a `double` value, 64.
Since:
1.5
• ### PRECISION

public static final int PRECISION
The number of bits in the significand of a `double` value, 53. This is the parameter N in section 4.2.3 of The Java Language Specification.
Since:
19
• ### MAX_EXPONENT

public static final int MAX_EXPONENT
Maximum exponent a finite `double` variable may have, 1023. It is equal to the value returned by ``` Math.getExponent(Double.MAX_VALUE)```.
Since:
1.6
• ### MIN_EXPONENT

public static final int MIN_EXPONENT
Minimum exponent a normalized `double` variable may have, -1022. It is equal to the value returned by ``` Math.getExponent(Double.MIN_NORMAL)```.
Since:
1.6
• ### BYTES

public static final int BYTES
The number of bytes used to represent a `double` value, 8.
Since:
1.8
• ### TYPE

public static final  TYPE
The `Class` instance representing the primitive type `double`.
Since:
1.1
• ## Constructor Details

• ### Double

@Deprecated(since="9", forRemoval=true) public Double(double value)
Deprecated, for removal: This API element is subject to removal in a future version.
It is rarely appropriate to use this constructor. The static factory `valueOf(double)` is generally a better choice, as it is likely to yield significantly better space and time performance.
Constructs a newly allocated `Double` object that represents the primitive `double` argument.
Parameters:
`value` - the value to be represented by the `Double`.
• ### Double

@Deprecated(since="9", forRemoval=true) public Double(String s) throws NumberFormatException
Deprecated, for removal: This API element is subject to removal in a future version.
It is rarely appropriate to use this constructor. Use `parseDouble(String)` to convert a string to a `double` primitive, or use `valueOf(String)` to convert a string to a `Double` object.
Constructs a newly allocated `Double` object that represents the floating-point value of type `double` represented by the string. The string is converted to a `double` value as if by the `valueOf` method.
Parameters:
`s` - a string to be converted to a `Double`.
Throws:
`NumberFormatException` - if the string does not contain a parsable number.
• ## Method Details

• ### toString

public static String toString(double d)
Returns a string representation of the `double` argument. All characters mentioned below are ASCII characters.
• If the argument is NaN, the result is the string "`NaN`".
• Otherwise, the result is a string that represents the sign and magnitude (absolute value) of the argument. If the sign is negative, the first character of the result is '`-`' (`'\u002D'`); if the sign is positive, no sign character appears in the result. As for the magnitude m:
• If m is infinity, it is represented by the characters `"Infinity"`; thus, positive infinity produces the result `"Infinity"` and negative infinity produces the result `"-Infinity"`.
• If m is zero, it is represented by the characters `"0.0"`; thus, negative zero produces the result `"-0.0"` and positive zero produces the result `"0.0"`.
• Otherwise m is positive and finite. It is converted to a string in two stages:
• Selection of a decimal: A well-defined decimal dm is selected to represent m. This decimal is (almost always) the shortest one that rounds to m according to the round to nearest rounding policy of IEEE 754 floating-point arithmetic.
• Formatting as a string: The decimal dm is formatted as a string, either in plain or in computerized scientific notation, depending on its value.

A decimal is a number of the form s×10i for some (unique) integers s > 0 and i such that s is not a multiple of 10. These integers are the significand and the exponent, respectively, of the decimal. The length of the decimal is the (unique) positive integer n meeting 10n-1s < 10n.

The decimal dm for a finite positive m is defined as follows:

• Let R be the set of all decimals that round to m according to the usual round to nearest rounding policy of IEEE 754 floating-point arithmetic.
• Let p be the minimal length over all decimals in R.
• When p ≥ 2, let T be the set of all decimals in R with length p. Otherwise, let T be the set of all decimals in R with length 1 or 2.
• Define dm as the decimal in T that is closest to m. Or if there are two such decimals in T, select the one with the even significand.

The (uniquely) selected decimal dm is then formatted. Let s, i and n be the significand, exponent and length of dm, respectively. Further, let e = n + i - 1 and let s1sn be the usual decimal expansion of s. Note that s1 ≠ 0 and sn ≠ 0. Below, the decimal point `'.'` is `'\u002E'` and the exponent indicator `'E'` is `'\u0045'`.

• Case -3 ≤ e < 0: dm is formatted as `0.0``0`s1sn, where there are exactly -(n + i) zeroes between the decimal point and s1. For example, 123 × 10-4 is formatted as `0.0123`.
• Case 0 ≤ e < 7:
• Subcase i ≥ 0: dm is formatted as s1sn`0``0.0`, where there are exactly i zeroes between sn and the decimal point. For example, 123 × 102 is formatted as `12300.0`.
• Subcase i < 0: dm is formatted as s1sn+i`.`sn+i+1sn, where there are exactly -i digits to the right of the decimal point. For example, 123 × 10-1 is formatted as `12.3`.
• Case e < -3 or e ≥ 7: computerized scientific notation is used to format dm. Here e is formatted as by `Integer.toString(int)`.
• Subcase n = 1: dm is formatted as s1`.0E`e. For example, 1 × 1023 is formatted as `1.0E23`.
• Subcase n > 1: dm is formatted as s1`.`s2sn`E`e. For example, 123 × 10-21 is formatted as `1.23E-19`.

To create localized string representations of a floating-point value, use subclasses of `NumberFormat`.

API Note:
This method corresponds to the general functionality of the convertToDecimalCharacter operation defined in IEEE 754; however, that operation is defined in terms of specifying the number of significand digits used in the conversion. Code to do such a conversion in the Java platform includes converting the `double` to a `BigDecimal` exactly and then rounding the `BigDecimal` to the desired number of digits; sample code:
``````double d = 0.1;
int digits = 25;
BigDecimal bd = new BigDecimal(d);
String result = bd.round(new MathContext(digits,  RoundingMode.HALF_UP));
// 0.1000000000000000055511151
``````
Parameters:
`d` - the `double` to be converted.
Returns:
a string representation of the argument.
• ### toHexString

public static String toHexString(double d)
Returns a hexadecimal string representation of the `double` argument. All characters mentioned below are ASCII characters.
• If the argument is NaN, the result is the string "`NaN`".
• Otherwise, the result is a string that represents the sign and magnitude of the argument. If the sign is negative, the first character of the result is '`-`' (`'\u002D'`); if the sign is positive, no sign character appears in the result. As for the magnitude m:
• If m is infinity, it is represented by the string `"Infinity"`; thus, positive infinity produces the result `"Infinity"` and negative infinity produces the result `"-Infinity"`.
• If m is zero, it is represented by the string `"0x0.0p0"`; thus, negative zero produces the result `"-0x0.0p0"` and positive zero produces the result `"0x0.0p0"`.
• If m is a `double` value with a normalized representation, substrings are used to represent the significand and exponent fields. The significand is represented by the characters `"0x1."` followed by a lowercase hexadecimal representation of the rest of the significand as a fraction. Trailing zeros in the hexadecimal representation are removed unless all the digits are zero, in which case a single zero is used. Next, the exponent is represented by `"p"` followed by a decimal string of the unbiased exponent as if produced by a call to `Integer.toString` on the exponent value.
• If m is a `double` value with a subnormal representation, the significand is represented by the characters `"0x0."` followed by a hexadecimal representation of the rest of the significand as a fraction. Trailing zeros in the hexadecimal representation are removed. Next, the exponent is represented by `"p-1022"`. Note that there must be at least one nonzero digit in a subnormal significand.
Examples
`1.0` `0x1.0p0`
`-1.0` `-0x1.0p0`
`2.0` `0x1.0p1`
`3.0` `0x1.8p1`
`0.5` `0x1.0p-1`
`0.25` `0x1.0p-2`
`Double.MAX_VALUE` `0x1.fffffffffffffp1023`
`Minimum Normal Value` `0x1.0p-1022`
`Maximum Subnormal Value` `0x0.fffffffffffffp-1022`
`Double.MIN_VALUE` `0x0.0000000000001p-1022`
API Note:
This method corresponds to the convertToHexCharacter operation defined in IEEE 754.
Parameters:
`d` - the `double` to be converted.
Returns:
a hex string representation of the argument.
Since:
1.5
• ### valueOf

public static Double valueOf(String s) throws NumberFormatException
Returns a `Double` object holding the `double` value represented by the argument string `s`.

If `s` is `null`, then a `NullPointerException` is thrown.

Leading and trailing whitespace characters in `s` are ignored. Whitespace is removed as if by the `String.trim()` method; that is, both ASCII space and control characters are removed. The rest of `s` should constitute a FloatValue as described by the lexical syntax rules:

FloatValue:
Signopt `NaN`
Signopt `Infinity`
Signopt FloatingPointLiteral
Signopt HexFloatingPointLiteral
SignedInteger
HexFloatingPointLiteral:
HexSignificand BinaryExponent FloatTypeSuffixopt
HexSignificand:
HexNumeral
HexNumeral `.`
`0x` HexDigitsopt `.` HexDigits
`0X` HexDigitsopt `.` HexDigits
BinaryExponent:
BinaryExponentIndicator SignedInteger
BinaryExponentIndicator:
`p`
`P`
where Sign, FloatingPointLiteral, HexNumeral, HexDigits, SignedInteger and FloatTypeSuffix are as defined in the lexical structure sections of The Java Language Specification, except that underscores are not accepted between digits. If `s` does not have the form of a FloatValue, then a `NumberFormatException` is thrown. Otherwise, `s` is regarded as representing an exact decimal value in the usual "computerized scientific notation" or as an exact hexadecimal value; this exact numerical value is then conceptually converted to an "infinitely precise" binary value that is then rounded to type `double` by the usual round-to-nearest rule of IEEE 754 floating-point arithmetic, which includes preserving the sign of a zero value. Note that the round-to-nearest rule also implies overflow and underflow behaviour; if the exact value of `s` is large enough in magnitude (greater than or equal to (`MAX_VALUE` + `ulp(MAX_VALUE)`/2), rounding to `double` will result in an infinity and if the exact value of `s` is small enough in magnitude (less than or equal to `MIN_VALUE`/2), rounding to float will result in a zero. Finally, after rounding a `Double` object representing this `double` value is returned.

Note that trailing format specifiers, specifiers that determine the type of a floating-point literal (`1.0f` is a `float` value; `1.0d` is a `double` value), do not influence the results of this method. In other words, the numerical value of the input string is converted directly to the target floating-point type. The two-step sequence of conversions, string to `float` followed by `float` to `double`, is not equivalent to converting a string directly to `double`. For example, the `float` literal `0.1f` is equal to the `double` value `0.10000000149011612`; the `float` literal `0.1f` represents a different numerical value than the `double` literal `0.1`. (The numerical value 0.1 cannot be exactly represented in a binary floating-point number.)

To avoid calling this method on an invalid string and having a `NumberFormatException` be thrown, the regular expression below can be used to screen the input string:

`````` final String Digits     = "(\\p{Digit}+)";
final String HexDigits  = "(\\p{XDigit}+)";
// an exponent is 'e' or 'E' followed by an optionally
// signed decimal integer.
final String Exp        = "[eE][+-]?"+Digits;
final String fpRegex    =
"[+-]?(" + // Optional sign character
"NaN|" +           // "NaN" string
"Infinity|" +      // "Infinity" string

// A decimal floating-point string representing a finite positive
// number without a leading sign has at most five basic pieces:
// Digits . Digits ExponentPart FloatTypeSuffix
//
// Since this method allows integer-only strings as input
// in addition to strings of floating-point literals, the
// two sub-patterns below are simplifications of the grammar
// productions from section 3.10.2 of
// The Java Language Specification.

// Digits ._opt Digits_opt ExponentPart_opt FloatTypeSuffix_opt
"((("+Digits+"(\\.)?("+Digits+"?)("+Exp+")?)|"+

// . Digits ExponentPart_opt FloatTypeSuffix_opt
"(\\.("+Digits+")("+Exp+")?)|"+

"((" +
// 0[xX] HexDigits ._opt BinaryExponent FloatTypeSuffix_opt
"(0[xX]" + HexDigits + "(\\.)?)|" +

// 0[xX] HexDigits_opt . HexDigits BinaryExponent FloatTypeSuffix_opt
"(0[xX]" + HexDigits + "?(\\.)" + HexDigits + ")" +

")[pP][+-]?" + Digits + "))" +
"[fFdD]?))" +
"[\\x00-\\x20]*");// Optional trailing "whitespace"
if (Pattern.matches(fpRegex, myString))
Double.valueOf(myString); // Will not throw NumberFormatException
else {
// Perform suitable alternative action
}
``````
API Note:
To interpret localized string representations of a floating-point value, or string representations that have non-ASCII digits, use `NumberFormat`. For example,
``````    NumberFormat.getInstance(l).parse(s).doubleValue();
``````
where `l` is the desired locale, or `Locale.ROOT` if locale insensitive., This method corresponds to the convertFromDecimalCharacter and convertFromHexCharacter operations defined in IEEE 754.
Parameters:
`s` - the string to be parsed.
Returns:
a `Double` object holding the value represented by the `String` argument.
Throws:
`NumberFormatException` - if the string does not contain a parsable number.
• ### valueOf

public static Double valueOf(double d)
Returns a `Double` instance representing the specified `double` value. If a new `Double` instance is not required, this method should generally be used in preference to the constructor `Double(double)`, as this method is likely to yield significantly better space and time performance by caching frequently requested values.
Parameters:
`d` - a double value.
Returns:
a `Double` instance representing `d`.
Since:
1.5
• ### parseDouble

public static double parseDouble(String s) throws NumberFormatException
Returns a new `double` initialized to the value represented by the specified `String`, as performed by the `valueOf` method of class `Double`.
Parameters:
`s` - the string to be parsed.
Returns:
the `double` value represented by the string argument.
Throws:
`NullPointerException` - if the string is null
`NumberFormatException` - if the string does not contain a parsable `double`.
Since:
1.2
• ### isNaN

public static boolean isNaN(double v)
Returns `true` if the specified number is a Not-a-Number (NaN) value, `false` otherwise.
API Note:
This method corresponds to the isNaN operation defined in IEEE 754.
Parameters:
`v` - the value to be tested.
Returns:
`true` if the value of the argument is NaN; `false` otherwise.
• ### isInfinite

public static boolean isInfinite(double v)
Returns `true` if the specified number is infinitely large in magnitude, `false` otherwise.
API Note:
This method corresponds to the isInfinite operation defined in IEEE 754.
Parameters:
`v` - the value to be tested.
Returns:
`true` if the value of the argument is positive infinity or negative infinity; `false` otherwise.
• ### isFinite

public static boolean isFinite(double d)
Returns `true` if the argument is a finite floating-point value; returns `false` otherwise (for NaN and infinity arguments).
API Note:
This method corresponds to the isFinite operation defined in IEEE 754.
Parameters:
`d` - the `double` value to be tested
Returns:
`true` if the argument is a finite floating-point value, `false` otherwise.
Since:
1.8
• ### isNaN

public boolean isNaN()
Returns `true` if this `Double` value is a Not-a-Number (NaN), `false` otherwise.
Returns:
`true` if the value represented by this object is NaN; `false` otherwise.
• ### isInfinite

public boolean isInfinite()
Returns `true` if this `Double` value is infinitely large in magnitude, `false` otherwise.
Returns:
`true` if the value represented by this object is positive infinity or negative infinity; `false` otherwise.
• ### toString

public String toString()
Returns a string representation of this `Double` object. The primitive `double` value represented by this object is converted to a string exactly as if by the method `toString` of one argument.
Overrides:
`toString` in class `Object`
Returns:
a `String` representation of this object.
• ### byteValue

public byte byteValue()
Returns the value of this `Double` as a `byte` after a narrowing primitive conversion.
Overrides:
`byteValue` in class `Number`
Returns:
the `double` value represented by this object converted to type `byte`
See Java Language Specification:
5.1.3 Narrowing Primitive Conversion
Since:
1.1
• ### shortValue

public short shortValue()
Returns the value of this `Double` as a `short` after a narrowing primitive conversion.
Overrides:
`shortValue` in class `Number`
Returns:
the `double` value represented by this object converted to type `short`
See Java Language Specification:
5.1.3 Narrowing Primitive Conversion
Since:
1.1
• ### intValue

public int intValue()
Returns the value of this `Double` as an `int` after a narrowing primitive conversion.
Specified by:
`intValue` in class `Number`
API Note:
This method corresponds to the convertToIntegerTowardZero operation defined in IEEE 754.
Returns:
the `double` value represented by this object converted to type `int`
See Java Language Specification:
5.1.3 Narrowing Primitive Conversion
• ### longValue

public long longValue()
Returns the value of this `Double` as a `long` after a narrowing primitive conversion.
Specified by:
`longValue` in class `Number`
API Note:
This method corresponds to the convertToIntegerTowardZero operation defined in IEEE 754.
Returns:
the `double` value represented by this object converted to type `long`
See Java Language Specification:
5.1.3 Narrowing Primitive Conversion
• ### floatValue

public float floatValue()
Returns the value of this `Double` as a `float` after a narrowing primitive conversion.
Specified by:
`floatValue` in class `Number`
API Note:
This method corresponds to the convertFormat operation defined in IEEE 754.
Returns:
the `double` value represented by this object converted to type `float`
See Java Language Specification:
5.1.3 Narrowing Primitive Conversion
Since:
1.0
• ### doubleValue

public double doubleValue()
Returns the `double` value of this `Double` object.
Specified by:
`doubleValue` in class `Number`
Returns:
the `double` value represented by this object
• ### hashCode

public int hashCode()
Returns a hash code for this `Double` object. The result is the exclusive OR of the two halves of the `long` integer bit representation, exactly as produced by the method `doubleToLongBits(double)`, of the primitive `double` value represented by this `Double` object. That is, the hash code is the value of the expression:
`(int)(v^(v>>>32))`
where `v` is defined by:
`long v = Double.doubleToLongBits(this.doubleValue());`
Overrides:
`hashCode` in class `Object`
Returns:
a `hash code` value for this object.
• ### hashCode

public static int hashCode(double value)
Returns a hash code for a `double` value; compatible with `Double.hashCode()`.
Parameters:
`value` - the value to hash
Returns:
a hash code value for a `double` value.
Since:
1.8
• ### equals

public boolean equals(Object obj)
Compares this object against the specified object. The result is `true` if and only if the argument is not `null` and is a `Double` object that represents a `double` that has the same value as the `double` represented by this object. For this purpose, two `double` values are considered to be the same if and only if the method `doubleToLongBits(double)` returns the identical `long` value when applied to each.
Overrides:
`equals` in class `Object`
API Note:
This method is defined in terms of `doubleToLongBits(double)` rather than the `==` operator on `double` values since the `==` operator does not define an equivalence relation and to satisfy the equals contract an equivalence relation must be implemented; see this discussion for details of floating-point equality and equivalence.
Parameters:
`obj` - the reference object with which to compare.
Returns:
`true` if this object is the same as the obj argument; `false` otherwise.
See Java Language Specification:
15.21.1 Numerical Equality Operators == and !=
• ### doubleToLongBits

public static long doubleToLongBits(double value)
Returns a representation of the specified floating-point value according to the IEEE 754 floating-point "double format" bit layout.

Bit 63 (the bit that is selected by the mask `0x8000000000000000L`) represents the sign of the floating-point number. Bits 62-52 (the bits that are selected by the mask `0x7ff0000000000000L`) represent the exponent. Bits 51-0 (the bits that are selected by the mask `0x000fffffffffffffL`) represent the significand (sometimes called the mantissa) of the floating-point number.

If the argument is positive infinity, the result is `0x7ff0000000000000L`.

If the argument is negative infinity, the result is `0xfff0000000000000L`.

If the argument is NaN, the result is `0x7ff8000000000000L`.

In all cases, the result is a `long` integer that, when given to the `longBitsToDouble(long)` method, will produce a floating-point value the same as the argument to `doubleToLongBits` (except all NaN values are collapsed to a single "canonical" NaN value).

Parameters:
`value` - a `double` precision floating-point number.
Returns:
the bits that represent the floating-point number.
• ### doubleToRawLongBits

public static long doubleToRawLongBits(double value)
Returns a representation of the specified floating-point value according to the IEEE 754 floating-point "double format" bit layout, preserving Not-a-Number (NaN) values.

Bit 63 (the bit that is selected by the mask `0x8000000000000000L`) represents the sign of the floating-point number. Bits 62-52 (the bits that are selected by the mask `0x7ff0000000000000L`) represent the exponent. Bits 51-0 (the bits that are selected by the mask `0x000fffffffffffffL`) represent the significand (sometimes called the mantissa) of the floating-point number.

If the argument is positive infinity, the result is `0x7ff0000000000000L`.

If the argument is negative infinity, the result is `0xfff0000000000000L`.

If the argument is NaN, the result is the `long` integer representing the actual NaN value. Unlike the `doubleToLongBits` method, `doubleToRawLongBits` does not collapse all the bit patterns encoding a NaN to a single "canonical" NaN value.

In all cases, the result is a `long` integer that, when given to the `longBitsToDouble(long)` method, will produce a floating-point value the same as the argument to `doubleToRawLongBits`.

Parameters:
`value` - a `double` precision floating-point number.
Returns:
the bits that represent the floating-point number.
Since:
1.3
• ### longBitsToDouble

public static double longBitsToDouble(long bits)
Returns the `double` value corresponding to a given bit representation. The argument is considered to be a representation of a floating-point value according to the IEEE 754 floating-point "double format" bit layout.

If the argument is `0x7ff0000000000000L`, the result is positive infinity.

If the argument is `0xfff0000000000000L`, the result is negative infinity.

If the argument is any value in the range `0x7ff0000000000001L` through `0x7fffffffffffffffL` or in the range `0xfff0000000000001L` through `0xffffffffffffffffL`, the result is a NaN. No IEEE 754 floating-point operation provided by Java can distinguish between two NaN values of the same type with different bit patterns. Distinct values of NaN are only distinguishable by use of the `Double.doubleToRawLongBits` method.

In all other cases, let s, e, and m be three values that can be computed from the argument:

``````int s = ((bits >> 63) == 0) ? 1 : -1;
int e = (int)((bits >> 52) & 0x7ffL);
long m = (e == 0) ?
(bits & 0xfffffffffffffL) << 1 :
(bits & 0xfffffffffffffL) | 0x10000000000000L;
``````
Then the floating-point result equals the value of the mathematical expression s·m·2e-1075.

Note that this method may not be able to return a `double` NaN with exactly same bit pattern as the `long` argument. IEEE 754 distinguishes between two kinds of NaNs, quiet NaNs and signaling NaNs. The differences between the two kinds of NaN are generally not visible in Java. Arithmetic operations on signaling NaNs turn them into quiet NaNs with a different, but often similar, bit pattern. However, on some processors merely copying a signaling NaN also performs that conversion. In particular, copying a signaling NaN to return it to the calling method may perform this conversion. So `longBitsToDouble` may not be able to return a `double` with a signaling NaN bit pattern. Consequently, for some `long` values, `doubleToRawLongBits(longBitsToDouble(start))` may not equal `start`. Moreover, which particular bit patterns represent signaling NaNs is platform dependent; although all NaN bit patterns, quiet or signaling, must be in the NaN range identified above.

Parameters:
`bits` - any `long` integer.
Returns:
the `double` floating-point value with the same bit pattern.
• ### compareTo

public int compareTo(Double anotherDouble)
Compares two `Double` objects numerically. This method imposes a total order on `Double` objects with two differences compared to the incomplete order defined by the Java language numerical comparison operators (```<, <=, ==, >=, >```) on `double` values.
• A NaN is unordered with respect to other values and unequal to itself under the comparison operators. This method chooses to define ``` Double.NaN``` to be equal to itself and greater than all other `double` values (including ``` Double.POSITIVE_INFINITY```).
• Positive zero and negative zero compare equal numerically, but are distinct and distinguishable values. This method chooses to define positive zero (`+0.0d`), to be greater than negative zero (`-0.0d`).
This ensures that the natural ordering of `Double` objects imposed by this method is consistent with equals; see this discussion for details of floating-point comparison and ordering.
Specified by:
`compareTo` in interface `Comparable<Double>`
Parameters:
`anotherDouble` - the `Double` to be compared.
Returns:
the value `0` if `anotherDouble` is numerically equal to this `Double`; a value less than `0` if this `Double` is numerically less than `anotherDouble`; and a value greater than `0` if this `Double` is numerically greater than `anotherDouble`.
See Java Language Specification:
15.20.1 Numerical Comparison Operators `<`, `<=`, `>`, and `>=`
Since:
1.2
• ### compare

public static int compare(double d1, double d2)
Compares the two specified `double` values. The sign of the integer value returned is the same as that of the integer that would be returned by the call:
```    Double.valueOf(d1).compareTo(Double.valueOf(d2))
```
Parameters:
`d1` - the first `double` to compare
`d2` - the second `double` to compare
Returns:
the value `0` if `d1` is numerically equal to `d2`; a value less than `0` if `d1` is numerically less than `d2`; and a value greater than `0` if `d1` is numerically greater than `d2`.
Since:
1.4
• ### sum

public static double sum(double a, double b)
Adds two `double` values together as per the + operator.
API Note:
This method corresponds to the addition operation defined in IEEE 754.
Parameters:
`a` - the first operand
`b` - the second operand
Returns:
the sum of `a` and `b`
See Java Language Specification:
4.2.4 Floating-Point Operations
Since:
1.8
• ### max

public static double max(double a, double b)
Returns the greater of two `double` values as if by calling `Math.max`.
API Note:
This method corresponds to the maximum operation defined in IEEE 754.
Parameters:
`a` - the first operand
`b` - the second operand
Returns:
the greater of `a` and `b`
Since:
1.8
• ### min

public static double min(double a, double b)
Returns the smaller of two `double` values as if by calling `Math.min`.
API Note:
This method corresponds to the minimum operation defined in IEEE 754.
Parameters:
`a` - the first operand
`b` - the second operand
Returns:
the smaller of `a` and `b`.
Since:
1.8
• ### describeConstable

public  describeConstable()
Returns an `Optional` containing the nominal descriptor for this instance, which is the instance itself.
Specified by:
`describeConstable` in interface `Constable`
Returns:
an `Optional` describing the Double instance
Since:
12
• ### resolveConstantDesc

public Double resolveConstantDesc(MethodHandles.Lookup lookup)
Resolves this instance as a `ConstantDesc`, the result of which is the instance itself.
Specified by:
`resolveConstantDesc` in interface `ConstantDesc`
Parameters:
`lookup` - ignored
Returns:
the Double instance
Since:
12