Quelle Double.java

Sprache: JAVA

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package java.lang;

import java.lang.invoke.MethodHandles;
import java.lang.constant.Constable;
import java.lang.constant.ConstantDesc;
import java.util.Optional;

import jdk.internal.math.FloatingDecimal;
import jdk.internal.math.DoubleConsts;
import jdk.internal.math.DoubleToDecimal;
import jdk.internal.vm.annotation.IntrinsicCandidate;

/**
* The {@code Double} class wraps a value of the primitive type
* {@code double} in an object. An object of type
* {@code Double} contains a single field whose type is
* {@code double}.
*
* In addition, this class provides several methods for converting a
* {@code double} to a {@code String} and a
* {@code String} to a {@code double}, as well as other
* constants and methods useful when dealing with a
* {@code double}.
*
* This is a <a href="{@docRoot}/java.base/java/lang/doc-files/ValueBased.html">value-based</a>
* class; programmers should treat instances that are
* {@linkplain #equals(Object) equal} as interchangeable and should not
* use instances for synchronization, or unpredictable behavior may
* occur. For example, in a future release, synchronization may fail.
*
* <h2><a id=equivalenceRelation>Floating-point Equality, Equivalence,
* and Comparison</a></h2>
*
* IEEE 754 floating-point values include finite nonzero values,
* signed zeros ({@code +0.0} and {@code -0.0}), signed infinities
* ({@linkplain Double#POSITIVE_INFINITY positive infinity} and
* {@linkplain Double#NEGATIVE_INFINITY negative infinity}), and
* {@linkplain Double#NaN 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 {@link Object#equals 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 {@code ==} operation on floating-point
* values is not an equivalence relation. Despite not
* defining an equivalence relation, the semantics of the IEEE 754
* {@code ==} 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 {@code
* ==} on floating-point values:
*
* <ul>
*
* <li>If {@code v1} and {@code v2} are both NaN, then {@code v1
* == v2} has the value {@code false}. Therefore, for two NaN
* arguments the reflexive property of an equivalence
* relation is not satisfied by the {@code ==} operator.
*
* <li>If {@code v1} represents {@code +0.0} while {@code v2}
* represents {@code -0.0}, or vice versa, then {@code v1 == v2} has
* the value {@code true} even though {@code +0.0} and {@code -0.0}
* are distinguishable under various floating-point operations. For
* example, {@code 1.0/+0.0} evaluates to positive infinity while
* {@code 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, {@code +0.0} and {@code -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.
*
* </ul>
*
* For ordered comparisons using the built-in comparison operators
* ({@code <}, {@code <=}, 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 {@code equals} and
* {@code compareTo} methods, those methods cannot simply be wrappers
* around {@code ==} or ordered comparison operations. Instead, {@link
* Double#equals equals} uses <a href=#repEquivalence> representation
* equivalence</a>, defining NaN arguments to be equal to each other,
* restoring reflexivity, and defining {@code +0.0} to not be
* equal to {@code -0.0}. For comparisons, {@link Double#compareTo
* compareTo} defines a total order where {@code -0.0} is less than
* {@code +0.0} and where a NaN is equal to itself and considered
* greater than positive infinity.
*
* The operational semantics of {@code equals} and {@code
* compareTo} are expressed in terms of {@linkplain #doubleToLongBits
* bit-wise converting} the floating-point values to integral values.
*
* The natural ordering implemented by {@link #compareTo
* compareTo} is {@linkplain Comparable consistent with equals}. That
* is, two objects are reported as equal by {@code equals} if and only
* if {@code compareTo} on those objects returns zero.
*
* The adjusted behaviors defined for {@code equals} and {@code
* compareTo} allow instances of wrapper classes to work properly with
* conventional data structures. For example, defining NaN
* values to be {@code equals} to one another allows NaN to be used as
* an element of a {@link java.util.HashSet HashSet} or as the key of
* a {@link java.util.HashMap HashMap}. Similarly, defining {@code
* compareTo} as a total ordering, including {@code +0.0}, {@code
* -0.0}, and NaN, allows instances of wrapper classes to be used as
* elements of a {@link java.util.SortedSet SortedSet} or as keys of a
* {@link java.util.SortedMap SortedMap}.
*
* Comparing numerical equality to various useful equivalence
* relations that can be defined over floating-point values:
*
* <dl>
* <dt><a id=fpNumericalEq>numerical equality</a> ({@code ==}
* operator): (Not an equivalence relation)</dt>
* <dd>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, {@code +0.0} and {@code -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.
* </dd>
*
* <dt>bit-wise equivalence:</dt>
* <dd>The bits of the two floating-point values are the same. This
* equivalence relation for {@code double} values {@code a} and {@code
* b} is implemented by the expression
* {@code Double.doubleTo}<code>Raw</code>{@code LongBits(a) == Double.doubleTo}<code>Raw</code>{@code LongBits(b)} 
* Under this relation, {@code +0.0} and {@code -0.0} are
* distinguished from each other and every bit pattern encoding a NaN
* is distinguished from every other bit pattern encoding a NaN.
* </dd>
*
* <dt><a id=repEquivalence>representation equivalence</a>:</dt>
* <dd>The two floating-point values represent the same IEEE 754
* datum. In particular, for {@linkplain #isFinite(double)
* finite} values, the sign, {@linkplain Math#getExponent(double)
* exponent}, and significand components of the floating-point values
* are the same. Under this relation:
* <ul>
* <li> {@code +0.0} and {@code -0.0} are distinguished from each other.
* <li> every bit pattern encoding a NaN is considered equivalent to each other
* <li> positive infinity is equivalent to positive infinity; negative
* infinity is equivalent to negative infinity.
* </ul>
* Expressions implementing this equivalence relation include:
* <ul>
* <li>{@code Double.doubleToLongBits(a) == Double.doubleToLongBits(b)}
* <li>{@code Double.valueOf(a).equals(Double.valueOf(b))}
* <li>{@code Double.compare(a, b) == 0}
* </ul>
* Note that representation equivalence is often an appropriate notion
* of equivalence to test the behavior of {@linkplain StrictMath math
* libraries}.
* </dd>
* </dl>
*
* For two binary floating-point values {@code a} and {@code b}, if
* neither of {@code a} and {@code b} is zero or NaN, then the three
* relations numerical equality, bit-wise equivalence, and
* representation equivalence of {@code a} and {@code b} have the same
* {@code true}/{@code false} value. In other words, for binary
* floating-point values, the three relations only differ if at least
* one argument is zero or NaN.
*
* @jls 4.2.3 Floating-Point Types, Formats, and Values
* @jls 4.2.4. Floating-Point Operations
* @jls 15.21.1 Numerical Equality Operators == and !=
* @jls 15.20.1 Numerical Comparison Operators {@code <}, {@code <=}, {@code >}, and {@code >=}
*
* @see <a href="https://standards.ieee.org/ieee/754/6210/">
* <cite>IEEE Standard for Floating-Point Arithmetic</cite></a>
*
* @author Lee Boynton
* @author Arthur van Hoff
* @author Joseph D. Darcy
* @since 1.0
*/
@jdk.internal.ValueBased
public final class Double extends Number
 implements Comparable<Double>, Constable, ConstantDesc {
 /**
 * A constant holding the positive infinity of type
 * {@code double}. It is equal to the value returned by
 * {@code Double.longBitsToDouble(0x7ff0000000000000L)}.
 */
 public static final double POSITIVE_INFINITY = 1.0 / 0.0;

 /**
 * A constant holding the negative infinity of type
 * {@code double}. It is equal to the value returned by
 * {@code Double.longBitsToDouble(0xfff0000000000000L)}.
 */
 public static final double NEGATIVE_INFINITY = -1.0 / 0.0;

 /**
 * A constant holding a Not-a-Number (NaN) value of type
 * {@code double}. It is equivalent to the value returned by
 * {@code Double.longBitsToDouble(0x7ff8000000000000L)}.
 */
 public static final double NaN = 0.0d / 0.0;

 /**
 * A constant holding the largest positive finite value of type
 * {@code double},
 * (2-2-52)·21023. It is equal to
 * the hexadecimal floating-point literal
 * {@code 0x1.fffffffffffffP+1023} and also equal to
 * {@code Double.longBitsToDouble(0x7fefffffffffffffL)}.
 */
 public static final double MAX_VALUE = 0x1.fffffffffffffP+1023; // 1.7976931348623157e+308

 /**
 * A constant holding the smallest positive normal value of type
 * {@code double}, 2-1022. It is equal to the
 * hexadecimal floating-point literal {@code 0x1.0p-1022} and also
 * equal to {@code Double.longBitsToDouble(0x0010000000000000L)}.
 *
 * @since 1.6
 */
 public static final double MIN_NORMAL = 0x1.0p-1022; // 2.2250738585072014E-308

 /**
 * A constant holding the smallest positive nonzero value of type
 * {@code double}, 2-1074. It is equal to the
 * hexadecimal floating-point literal
 * {@code 0x0.0000000000001P-1022} and also equal to
 * {@code Double.longBitsToDouble(0x1L)}.
 */
 public static final double MIN_VALUE = 0x0.0000000000001P-1022; // 4.9e-324

 /**
 * The number of bits used to represent a {@code double} value.
 *
 * @since 1.5
 */
 public static final int SIZE = 64;

 /**
 * The number of bits in the significand of a {@code double} value.
 * This is the parameter N in section {@jls 4.2.3} of
 * <cite>The Java Language Specification</cite>.
 *
 * @since 19
 */
 public static final int PRECISION = 53;

 /**
 * Maximum exponent a finite {@code double} variable may have.
 * It is equal to the value returned by
 * {@code Math.getExponent(Double.MAX_VALUE)}.
 *
 * @since 1.6
 */
 public static final int MAX_EXPONENT = (1 << (SIZE - PRECISION - 1)) - 1; // 1023

 /**
 * Minimum exponent a normalized {@code double} variable may
 * have. It is equal to the value returned by
 * {@code Math.getExponent(Double.MIN_NORMAL)}.
 *
 * @since 1.6
 */
 public static final int MIN_EXPONENT = 1 - MAX_EXPONENT; // -1022

 /**
 * The number of bytes used to represent a {@code double} value.
 *
 * @since 1.8
 */
 public static final int BYTES = SIZE / Byte.SIZE;

 /**
 * The {@code Class} instance representing the primitive type
 * {@code double}.
 *
 * @since 1.1
 */
 @SuppressWarnings("unchecked")
 public static final Class<Double> TYPE = (Class<Double>) Class.getPrimitiveClass("double");

 /**
 * Returns a string representation of the {@code double}
 * argument. All characters mentioned below are ASCII characters.
 * <ul>
 * <li>If the argument is NaN, the result is the string
 * "{@code NaN}".
 * <li>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 '{@code -}'
 * ({@code '\u005Cu002D'}); if the sign is positive, no sign character
 * appears in the result. As for the magnitude m:
 * <ul>
 * <li>If m is infinity, it is represented by the characters
 * {@code "Infinity"}; thus, positive infinity produces the result
 * {@code "Infinity"} and negative infinity produces the result
 * {@code "-Infinity"}.
 *
 * <li>If m is zero, it is represented by the characters
 * {@code "0.0"}; thus, negative zero produces the result
 * {@code "-0.0"} and positive zero produces the result
 * {@code "0.0"}.
 *
 * <li> Otherwise m is positive and finite.
 * It is converted to a string in two stages:
 * <ul>
 * <li> 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.
 * <li> Formatting as a string:
 * The decimal dm is formatted as a string,
 * either in plain or in computerized scientific notation,
 * depending on its value.
 * </ul>
 * </ul>
 * </ul>
 *
 * 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-1 ≤ s < 10n.
 *
 * The decimal dm for a finite positive m
 * is defined as follows:
 * <ul>
 * <li>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.
 * <li>Let p be the minimal length over all decimals in R.
 * <li>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.
 * <li>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.
 * </ul>
 *
 * 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
 * s1…sn
 * be the usual decimal expansion of s.
 * Note that s1 ≠ 0
 * and sn ≠ 0.
 * Below, the decimal point {@code '.'} is {@code '\u005Cu002E'}
 * and the exponent indicator {@code 'E'} is {@code '\u005Cu0045'}.
 * <ul>
 * <li>Case -3 ≤ e < 0:
 * dm is formatted as
 * <code>0.0</code>…<code>0</code>s1…sn,
 * where there are exactly -(n + i) zeroes between
 * the decimal point and s1.
 * For example, 123 × 10-4 is formatted as
 * {@code 0.0123}.
 * <li>Case 0 ≤ e < 7:
 * <ul>
 * <li>Subcase i ≥ 0:
 * dm is formatted as
 * s1…sn<code>0</code>…<code>0.0</code>,
 * where there are exactly i zeroes
 * between sn and the decimal point.
 * For example, 123 × 102 is formatted as
 * {@code 12300.0}.
 * <li>Subcase i < 0:
 * dm is formatted as
 * s1…sn+i<code>.</code>sn+i+1…sn,
 * where there are exactly -i digits to the right of
 * the decimal point.
 * For example, 123 × 10-1 is formatted as
 * {@code 12.3}.
 * </ul>
 * <li>Case e < -3 or e ≥ 7:
 * computerized scientific notation is used to format
 * dm.
 * Here e is formatted as by {@link Integer#toString(int)}.
 * <ul>
 * <li>Subcase n = 1:
 * dm is formatted as
 * s1<code>.0E</code>e.
 * For example, 1 × 1023 is formatted as
 * {@code 1.0E23}.
 * <li>Subcase n > 1:
 * dm is formatted as
 * s1<code>.</code>s2…sn<code>E</code>e.
 * For example, 123 × 10-21 is formatted as
 * {@code 1.23E-19}.
 * </ul>
 * </ul>
 *
 * To create localized string representations of a floating-point
 * value, use subclasses of {@link java.text.NumberFormat}.
 *
 * @param d the {@code double} to be converted.
 * @return a string representation of the argument.
 */
 public static String toString(double d) {
 return DoubleToDecimal.toString(d);
 }

 /**
 * Returns a hexadecimal string representation of the
 * {@code double} argument. All characters mentioned below
 * are ASCII characters.
 *
 * <ul>
 * <li>If the argument is NaN, the result is the string
 * "{@code NaN}".
 * <li>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 '{@code -}'
 * ({@code '\u005Cu002D'}); if the sign is positive, no sign
 * character appears in the result. As for the magnitude m:
 *
 * <ul>
 * <li>If m is infinity, it is represented by the string
 * {@code "Infinity"}; thus, positive infinity produces the
 * result {@code "Infinity"} and negative infinity produces
 * the result {@code "-Infinity"}.
 *
 * <li>If m is zero, it is represented by the string
 * {@code "0x0.0p0"}; thus, negative zero produces the result
 * {@code "-0x0.0p0"} and positive zero produces the result
 * {@code "0x0.0p0"}.
 *
 * <li>If m is a {@code double} value with a
 * normalized representation, substrings are used to represent the
 * significand and exponent fields. The significand is
 * represented by the characters {@code "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 {@code "p"} followed
 * by a decimal string of the unbiased exponent as if produced by
 * a call to {@link Integer#toString(int) Integer.toString} on the
 * exponent value.
 *
 * <li>If m is a {@code double} value with a subnormal
 * representation, the significand is represented by the
 * characters {@code "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
 * {@code "p-1022"}. Note that there must be at
 * least one nonzero digit in a subnormal significand.
 *
 * </ul>
 *
 * </ul>
 *
 * <table class="striped">
 * <caption>Examples</caption>
 * <thead>
 * <tr><th scope="col">Floating-point Value</th><th scope="col">Hexadecimal String</th>
 * </thead>
 * <tbody style="text-align:right">
 * <tr><th scope="row">{@code 1.0}</th> <td>{@code 0x1.0p0}</td>
 * <tr><th scope="row">{@code -1.0}</th> <td>{@code -0x1.0p0}</td>
 * <tr><th scope="row">{@code 2.0}</th> <td>{@code 0x1.0p1}</td>
 * <tr><th scope="row">{@code 3.0}</th> <td>{@code 0x1.8p1}</td>
 * <tr><th scope="row">{@code 0.5}</th> <td>{@code 0x1.0p-1}</td>
 * <tr><th scope="row">{@code 0.25}</th> <td>{@code 0x1.0p-2}</td>
 * <tr><th scope="row">{@code Double.MAX_VALUE}</th>
 * <td>{@code 0x1.fffffffffffffp1023}</td>
 * <tr><th scope="row">{@code Minimum Normal Value}</th>
 * <td>{@code 0x1.0p-1022}</td>
 * <tr><th scope="row">{@code Maximum Subnormal Value}</th>
 * <td>{@code 0x0.fffffffffffffp-1022}</td>
 * <tr><th scope="row">{@code Double.MIN_VALUE}</th>
 * <td>{@code 0x0.0000000000001p-1022}</td>
 * </tbody>
 * </table>
 * @param d the {@code double} to be converted.
 * @return a hex string representation of the argument.
 * @since 1.5
 * @author Joseph D. Darcy
 */
 public static String toHexString(double d) {
 /*
 * Modeled after the "a" conversion specifier in C99, section
 * 7.19.6.1; however, the output of this method is more
 * tightly specified.
 */
 if (!isFinite(d) )
 // For infinity and NaN, use the decimal output.
 return Double.toString(d);
 else {
 // Initialized to maximum size of output.
 StringBuilder answer = new StringBuilder(24);

 if (Math.copySign(1.0, d) == -1.0) // value is negative,
 answer.append("-"); // so append sign info

 answer.append("0x");

 d = Math.abs(d);

 if(d == 0.0) {
 answer.append("0.0p0");
 } else {
 boolean subnormal = (d < Double.MIN_NORMAL);

 // Isolate significand bits and OR in a high-order bit
 // so that the string representation has a known
 // length.
 long signifBits = (Double.doubleToLongBits(d)
 & DoubleConsts.SIGNIF_BIT_MASK) |
 0x1000000000000000L;

 // Subnormal values have a 0 implicit bit; normal
 // values have a 1 implicit bit.
 answer.append(subnormal ? "0." : "1.");

 // Isolate the low-order 13 digits of the hex
 // representation. If all the digits are zero,
 // replace with a single 0; otherwise, remove all
 // trailing zeros.
 String signif = Long.toHexString(signifBits).substring(3,16);
 answer.append(signif.equals("0000000000000") ? // 13 zeros
 "0":
 signif.replaceFirst("0{1,12}$", ""));

 answer.append('p');
 // If the value is subnormal, use the E_min exponent
 // value for double; otherwise, extract and report d's
 // exponent (the representation of a subnormal uses
 // E_min -1).
 answer.append(subnormal ?
 Double.MIN_EXPONENT:
 Math.getExponent(d));
 }
 return answer.toString();
 }
 }

 /**
 * Returns a {@code Double} object holding the
 * {@code double} value represented by the argument string
 * {@code s}.
 *
 * If {@code s} is {@code null}, then a
 * {@code NullPointerException} is thrown.
 *
 * Leading and trailing whitespace characters in {@code s}
 * are ignored. Whitespace is removed as if by the {@link
 * String#trim} method; that is, both ASCII space and control
 * characters are removed. The rest of {@code s} should
 * constitute a FloatValue as described by the lexical
 * syntax rules:
 *
 * <blockquote>
 * <dl>
 * <dt>FloatValue:
 * <dd>Signopt {@code NaN}
 * <dd>Signopt {@code Infinity}
 * <dd>Signopt FloatingPointLiteral
 * <dd>Signopt HexFloatingPointLiteral
 * <dd>SignedInteger
 * </dl>
 *
 * <dl>
 * <dt>HexFloatingPointLiteral:
 * <dd> HexSignificand BinaryExponent FloatTypeSuffixopt
 * </dl>
 *
 * <dl>
 * <dt>HexSignificand:
 * <dd>HexNumeral
 * <dd>HexNumeral {@code .}
 * <dd>{@code 0x} HexDigitsopt
 * {@code .} HexDigits
 * <dd>{@code 0X} HexDigitsopt
 * {@code .} HexDigits
 * </dl>
 *
 * <dl>
 * <dt>BinaryExponent:
 * <dd>BinaryExponentIndicator SignedInteger
 * </dl>
 *
 * <dl>
 * <dt>BinaryExponentIndicator:
 * <dd>{@code p}
 * <dd>{@code P}
 * </dl>
 *
 * </blockquote>
 *
 * where Sign, FloatingPointLiteral,
 * HexNumeral, HexDigits, SignedInteger and
 * FloatTypeSuffix are as defined in the lexical structure
 * sections of
 * <cite>The Java Language Specification</cite>,
 * except that underscores are not accepted between digits.
 * If {@code s} does not have the form of
 * a FloatValue, then a {@code NumberFormatException}
 * is thrown. Otherwise, {@code 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 {@code 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 {@code s} is large
 * enough in magnitude (greater than or equal to ({@link
 * #MAX_VALUE} + {@link Math#ulp(double) ulp(MAX_VALUE)}/2),
 * rounding to {@code double} will result in an infinity and if the
 * exact value of {@code s} is small enough in magnitude (less
 * than or equal to {@link #MIN_VALUE}/2), rounding to float will
 * result in a zero.
 *
 * Finally, after rounding a {@code Double} object representing
 * this {@code double} value is returned.
 *
 * To interpret localized string representations of a
 * floating-point value, use subclasses of {@link
 * java.text.NumberFormat}.
 *
 * Note that trailing format specifiers, specifiers that
 * determine the type of a floating-point literal
 * ({@code 1.0f} is a {@code float} value;
 * {@code 1.0d} is a {@code 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 {@code float} followed
 * by {@code float} to {@code double}, is not
 * equivalent to converting a string directly to
 * {@code double}. For example, the {@code float}
 * literal {@code 0.1f} is equal to the {@code double}
 * value {@code 0.10000000149011612}; the {@code float}
 * literal {@code 0.1f} represents a different numerical
 * value than the {@code double} literal
 * {@code 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 {@code NumberFormatException} be thrown, the regular
 * expression below can be used to screen the input string:
 *
 * {@snippet lang="java" :
 * 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 =
 * ("[\\x00-\\x20]*"+ // Optional leading "whitespace"
 * "[+-]?(" + // 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+")?)|"+
 *
 * // Hexadecimal strings
 * "((" +
 * // 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"
 * // @link region substring="Pattern.matches" target ="java.util.regex.Pattern#matches"
 * if (Pattern.matches(fpRegex, myString))
 * Double.valueOf(myString); // Will not throw NumberFormatException
 * // @end
 * else {
 * // Perform suitable alternative action
 * }
 * }
 *
 * @param s the string to be parsed.
 * @return a {@code Double} object holding the value
 * represented by the {@code String} argument.
 * @throws NumberFormatException if the string does not contain a
 * parsable number.
 */
 public static Double valueOf(String s) throws NumberFormatException {
 return new Double(parseDouble(s));
 }

 /**
 * Returns a {@code Double} instance representing the specified
 * {@code double} value.
 * If a new {@code Double} instance is not required, this method
 * should generally be used in preference to the constructor
 * {@link #Double(double)}, as this method is likely to yield
 * significantly better space and time performance by caching
 * frequently requested values.
 *
 * @param d a double value.
 * @return a {@code Double} instance representing {@code d}.
 * @since 1.5
 */
 @IntrinsicCandidate
 public static Double valueOf(double d) {
 return new Double(d);
 }

 /**
 * Returns a new {@code double} initialized to the value
 * represented by the specified {@code String}, as performed
 * by the {@code valueOf} method of class
 * {@code Double}.
 *
 * @param s the string to be parsed.
 * @return the {@code double} value represented by the string
 * argument.
 * @throws NullPointerException if the string is null
 * @throws NumberFormatException if the string does not contain
 * a parsable {@code double}.
 * @see java.lang.Double#valueOf(String)
 * @since 1.2
 */
 public static double parseDouble(String s) throws NumberFormatException {
 return FloatingDecimal.parseDouble(s);
 }

 /**
 * Returns {@code true} if the specified number is a
 * Not-a-Number (NaN) value, {@code false} otherwise.
 *
 * @apiNote
 * This method corresponds to the isNaN operation defined in IEEE
 * 754.
 *
 * @param v the value to be tested.
 * @return {@code true} if the value of the argument is NaN;
 * {@code false} otherwise.
 */
 public static boolean isNaN(double v) {
 return (v != v);
 }

 /**
 * Returns {@code true} if the specified number is infinitely
 * large in magnitude, {@code false} otherwise.
 *
 * @apiNote
 * This method corresponds to the isInfinite operation defined in
 * IEEE 754.
 *
 * @param v the value to be tested.
 * @return {@code true} if the value of the argument is positive
 * infinity or negative infinity; {@code false} otherwise.
 */
 @IntrinsicCandidate
 public static boolean isInfinite(double v) {
 return Math.abs(v) > MAX_VALUE;
 }

 /**
 * Returns {@code true} if the argument is a finite floating-point
 * value; returns {@code false} otherwise (for NaN and infinity
 * arguments).
 *
 * @apiNote
 * This method corresponds to the isFinite operation defined in
 * IEEE 754.
 *
 * @param d the {@code double} value to be tested
 * @return {@code true} if the argument is a finite
 * floating-point value, {@code false} otherwise.
 * @since 1.8
 */
 @IntrinsicCandidate
 public static boolean isFinite(double d) {
 return Math.abs(d) <= Double.MAX_VALUE;
 }

 /**
 * The value of the Double.
 *
 * @serial
 */
 private final double value;

 /**
 * Constructs a newly allocated {@code Double} object that
 * represents the primitive {@code double} argument.
 *
 * @param value the value to be represented by the {@code Double}.
 *
 * @deprecated
 * It is rarely appropriate to use this constructor. The static factory
 * {@link #valueOf(double)} is generally a better choice, as it is
 * likely to yield significantly better space and time performance.
 */
 @Deprecated(since="9", forRemoval = true)
 public Double(double value) {
 this.value = value;
 }

 /**
 * Constructs a newly allocated {@code Double} object that
 * represents the floating-point value of type {@code double}
 * represented by the string. The string is converted to a
 * {@code double} value as if by the {@code valueOf} method.
 *
 * @param s a string to be converted to a {@code Double}.
 * @throws NumberFormatException if the string does not contain a
 * parsable number.
 *
 * @deprecated
 * It is rarely appropriate to use this constructor.
 * Use {@link #parseDouble(String)} to convert a string to a
 * {@code double} primitive, or use {@link #valueOf(String)}
 * to convert a string to a {@code Double} object.
 */
 @Deprecated(since="9", forRemoval = true)
 public Double(String s) throws NumberFormatException {
 value = parseDouble(s);
 }

 /**
 * Returns {@code true} if this {@code Double} value is
 * a Not-a-Number (NaN), {@code false} otherwise.
 *
 * @return {@code true} if the value represented by this object is
 * NaN; {@code false} otherwise.
 */
 public boolean isNaN() {
 return isNaN(value);
 }

 /**
 * Returns {@code true} if this {@code Double} value is
 * infinitely large in magnitude, {@code false} otherwise.
 *
 * @return {@code true} if the value represented by this object is
 * positive infinity or negative infinity;
 * {@code false} otherwise.
 */
 public boolean isInfinite() {
 return isInfinite(value);
 }

 /**
 * Returns a string representation of this {@code Double} object.
 * The primitive {@code double} value represented by this
 * object is converted to a string exactly as if by the method
 * {@code toString} of one argument.
 *
 * @return a {@code String} representation of this object.
 * @see java.lang.Double#toString(double)
 */
 public String toString() {
 return toString(value);
 }

 /**
 * Returns the value of this {@code Double} as a {@code byte}
 * after a narrowing primitive conversion.
 *
 * @return the {@code double} value represented by this object
 * converted to type {@code byte}
 * @jls 5.1.3 Narrowing Primitive Conversion
 * @since 1.1
 */
 public byte byteValue() {
 return (byte)value;
 }

 /**
 * Returns the value of this {@code Double} as a {@code short}
 * after a narrowing primitive conversion.
 *
 * @return the {@code double} value represented by this object
 * converted to type {@code short}
 * @jls 5.1.3 Narrowing Primitive Conversion
 * @since 1.1
 */
 public short shortValue() {
 return (short)value;
 }

 /**
 * Returns the value of this {@code Double} as an {@code int}
 * after a narrowing primitive conversion.
 * @jls 5.1.3 Narrowing Primitive Conversion
 *
 * @return the {@code double} value represented by this object
 * converted to type {@code int}
 */
 public int intValue() {
 return (int)value;
 }

 /**
 * Returns the value of this {@code Double} as a {@code long}
 * after a narrowing primitive conversion.
 *
 * @return the {@code double} value represented by this object
 * converted to type {@code long}
 * @jls 5.1.3 Narrowing Primitive Conversion
 */
 public long longValue() {
 return (long)value;
 }

 /**
 * Returns the value of this {@code Double} as a {@code float}
 * after a narrowing primitive conversion.
 *
 * @apiNote
 * This method corresponds to the convertFormat operation defined
 * in IEEE 754.
 *
 * @return the {@code double} value represented by this object
 * converted to type {@code float}
 * @jls 5.1.3 Narrowing Primitive Conversion
 * @since 1.0
 */
 public float floatValue() {
 return (float)value;
 }

 /**
 * Returns the {@code double} value of this {@code Double} object.
 *
 * @return the {@code double} value represented by this object
 */
 @IntrinsicCandidate
 public double doubleValue() {
 return value;
 }

 /**
 * Returns a hash code for this {@code Double} object. The
 * result is the exclusive OR of the two halves of the
 * {@code long} integer bit representation, exactly as
 * produced by the method {@link #doubleToLongBits(double)}, of
 * the primitive {@code double} value represented by this
 * {@code Double} object. That is, the hash code is the value
 * of the expression:
 *
 * <blockquote>
 * {@code (int)(v^(v>>>32))}
 * </blockquote>
 *
 * where {@code v} is defined by:
 *
 * <blockquote>
 * {@code long v = Double.doubleToLongBits(this.doubleValue());}
 * </blockquote>
 *
 * @return a {@code hash code} value for this object.
 */
 @Override
 public int hashCode() {
 return Double.hashCode(value);
 }

 /**
 * Returns a hash code for a {@code double} value; compatible with
 * {@code Double.hashCode()}.
 *
 * @param value the value to hash
 * @return a hash code value for a {@code double} value.
 * @since 1.8
 */
 public static int hashCode(double value) {
 return Long.hashCode(doubleToLongBits(value));
 }

 /**
 * Compares this object against the specified object. The result
 * is {@code true} if and only if the argument is not
 * {@code null} and is a {@code Double} object that
 * represents a {@code double} that has the same value as the
 * {@code double} represented by this object. For this
 * purpose, two {@code double} values are considered to be
 * the same if and only if the method {@link
 * #doubleToLongBits(double)} returns the identical
 * {@code long} value when applied to each.
 *
 * @apiNote
 * This method is defined in terms of {@link
 * #doubleToLongBits(double)} rather than the {@code ==} operator
 * on {@code double} values since the {@code ==} operator does
 * not define an equivalence relation and to satisfy the
 * {@linkplain Object#equals equals contract} an equivalence
 * relation must be implemented; see <a
 * href="#equivalenceRelation">this discussion</a> for details of
 * floating-point equality and equivalence.
 *
 * @see java.lang.Double#doubleToLongBits(double)
 * @jls 15.21.1 Numerical Equality Operators == and !=
 */
 public boolean equals(Object obj) {
 return (obj instanceof Double)
 && (doubleToLongBits(((Double)obj).value) ==
 doubleToLongBits(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
 * {@code 0x8000000000000000L}) represents the sign of the
 * floating-point number. Bits
 * 62-52 (the bits that are selected by the mask
 * {@code 0x7ff0000000000000L}) represent the exponent. Bits 51-0
 * (the bits that are selected by the mask
 * {@code 0x000fffffffffffffL}) represent the significand
 * (sometimes called the mantissa) of the floating-point number.
 *
 * If the argument is positive infinity, the result is
 * {@code 0x7ff0000000000000L}.
 *
 * If the argument is negative infinity, the result is
 * {@code 0xfff0000000000000L}.
 *
 * If the argument is NaN, the result is
 * {@code 0x7ff8000000000000L}.
 *
 * In all cases, the result is a {@code long} integer that, when
 * given to the {@link #longBitsToDouble(long)} method, will produce a
 * floating-point value the same as the argument to
 * {@code doubleToLongBits} (except all NaN values are
 * collapsed to a single "canonical" NaN value).
 *
 * @param value a {@code double} precision floating-point number.
 * @return the bits that represent the floating-point number.
 */
 @IntrinsicCandidate
 public static long doubleToLongBits(double value) {
 if (!isNaN(value)) {
 return doubleToRawLongBits(value);
 }
 return 0x7ff8000000000000L;
 }

 /**
 * 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
 * {@code 0x8000000000000000L}) represents the sign of the
 * floating-point number. Bits
 * 62-52 (the bits that are selected by the mask
 * {@code 0x7ff0000000000000L}) represent the exponent. Bits 51-0
 * (the bits that are selected by the mask
 * {@code 0x000fffffffffffffL}) represent the significand
 * (sometimes called the mantissa) of the floating-point number.
 *
 * If the argument is positive infinity, the result is
 * {@code 0x7ff0000000000000L}.
 *
 * If the argument is negative infinity, the result is
 * {@code 0xfff0000000000000L}.
 *
 * If the argument is NaN, the result is the {@code long}
 * integer representing the actual NaN value. Unlike the
 * {@code doubleToLongBits} method,
 * {@code doubleToRawLongBits} does not collapse all the bit
 * patterns encoding a NaN to a single "canonical" NaN
 * value.
 *
 * In all cases, the result is a {@code long} integer that,
 * when given to the {@link #longBitsToDouble(long)} method, will
 * produce a floating-point value the same as the argument to
 * {@code doubleToRawLongBits}.
 *
 * @param value a {@code double} precision floating-point number.
 * @return the bits that represent the floating-point number.
 * @since 1.3
 */
 @IntrinsicCandidate
 public static native long doubleToRawLongBits(double value);

 /**
 * Returns the {@code 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 {@code 0x7ff0000000000000L}, the result
 * is positive infinity.
 *
 * If the argument is {@code 0xfff0000000000000L}, the result
 * is negative infinity.
 *
 * If the argument is any value in the range
 * {@code 0x7ff0000000000001L} through
 * {@code 0x7fffffffffffffffL} or in the range
 * {@code 0xfff0000000000001L} through
 * {@code 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 {@code Double.doubleToRawLongBits} method.
 *
 * In all other cases, let s, e, and m be three
 * values that can be computed from the argument:
 *
 * {@snippet lang="java" :
 * 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
 * {@code double} NaN with exactly same bit pattern as the
 * {@code 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 {@code longBitsToDouble}
 * may not be able to return a {@code double} with a
 * signaling NaN bit pattern. Consequently, for some
 * {@code long} values,
 * {@code doubleToRawLongBits(longBitsToDouble(start))} may
 * not equal {@code 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.
 *
 * @param bits any {@code long} integer.
 * @return the {@code double} floating-point value with the same
 * bit pattern.
 */
 @IntrinsicCandidate
 public static native double longBitsToDouble(long bits);

 /**
 * Compares two {@code Double} objects numerically.
 *
 * This method imposes a total order on {@code Double} objects
 * with two differences compared to the incomplete order defined by
 * the Java language numerical comparison operators ({@code <, <=,
 * ==, >=, >}) on {@code double} values.
 *
 * <ul><li> A NaN is unordered with respect to other
 * values and unequal to itself under the comparison
 * operators. This method chooses to define {@code
 * Double.NaN} to be equal to itself and greater than all
 * other {@code double} values (including {@code
 * Double.POSITIVE_INFINITY}).
 *
 * <li> Positive zero and negative zero compare equal
 * numerically, but are distinct and distinguishable values.
 * This method chooses to define positive zero ({@code +0.0d}),
 * to be greater than negative zero ({@code -0.0d}).
 * </ul>

 * This ensures that the natural ordering of {@code Double}
 * objects imposed by this method is consistent with
 * equals; see <a href="#equivalenceRelation">this
 * discussion</a> for details of floating-point comparison and
 * ordering.
 *
 * @param anotherDouble the {@code Double} to be compared.
 * @return the value {@code 0} if {@code anotherDouble} is
 * numerically equal to this {@code Double}; a value
 * less than {@code 0} if this {@code Double}
 * is numerically less than {@code anotherDouble};
 * and a value greater than {@code 0} if this
 * {@code Double} is numerically greater than
 * {@code anotherDouble}.
 *
 * @jls 15.20.1 Numerical Comparison Operators {@code <}, {@code <=}, {@code >}, and {@code >=}
 * @since 1.2
 */
 public int compareTo(Double anotherDouble) {
 return Double.compare(value, anotherDouble.value);
 }

 /**
 * Compares the two specified {@code double} values. The sign
 * of the integer value returned is the same as that of the
 * integer that would be returned by the call:
 * <pre>
 * Double.valueOf(d1).compareTo(Double.valueOf(d2))
 * </pre>
 *
 * @param d1 the first {@code double} to compare
 * @param d2 the second {@code double} to compare
 * @return the value {@code 0} if {@code d1} is
 * numerically equal to {@code d2}; a value less than
 * {@code 0} if {@code d1} is numerically less than
 * {@code d2}; and a value greater than {@code 0}
 * if {@code d1} is numerically greater than
 * {@code d2}.
 * @since 1.4
 */
 public static int compare(double d1, double d2) {
 if (d1 < d2)
 return -1; // Neither val is NaN, thisVal is smaller
 if (d1 > d2)
 return 1; // Neither val is NaN, thisVal is larger

 // Cannot use doubleToRawLongBits because of possibility of NaNs.
 long thisBits = Double.doubleToLongBits(d1);
 long anotherBits = Double.doubleToLongBits(d2);

 return (thisBits == anotherBits ? 0 : // Values are equal
 (thisBits < anotherBits ? -1 : // (-0.0, 0.0) or (!NaN, NaN)
 1)); // (0.0, -0.0) or (NaN, !NaN)
 }

 /**
 * Adds two {@code double} values together as per the + operator.
 *
 * @apiNote This method corresponds to the addition operation
 * defined in IEEE 754.
 *
 * @param a the first operand
 * @param b the second operand
 * @return the sum of {@code a} and {@code b}
 * @jls 4.2.4 Floating-Point Operations
 * @see java.util.function.BinaryOperator
 * @since 1.8
 */
 public static double sum(double a, double b) {
 return a + b;
 }

 /**
 * Returns the greater of two {@code double} values
 * as if by calling {@link Math#max(double, double) Math.max}.
 *
 * @apiNote
 * This method corresponds to the maximum operation defined in
 * IEEE 754.
 *
 * @param a the first operand
 * @param b the second operand
 * @return the greater of {@code a} and {@code b}
 * @see java.util.function.BinaryOperator
 * @since 1.8
 */
 public static double max(double a, double b) {
 return Math.max(a, b);
 }

 /**
 * Returns the smaller of two {@code double} values
 * as if by calling {@link Math#min(double, double) Math.min}.
 *
 * @apiNote
 * This method corresponds to the minimum operation defined in
 * IEEE 754.
 *
 * @param a the first operand
 * @param b the second operand
 * @return the smaller of {@code a} and {@code b}.
 * @see java.util.function.BinaryOperator
 * @since 1.8
 */
 public static double min(double a, double b) {
 return Math.min(a, b);
 }

 /**
 * Returns an {@link Optional} containing the nominal descriptor for this
 * instance, which is the instance itself.
 *
 * @return an {@link Optional} describing the {@linkplain Double} instance
 * @since 12
 */
 @Override
 public Optional<Double> describeConstable() {
 return Optional.of(this);
 }

 /**
 * Resolves this instance as a {@link ConstantDesc}, the result of which is
 * the instance itself.
 *
 * @param lookup ignored
 * @return the {@linkplain Double} instance
 * @since 12
 */
 @Override
 public Double resolveConstantDesc(MethodHandles.Lookup lookup) {
 return this;
 }

 /** use serialVersionUID from JDK 1.0.2 for interoperability */
 @java.io.Serial
 private static final long serialVersionUID = -9172774392245257468L;
}

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