Quelle Double.java Sprache: JAVA

/*
* Copyright (c) 1994, 2023, Oracle and/or its affiliates. All rights reserved.
* DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER.
*
* This code is free software; you can redistribute it and/or modify it
* under the terms of the GNU General Public License version 2 only, as
* published by the Free Software Foundation. Oracle designates this
* particular file as subject to the "Classpath" exception as provided
* by Oracle in the LICENSE file that accompanied this code.
*
* This code is distributed in the hope that it will be useful, but WITHOUT
* ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
* FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
* version 2 for more details (a copy is included in the LICENSE file that
* accompanied this code).
*
* You should have received a copy of the GNU General Public License version
* 2 along with this work; if not, write to the Free Software Foundation,
* Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA.
*
* Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA
* or visit www.oracle.com if you need additional information or have any
* questions.
*/

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;
}

Messung V0.5

¤ Dauer der Verarbeitung: 0.9 Sekunden (vorverarbeitet) ¤

Wurzel

Suchen

Beweissystem der NASA

Beweissystem Isabelle

NIST Cobol Testsuite

Cephes Mathematical Library

Wiener Entwicklungsmethode

Haftungshinweis

Die Informationen auf dieser Webseite wurden nach bestem Wissen sorgfältig zusammengestellt. Es wird jedoch weder Vollständigkeit, noch Richtigkeit, noch Qualität der bereit gestellten Informationen zugesichert.

Bemerkung:

Die farbliche Syntaxdarstellung und die Messung sind noch experimentell.