Double.java

/*
 * Copyright (c) 1994, 2017, 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 jdk.internal.HotSpotIntrinsicCandidate;
import jdk.internal.math.DoubleConsts;
import jdk.internal.math.FloatingDecimal;

/**
 * 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}.
 *
 * <p>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}.
 *
 * @author Lee Boynton
 * @author Arthur van Hoff
 * @author Joseph D. Darcy
 * @since 1.0
 */
// double的包装类
public final class Double extends Number implements Comparable<Double> {
    
    /** use serialVersionUID from JDK 1.0.2 for interoperability */
    private static final long serialVersionUID = -9172774392245257468L;
    
    /**
     * The {@code Class} instance representing the primitive type
     * {@code double}.
     *
     * @since 1.1
     */
    // 相当于double.class
    @SuppressWarnings("unchecked")
    public static final Class<Double> TYPE = (Class<Double>) Class.getPrimitiveClass("double");
    
    /**
     * 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; // 代表正无穷大
    
    /**
     * 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; // 代表负无穷大
    
    /**
     * 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; // 代表非数字
    
    /**
     * A constant holding the largest positive finite value of type
     * {@code double},
     * (2-2<sup>-52</sup>)&middot;2<sup>1023</sup>.  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; // double最大值：1.7976931348623157e+308
    
    /**
     * A constant holding the smallest positive normal value of type
     * {@code double}, 2<sup>-1022</sup>.  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; // double最小正值：2.2250738585072014E-308，正规数
    
    /**
     * A constant holding the smallest positive nonzero value of type
     * {@code double}, 2<sup>-1074</sup>. 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; // double最小正值：4.9e-324，次正规数
    
    /**
     * 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 = 1023; // double二进制形式指数部分最大值
    
    /**
     * 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 = -1022; // double二进制形式指数部分最大值
    
    /**
     * The number of bits used to represent a {@code double} value.
     *
     * @since 1.5
     */
    public static final int SIZE = 64;  // 当前类型所占bit[位]数
    
    /**
     * The number of bytes used to represent a {@code double} value.
     *
     * @since 1.8
     */
    public static final int BYTES = SIZE / Byte.SIZE;   // 当前类型所占字节数
    
    /**
     * The value of the Double.
     *
     * @serial
     */
    private final double value; // 当前类包装的值
    
    
    
    /*▼ 构造方法 ████████████████████████████████████████████████████████████████████████████████┓ */
    
    /**
     * 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")
    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")
    public Double(String s) throws NumberFormatException {
        value = parseDouble(s);
    }
    
    /*▲ 构造方法 ████████████████████████████████████████████████████████████████████████████████┛ */
    
    
    
    /*▼ [装箱] ████████████████████████████████████████████████████████████████████████████████┓ */
    
    /**
     * 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
     */
    // double-->Double 默认的装箱行为
    @HotSpotIntrinsicCandidate
    public static Double valueOf(double d) {
        return new Double(d);
    }
    
    /**
     * Returns a {@code Double} object holding the
     * {@code double} value represented by the argument string
     * {@code s}.
     *
     * <p>If {@code s} is {@code null}, then a
     * {@code NullPointerException} is thrown.
     *
     * <p>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 <i>FloatValue</i> as described by the lexical
     * syntax rules:
     *
     * <blockquote>
     * <dl>
     * <dt><i>FloatValue:</i>
     * <dd><i>Sign<sub>opt</sub></i> {@code NaN}
     * <dd><i>Sign<sub>opt</sub></i> {@code Infinity}
     * <dd><i>Sign<sub>opt</sub> FloatingPointLiteral</i>
     * <dd><i>Sign<sub>opt</sub> HexFloatingPointLiteral</i>
     * <dd><i>SignedInteger</i>
     * </dl>
     *
     * <dl>
     * <dt><i>HexFloatingPointLiteral</i>:
     * <dd> <i>HexSignificand BinaryExponent FloatTypeSuffix<sub>opt</sub></i>
     * </dl>
     *
     * <dl>
     * <dt><i>HexSignificand:</i>
     * <dd><i>HexNumeral</i>
     * <dd><i>HexNumeral</i> {@code .}
     * <dd>{@code 0x} <i>HexDigits<sub>opt</sub>
     * </i>{@code .}<i> HexDigits</i>
     * <dd>{@code 0X}<i> HexDigits<sub>opt</sub>
     * </i>{@code .} <i>HexDigits</i>
     * </dl>
     *
     * <dl>
     * <dt><i>BinaryExponent:</i>
     * <dd><i>BinaryExponentIndicator SignedInteger</i>
     * </dl>
     *
     * <dl>
     * <dt><i>BinaryExponentIndicator:</i>
     * <dd>{@code p}
     * <dd>{@code P}
     * </dl>
     *
     * </blockquote>
     *
     * where <i>Sign</i>, <i>FloatingPointLiteral</i>,
     * <i>HexNumeral</i>, <i>HexDigits</i>, <i>SignedInteger</i> and
     * <i>FloatTypeSuffix</i> are as defined in the lexical structure
     * sections of
     * <cite>The Java&trade; Language Specification</cite>,
     * except that underscores are not accepted between digits.
     * If {@code s} does not have the form of
     * a <i>FloatValue</i>, 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.
     *
     * <p> To interpret localized string representations of a
     * floating-point value, use subclasses of {@link
     * java.text.NumberFormat}.
     *
     * <p>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
     * <em>not</em> 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 <em>not</em>
     * 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.)
     *
     * <p>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:
     *
     * <pre>{@code
     *  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"
     *
     *  if (Pattern.matches(fpRegex, myString))
     *      Double.valueOf(myString); // Will not throw NumberFormatException
     *  else {
     *      // Perform suitable alternative action
     *  }
     * }</pre>
     *
     * @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.
     */
    // 将字符串s解析为double值，然后再装箱
    public static Double valueOf(String s) throws NumberFormatException {
        return new Double(parseDouble(s));
    }
    
    /*▲ [装箱] ████████████████████████████████████████████████████████████████████████████████┛ */
    
    
    
    /*▼ [拆箱] ████████████████████████████████████████████████████████████████████████████████┓ */
    
    /**
     * 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 Conversions
     * @since 1.1
     */
    // 以byte形式返回当前对象的值
    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 Conversions
     * @since 1.1
     */
    // 以short形式返回当前对象的值
    public short shortValue() {
        return (short) value;
    }
    
    /**
     * Returns the value of this {@code Double} as an {@code int}
     * after a narrowing primitive conversion.
     *
     * @return the {@code double} value represented by this object
     * converted to type {@code int}
     *
     * @jls 5.1.3 Narrowing Primitive Conversions
     */
    // 以int形式返回当前对象的值
    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 Conversions
     */
    // 以long形式返回当前对象的值
    public long longValue() {
        return (long) value;
    }
    
    /**
     * Returns the value of this {@code Double} as a {@code float}
     * after a narrowing primitive conversion.
     *
     * @return the {@code double} value represented by this object
     * converted to type {@code float}
     *
     * @jls 5.1.3 Narrowing Primitive Conversions
     * @since 1.0
     */
    // 以float形式返回当前对象的值
    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
     */
    // Double-->double 默认的拆箱行为
    @HotSpotIntrinsicCandidate
    public double doubleValue() {
        return value;
    }
    
    /*▲ [拆箱] ████████████████████████████████████████████████████████████████████████████████┛ */
    
    
    
    /*▼ 逆字符串化 ████████████████████████████████████████████████████████████████████████████████┓ */
    
    /**
     * 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
     */
    // 将字符串s解析为double值
    public static double parseDouble(String s) throws NumberFormatException {
        return FloatingDecimal.parseDouble(s);
    }
    
    /*▲ 逆字符串化 ████████████████████████████████████████████████████████████████████████████████┛ */
    
    
    
    /*▼ 字符串化 ████████████████████████████████████████████████████████████████████████████████┓ */
    
    /**
     * 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 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 <i>m</i>:
     * <ul>
     * <li>If <i>m</i> 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 <i>m</i> 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>If <i>m</i> is greater than or equal to 10<sup>-3</sup> but less
     * than 10<sup>7</sup>, then it is represented as the integer part of
     * <i>m</i>, in decimal form with no leading zeroes, followed by
     * '{@code .}' ({@code '\u005Cu002E'}), followed by one or
     * more decimal digits representing the fractional part of <i>m</i>.
     *
     * <li>If <i>m</i> is less than 10<sup>-3</sup> or greater than or
     * equal to 10<sup>7</sup>, then it is represented in so-called
     * "computerized scientific notation." Let <i>n</i> be the unique
     * integer such that 10<sup><i>n</i></sup> &le; <i>m</i> {@literal <}
     * 10<sup><i>n</i>+1</sup>; then let <i>a</i> be the
     * mathematically exact quotient of <i>m</i> and
     * 10<sup><i>n</i></sup> so that 1 &le; <i>a</i> {@literal <} 10. The
     * magnitude is then represented as the integer part of <i>a</i>,
     * as a single decimal digit, followed by '{@code .}'
     * ({@code '\u005Cu002E'}), followed by decimal digits
     * representing the fractional part of <i>a</i>, followed by the
     * letter '{@code E}' ({@code '\u005Cu0045'}), followed
     * by a representation of <i>n</i> as a decimal integer, as
     * produced by the method {@link Integer#toString(int)}.
     * </ul>
     * </ul>
     * How many digits must be printed for the fractional part of
     * <i>m</i> or <i>a</i>? There must be at least one digit to represent
     * the fractional part, and beyond that as many, but only as many, more
     * digits as are needed to uniquely distinguish the argument value from
     * adjacent values of type {@code double}. That is, suppose that
     * <i>x</i> is the exact mathematical value represented by the decimal
     * representation produced by this method for a finite nonzero argument
     * <i>d</i>. Then <i>d</i> must be the {@code double} value nearest
     * to <i>x</i>; or if two {@code double} values are equally close
     * to <i>x</i>, then <i>d</i> must be one of them and the least
     * significant bit of the significand of <i>d</i> must be {@code 0}.
     *
     * <p>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 FloatingDecimal.toJavaFormatString(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 <i>m</i>:
     *
     * <ul>
     * <li>If <i>m</i> 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 <i>m</i> 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 <i>m</i> 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 <i>m</i> 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.
     *
     * @author Joseph D. Darcy
     * @since 1.5
     */
    // 返回浮点值f的十六进制形式
    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();
        }
    }
    
    /*▲ 字符串化 ████████████████████████████████████████████████████████████████████████████████┛ */
    
    
    
    /*▼ 比较 ████████████████████████████████████████████████████████████████████████████████┓ */
    
    /**
     * 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>
     *    new Double(d1).compareTo(new Double(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
     */
    // 比较两个double
    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)
        );
    }
    
    /**
     * Compares two {@code Double} objects numerically.  There
     * are two ways in which comparisons performed by this method
     * differ from those performed by the Java language numerical
     * comparison operators ({@code <, <=, ==, >=, >})
     * when applied to primitive {@code double} values:
     * <ul><li>
     * {@code Double.NaN} is considered by this method
     * to be equal to itself and greater than all other
     * {@code double} values (including
     * {@code Double.POSITIVE_INFINITY}).
     * <li>
     * {@code 0.0d} is considered by this method to be greater
     * than {@code -0.0d}.
     * </ul>
     * This ensures that the <i>natural ordering</i> of
     * {@code Double} objects imposed by this method is <i>consistent
     * with equals</i>.
     *
     * @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}.
     *
     * @since 1.2
     */
    // 比较两个Double
    public int compareTo(Double anotherDouble) {
        return Double.compare(value, anotherDouble.value);
    }
    
    /*▲ 比较 ████████████████████████████████████████████████████████████████████████████████┛ */
    
    
    
    /*▼ 位操作 ████████████████████████████████████████████████████████████████████████████████┓ */
    
    /**
     * Returns a representation of the specified floating-point value
     * according to the IEEE 754 floating-point "double
     * format" bit layout.
     *
     * <p>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.
     *
     * <p>If the argument is positive infinity, the result is
     * {@code 0x7ff0000000000000L}.
     *
     * <p>If the argument is negative infinity, the result is
     * {@code 0xfff0000000000000L}.
     *
     * <p>If the argument is NaN, the result is
     * {@code 0x7ff8000000000000L}.
     *
     * <p>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.
     */
    // 先计算value的二进制格式，然后返回该二进制格式表示的long
    @HotSpotIntrinsicCandidate
    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.
     *
     * <p>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.
     *
     * <p>If the argument is positive infinity, the result is
     * {@code 0x7ff0000000000000L}.
     *
     * <p>If the argument is negative infinity, the result is
     * {@code 0xfff0000000000000L}.
     *
     * <p>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.
     *
     * <p>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
     */
    // 先计算value的二进制格式，然后返回该二进制格式表示的long
    @HotSpotIntrinsicCandidate
    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.
     *
     * <p>If the argument is {@code 0x7ff0000000000000L}, the result
     * is positive infinity.
     *
     * <p>If the argument is {@code 0xfff0000000000000L}, the result
     * is negative infinity.
     *
     * <p>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.
     *
     * <p>In all other cases, let <i>s</i>, <i>e</i>, and <i>m</i> be three
     * values that can be computed from the argument:
     *
     * <blockquote><pre>{@code
     * int s = ((bits >> 63) == 0) ? 1 : -1;
     * int e = (int)((bits >> 52) & 0x7ffL);
     * long m = (e == 0) ?
     *                 (bits & 0xfffffffffffffL) << 1 :
     *                 (bits & 0xfffffffffffffL) | 0x10000000000000L;
     * }</pre></blockquote>
     *
     * Then the floating-point result equals the value of the mathematical
     * expression <i>s</i>&middot;<i>m</i>&middot;2<sup><i>e</i>-1075</sup>.
     *
     * <p>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 <i>signaling NaNs</i>.  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
     * <i>not</i> 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.
     */
    // 先计算bits的二进制格式，然后返回该二进制格式表示的double
    @HotSpotIntrinsicCandidate
    public static native double longBitsToDouble(long bits);
    
    /*▲ 位操作 ████████████████████████████████████████████████████████████████████████████████┛ */
    
    
    /*▼ 简单运算 ████████████████████████████████████████████████████████████████████████████████┓ */
    
    /**
     * Adds two {@code double} values together as per the + operator.
     *
     * @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
     */
    // 求和
    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}.
     *
     * @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
     */
    // 最大值
    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}.
     *
     * @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
     */
    // 最小值
    public static double min(double a, double b) {
        return Math.min(a, b);
    }
    
    /*▲ 简单运算 ████████████████████████████████████████████████████████████████████████████████┛ */
    
    
    
    /*▼ 非常规数值 ████████████████████████████████████████████████████████████████████████████████┓ */
    
    /**
     * 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.
     */
    // 判断当前double值是否为NaN
    public boolean isNaN() {
        return isNaN(value);
    }
    
    /**
     * Returns {@code true} if the specified number is a
     * Not-a-Number (NaN) value, {@code false} otherwise.
     *
     * @param v the value to be tested.
     *
     * @return {@code true} if the value of the argument is NaN;
     * {@code false} otherwise.
     */
    // 判断v是否为NaN
    public static boolean isNaN(double v) {
        return (v != v);
    }
    
    /**
     * 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.
     */
    // 判断当前double值是否为正无穷大/负无穷大
    public boolean isInfinite() {
        return isInfinite(value);
    }
    
    /**
     * Returns {@code true} if the specified number is infinitely
     * large in magnitude, {@code false} otherwise.
     *
     * @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.
     */
    // 判断v是否为正无穷大/负无穷大
    public static boolean isInfinite(double v) {
        return (v == POSITIVE_INFINITY) || (v == NEGATIVE_INFINITY);
    }
    
    /**
     * Returns {@code true} if the argument is a finite floating-point
     * value; returns {@code false} otherwise (for NaN and infinity
     * arguments).
     *
     * @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
     */
    // 判断d是否为有限值
    public static boolean isFinite(double d) {
        return Math.abs(d)<=Double.MAX_VALUE;
    }
    
    /*▲ 非常规数值 ████████████████████████████████████████████████████████████████████████████████┛ */
    
    
    
    /**
     * 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) {
        long bits = doubleToLongBits(value);
        return (int) (bits ^ (bits >>> 32));
    }
    
    /**
     * 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.
     *
     * <p>Note that in most cases, for two instances of class
     * {@code Double}, {@code d1} and {@code d2}, the
     * value of {@code d1.equals(d2)} is {@code true} if and
     * only if
     *
     * <blockquote>
     * {@code d1.doubleValue() == d2.doubleValue()}
     * </blockquote>
     *
     * <p>also has the value {@code true}. However, there are two
     * exceptions:
     * <ul>
     * <li>If {@code d1} and {@code d2} both represent
     * {@code Double.NaN}, then the {@code equals} method
     * returns {@code true}, even though
     * {@code Double.NaN==Double.NaN} has the value
     * {@code false}.
     * <li>If {@code d1} represents {@code +0.0} while
     * {@code d2} represents {@code -0.0}, or vice versa,
     * the {@code equal} test has the value {@code false},
     * even though {@code +0.0==-0.0} has the value {@code true}.
     * </ul>
     * This definition allows hash tables to operate properly.
     *
     * @param obj the object to compare with.
     *
     * @return {@code true} if the objects are the same;
     * {@code false} otherwise.
     *
     * @see java.lang.Double#doubleToLongBits(double)
     */
    public boolean equals(Object obj) {
        return (obj instanceof Double) && (doubleToLongBits(((Double) obj).value) == doubleToLongBits(value));
    }
    
}