1 /*
   2  * Copyright (c) 1994, 2014, Oracle and/or its affiliates. All rights reserved.
   3  * DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER.
   4  *
   5  * This code is free software; you can redistribute it and/or modify it
   6  * under the terms of the GNU General Public License version 2 only, as
   7  * published by the Free Software Foundation.  Oracle designates this
   8  * particular file as subject to the "Classpath" exception as provided
   9  * by Oracle in the LICENSE file that accompanied this code.
  10  *
  11  * This code is distributed in the hope that it will be useful, but WITHOUT
  12  * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
  13  * FITNESS FOR A PARTICULAR PURPOSE.  See the GNU General Public License
  14  * version 2 for more details (a copy is included in the LICENSE file that
  15  * accompanied this code).
  16  *
  17  * You should have received a copy of the GNU General Public License version
  18  * 2 along with this work; if not, write to the Free Software Foundation,
  19  * Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA.
  20  *
  21  * Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA
  22  * or visit www.oracle.com if you need additional information or have any
  23  * questions.
  24  */
  25 
  26 package java.lang;
  27 
  28 import sun.misc.FloatingDecimal;
  29 import sun.misc.DoubleConsts;
  30 
  31 /**
  32  * The {@code Double} class wraps a value of the primitive type
  33  * {@code double} in an object. An object of type
  34  * {@code Double} contains a single field whose type is
  35  * {@code double}.
  36  *
  37  * <p>In addition, this class provides several methods for converting a
  38  * {@code double} to a {@code String} and a
  39  * {@code String} to a {@code double}, as well as other
  40  * constants and methods useful when dealing with a
  41  * {@code double}.
  42  *
  43  * @author  Lee Boynton
  44  * @author  Arthur van Hoff
  45  * @author  Joseph D. Darcy
  46  * @since 1.0
  47  */
  48 public final class Double extends Number implements Comparable<Double> {
  49     /**
  50      * A constant holding the positive infinity of type
  51      * {@code double}. It is equal to the value returned by
  52      * {@code Double.longBitsToDouble(0x7ff0000000000000L)}.
  53      */
  54     public static final double POSITIVE_INFINITY = 1.0 / 0.0;
  55 
  56     /**
  57      * A constant holding the negative infinity of type
  58      * {@code double}. It is equal to the value returned by
  59      * {@code Double.longBitsToDouble(0xfff0000000000000L)}.
  60      */
  61     public static final double NEGATIVE_INFINITY = -1.0 / 0.0;
  62 
  63     /**
  64      * A constant holding a Not-a-Number (NaN) value of type
  65      * {@code double}. It is equivalent to the value returned by
  66      * {@code Double.longBitsToDouble(0x7ff8000000000000L)}.
  67      */
  68     public static final double NaN = 0.0d / 0.0;
  69 
  70     /**
  71      * A constant holding the largest positive finite value of type
  72      * {@code double},
  73      * (2-2<sup>-52</sup>)&middot;2<sup>1023</sup>.  It is equal to
  74      * the hexadecimal floating-point literal
  75      * {@code 0x1.fffffffffffffP+1023} and also equal to
  76      * {@code Double.longBitsToDouble(0x7fefffffffffffffL)}.
  77      */
  78     public static final double MAX_VALUE = 0x1.fffffffffffffP+1023; // 1.7976931348623157e+308
  79 
  80     /**
  81      * A constant holding the smallest positive normal value of type
  82      * {@code double}, 2<sup>-1022</sup>.  It is equal to the
  83      * hexadecimal floating-point literal {@code 0x1.0p-1022} and also
  84      * equal to {@code Double.longBitsToDouble(0x0010000000000000L)}.
  85      *
  86      * @since 1.6
  87      */
  88     public static final double MIN_NORMAL = 0x1.0p-1022; // 2.2250738585072014E-308
  89 
  90     /**
  91      * A constant holding the smallest positive nonzero value of type
  92      * {@code double}, 2<sup>-1074</sup>. It is equal to the
  93      * hexadecimal floating-point literal
  94      * {@code 0x0.0000000000001P-1022} and also equal to
  95      * {@code Double.longBitsToDouble(0x1L)}.
  96      */
  97     public static final double MIN_VALUE = 0x0.0000000000001P-1022; // 4.9e-324
  98 
  99     /**
 100      * Maximum exponent a finite {@code double} variable may have.
 101      * It is equal to the value returned by
 102      * {@code Math.getExponent(Double.MAX_VALUE)}.
 103      *
 104      * @since 1.6
 105      */
 106     public static final int MAX_EXPONENT = 1023;
 107 
 108     /**
 109      * Minimum exponent a normalized {@code double} variable may
 110      * have.  It is equal to the value returned by
 111      * {@code Math.getExponent(Double.MIN_NORMAL)}.
 112      *
 113      * @since 1.6
 114      */
 115     public static final int MIN_EXPONENT = -1022;
 116 
 117     /**
 118      * The number of bits used to represent a {@code double} value.
 119      *
 120      * @since 1.5
 121      */
 122     public static final int SIZE = 64;
 123 
 124     /**
 125      * The number of bytes used to represent a {@code double} value.
 126      *
 127      * @since 1.8
 128      */
 129     public static final int BYTES = SIZE / Byte.SIZE;
 130 
 131     /**
 132      * The {@code Class} instance representing the primitive type
 133      * {@code double}.
 134      *
 135      * @since 1.1
 136      */
 137     @SuppressWarnings("unchecked")
 138     public static final Class<Double>   TYPE = (Class<Double>) Class.getPrimitiveClass("double");
 139 
 140     /**
 141      * Returns a string representation of the {@code double}
 142      * argument. All characters mentioned below are ASCII characters.
 143      * <ul>
 144      * <li>If the argument is NaN, the result is the string
 145      *     "{@code NaN}".
 146      * <li>Otherwise, the result is a string that represents the sign and
 147      * magnitude (absolute value) of the argument. If the sign is negative,
 148      * the first character of the result is '{@code -}'
 149      * ({@code '\u005Cu002D'}); if the sign is positive, no sign character
 150      * appears in the result. As for the magnitude <i>m</i>:
 151      * <ul>
 152      * <li>If <i>m</i> is infinity, it is represented by the characters
 153      * {@code "Infinity"}; thus, positive infinity produces the result
 154      * {@code "Infinity"} and negative infinity produces the result
 155      * {@code "-Infinity"}.
 156      *
 157      * <li>If <i>m</i> is zero, it is represented by the characters
 158      * {@code "0.0"}; thus, negative zero produces the result
 159      * {@code "-0.0"} and positive zero produces the result
 160      * {@code "0.0"}.
 161      *
 162      * <li>If <i>m</i> is greater than or equal to 10<sup>-3</sup> but less
 163      * than 10<sup>7</sup>, then it is represented as the integer part of
 164      * <i>m</i>, in decimal form with no leading zeroes, followed by
 165      * '{@code .}' ({@code '\u005Cu002E'}), followed by one or
 166      * more decimal digits representing the fractional part of <i>m</i>.
 167      *
 168      * <li>If <i>m</i> is less than 10<sup>-3</sup> or greater than or
 169      * equal to 10<sup>7</sup>, then it is represented in so-called
 170      * "computerized scientific notation." Let <i>n</i> be the unique
 171      * integer such that 10<sup><i>n</i></sup> &le; <i>m</i> {@literal <}
 172      * 10<sup><i>n</i>+1</sup>; then let <i>a</i> be the
 173      * mathematically exact quotient of <i>m</i> and
 174      * 10<sup><i>n</i></sup> so that 1 &le; <i>a</i> {@literal <} 10. The
 175      * magnitude is then represented as the integer part of <i>a</i>,
 176      * as a single decimal digit, followed by '{@code .}'
 177      * ({@code '\u005Cu002E'}), followed by decimal digits
 178      * representing the fractional part of <i>a</i>, followed by the
 179      * letter '{@code E}' ({@code '\u005Cu0045'}), followed
 180      * by a representation of <i>n</i> as a decimal integer, as
 181      * produced by the method {@link Integer#toString(int)}.
 182      * </ul>
 183      * </ul>
 184      * How many digits must be printed for the fractional part of
 185      * <i>m</i> or <i>a</i>? There must be at least one digit to represent
 186      * the fractional part, and beyond that as many, but only as many, more
 187      * digits as are needed to uniquely distinguish the argument value from
 188      * adjacent values of type {@code double}. That is, suppose that
 189      * <i>x</i> is the exact mathematical value represented by the decimal
 190      * representation produced by this method for a finite nonzero argument
 191      * <i>d</i>. Then <i>d</i> must be the {@code double} value nearest
 192      * to <i>x</i>; or if two {@code double} values are equally close
 193      * to <i>x</i>, then <i>d</i> must be one of them and the least
 194      * significant bit of the significand of <i>d</i> must be {@code 0}.
 195      *
 196      * <p>To create localized string representations of a floating-point
 197      * value, use subclasses of {@link java.text.NumberFormat}.
 198      *
 199      * @param   d   the {@code double} to be converted.
 200      * @return a string representation of the argument.
 201      */
 202     public static String toString(double d) {
 203         return FloatingDecimal.toJavaFormatString(d);
 204     }
 205 
 206     /**
 207      * Returns a hexadecimal string representation of the
 208      * {@code double} argument. All characters mentioned below
 209      * are ASCII characters.
 210      *
 211      * <ul>
 212      * <li>If the argument is NaN, the result is the string
 213      *     "{@code NaN}".
 214      * <li>Otherwise, the result is a string that represents the sign
 215      * and magnitude of the argument. If the sign is negative, the
 216      * first character of the result is '{@code -}'
 217      * ({@code '\u005Cu002D'}); if the sign is positive, no sign
 218      * character appears in the result. As for the magnitude <i>m</i>:
 219      *
 220      * <ul>
 221      * <li>If <i>m</i> is infinity, it is represented by the string
 222      * {@code "Infinity"}; thus, positive infinity produces the
 223      * result {@code "Infinity"} and negative infinity produces
 224      * the result {@code "-Infinity"}.
 225      *
 226      * <li>If <i>m</i> is zero, it is represented by the string
 227      * {@code "0x0.0p0"}; thus, negative zero produces the result
 228      * {@code "-0x0.0p0"} and positive zero produces the result
 229      * {@code "0x0.0p0"}.
 230      *
 231      * <li>If <i>m</i> is a {@code double} value with a
 232      * normalized representation, substrings are used to represent the
 233      * significand and exponent fields.  The significand is
 234      * represented by the characters {@code "0x1."}
 235      * followed by a lowercase hexadecimal representation of the rest
 236      * of the significand as a fraction.  Trailing zeros in the
 237      * hexadecimal representation are removed unless all the digits
 238      * are zero, in which case a single zero is used. Next, the
 239      * exponent is represented by {@code "p"} followed
 240      * by a decimal string of the unbiased exponent as if produced by
 241      * a call to {@link Integer#toString(int) Integer.toString} on the
 242      * exponent value.
 243      *
 244      * <li>If <i>m</i> is a {@code double} value with a subnormal
 245      * representation, the significand is represented by the
 246      * characters {@code "0x0."} followed by a
 247      * hexadecimal representation of the rest of the significand as a
 248      * fraction.  Trailing zeros in the hexadecimal representation are
 249      * removed. Next, the exponent is represented by
 250      * {@code "p-1022"}.  Note that there must be at
 251      * least one nonzero digit in a subnormal significand.
 252      *
 253      * </ul>
 254      *
 255      * </ul>
 256      *
 257      * <table border>
 258      * <caption>Examples</caption>
 259      * <tr><th>Floating-point Value</th><th>Hexadecimal String</th>
 260      * <tr><td>{@code 1.0}</td> <td>{@code 0x1.0p0}</td>
 261      * <tr><td>{@code -1.0}</td>        <td>{@code -0x1.0p0}</td>
 262      * <tr><td>{@code 2.0}</td> <td>{@code 0x1.0p1}</td>
 263      * <tr><td>{@code 3.0}</td> <td>{@code 0x1.8p1}</td>
 264      * <tr><td>{@code 0.5}</td> <td>{@code 0x1.0p-1}</td>
 265      * <tr><td>{@code 0.25}</td>        <td>{@code 0x1.0p-2}</td>
 266      * <tr><td>{@code Double.MAX_VALUE}</td>
 267      *     <td>{@code 0x1.fffffffffffffp1023}</td>
 268      * <tr><td>{@code Minimum Normal Value}</td>
 269      *     <td>{@code 0x1.0p-1022}</td>
 270      * <tr><td>{@code Maximum Subnormal Value}</td>
 271      *     <td>{@code 0x0.fffffffffffffp-1022}</td>
 272      * <tr><td>{@code Double.MIN_VALUE}</td>
 273      *     <td>{@code 0x0.0000000000001p-1022}</td>
 274      * </table>
 275      * @param   d   the {@code double} to be converted.
 276      * @return a hex string representation of the argument.
 277      * @since 1.5
 278      * @author Joseph D. Darcy
 279      */
 280     public static String toHexString(double d) {
 281         /*
 282          * Modeled after the "a" conversion specifier in C99, section
 283          * 7.19.6.1; however, the output of this method is more
 284          * tightly specified.
 285          */
 286         if (!isFinite(d) )
 287             // For infinity and NaN, use the decimal output.
 288             return Double.toString(d);
 289         else {
 290             // Initialized to maximum size of output.
 291             StringBuilder answer = new StringBuilder(24);
 292 
 293             if (Math.copySign(1.0, d) == -1.0)    // value is negative,
 294                 answer.append("-");                  // so append sign info
 295 
 296             answer.append("0x");
 297 
 298             d = Math.abs(d);
 299 
 300             if(d == 0.0) {
 301                 answer.append("0.0p0");
 302             } else {
 303                 boolean subnormal = (d < DoubleConsts.MIN_NORMAL);
 304 
 305                 // Isolate significand bits and OR in a high-order bit
 306                 // so that the string representation has a known
 307                 // length.
 308                 long signifBits = (Double.doubleToLongBits(d)
 309                                    & DoubleConsts.SIGNIF_BIT_MASK) |
 310                     0x1000000000000000L;
 311 
 312                 // Subnormal values have a 0 implicit bit; normal
 313                 // values have a 1 implicit bit.
 314                 answer.append(subnormal ? "0." : "1.");
 315 
 316                 // Isolate the low-order 13 digits of the hex
 317                 // representation.  If all the digits are zero,
 318                 // replace with a single 0; otherwise, remove all
 319                 // trailing zeros.
 320                 String signif = Long.toHexString(signifBits).substring(3,16);
 321                 answer.append(signif.equals("0000000000000") ? // 13 zeros
 322                               "0":
 323                               signif.replaceFirst("0{1,12}$", ""));
 324 
 325                 answer.append('p');
 326                 // If the value is subnormal, use the E_min exponent
 327                 // value for double; otherwise, extract and report d's
 328                 // exponent (the representation of a subnormal uses
 329                 // E_min -1).
 330                 answer.append(subnormal ?
 331                               DoubleConsts.MIN_EXPONENT:
 332                               Math.getExponent(d));
 333             }
 334             return answer.toString();
 335         }
 336     }
 337 
 338     /**
 339      * Returns a {@code Double} object holding the
 340      * {@code double} value represented by the argument string
 341      * {@code s}.
 342      *
 343      * <p>If {@code s} is {@code null}, then a
 344      * {@code NullPointerException} is thrown.
 345      *
 346      * <p>Leading and trailing whitespace characters in {@code s}
 347      * are ignored.  Whitespace is removed as if by the {@link
 348      * String#trim} method; that is, both ASCII space and control
 349      * characters are removed. The rest of {@code s} should
 350      * constitute a <i>FloatValue</i> as described by the lexical
 351      * syntax rules:
 352      *
 353      * <blockquote>
 354      * <dl>
 355      * <dt><i>FloatValue:</i>
 356      * <dd><i>Sign<sub>opt</sub></i> {@code NaN}
 357      * <dd><i>Sign<sub>opt</sub></i> {@code Infinity}
 358      * <dd><i>Sign<sub>opt</sub> FloatingPointLiteral</i>
 359      * <dd><i>Sign<sub>opt</sub> HexFloatingPointLiteral</i>
 360      * <dd><i>SignedInteger</i>
 361      * </dl>
 362      *
 363      * <dl>
 364      * <dt><i>HexFloatingPointLiteral</i>:
 365      * <dd> <i>HexSignificand BinaryExponent FloatTypeSuffix<sub>opt</sub></i>
 366      * </dl>
 367      *
 368      * <dl>
 369      * <dt><i>HexSignificand:</i>
 370      * <dd><i>HexNumeral</i>
 371      * <dd><i>HexNumeral</i> {@code .}
 372      * <dd>{@code 0x} <i>HexDigits<sub>opt</sub>
 373      *     </i>{@code .}<i> HexDigits</i>
 374      * <dd>{@code 0X}<i> HexDigits<sub>opt</sub>
 375      *     </i>{@code .} <i>HexDigits</i>
 376      * </dl>
 377      *
 378      * <dl>
 379      * <dt><i>BinaryExponent:</i>
 380      * <dd><i>BinaryExponentIndicator SignedInteger</i>
 381      * </dl>
 382      *
 383      * <dl>
 384      * <dt><i>BinaryExponentIndicator:</i>
 385      * <dd>{@code p}
 386      * <dd>{@code P}
 387      * </dl>
 388      *
 389      * </blockquote>
 390      *
 391      * where <i>Sign</i>, <i>FloatingPointLiteral</i>,
 392      * <i>HexNumeral</i>, <i>HexDigits</i>, <i>SignedInteger</i> and
 393      * <i>FloatTypeSuffix</i> are as defined in the lexical structure
 394      * sections of
 395      * <cite>The Java&trade; Language Specification</cite>,
 396      * except that underscores are not accepted between digits.
 397      * If {@code s} does not have the form of
 398      * a <i>FloatValue</i>, then a {@code NumberFormatException}
 399      * is thrown. Otherwise, {@code s} is regarded as
 400      * representing an exact decimal value in the usual
 401      * "computerized scientific notation" or as an exact
 402      * hexadecimal value; this exact numerical value is then
 403      * conceptually converted to an "infinitely precise"
 404      * binary value that is then rounded to type {@code double}
 405      * by the usual round-to-nearest rule of IEEE 754 floating-point
 406      * arithmetic, which includes preserving the sign of a zero
 407      * value.
 408      *
 409      * Note that the round-to-nearest rule also implies overflow and
 410      * underflow behaviour; if the exact value of {@code s} is large
 411      * enough in magnitude (greater than or equal to ({@link
 412      * #MAX_VALUE} + {@link Math#ulp(double) ulp(MAX_VALUE)}/2),
 413      * rounding to {@code double} will result in an infinity and if the
 414      * exact value of {@code s} is small enough in magnitude (less
 415      * than or equal to {@link #MIN_VALUE}/2), rounding to float will
 416      * result in a zero.
 417      *
 418      * Finally, after rounding a {@code Double} object representing
 419      * this {@code double} value is returned.
 420      *
 421      * <p> To interpret localized string representations of a
 422      * floating-point value, use subclasses of {@link
 423      * java.text.NumberFormat}.
 424      *
 425      * <p>Note that trailing format specifiers, specifiers that
 426      * determine the type of a floating-point literal
 427      * ({@code 1.0f} is a {@code float} value;
 428      * {@code 1.0d} is a {@code double} value), do
 429      * <em>not</em> influence the results of this method.  In other
 430      * words, the numerical value of the input string is converted
 431      * directly to the target floating-point type.  The two-step
 432      * sequence of conversions, string to {@code float} followed
 433      * by {@code float} to {@code double}, is <em>not</em>
 434      * equivalent to converting a string directly to
 435      * {@code double}. For example, the {@code float}
 436      * literal {@code 0.1f} is equal to the {@code double}
 437      * value {@code 0.10000000149011612}; the {@code float}
 438      * literal {@code 0.1f} represents a different numerical
 439      * value than the {@code double} literal
 440      * {@code 0.1}. (The numerical value 0.1 cannot be exactly
 441      * represented in a binary floating-point number.)
 442      *
 443      * <p>To avoid calling this method on an invalid string and having
 444      * a {@code NumberFormatException} be thrown, the regular
 445      * expression below can be used to screen the input string:
 446      *
 447      * <pre>{@code
 448      *  final String Digits     = "(\\p{Digit}+)";
 449      *  final String HexDigits  = "(\\p{XDigit}+)";
 450      *  // an exponent is 'e' or 'E' followed by an optionally
 451      *  // signed decimal integer.
 452      *  final String Exp        = "[eE][+-]?"+Digits;
 453      *  final String fpRegex    =
 454      *      ("[\\x00-\\x20]*"+  // Optional leading "whitespace"
 455      *       "[+-]?(" + // Optional sign character
 456      *       "NaN|" +           // "NaN" string
 457      *       "Infinity|" +      // "Infinity" string
 458      *
 459      *       // A decimal floating-point string representing a finite positive
 460      *       // number without a leading sign has at most five basic pieces:
 461      *       // Digits . Digits ExponentPart FloatTypeSuffix
 462      *       //
 463      *       // Since this method allows integer-only strings as input
 464      *       // in addition to strings of floating-point literals, the
 465      *       // two sub-patterns below are simplifications of the grammar
 466      *       // productions from section 3.10.2 of
 467      *       // The Java Language Specification.
 468      *
 469      *       // Digits ._opt Digits_opt ExponentPart_opt FloatTypeSuffix_opt
 470      *       "((("+Digits+"(\\.)?("+Digits+"?)("+Exp+")?)|"+
 471      *
 472      *       // . Digits ExponentPart_opt FloatTypeSuffix_opt
 473      *       "(\\.("+Digits+")("+Exp+")?)|"+
 474      *
 475      *       // Hexadecimal strings
 476      *       "((" +
 477      *        // 0[xX] HexDigits ._opt BinaryExponent FloatTypeSuffix_opt
 478      *        "(0[xX]" + HexDigits + "(\\.)?)|" +
 479      *
 480      *        // 0[xX] HexDigits_opt . HexDigits BinaryExponent FloatTypeSuffix_opt
 481      *        "(0[xX]" + HexDigits + "?(\\.)" + HexDigits + ")" +
 482      *
 483      *        ")[pP][+-]?" + Digits + "))" +
 484      *       "[fFdD]?))" +
 485      *       "[\\x00-\\x20]*");// Optional trailing "whitespace"
 486      *
 487      *  if (Pattern.matches(fpRegex, myString))
 488      *      Double.valueOf(myString); // Will not throw NumberFormatException
 489      *  else {
 490      *      // Perform suitable alternative action
 491      *  }
 492      * }</pre>
 493      *
 494      * @param      s   the string to be parsed.
 495      * @return     a {@code Double} object holding the value
 496      *             represented by the {@code String} argument.
 497      * @throws     NumberFormatException  if the string does not contain a
 498      *             parsable number.
 499      */
 500     public static Double valueOf(String s) throws NumberFormatException {
 501         return new Double(parseDouble(s));
 502     }
 503 
 504     /**
 505      * Returns a {@code Double} instance representing the specified
 506      * {@code double} value.
 507      * If a new {@code Double} instance is not required, this method
 508      * should generally be used in preference to the constructor
 509      * {@link #Double(double)}, as this method is likely to yield
 510      * significantly better space and time performance by caching
 511      * frequently requested values.
 512      *
 513      * @param  d a double value.
 514      * @return a {@code Double} instance representing {@code d}.
 515      * @since  1.5
 516      */
 517     public static Double valueOf(double d) {
 518         return new Double(d);
 519     }
 520 
 521     /**
 522      * Returns a new {@code double} initialized to the value
 523      * represented by the specified {@code String}, as performed
 524      * by the {@code valueOf} method of class
 525      * {@code Double}.
 526      *
 527      * @param  s   the string to be parsed.
 528      * @return the {@code double} value represented by the string
 529      *         argument.
 530      * @throws NullPointerException  if the string is null
 531      * @throws NumberFormatException if the string does not contain
 532      *         a parsable {@code double}.
 533      * @see    java.lang.Double#valueOf(String)
 534      * @since 1.2
 535      */
 536     public static double parseDouble(String s) throws NumberFormatException {
 537         return FloatingDecimal.parseDouble(s);
 538     }
 539 
 540     /**
 541      * Returns {@code true} if the specified number is a
 542      * Not-a-Number (NaN) value, {@code false} otherwise.
 543      *
 544      * @param   v   the value to be tested.
 545      * @return  {@code true} if the value of the argument is NaN;
 546      *          {@code false} otherwise.
 547      */
 548     public static boolean isNaN(double v) {
 549         return (v != v);
 550     }
 551 
 552     /**
 553      * Returns {@code true} if the specified number is infinitely
 554      * large in magnitude, {@code false} otherwise.
 555      *
 556      * @param   v   the value to be tested.
 557      * @return  {@code true} if the value of the argument is positive
 558      *          infinity or negative infinity; {@code false} otherwise.
 559      */
 560     public static boolean isInfinite(double v) {
 561         return (v == POSITIVE_INFINITY) || (v == NEGATIVE_INFINITY);
 562     }
 563 
 564     /**
 565      * Returns {@code true} if the argument is a finite floating-point
 566      * value; returns {@code false} otherwise (for NaN and infinity
 567      * arguments).
 568      *
 569      * @param d the {@code double} value to be tested
 570      * @return {@code true} if the argument is a finite
 571      * floating-point value, {@code false} otherwise.
 572      * @since 1.8
 573      */
 574     public static boolean isFinite(double d) {
 575         return Math.abs(d) <= DoubleConsts.MAX_VALUE;
 576     }
 577 
 578     /**
 579      * The value of the Double.
 580      *
 581      * @serial
 582      */
 583     private final double value;
 584 
 585     /**
 586      * Constructs a newly allocated {@code Double} object that
 587      * represents the primitive {@code double} argument.
 588      *
 589      * @param   value   the value to be represented by the {@code Double}.
 590      */
 591     public Double(double value) {
 592         this.value = value;
 593     }
 594 
 595     /**
 596      * Constructs a newly allocated {@code Double} object that
 597      * represents the floating-point value of type {@code double}
 598      * represented by the string. The string is converted to a
 599      * {@code double} value as if by the {@code valueOf} method.
 600      *
 601      * @param  s  a string to be converted to a {@code Double}.
 602      * @throws    NumberFormatException  if the string does not contain a
 603      *            parsable number.
 604      * @see       java.lang.Double#valueOf(java.lang.String)
 605      */
 606     public Double(String s) throws NumberFormatException {
 607         value = parseDouble(s);
 608     }
 609 
 610     /**
 611      * Returns {@code true} if this {@code Double} value is
 612      * a Not-a-Number (NaN), {@code false} otherwise.
 613      *
 614      * @return  {@code true} if the value represented by this object is
 615      *          NaN; {@code false} otherwise.
 616      */
 617     public boolean isNaN() {
 618         return isNaN(value);
 619     }
 620 
 621     /**
 622      * Returns {@code true} if this {@code Double} value is
 623      * infinitely large in magnitude, {@code false} otherwise.
 624      *
 625      * @return  {@code true} if the value represented by this object is
 626      *          positive infinity or negative infinity;
 627      *          {@code false} otherwise.
 628      */
 629     public boolean isInfinite() {
 630         return isInfinite(value);
 631     }
 632 
 633     /**
 634      * Returns a string representation of this {@code Double} object.
 635      * The primitive {@code double} value represented by this
 636      * object is converted to a string exactly as if by the method
 637      * {@code toString} of one argument.
 638      *
 639      * @return  a {@code String} representation of this object.
 640      * @see java.lang.Double#toString(double)
 641      */
 642     public String toString() {
 643         return toString(value);
 644     }
 645 
 646     /**
 647      * Returns the value of this {@code Double} as a {@code byte}
 648      * after a narrowing primitive conversion.
 649      *
 650      * @return  the {@code double} value represented by this object
 651      *          converted to type {@code byte}
 652      * @jls 5.1.3 Narrowing Primitive Conversions
 653      * @since 1.1
 654      */
 655     public byte byteValue() {
 656         return (byte)value;
 657     }
 658 
 659     /**
 660      * Returns the value of this {@code Double} as a {@code short}
 661      * after a narrowing primitive conversion.
 662      *
 663      * @return  the {@code double} value represented by this object
 664      *          converted to type {@code short}
 665      * @jls 5.1.3 Narrowing Primitive Conversions
 666      * @since 1.1
 667      */
 668     public short shortValue() {
 669         return (short)value;
 670     }
 671 
 672     /**
 673      * Returns the value of this {@code Double} as an {@code int}
 674      * after a narrowing primitive conversion.
 675      * @jls 5.1.3 Narrowing Primitive Conversions
 676      *
 677      * @return  the {@code double} value represented by this object
 678      *          converted to type {@code int}
 679      */
 680     public int intValue() {
 681         return (int)value;
 682     }
 683 
 684     /**
 685      * Returns the value of this {@code Double} as a {@code long}
 686      * after a narrowing primitive conversion.
 687      *
 688      * @return  the {@code double} value represented by this object
 689      *          converted to type {@code long}
 690      * @jls 5.1.3 Narrowing Primitive Conversions
 691      */
 692     public long longValue() {
 693         return (long)value;
 694     }
 695 
 696     /**
 697      * Returns the value of this {@code Double} as a {@code float}
 698      * after a narrowing primitive conversion.
 699      *
 700      * @return  the {@code double} value represented by this object
 701      *          converted to type {@code float}
 702      * @jls 5.1.3 Narrowing Primitive Conversions
 703      * @since 1.0
 704      */
 705     public float floatValue() {
 706         return (float)value;
 707     }
 708 
 709     /**
 710      * Returns the {@code double} value of this {@code Double} object.
 711      *
 712      * @return the {@code double} value represented by this object
 713      */
 714     public double doubleValue() {
 715         return value;
 716     }
 717 
 718     /**
 719      * Returns a hash code for this {@code Double} object. The
 720      * result is the exclusive OR of the two halves of the
 721      * {@code long} integer bit representation, exactly as
 722      * produced by the method {@link #doubleToLongBits(double)}, of
 723      * the primitive {@code double} value represented by this
 724      * {@code Double} object. That is, the hash code is the value
 725      * of the expression:
 726      *
 727      * <blockquote>
 728      *  {@code (int)(v^(v>>>32))}
 729      * </blockquote>
 730      *
 731      * where {@code v} is defined by:
 732      *
 733      * <blockquote>
 734      *  {@code long v = Double.doubleToLongBits(this.doubleValue());}
 735      * </blockquote>
 736      *
 737      * @return  a {@code hash code} value for this object.
 738      */
 739     @Override
 740     public int hashCode() {
 741         return Double.hashCode(value);
 742     }
 743 
 744     /**
 745      * Returns a hash code for a {@code double} value; compatible with
 746      * {@code Double.hashCode()}.
 747      *
 748      * @param value the value to hash
 749      * @return a hash code value for a {@code double} value.
 750      * @since 1.8
 751      */
 752     public static int hashCode(double value) {
 753         long bits = doubleToLongBits(value);
 754         return (int)(bits ^ (bits >>> 32));
 755     }
 756 
 757     /**
 758      * Compares this object against the specified object.  The result
 759      * is {@code true} if and only if the argument is not
 760      * {@code null} and is a {@code Double} object that
 761      * represents a {@code double} that has the same value as the
 762      * {@code double} represented by this object. For this
 763      * purpose, two {@code double} values are considered to be
 764      * the same if and only if the method {@link
 765      * #doubleToLongBits(double)} returns the identical
 766      * {@code long} value when applied to each.
 767      *
 768      * <p>Note that in most cases, for two instances of class
 769      * {@code Double}, {@code d1} and {@code d2}, the
 770      * value of {@code d1.equals(d2)} is {@code true} if and
 771      * only if
 772      *
 773      * <blockquote>
 774      *  {@code d1.doubleValue() == d2.doubleValue()}
 775      * </blockquote>
 776      *
 777      * <p>also has the value {@code true}. However, there are two
 778      * exceptions:
 779      * <ul>
 780      * <li>If {@code d1} and {@code d2} both represent
 781      *     {@code Double.NaN}, then the {@code equals} method
 782      *     returns {@code true}, even though
 783      *     {@code Double.NaN==Double.NaN} has the value
 784      *     {@code false}.
 785      * <li>If {@code d1} represents {@code +0.0} while
 786      *     {@code d2} represents {@code -0.0}, or vice versa,
 787      *     the {@code equal} test has the value {@code false},
 788      *     even though {@code +0.0==-0.0} has the value {@code true}.
 789      * </ul>
 790      * This definition allows hash tables to operate properly.
 791      * @param   obj   the object to compare with.
 792      * @return  {@code true} if the objects are the same;
 793      *          {@code false} otherwise.
 794      * @see java.lang.Double#doubleToLongBits(double)
 795      */
 796     public boolean equals(Object obj) {
 797         return (obj instanceof Double)
 798                && (doubleToLongBits(((Double)obj).value) ==
 799                       doubleToLongBits(value));
 800     }
 801 
 802     /**
 803      * Returns a representation of the specified floating-point value
 804      * according to the IEEE 754 floating-point "double
 805      * format" bit layout.
 806      *
 807      * <p>Bit 63 (the bit that is selected by the mask
 808      * {@code 0x8000000000000000L}) represents the sign of the
 809      * floating-point number. Bits
 810      * 62-52 (the bits that are selected by the mask
 811      * {@code 0x7ff0000000000000L}) represent the exponent. Bits 51-0
 812      * (the bits that are selected by the mask
 813      * {@code 0x000fffffffffffffL}) represent the significand
 814      * (sometimes called the mantissa) of the floating-point number.
 815      *
 816      * <p>If the argument is positive infinity, the result is
 817      * {@code 0x7ff0000000000000L}.
 818      *
 819      * <p>If the argument is negative infinity, the result is
 820      * {@code 0xfff0000000000000L}.
 821      *
 822      * <p>If the argument is NaN, the result is
 823      * {@code 0x7ff8000000000000L}.
 824      *
 825      * <p>In all cases, the result is a {@code long} integer that, when
 826      * given to the {@link #longBitsToDouble(long)} method, will produce a
 827      * floating-point value the same as the argument to
 828      * {@code doubleToLongBits} (except all NaN values are
 829      * collapsed to a single "canonical" NaN value).
 830      *
 831      * @param   value   a {@code double} precision floating-point number.
 832      * @return the bits that represent the floating-point number.
 833      */
 834     public static long doubleToLongBits(double value) {
 835         if (!isNaN(value)) {
 836             return doubleToRawLongBits(value);
 837         }
 838         return 0x7ff8000000000000L;
 839     }
 840 
 841     /**
 842      * Returns a representation of the specified floating-point value
 843      * according to the IEEE 754 floating-point "double
 844      * format" bit layout, preserving Not-a-Number (NaN) values.
 845      *
 846      * <p>Bit 63 (the bit that is selected by the mask
 847      * {@code 0x8000000000000000L}) represents the sign of the
 848      * floating-point number. Bits
 849      * 62-52 (the bits that are selected by the mask
 850      * {@code 0x7ff0000000000000L}) represent the exponent. Bits 51-0
 851      * (the bits that are selected by the mask
 852      * {@code 0x000fffffffffffffL}) represent the significand
 853      * (sometimes called the mantissa) of the floating-point number.
 854      *
 855      * <p>If the argument is positive infinity, the result is
 856      * {@code 0x7ff0000000000000L}.
 857      *
 858      * <p>If the argument is negative infinity, the result is
 859      * {@code 0xfff0000000000000L}.
 860      *
 861      * <p>If the argument is NaN, the result is the {@code long}
 862      * integer representing the actual NaN value.  Unlike the
 863      * {@code doubleToLongBits} method,
 864      * {@code doubleToRawLongBits} does not collapse all the bit
 865      * patterns encoding a NaN to a single "canonical" NaN
 866      * value.
 867      *
 868      * <p>In all cases, the result is a {@code long} integer that,
 869      * when given to the {@link #longBitsToDouble(long)} method, will
 870      * produce a floating-point value the same as the argument to
 871      * {@code doubleToRawLongBits}.
 872      *
 873      * @param   value   a {@code double} precision floating-point number.
 874      * @return the bits that represent the floating-point number.
 875      * @since 1.3
 876      */
 877     public static native long doubleToRawLongBits(double value);
 878 
 879     /**
 880      * Returns the {@code double} value corresponding to a given
 881      * bit representation.
 882      * The argument is considered to be a representation of a
 883      * floating-point value according to the IEEE 754 floating-point
 884      * "double format" bit layout.
 885      *
 886      * <p>If the argument is {@code 0x7ff0000000000000L}, the result
 887      * is positive infinity.
 888      *
 889      * <p>If the argument is {@code 0xfff0000000000000L}, the result
 890      * is negative infinity.
 891      *
 892      * <p>If the argument is any value in the range
 893      * {@code 0x7ff0000000000001L} through
 894      * {@code 0x7fffffffffffffffL} or in the range
 895      * {@code 0xfff0000000000001L} through
 896      * {@code 0xffffffffffffffffL}, the result is a NaN.  No IEEE
 897      * 754 floating-point operation provided by Java can distinguish
 898      * between two NaN values of the same type with different bit
 899      * patterns.  Distinct values of NaN are only distinguishable by
 900      * use of the {@code Double.doubleToRawLongBits} method.
 901      *
 902      * <p>In all other cases, let <i>s</i>, <i>e</i>, and <i>m</i> be three
 903      * values that can be computed from the argument:
 904      *
 905      * <blockquote><pre>{@code
 906      * int s = ((bits >> 63) == 0) ? 1 : -1;
 907      * int e = (int)((bits >> 52) & 0x7ffL);
 908      * long m = (e == 0) ?
 909      *                 (bits & 0xfffffffffffffL) << 1 :
 910      *                 (bits & 0xfffffffffffffL) | 0x10000000000000L;
 911      * }</pre></blockquote>
 912      *
 913      * Then the floating-point result equals the value of the mathematical
 914      * expression <i>s</i>&middot;<i>m</i>&middot;2<sup><i>e</i>-1075</sup>.
 915      *
 916      * <p>Note that this method may not be able to return a
 917      * {@code double} NaN with exactly same bit pattern as the
 918      * {@code long} argument.  IEEE 754 distinguishes between two
 919      * kinds of NaNs, quiet NaNs and <i>signaling NaNs</i>.  The
 920      * differences between the two kinds of NaN are generally not
 921      * visible in Java.  Arithmetic operations on signaling NaNs turn
 922      * them into quiet NaNs with a different, but often similar, bit
 923      * pattern.  However, on some processors merely copying a
 924      * signaling NaN also performs that conversion.  In particular,
 925      * copying a signaling NaN to return it to the calling method
 926      * may perform this conversion.  So {@code longBitsToDouble}
 927      * may not be able to return a {@code double} with a
 928      * signaling NaN bit pattern.  Consequently, for some
 929      * {@code long} values,
 930      * {@code doubleToRawLongBits(longBitsToDouble(start))} may
 931      * <i>not</i> equal {@code start}.  Moreover, which
 932      * particular bit patterns represent signaling NaNs is platform
 933      * dependent; although all NaN bit patterns, quiet or signaling,
 934      * must be in the NaN range identified above.
 935      *
 936      * @param   bits   any {@code long} integer.
 937      * @return  the {@code double} floating-point value with the same
 938      *          bit pattern.
 939      */
 940     public static native double longBitsToDouble(long bits);
 941 
 942     /**
 943      * Compares two {@code Double} objects numerically.  There
 944      * are two ways in which comparisons performed by this method
 945      * differ from those performed by the Java language numerical
 946      * comparison operators ({@code <, <=, ==, >=, >})
 947      * when applied to primitive {@code double} values:
 948      * <ul><li>
 949      *          {@code Double.NaN} is considered by this method
 950      *          to be equal to itself and greater than all other
 951      *          {@code double} values (including
 952      *          {@code Double.POSITIVE_INFINITY}).
 953      * <li>
 954      *          {@code 0.0d} is considered by this method to be greater
 955      *          than {@code -0.0d}.
 956      * </ul>
 957      * This ensures that the <i>natural ordering</i> of
 958      * {@code Double} objects imposed by this method is <i>consistent
 959      * with equals</i>.
 960      *
 961      * @param   anotherDouble   the {@code Double} to be compared.
 962      * @return  the value {@code 0} if {@code anotherDouble} is
 963      *          numerically equal to this {@code Double}; a value
 964      *          less than {@code 0} if this {@code Double}
 965      *          is numerically less than {@code anotherDouble};
 966      *          and a value greater than {@code 0} if this
 967      *          {@code Double} is numerically greater than
 968      *          {@code anotherDouble}.
 969      *
 970      * @since   1.2
 971      */
 972     public int compareTo(Double anotherDouble) {
 973         return Double.compare(value, anotherDouble.value);
 974     }
 975 
 976     /**
 977      * Compares the two specified {@code double} values. The sign
 978      * of the integer value returned is the same as that of the
 979      * integer that would be returned by the call:
 980      * <pre>
 981      *    new Double(d1).compareTo(new Double(d2))
 982      * </pre>
 983      *
 984      * @param   d1        the first {@code double} to compare
 985      * @param   d2        the second {@code double} to compare
 986      * @return  the value {@code 0} if {@code d1} is
 987      *          numerically equal to {@code d2}; a value less than
 988      *          {@code 0} if {@code d1} is numerically less than
 989      *          {@code d2}; and a value greater than {@code 0}
 990      *          if {@code d1} is numerically greater than
 991      *          {@code d2}.
 992      * @since 1.4
 993      */
 994     public static int compare(double d1, double d2) {
 995         if (d1 < d2)
 996             return -1;           // Neither val is NaN, thisVal is smaller
 997         if (d1 > d2)
 998             return 1;            // Neither val is NaN, thisVal is larger
 999 
1000         // Cannot use doubleToRawLongBits because of possibility of NaNs.
1001         long thisBits    = Double.doubleToLongBits(d1);
1002         long anotherBits = Double.doubleToLongBits(d2);
1003 
1004         return (thisBits == anotherBits ?  0 : // Values are equal
1005                 (thisBits < anotherBits ? -1 : // (-0.0, 0.0) or (!NaN, NaN)
1006                  1));                          // (0.0, -0.0) or (NaN, !NaN)
1007     }
1008 
1009     /**
1010      * Adds two {@code double} values together as per the + operator.
1011      *
1012      * @param a the first operand
1013      * @param b the second operand
1014      * @return the sum of {@code a} and {@code b}
1015      * @jls 4.2.4 Floating-Point Operations
1016      * @see java.util.function.BinaryOperator
1017      * @since 1.8
1018      */
1019     public static double sum(double a, double b) {
1020         return a + b;
1021     }
1022 
1023     /**
1024      * Returns the greater of two {@code double} values
1025      * as if by calling {@link Math#max(double, double) Math.max}.
1026      *
1027      * @param a the first operand
1028      * @param b the second operand
1029      * @return the greater of {@code a} and {@code b}
1030      * @see java.util.function.BinaryOperator
1031      * @since 1.8
1032      */
1033     public static double max(double a, double b) {
1034         return Math.max(a, b);
1035     }
1036 
1037     /**
1038      * Returns the smaller of two {@code double} values
1039      * as if by calling {@link Math#min(double, double) Math.min}.
1040      *
1041      * @param a the first operand
1042      * @param b the second operand
1043      * @return the smaller of {@code a} and {@code b}.
1044      * @see java.util.function.BinaryOperator
1045      * @since 1.8
1046      */
1047     public static double min(double a, double b) {
1048         return Math.min(a, b);
1049     }
1050 
1051     /** use serialVersionUID from JDK 1.0.2 for interoperability */
1052     private static final long serialVersionUID = -9172774392245257468L;
1053 }