1 /* 2 * Copyright (c) 1994, 2024, 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 java.lang.invoke.MethodHandles; 29 import java.lang.constant.Constable; 30 import java.lang.constant.ConstantDesc; 31 import java.util.Optional; 32 33 import jdk.internal.math.FloatingDecimal; 34 import jdk.internal.math.DoubleConsts; 35 import jdk.internal.math.DoubleToDecimal; 36 import jdk.internal.vm.annotation.IntrinsicCandidate; 37 38 /** 39 * The {@code Double} class wraps a value of the primitive type 40 * {@code double} in an object. An object of type 41 * {@code Double} contains a single field whose type is 42 * {@code double}. 43 * 44 * <p>In addition, this class provides several methods for converting a 45 * {@code double} to a {@code String} and a 46 * {@code String} to a {@code double}, as well as other 47 * constants and methods useful when dealing with a 48 * {@code double}. 49 * 50 * <p>This is a <a href="{@docRoot}/java.base/java/lang/doc-files/ValueBased.html">value-based</a> 51 * class; programmers should treat instances that are 52 * {@linkplain #equals(Object) equal} as interchangeable and should not 53 * use instances for synchronization, or unpredictable behavior may 54 * occur. For example, in a future release, synchronization may fail. 55 * 56 * <h2><a id=equivalenceRelation>Floating-point Equality, Equivalence, 57 * and Comparison</a></h2> 58 * 59 * IEEE 754 floating-point values include finite nonzero values, 60 * signed zeros ({@code +0.0} and {@code -0.0}), signed infinities 61 * ({@linkplain Double#POSITIVE_INFINITY positive infinity} and 62 * {@linkplain Double#NEGATIVE_INFINITY negative infinity}), and 63 * {@linkplain Double#NaN NaN} (not-a-number). 64 * 65 * <p>An <em>equivalence relation</em> on a set of values is a boolean 66 * relation on pairs of values that is reflexive, symmetric, and 67 * transitive. For more discussion of equivalence relations and object 68 * equality, see the {@link Object#equals Object.equals} 69 * specification. An equivalence relation partitions the values it 70 * operates over into sets called <i>equivalence classes</i>. All the 71 * members of the equivalence class are equal to each other under the 72 * relation. An equivalence class may contain only a single member. At 73 * least for some purposes, all the members of an equivalence class 74 * are substitutable for each other. In particular, in a numeric 75 * expression equivalent values can be <em>substituted</em> for one 76 * another without changing the result of the expression, meaning 77 * changing the equivalence class of the result of the expression. 78 * 79 * <p>Notably, the built-in {@code ==} operation on floating-point 80 * values is <em>not</em> an equivalence relation. Despite not 81 * defining an equivalence relation, the semantics of the IEEE 754 82 * {@code ==} operator were deliberately designed to meet other needs 83 * of numerical computation. There are two exceptions where the 84 * properties of an equivalence relation are not satisfied by {@code 85 * ==} on floating-point values: 86 * 87 * <ul> 88 * 89 * <li>If {@code v1} and {@code v2} are both NaN, then {@code v1 90 * == v2} has the value {@code false}. Therefore, for two NaN 91 * arguments the <em>reflexive</em> property of an equivalence 92 * relation is <em>not</em> satisfied by the {@code ==} operator. 93 * 94 * <li>If {@code v1} represents {@code +0.0} while {@code v2} 95 * represents {@code -0.0}, or vice versa, then {@code v1 == v2} has 96 * the value {@code true} even though {@code +0.0} and {@code -0.0} 97 * are distinguishable under various floating-point operations. For 98 * example, {@code 1.0/+0.0} evaluates to positive infinity while 99 * {@code 1.0/-0.0} evaluates to <em>negative</em> infinity and 100 * positive infinity and negative infinity are neither equal to each 101 * other nor equivalent to each other. Thus, while a signed zero input 102 * most commonly determines the sign of a zero result, because of 103 * dividing by zero, {@code +0.0} and {@code -0.0} may not be 104 * substituted for each other in general. The sign of a zero input 105 * also has a non-substitutable effect on the result of some math 106 * library methods. 107 * 108 * </ul> 109 * 110 * <p>For ordered comparisons using the built-in comparison operators 111 * ({@code <}, {@code <=}, etc.), NaN values have another anomalous 112 * situation: a NaN is neither less than, nor greater than, nor equal 113 * to any value, including itself. This means the <i>trichotomy of 114 * comparison</i> does <em>not</em> hold. 115 * 116 * <p>To provide the appropriate semantics for {@code equals} and 117 * {@code compareTo} methods, those methods cannot simply be wrappers 118 * around {@code ==} or ordered comparison operations. Instead, {@link 119 * Double#equals equals} uses <a href=#repEquivalence> representation 120 * equivalence</a>, defining NaN arguments to be equal to each other, 121 * restoring reflexivity, and defining {@code +0.0} to <em>not</em> be 122 * equal to {@code -0.0}. For comparisons, {@link Double#compareTo 123 * compareTo} defines a total order where {@code -0.0} is less than 124 * {@code +0.0} and where a NaN is equal to itself and considered 125 * greater than positive infinity. 126 * 127 * <p>The operational semantics of {@code equals} and {@code 128 * compareTo} are expressed in terms of {@linkplain #doubleToLongBits 129 * bit-wise converting} the floating-point values to integral values. 130 * 131 * <p>The <em>natural ordering</em> implemented by {@link #compareTo 132 * compareTo} is {@linkplain Comparable consistent with equals}. That 133 * is, two objects are reported as equal by {@code equals} if and only 134 * if {@code compareTo} on those objects returns zero. 135 * 136 * <p>The adjusted behaviors defined for {@code equals} and {@code 137 * compareTo} allow instances of wrapper classes to work properly with 138 * conventional data structures. For example, defining NaN 139 * values to be {@code equals} to one another allows NaN to be used as 140 * an element of a {@link java.util.HashSet HashSet} or as the key of 141 * a {@link java.util.HashMap HashMap}. Similarly, defining {@code 142 * compareTo} as a total ordering, including {@code +0.0}, {@code 143 * -0.0}, and NaN, allows instances of wrapper classes to be used as 144 * elements of a {@link java.util.SortedSet SortedSet} or as keys of a 145 * {@link java.util.SortedMap SortedMap}. 146 * 147 * <p>Comparing numerical equality to various useful equivalence 148 * relations that can be defined over floating-point values: 149 * 150 * <dl> 151 * <dt><a id=fpNumericalEq><i>numerical equality</i></a> ({@code ==} 152 * operator): (<em>Not</em> an equivalence relation)</dt> 153 * <dd>Two floating-point values represent the same extended real 154 * number. The extended real numbers are the real numbers augmented 155 * with positive infinity and negative infinity. Under numerical 156 * equality, {@code +0.0} and {@code -0.0} are equal since they both 157 * map to the same real value, 0. A NaN does not map to any real 158 * number and is not equal to any value, including itself. 159 * </dd> 160 * 161 * <dt><i>bit-wise equivalence</i>:</dt> 162 * <dd>The bits of the two floating-point values are the same. This 163 * equivalence relation for {@code double} values {@code a} and {@code 164 * b} is implemented by the expression 165 * <br>{@code Double.doubleTo}<code><b>Raw</b></code>{@code LongBits(a) == Double.doubleTo}<code><b>Raw</b></code>{@code LongBits(b)}<br> 166 * Under this relation, {@code +0.0} and {@code -0.0} are 167 * distinguished from each other and every bit pattern encoding a NaN 168 * is distinguished from every other bit pattern encoding a NaN. 169 * </dd> 170 * 171 * <dt><i><a id=repEquivalence>representation equivalence</a></i>:</dt> 172 * <dd>The two floating-point values represent the same IEEE 754 173 * <i>datum</i>. In particular, for {@linkplain #isFinite(double) 174 * finite} values, the sign, {@linkplain Math#getExponent(double) 175 * exponent}, and significand components of the floating-point values 176 * are the same. Under this relation: 177 * <ul> 178 * <li> {@code +0.0} and {@code -0.0} are distinguished from each other. 179 * <li> every bit pattern encoding a NaN is considered equivalent to each other 180 * <li> positive infinity is equivalent to positive infinity; negative 181 * infinity is equivalent to negative infinity. 182 * </ul> 183 * Expressions implementing this equivalence relation include: 184 * <ul> 185 * <li>{@code Double.doubleToLongBits(a) == Double.doubleToLongBits(b)} 186 * <li>{@code Double.valueOf(a).equals(Double.valueOf(b))} 187 * <li>{@code Double.compare(a, b) == 0} 188 * </ul> 189 * Note that representation equivalence is often an appropriate notion 190 * of equivalence to test the behavior of {@linkplain StrictMath math 191 * libraries}. 192 * </dd> 193 * </dl> 194 * 195 * For two binary floating-point values {@code a} and {@code b}, if 196 * neither of {@code a} and {@code b} is zero or NaN, then the three 197 * relations numerical equality, bit-wise equivalence, and 198 * representation equivalence of {@code a} and {@code b} have the same 199 * {@code true}/{@code false} value. In other words, for binary 200 * floating-point values, the three relations only differ if at least 201 * one argument is zero or NaN. 202 * 203 * <h2><a id=decimalToBinaryConversion>Decimal ↔ Binary Conversion Issues</a></h2> 204 * 205 * Many surprising results of binary floating-point arithmetic trace 206 * back to aspects of decimal to binary conversion and binary to 207 * decimal conversion. While integer values can be exactly represented 208 * in any base, which fractional values can be exactly represented in 209 * a base is a function of the base. For example, in base 10, 1/3 is a 210 * repeating fraction (0.33333....); but in base 3, 1/3 is exactly 211 * 0.1<sub>(3)</sub>, that is 1 × 3<sup>-1</sup>. 212 * Similarly, in base 10, 1/10 is exactly representable as 0.1 213 * (1 × 10<sup>-1</sup>), but in base 2, it is a 214 * repeating fraction (0.0001100110011...<sub>(2)</sub>). 215 * 216 * <p>Values of the {@code float} type have {@value Float#PRECISION} 217 * bits of precision and values of the {@code double} type have 218 * {@value Double#PRECISION} bits of precision. Therefore, since 0.1 219 * is a repeating fraction in base 2 with a four-bit repeat, {@code 220 * 0.1f} != {@code 0.1d}. In more detail, including hexadecimal 221 * floating-point literals: 222 * 223 * <ul> 224 * <li>The exact numerical value of {@code 0.1f} ({@code 0x1.99999a0000000p-4f}) is 225 * 0.100000001490116119384765625. 226 * <li>The exact numerical value of {@code 0.1d} ({@code 0x1.999999999999ap-4d}) is 227 * 0.1000000000000000055511151231257827021181583404541015625. 228 * </ul> 229 * 230 * These are the closest {@code float} and {@code double} values, 231 * respectively, to the numerical value of 0.1. These results are 232 * consistent with a {@code float} value having the equivalent of 6 to 233 * 9 digits of decimal precision and a {@code double} value having the 234 * equivalent of 15 to 17 digits of decimal precision. (The 235 * equivalent precision varies according to the different relative 236 * densities of binary and decimal values at different points along the 237 * real number line.) 238 * 239 * <p>This representation hazard of decimal fractions is one reason to 240 * use caution when storing monetary values as {@code float} or {@code 241 * double}. Alternatives include: 242 * <ul> 243 * <li>using {@link java.math.BigDecimal BigDecimal} to store decimal 244 * fractional values exactly 245 * 246 * <li>scaling up so the monetary value is an integer — for 247 * example, multiplying by 100 if the value is denominated in cents or 248 * multiplying by 1000 if the value is denominated in mills — 249 * and then storing that scaled value in an integer type 250 * 251 *</ul> 252 * 253 * <p>For each finite floating-point value and a given floating-point 254 * type, there is a contiguous region of the real number line which 255 * maps to that value. Under the default round to nearest rounding 256 * policy (JLS {@jls 15.4}), this contiguous region for a value is 257 * typically one {@linkplain Math#ulp ulp} (unit in the last place) 258 * wide and centered around the exactly representable value. (At 259 * exponent boundaries, the region is asymmetrical and larger on the 260 * side with the larger exponent.) For example, for {@code 0.1f}, the 261 * region can be computed as follows: 262 * 263 * <br>// Numeric values listed are exact values 264 * <br>oneTenthApproxAsFloat = 0.100000001490116119384765625; 265 * <br>ulpOfoneTenthApproxAsFloat = Math.ulp(0.1f) = 7.450580596923828125E-9; 266 * <br>// Numeric range that is converted to the float closest to 0.1, _excludes_ endpoints 267 * <br>(oneTenthApproxAsFloat - ½ulpOfoneTenthApproxAsFloat, oneTenthApproxAsFloat + ½ulpOfoneTenthApproxAsFloat) = 268 * <br>(0.0999999977648258209228515625, 0.1000000052154064178466796875) 269 * 270 * <p>In particular, a correctly rounded decimal to binary conversion 271 * of any string representing a number in this range, say by {@link 272 * Float#parseFloat(String)}, will be converted to the same value: 273 * 274 * {@snippet lang="java" : 275 * Float.parseFloat("0.0999999977648258209228515625000001"); // rounds up to oneTenthApproxAsFloat 276 * Float.parseFloat("0.099999998"); // rounds up to oneTenthApproxAsFloat 277 * Float.parseFloat("0.1"); // rounds up to oneTenthApproxAsFloat 278 * Float.parseFloat("0.100000001490116119384765625"); // exact conversion 279 * Float.parseFloat("0.100000005215406417846679687"); // rounds down to oneTenthApproxAsFloat 280 * Float.parseFloat("0.100000005215406417846679687499999"); // rounds down to oneTenthApproxAsFloat 281 * } 282 * 283 * <p>Similarly, an analogous range can be constructed for the {@code 284 * double} type based on the exact value of {@code double} 285 * approximation to {@code 0.1d} and the numerical value of {@code 286 * Math.ulp(0.1d)} and likewise for other particular numerical values 287 * in the {@code float} and {@code double} types. 288 * 289 * <p>As seen in the above conversions, compared to the exact 290 * numerical value the operation would have without rounding, the same 291 * floating-point value as a result can be: 292 * <ul> 293 * <li>greater than the exact result 294 * <li>equal to the exact result 295 * <li>less than the exact result 296 * </ul> 297 * 298 * A floating-point value doesn't "know" whether it was the result of 299 * rounding up, or rounding down, or an exact operation; it contains 300 * no history of how it was computed. Consequently, the sum of 301 * {@snippet lang="java" : 302 * 0.1f + 0.1f + 0.1f + 0.1f + 0.1f + 0.1f + 0.1f + 0.1f + 0.1f + 0.1f; 303 * // Numerical value of computed sum: 1.00000011920928955078125, 304 * // the next floating-point value larger than 1.0f, equal to Math.nextUp(1.0f). 305 * } 306 * or 307 * {@snippet lang="java" : 308 * 0.1d + 0.1d + 0.1d + 0.1d + 0.1d + 0.1d + 0.1d + 0.1d + 0.1d + 0.1d; 309 * // Numerical value of computed sum: 0.99999999999999988897769753748434595763683319091796875, 310 * // the next floating-point value smaller than 1.0d, equal to Math.nextDown(1.0d). 311 * } 312 * 313 * should <em>not</em> be expected to be exactly equal to 1.0, but 314 * only to be close to 1.0. Consequently, the following code is an 315 * infinite loop: 316 * 317 * {@snippet lang="java" : 318 * double d = 0.0; 319 * while (d != 1.0) { // Surprising infinite loop 320 * d += 0.1; // Sum never _exactly_ equals 1.0 321 * } 322 * } 323 * 324 * Instead, use an integer loop count for counted loops: 325 * 326 * {@snippet lang="java" : 327 * double d = 0.0; 328 * for (int i = 0; i < 10; i++) { 329 * d += 0.1; 330 * } // Value of d is equal to Math.nextDown(1.0). 331 * } 332 * 333 * or test against a floating-point limit using ordered comparisons 334 * ({@code <}, {@code <=}, {@code >}, {@code >=}): 335 * 336 * {@snippet lang="java" : 337 * double d = 0.0; 338 * while (d <= 1.0) { 339 * d += 0.1; 340 * } // Value of d approximately 1.0999999999999999 341 * } 342 * 343 * While floating-point arithmetic may have surprising results, IEEE 344 * 754 floating-point arithmetic follows a principled design and its 345 * behavior is predictable on the Java platform. 346 * 347 * @jls 4.2.3 Floating-Point Types, Formats, and Values 348 * @jls 4.2.4. Floating-Point Operations 349 * @jls 15.21.1 Numerical Equality Operators == and != 350 * @jls 15.20.1 Numerical Comparison Operators {@code <}, {@code <=}, {@code >}, and {@code >=} 351 * 352 * @see <a href="https://standards.ieee.org/ieee/754/6210/"> 353 * <cite>IEEE Standard for Floating-Point Arithmetic</cite></a> 354 * 355 * @author Lee Boynton 356 * @author Arthur van Hoff 357 * @author Joseph D. Darcy 358 * @since 1.0 359 */ 360 @jdk.internal.MigratedValueClass 361 @jdk.internal.ValueBased 362 public final class Double extends Number 363 implements Comparable<Double>, Constable, ConstantDesc { 364 /** 365 * A constant holding the positive infinity of type 366 * {@code double}. It is equal to the value returned by 367 * {@code Double.longBitsToDouble(0x7ff0000000000000L)}. 368 */ 369 public static final double POSITIVE_INFINITY = 1.0 / 0.0; 370 371 /** 372 * A constant holding the negative infinity of type 373 * {@code double}. It is equal to the value returned by 374 * {@code Double.longBitsToDouble(0xfff0000000000000L)}. 375 */ 376 public static final double NEGATIVE_INFINITY = -1.0 / 0.0; 377 378 /** 379 * A constant holding a Not-a-Number (NaN) value of type 380 * {@code double}. It is equivalent to the value returned by 381 * {@code Double.longBitsToDouble(0x7ff8000000000000L)}. 382 */ 383 public static final double NaN = 0.0d / 0.0; 384 385 /** 386 * A constant holding the largest positive finite value of type 387 * {@code double}, 388 * (2-2<sup>-52</sup>)·2<sup>1023</sup>. It is equal to 389 * the hexadecimal floating-point literal 390 * {@code 0x1.fffffffffffffP+1023} and also equal to 391 * {@code Double.longBitsToDouble(0x7fefffffffffffffL)}. 392 */ 393 public static final double MAX_VALUE = 0x1.fffffffffffffP+1023; // 1.7976931348623157e+308 394 395 /** 396 * A constant holding the smallest positive normal value of type 397 * {@code double}, 2<sup>-1022</sup>. It is equal to the 398 * hexadecimal floating-point literal {@code 0x1.0p-1022} and also 399 * equal to {@code Double.longBitsToDouble(0x0010000000000000L)}. 400 * 401 * @since 1.6 402 */ 403 public static final double MIN_NORMAL = 0x1.0p-1022; // 2.2250738585072014E-308 404 405 /** 406 * A constant holding the smallest positive nonzero value of type 407 * {@code double}, 2<sup>-1074</sup>. It is equal to the 408 * hexadecimal floating-point literal 409 * {@code 0x0.0000000000001P-1022} and also equal to 410 * {@code Double.longBitsToDouble(0x1L)}. 411 */ 412 public static final double MIN_VALUE = 0x0.0000000000001P-1022; // 4.9e-324 413 414 /** 415 * The number of bits used to represent a {@code double} value, 416 * {@value}. 417 * 418 * @since 1.5 419 */ 420 public static final int SIZE = 64; 421 422 /** 423 * The number of bits in the significand of a {@code double} 424 * value, {@value}. This is the parameter N in section {@jls 425 * 4.2.3} of <cite>The Java Language Specification</cite>. 426 * 427 * @since 19 428 */ 429 public static final int PRECISION = 53; 430 431 /** 432 * Maximum exponent a finite {@code double} variable may have, 433 * {@value}. It is equal to the value returned by {@code 434 * Math.getExponent(Double.MAX_VALUE)}. 435 * 436 * @since 1.6 437 */ 438 public static final int MAX_EXPONENT = (1 << (SIZE - PRECISION - 1)) - 1; // 1023 439 440 /** 441 * Minimum exponent a normalized {@code double} variable may have, 442 * {@value}. It is equal to the value returned by {@code 443 * Math.getExponent(Double.MIN_NORMAL)}. 444 * 445 * @since 1.6 446 */ 447 public static final int MIN_EXPONENT = 1 - MAX_EXPONENT; // -1022 448 449 /** 450 * The number of bytes used to represent a {@code double} value, 451 * {@value}. 452 * 453 * @since 1.8 454 */ 455 public static final int BYTES = SIZE / Byte.SIZE; 456 457 /** 458 * The {@code Class} instance representing the primitive type 459 * {@code double}. 460 * 461 * @since 1.1 462 */ 463 @SuppressWarnings("unchecked") 464 public static final Class<Double> TYPE = (Class<Double>) Class.getPrimitiveClass("double"); 465 466 /** 467 * Returns a string representation of the {@code double} 468 * argument. All characters mentioned below are ASCII characters. 469 * <ul> 470 * <li>If the argument is NaN, the result is the string 471 * "{@code NaN}". 472 * <li>Otherwise, the result is a string that represents the sign and 473 * magnitude (absolute value) of the argument. If the sign is negative, 474 * the first character of the result is '{@code -}' 475 * ({@code '\u005Cu002D'}); if the sign is positive, no sign character 476 * appears in the result. As for the magnitude <i>m</i>: 477 * <ul> 478 * <li>If <i>m</i> is infinity, it is represented by the characters 479 * {@code "Infinity"}; thus, positive infinity produces the result 480 * {@code "Infinity"} and negative infinity produces the result 481 * {@code "-Infinity"}. 482 * 483 * <li>If <i>m</i> is zero, it is represented by the characters 484 * {@code "0.0"}; thus, negative zero produces the result 485 * {@code "-0.0"} and positive zero produces the result 486 * {@code "0.0"}. 487 * 488 * <li> Otherwise <i>m</i> is positive and finite. 489 * It is converted to a string in two stages: 490 * <ul> 491 * <li> <em>Selection of a decimal</em>: 492 * A well-defined decimal <i>d</i><sub><i>m</i></sub> 493 * is selected to represent <i>m</i>. 494 * This decimal is (almost always) the <em>shortest</em> one that 495 * rounds to <i>m</i> according to the round to nearest 496 * rounding policy of IEEE 754 floating-point arithmetic. 497 * <li> <em>Formatting as a string</em>: 498 * The decimal <i>d</i><sub><i>m</i></sub> is formatted as a string, 499 * either in plain or in computerized scientific notation, 500 * depending on its value. 501 * </ul> 502 * </ul> 503 * </ul> 504 * 505 * <p>A <em>decimal</em> is a number of the form 506 * <i>s</i>×10<sup><i>i</i></sup> 507 * for some (unique) integers <i>s</i> > 0 and <i>i</i> such that 508 * <i>s</i> is not a multiple of 10. 509 * These integers are the <em>significand</em> and 510 * the <em>exponent</em>, respectively, of the decimal. 511 * The <em>length</em> of the decimal is the (unique) 512 * positive integer <i>n</i> meeting 513 * 10<sup><i>n</i>-1</sup> ≤ <i>s</i> < 10<sup><i>n</i></sup>. 514 * 515 * <p>The decimal <i>d</i><sub><i>m</i></sub> for a finite positive <i>m</i> 516 * is defined as follows: 517 * <ul> 518 * <li>Let <i>R</i> be the set of all decimals that round to <i>m</i> 519 * according to the usual <em>round to nearest</em> rounding policy of 520 * IEEE 754 floating-point arithmetic. 521 * <li>Let <i>p</i> be the minimal length over all decimals in <i>R</i>. 522 * <li>When <i>p</i> ≥ 2, let <i>T</i> be the set of all decimals 523 * in <i>R</i> with length <i>p</i>. 524 * Otherwise, let <i>T</i> be the set of all decimals 525 * in <i>R</i> with length 1 or 2. 526 * <li>Define <i>d</i><sub><i>m</i></sub> as the decimal in <i>T</i> 527 * that is closest to <i>m</i>. 528 * Or if there are two such decimals in <i>T</i>, 529 * select the one with the even significand. 530 * </ul> 531 * 532 * <p>The (uniquely) selected decimal <i>d</i><sub><i>m</i></sub> 533 * is then formatted. 534 * Let <i>s</i>, <i>i</i> and <i>n</i> be the significand, exponent and 535 * length of <i>d</i><sub><i>m</i></sub>, respectively. 536 * Further, let <i>e</i> = <i>n</i> + <i>i</i> - 1 and let 537 * <i>s</i><sub>1</sub>…<i>s</i><sub><i>n</i></sub> 538 * be the usual decimal expansion of <i>s</i>. 539 * Note that <i>s</i><sub>1</sub> ≠ 0 540 * and <i>s</i><sub><i>n</i></sub> ≠ 0. 541 * Below, the decimal point {@code '.'} is {@code '\u005Cu002E'} 542 * and the exponent indicator {@code 'E'} is {@code '\u005Cu0045'}. 543 * <ul> 544 * <li>Case -3 ≤ <i>e</i> < 0: 545 * <i>d</i><sub><i>m</i></sub> is formatted as 546 * <code>0.0</code>…<code>0</code><!-- 547 * --><i>s</i><sub>1</sub>…<i>s</i><sub><i>n</i></sub>, 548 * where there are exactly -(<i>n</i> + <i>i</i>) zeroes between 549 * the decimal point and <i>s</i><sub>1</sub>. 550 * For example, 123 × 10<sup>-4</sup> is formatted as 551 * {@code 0.0123}. 552 * <li>Case 0 ≤ <i>e</i> < 7: 553 * <ul> 554 * <li>Subcase <i>i</i> ≥ 0: 555 * <i>d</i><sub><i>m</i></sub> is formatted as 556 * <i>s</i><sub>1</sub>…<i>s</i><sub><i>n</i></sub><!-- 557 * --><code>0</code>…<code>0.0</code>, 558 * where there are exactly <i>i</i> zeroes 559 * between <i>s</i><sub><i>n</i></sub> and the decimal point. 560 * For example, 123 × 10<sup>2</sup> is formatted as 561 * {@code 12300.0}. 562 * <li>Subcase <i>i</i> < 0: 563 * <i>d</i><sub><i>m</i></sub> is formatted as 564 * <i>s</i><sub>1</sub>…<!-- 565 * --><i>s</i><sub><i>n</i>+<i>i</i></sub><code>.</code><!-- 566 * --><i>s</i><sub><i>n</i>+<i>i</i>+1</sub>…<!-- 567 * --><i>s</i><sub><i>n</i></sub>, 568 * where there are exactly -<i>i</i> digits to the right of 569 * the decimal point. 570 * For example, 123 × 10<sup>-1</sup> is formatted as 571 * {@code 12.3}. 572 * </ul> 573 * <li>Case <i>e</i> < -3 or <i>e</i> ≥ 7: 574 * computerized scientific notation is used to format 575 * <i>d</i><sub><i>m</i></sub>. 576 * Here <i>e</i> is formatted as by {@link Integer#toString(int)}. 577 * <ul> 578 * <li>Subcase <i>n</i> = 1: 579 * <i>d</i><sub><i>m</i></sub> is formatted as 580 * <i>s</i><sub>1</sub><code>.0E</code><i>e</i>. 581 * For example, 1 × 10<sup>23</sup> is formatted as 582 * {@code 1.0E23}. 583 * <li>Subcase <i>n</i> > 1: 584 * <i>d</i><sub><i>m</i></sub> is formatted as 585 * <i>s</i><sub>1</sub><code>.</code><i>s</i><sub>2</sub><!-- 586 * -->…<i>s</i><sub><i>n</i></sub><code>E</code><i>e</i>. 587 * For example, 123 × 10<sup>-21</sup> is formatted as 588 * {@code 1.23E-19}. 589 * </ul> 590 * </ul> 591 * 592 * <p>To create localized string representations of a floating-point 593 * value, use subclasses of {@link java.text.NumberFormat}. 594 * 595 * @param d the {@code double} to be converted. 596 * @return a string representation of the argument. 597 */ 598 public static String toString(double d) { 599 return DoubleToDecimal.toString(d); 600 } 601 602 /** 603 * Returns a hexadecimal string representation of the 604 * {@code double} argument. All characters mentioned below 605 * are ASCII characters. 606 * 607 * <ul> 608 * <li>If the argument is NaN, the result is the string 609 * "{@code NaN}". 610 * <li>Otherwise, the result is a string that represents the sign 611 * and magnitude of the argument. If the sign is negative, the 612 * first character of the result is '{@code -}' 613 * ({@code '\u005Cu002D'}); if the sign is positive, no sign 614 * character appears in the result. As for the magnitude <i>m</i>: 615 * 616 * <ul> 617 * <li>If <i>m</i> is infinity, it is represented by the string 618 * {@code "Infinity"}; thus, positive infinity produces the 619 * result {@code "Infinity"} and negative infinity produces 620 * the result {@code "-Infinity"}. 621 * 622 * <li>If <i>m</i> is zero, it is represented by the string 623 * {@code "0x0.0p0"}; thus, negative zero produces the result 624 * {@code "-0x0.0p0"} and positive zero produces the result 625 * {@code "0x0.0p0"}. 626 * 627 * <li>If <i>m</i> is a {@code double} value with a 628 * normalized representation, substrings are used to represent the 629 * significand and exponent fields. The significand is 630 * represented by the characters {@code "0x1."} 631 * followed by a lowercase hexadecimal representation of the rest 632 * of the significand as a fraction. Trailing zeros in the 633 * hexadecimal representation are removed unless all the digits 634 * are zero, in which case a single zero is used. Next, the 635 * exponent is represented by {@code "p"} followed 636 * by a decimal string of the unbiased exponent as if produced by 637 * a call to {@link Integer#toString(int) Integer.toString} on the 638 * exponent value. 639 * 640 * <li>If <i>m</i> is a {@code double} value with a subnormal 641 * representation, the significand is represented by the 642 * characters {@code "0x0."} followed by a 643 * hexadecimal representation of the rest of the significand as a 644 * fraction. Trailing zeros in the hexadecimal representation are 645 * removed. Next, the exponent is represented by 646 * {@code "p-1022"}. Note that there must be at 647 * least one nonzero digit in a subnormal significand. 648 * 649 * </ul> 650 * 651 * </ul> 652 * 653 * <table class="striped"> 654 * <caption>Examples</caption> 655 * <thead> 656 * <tr><th scope="col">Floating-point Value</th><th scope="col">Hexadecimal String</th> 657 * </thead> 658 * <tbody style="text-align:right"> 659 * <tr><th scope="row">{@code 1.0}</th> <td>{@code 0x1.0p0}</td> 660 * <tr><th scope="row">{@code -1.0}</th> <td>{@code -0x1.0p0}</td> 661 * <tr><th scope="row">{@code 2.0}</th> <td>{@code 0x1.0p1}</td> 662 * <tr><th scope="row">{@code 3.0}</th> <td>{@code 0x1.8p1}</td> 663 * <tr><th scope="row">{@code 0.5}</th> <td>{@code 0x1.0p-1}</td> 664 * <tr><th scope="row">{@code 0.25}</th> <td>{@code 0x1.0p-2}</td> 665 * <tr><th scope="row">{@code Double.MAX_VALUE}</th> 666 * <td>{@code 0x1.fffffffffffffp1023}</td> 667 * <tr><th scope="row">{@code Minimum Normal Value}</th> 668 * <td>{@code 0x1.0p-1022}</td> 669 * <tr><th scope="row">{@code Maximum Subnormal Value}</th> 670 * <td>{@code 0x0.fffffffffffffp-1022}</td> 671 * <tr><th scope="row">{@code Double.MIN_VALUE}</th> 672 * <td>{@code 0x0.0000000000001p-1022}</td> 673 * </tbody> 674 * </table> 675 * @param d the {@code double} to be converted. 676 * @return a hex string representation of the argument. 677 * @since 1.5 678 * @author Joseph D. Darcy 679 */ 680 public static String toHexString(double d) { 681 /* 682 * Modeled after the "a" conversion specifier in C99, section 683 * 7.19.6.1; however, the output of this method is more 684 * tightly specified. 685 */ 686 if (!isFinite(d) ) 687 // For infinity and NaN, use the decimal output. 688 return Double.toString(d); 689 else { 690 // Initialized to maximum size of output. 691 StringBuilder answer = new StringBuilder(24); 692 693 if (Math.copySign(1.0, d) == -1.0) // value is negative, 694 answer.append("-"); // so append sign info 695 696 answer.append("0x"); 697 698 d = Math.abs(d); 699 700 if(d == 0.0) { 701 answer.append("0.0p0"); 702 } else { 703 boolean subnormal = (d < Double.MIN_NORMAL); 704 705 // Isolate significand bits and OR in a high-order bit 706 // so that the string representation has a known 707 // length. 708 long signifBits = (Double.doubleToLongBits(d) 709 & DoubleConsts.SIGNIF_BIT_MASK) | 710 0x1000000000000000L; 711 712 // Subnormal values have a 0 implicit bit; normal 713 // values have a 1 implicit bit. 714 answer.append(subnormal ? "0." : "1."); 715 716 // Isolate the low-order 13 digits of the hex 717 // representation. If all the digits are zero, 718 // replace with a single 0; otherwise, remove all 719 // trailing zeros. 720 String signif = Long.toHexString(signifBits).substring(3,16); 721 answer.append(signif.equals("0000000000000") ? // 13 zeros 722 "0": 723 signif.replaceFirst("0{1,12}$", "")); 724 725 answer.append('p'); 726 // If the value is subnormal, use the E_min exponent 727 // value for double; otherwise, extract and report d's 728 // exponent (the representation of a subnormal uses 729 // E_min -1). 730 answer.append(subnormal ? 731 Double.MIN_EXPONENT: 732 Math.getExponent(d)); 733 } 734 return answer.toString(); 735 } 736 } 737 738 /** 739 * Returns a {@code Double} object holding the 740 * {@code double} value represented by the argument string 741 * {@code s}. 742 * 743 * <p>If {@code s} is {@code null}, then a 744 * {@code NullPointerException} is thrown. 745 * 746 * <p>Leading and trailing whitespace characters in {@code s} 747 * are ignored. Whitespace is removed as if by the {@link 748 * String#trim} method; that is, both ASCII space and control 749 * characters are removed. The rest of {@code s} should 750 * constitute a <i>FloatValue</i> as described by the lexical 751 * syntax rules: 752 * 753 * <blockquote> 754 * <dl> 755 * <dt><i>FloatValue:</i> 756 * <dd><i>Sign<sub>opt</sub></i> {@code NaN} 757 * <dd><i>Sign<sub>opt</sub></i> {@code Infinity} 758 * <dd><i>Sign<sub>opt</sub> FloatingPointLiteral</i> 759 * <dd><i>Sign<sub>opt</sub> HexFloatingPointLiteral</i> 760 * <dd><i>SignedInteger</i> 761 * </dl> 762 * 763 * <dl> 764 * <dt><i>HexFloatingPointLiteral</i>: 765 * <dd> <i>HexSignificand BinaryExponent FloatTypeSuffix<sub>opt</sub></i> 766 * </dl> 767 * 768 * <dl> 769 * <dt><i>HexSignificand:</i> 770 * <dd><i>HexNumeral</i> 771 * <dd><i>HexNumeral</i> {@code .} 772 * <dd>{@code 0x} <i>HexDigits<sub>opt</sub> 773 * </i>{@code .}<i> HexDigits</i> 774 * <dd>{@code 0X}<i> HexDigits<sub>opt</sub> 775 * </i>{@code .} <i>HexDigits</i> 776 * </dl> 777 * 778 * <dl> 779 * <dt><i>BinaryExponent:</i> 780 * <dd><i>BinaryExponentIndicator SignedInteger</i> 781 * </dl> 782 * 783 * <dl> 784 * <dt><i>BinaryExponentIndicator:</i> 785 * <dd>{@code p} 786 * <dd>{@code P} 787 * </dl> 788 * 789 * </blockquote> 790 * 791 * where <i>Sign</i>, <i>FloatingPointLiteral</i>, 792 * <i>HexNumeral</i>, <i>HexDigits</i>, <i>SignedInteger</i> and 793 * <i>FloatTypeSuffix</i> are as defined in the lexical structure 794 * sections of 795 * <cite>The Java Language Specification</cite>, 796 * except that underscores are not accepted between digits. 797 * If {@code s} does not have the form of 798 * a <i>FloatValue</i>, then a {@code NumberFormatException} 799 * is thrown. Otherwise, {@code s} is regarded as 800 * representing an exact decimal value in the usual 801 * "computerized scientific notation" or as an exact 802 * hexadecimal value; this exact numerical value is then 803 * conceptually converted to an "infinitely precise" 804 * binary value that is then rounded to type {@code double} 805 * by the usual round-to-nearest rule of IEEE 754 floating-point 806 * arithmetic, which includes preserving the sign of a zero 807 * value. 808 * 809 * Note that the round-to-nearest rule also implies overflow and 810 * underflow behaviour; if the exact value of {@code s} is large 811 * enough in magnitude (greater than or equal to ({@link 812 * #MAX_VALUE} + {@link Math#ulp(double) ulp(MAX_VALUE)}/2), 813 * rounding to {@code double} will result in an infinity and if the 814 * exact value of {@code s} is small enough in magnitude (less 815 * than or equal to {@link #MIN_VALUE}/2), rounding to float will 816 * result in a zero. 817 * 818 * Finally, after rounding a {@code Double} object representing 819 * this {@code double} value is returned. 820 * 821 * <p>Note that trailing format specifiers, specifiers that 822 * determine the type of a floating-point literal 823 * ({@code 1.0f} is a {@code float} value; 824 * {@code 1.0d} is a {@code double} value), do 825 * <em>not</em> influence the results of this method. In other 826 * words, the numerical value of the input string is converted 827 * directly to the target floating-point type. The two-step 828 * sequence of conversions, string to {@code float} followed 829 * by {@code float} to {@code double}, is <em>not</em> 830 * equivalent to converting a string directly to 831 * {@code double}. For example, the {@code float} 832 * literal {@code 0.1f} is equal to the {@code double} 833 * value {@code 0.10000000149011612}; the {@code float} 834 * literal {@code 0.1f} represents a different numerical 835 * value than the {@code double} literal 836 * {@code 0.1}. (The numerical value 0.1 cannot be exactly 837 * represented in a binary floating-point number.) 838 * 839 * <p>To avoid calling this method on an invalid string and having 840 * a {@code NumberFormatException} be thrown, the regular 841 * expression below can be used to screen the input string: 842 * 843 * {@snippet lang="java" : 844 * final String Digits = "(\\p{Digit}+)"; 845 * final String HexDigits = "(\\p{XDigit}+)"; 846 * // an exponent is 'e' or 'E' followed by an optionally 847 * // signed decimal integer. 848 * final String Exp = "[eE][+-]?"+Digits; 849 * final String fpRegex = 850 * ("[\\x00-\\x20]*"+ // Optional leading "whitespace" 851 * "[+-]?(" + // Optional sign character 852 * "NaN|" + // "NaN" string 853 * "Infinity|" + // "Infinity" string 854 * 855 * // A decimal floating-point string representing a finite positive 856 * // number without a leading sign has at most five basic pieces: 857 * // Digits . Digits ExponentPart FloatTypeSuffix 858 * // 859 * // Since this method allows integer-only strings as input 860 * // in addition to strings of floating-point literals, the 861 * // two sub-patterns below are simplifications of the grammar 862 * // productions from section 3.10.2 of 863 * // The Java Language Specification. 864 * 865 * // Digits ._opt Digits_opt ExponentPart_opt FloatTypeSuffix_opt 866 * "((("+Digits+"(\\.)?("+Digits+"?)("+Exp+")?)|"+ 867 * 868 * // . Digits ExponentPart_opt FloatTypeSuffix_opt 869 * "(\\.("+Digits+")("+Exp+")?)|"+ 870 * 871 * // Hexadecimal strings 872 * "((" + 873 * // 0[xX] HexDigits ._opt BinaryExponent FloatTypeSuffix_opt 874 * "(0[xX]" + HexDigits + "(\\.)?)|" + 875 * 876 * // 0[xX] HexDigits_opt . HexDigits BinaryExponent FloatTypeSuffix_opt 877 * "(0[xX]" + HexDigits + "?(\\.)" + HexDigits + ")" + 878 * 879 * ")[pP][+-]?" + Digits + "))" + 880 * "[fFdD]?))" + 881 * "[\\x00-\\x20]*");// Optional trailing "whitespace" 882 * // @link region substring="Pattern.matches" target ="java.util.regex.Pattern#matches" 883 * if (Pattern.matches(fpRegex, myString)) 884 * Double.valueOf(myString); // Will not throw NumberFormatException 885 * // @end 886 * else { 887 * // Perform suitable alternative action 888 * } 889 * } 890 * 891 * @apiNote To interpret localized string representations of a 892 * floating-point value, or string representations that have 893 * non-ASCII digits, use {@link java.text.NumberFormat}. For 894 * example, 895 * {@snippet lang="java" : 896 * NumberFormat.getInstance(l).parse(s).doubleValue(); 897 * } 898 * where {@code l} is the desired locale, or 899 * {@link java.util.Locale#ROOT} if locale insensitive. 900 * 901 * @param s the string to be parsed. 902 * @return a {@code Double} object holding the value 903 * represented by the {@code String} argument. 904 * @throws NumberFormatException if the string does not contain a 905 * parsable number. 906 * @see Double##decimalToBinaryConversion Decimal ↔ Binary Conversion Issues 907 */ 908 public static Double valueOf(String s) throws NumberFormatException { 909 return new Double(parseDouble(s)); 910 } 911 912 /** 913 * Returns a {@code Double} instance representing the specified 914 * {@code double} value. 915 * If a new {@code Double} instance is not required, this method 916 * should generally be used in preference to the constructor 917 * {@link #Double(double)}, as this method is likely to yield 918 * significantly better space and time performance by caching 919 * frequently requested values. 920 * 921 * @param d a double value. 922 * @return a {@code Double} instance representing {@code d}. 923 * @since 1.5 924 */ 925 @IntrinsicCandidate 926 public static Double valueOf(double d) { 927 return new Double(d); 928 } 929 930 /** 931 * Returns a new {@code double} initialized to the value 932 * represented by the specified {@code String}, as performed 933 * by the {@code valueOf} method of class 934 * {@code Double}. 935 * 936 * @param s the string to be parsed. 937 * @return the {@code double} value represented by the string 938 * argument. 939 * @throws NullPointerException if the string is null 940 * @throws NumberFormatException if the string does not contain 941 * a parsable {@code double}. 942 * @see java.lang.Double#valueOf(String) 943 * @see Double##decimalToBinaryConversion Decimal ↔ Binary Conversion Issues 944 * @since 1.2 945 */ 946 public static double parseDouble(String s) throws NumberFormatException { 947 return FloatingDecimal.parseDouble(s); 948 } 949 950 /** 951 * Returns {@code true} if the specified number is a 952 * Not-a-Number (NaN) value, {@code false} otherwise. 953 * 954 * @apiNote 955 * This method corresponds to the isNaN operation defined in IEEE 956 * 754. 957 * 958 * @param v the value to be tested. 959 * @return {@code true} if the value of the argument is NaN; 960 * {@code false} otherwise. 961 */ 962 public static boolean isNaN(double v) { 963 return (v != v); 964 } 965 966 /** 967 * Returns {@code true} if the specified number is infinitely 968 * large in magnitude, {@code false} otherwise. 969 * 970 * @apiNote 971 * This method corresponds to the isInfinite operation defined in 972 * IEEE 754. 973 * 974 * @param v the value to be tested. 975 * @return {@code true} if the value of the argument is positive 976 * infinity or negative infinity; {@code false} otherwise. 977 */ 978 @IntrinsicCandidate 979 public static boolean isInfinite(double v) { 980 return Math.abs(v) > MAX_VALUE; 981 } 982 983 /** 984 * Returns {@code true} if the argument is a finite floating-point 985 * value; returns {@code false} otherwise (for NaN and infinity 986 * arguments). 987 * 988 * @apiNote 989 * This method corresponds to the isFinite operation defined in 990 * IEEE 754. 991 * 992 * @param d the {@code double} value to be tested 993 * @return {@code true} if the argument is a finite 994 * floating-point value, {@code false} otherwise. 995 * @since 1.8 996 */ 997 @IntrinsicCandidate 998 public static boolean isFinite(double d) { 999 return Math.abs(d) <= Double.MAX_VALUE; 1000 } 1001 1002 /** 1003 * The value of the Double. 1004 * 1005 * @serial 1006 */ 1007 private final double value; 1008 1009 /** 1010 * Constructs a newly allocated {@code Double} object that 1011 * represents the primitive {@code double} argument. 1012 * 1013 * @param value the value to be represented by the {@code Double}. 1014 * 1015 * @deprecated 1016 * It is rarely appropriate to use this constructor. The static factory 1017 * {@link #valueOf(double)} is generally a better choice, as it is 1018 * likely to yield significantly better space and time performance. 1019 */ 1020 @Deprecated(since="9", forRemoval = true) 1021 public Double(double value) { 1022 this.value = value; 1023 } 1024 1025 /** 1026 * Constructs a newly allocated {@code Double} object that 1027 * represents the floating-point value of type {@code double} 1028 * represented by the string. The string is converted to a 1029 * {@code double} value as if by the {@code valueOf} method. 1030 * 1031 * @param s a string to be converted to a {@code Double}. 1032 * @throws NumberFormatException if the string does not contain a 1033 * parsable number. 1034 * 1035 * @deprecated 1036 * It is rarely appropriate to use this constructor. 1037 * Use {@link #parseDouble(String)} to convert a string to a 1038 * {@code double} primitive, or use {@link #valueOf(String)} 1039 * to convert a string to a {@code Double} object. 1040 */ 1041 @Deprecated(since="9", forRemoval = true) 1042 public Double(String s) throws NumberFormatException { 1043 value = parseDouble(s); 1044 } 1045 1046 /** 1047 * Returns {@code true} if this {@code Double} value is 1048 * a Not-a-Number (NaN), {@code false} otherwise. 1049 * 1050 * @return {@code true} if the value represented by this object is 1051 * NaN; {@code false} otherwise. 1052 */ 1053 public boolean isNaN() { 1054 return isNaN(value); 1055 } 1056 1057 /** 1058 * Returns {@code true} if this {@code Double} value is 1059 * infinitely large in magnitude, {@code false} otherwise. 1060 * 1061 * @return {@code true} if the value represented by this object is 1062 * positive infinity or negative infinity; 1063 * {@code false} otherwise. 1064 */ 1065 public boolean isInfinite() { 1066 return isInfinite(value); 1067 } 1068 1069 /** 1070 * Returns a string representation of this {@code Double} object. 1071 * The primitive {@code double} value represented by this 1072 * object is converted to a string exactly as if by the method 1073 * {@code toString} of one argument. 1074 * 1075 * @return a {@code String} representation of this object. 1076 * @see java.lang.Double#toString(double) 1077 */ 1078 public String toString() { 1079 return toString(value); 1080 } 1081 1082 /** 1083 * Returns the value of this {@code Double} as a {@code byte} 1084 * after a narrowing primitive conversion. 1085 * 1086 * @return the {@code double} value represented by this object 1087 * converted to type {@code byte} 1088 * @jls 5.1.3 Narrowing Primitive Conversion 1089 * @since 1.1 1090 */ 1091 public byte byteValue() { 1092 return (byte)value; 1093 } 1094 1095 /** 1096 * Returns the value of this {@code Double} as a {@code short} 1097 * after a narrowing primitive conversion. 1098 * 1099 * @return the {@code double} value represented by this object 1100 * converted to type {@code short} 1101 * @jls 5.1.3 Narrowing Primitive Conversion 1102 * @since 1.1 1103 */ 1104 public short shortValue() { 1105 return (short)value; 1106 } 1107 1108 /** 1109 * Returns the value of this {@code Double} as an {@code int} 1110 * after a narrowing primitive conversion. 1111 * @jls 5.1.3 Narrowing Primitive Conversion 1112 * 1113 * @return the {@code double} value represented by this object 1114 * converted to type {@code int} 1115 */ 1116 public int intValue() { 1117 return (int)value; 1118 } 1119 1120 /** 1121 * Returns the value of this {@code Double} as a {@code long} 1122 * after a narrowing primitive conversion. 1123 * 1124 * @return the {@code double} value represented by this object 1125 * converted to type {@code long} 1126 * @jls 5.1.3 Narrowing Primitive Conversion 1127 */ 1128 public long longValue() { 1129 return (long)value; 1130 } 1131 1132 /** 1133 * Returns the value of this {@code Double} as a {@code float} 1134 * after a narrowing primitive conversion. 1135 * 1136 * @apiNote 1137 * This method corresponds to the convertFormat operation defined 1138 * in IEEE 754. 1139 * 1140 * @return the {@code double} value represented by this object 1141 * converted to type {@code float} 1142 * @jls 5.1.3 Narrowing Primitive Conversion 1143 * @since 1.0 1144 */ 1145 public float floatValue() { 1146 return (float)value; 1147 } 1148 1149 /** 1150 * Returns the {@code double} value of this {@code Double} object. 1151 * 1152 * @return the {@code double} value represented by this object 1153 */ 1154 @IntrinsicCandidate 1155 public double doubleValue() { 1156 return value; 1157 } 1158 1159 /** 1160 * Returns a hash code for this {@code Double} object. The 1161 * result is the exclusive OR of the two halves of the 1162 * {@code long} integer bit representation, exactly as 1163 * produced by the method {@link #doubleToLongBits(double)}, of 1164 * the primitive {@code double} value represented by this 1165 * {@code Double} object. That is, the hash code is the value 1166 * of the expression: 1167 * 1168 * <blockquote> 1169 * {@code (int)(v^(v>>>32))} 1170 * </blockquote> 1171 * 1172 * where {@code v} is defined by: 1173 * 1174 * <blockquote> 1175 * {@code long v = Double.doubleToLongBits(this.doubleValue());} 1176 * </blockquote> 1177 * 1178 * @return a {@code hash code} value for this object. 1179 */ 1180 @Override 1181 public int hashCode() { 1182 return Double.hashCode(value); 1183 } 1184 1185 /** 1186 * Returns a hash code for a {@code double} value; compatible with 1187 * {@code Double.hashCode()}. 1188 * 1189 * @param value the value to hash 1190 * @return a hash code value for a {@code double} value. 1191 * @since 1.8 1192 */ 1193 public static int hashCode(double value) { 1194 return Long.hashCode(doubleToLongBits(value)); 1195 } 1196 1197 /** 1198 * Compares this object against the specified object. The result 1199 * is {@code true} if and only if the argument is not 1200 * {@code null} and is a {@code Double} object that 1201 * represents a {@code double} that has the same value as the 1202 * {@code double} represented by this object. For this 1203 * purpose, two {@code double} values are considered to be 1204 * the same if and only if the method {@link 1205 * #doubleToLongBits(double)} returns the identical 1206 * {@code long} value when applied to each. 1207 * 1208 * @apiNote 1209 * This method is defined in terms of {@link 1210 * #doubleToLongBits(double)} rather than the {@code ==} operator 1211 * on {@code double} values since the {@code ==} operator does 1212 * <em>not</em> define an equivalence relation and to satisfy the 1213 * {@linkplain Object#equals equals contract} an equivalence 1214 * relation must be implemented; see <a 1215 * href="#equivalenceRelation">this discussion</a> for details of 1216 * floating-point equality and equivalence. 1217 * 1218 * @see java.lang.Double#doubleToLongBits(double) 1219 * @jls 15.21.1 Numerical Equality Operators == and != 1220 */ 1221 public boolean equals(Object obj) { 1222 return (obj instanceof Double) 1223 && (doubleToLongBits(((Double)obj).value) == 1224 doubleToLongBits(value)); 1225 } 1226 1227 /** 1228 * Returns a representation of the specified floating-point value 1229 * according to the IEEE 754 floating-point "double 1230 * format" bit layout. 1231 * 1232 * <p>Bit 63 (the bit that is selected by the mask 1233 * {@code 0x8000000000000000L}) represents the sign of the 1234 * floating-point number. Bits 1235 * 62-52 (the bits that are selected by the mask 1236 * {@code 0x7ff0000000000000L}) represent the exponent. Bits 51-0 1237 * (the bits that are selected by the mask 1238 * {@code 0x000fffffffffffffL}) represent the significand 1239 * (sometimes called the mantissa) of the floating-point number. 1240 * 1241 * <p>If the argument is positive infinity, the result is 1242 * {@code 0x7ff0000000000000L}. 1243 * 1244 * <p>If the argument is negative infinity, the result is 1245 * {@code 0xfff0000000000000L}. 1246 * 1247 * <p>If the argument is NaN, the result is 1248 * {@code 0x7ff8000000000000L}. 1249 * 1250 * <p>In all cases, the result is a {@code long} integer that, when 1251 * given to the {@link #longBitsToDouble(long)} method, will produce a 1252 * floating-point value the same as the argument to 1253 * {@code doubleToLongBits} (except all NaN values are 1254 * collapsed to a single "canonical" NaN value). 1255 * 1256 * @param value a {@code double} precision floating-point number. 1257 * @return the bits that represent the floating-point number. 1258 */ 1259 @IntrinsicCandidate 1260 public static long doubleToLongBits(double value) { 1261 if (!isNaN(value)) { 1262 return doubleToRawLongBits(value); 1263 } 1264 return 0x7ff8000000000000L; 1265 } 1266 1267 /** 1268 * Returns a representation of the specified floating-point value 1269 * according to the IEEE 754 floating-point "double 1270 * format" bit layout, preserving Not-a-Number (NaN) values. 1271 * 1272 * <p>Bit 63 (the bit that is selected by the mask 1273 * {@code 0x8000000000000000L}) represents the sign of the 1274 * floating-point number. Bits 1275 * 62-52 (the bits that are selected by the mask 1276 * {@code 0x7ff0000000000000L}) represent the exponent. Bits 51-0 1277 * (the bits that are selected by the mask 1278 * {@code 0x000fffffffffffffL}) represent the significand 1279 * (sometimes called the mantissa) of the floating-point number. 1280 * 1281 * <p>If the argument is positive infinity, the result is 1282 * {@code 0x7ff0000000000000L}. 1283 * 1284 * <p>If the argument is negative infinity, the result is 1285 * {@code 0xfff0000000000000L}. 1286 * 1287 * <p>If the argument is NaN, the result is the {@code long} 1288 * integer representing the actual NaN value. Unlike the 1289 * {@code doubleToLongBits} method, 1290 * {@code doubleToRawLongBits} does not collapse all the bit 1291 * patterns encoding a NaN to a single "canonical" NaN 1292 * value. 1293 * 1294 * <p>In all cases, the result is a {@code long} integer that, 1295 * when given to the {@link #longBitsToDouble(long)} method, will 1296 * produce a floating-point value the same as the argument to 1297 * {@code doubleToRawLongBits}. 1298 * 1299 * @param value a {@code double} precision floating-point number. 1300 * @return the bits that represent the floating-point number. 1301 * @since 1.3 1302 */ 1303 @IntrinsicCandidate 1304 public static native long doubleToRawLongBits(double value); 1305 1306 /** 1307 * Returns the {@code double} value corresponding to a given 1308 * bit representation. 1309 * The argument is considered to be a representation of a 1310 * floating-point value according to the IEEE 754 floating-point 1311 * "double format" bit layout. 1312 * 1313 * <p>If the argument is {@code 0x7ff0000000000000L}, the result 1314 * is positive infinity. 1315 * 1316 * <p>If the argument is {@code 0xfff0000000000000L}, the result 1317 * is negative infinity. 1318 * 1319 * <p>If the argument is any value in the range 1320 * {@code 0x7ff0000000000001L} through 1321 * {@code 0x7fffffffffffffffL} or in the range 1322 * {@code 0xfff0000000000001L} through 1323 * {@code 0xffffffffffffffffL}, the result is a NaN. No IEEE 1324 * 754 floating-point operation provided by Java can distinguish 1325 * between two NaN values of the same type with different bit 1326 * patterns. Distinct values of NaN are only distinguishable by 1327 * use of the {@code Double.doubleToRawLongBits} method. 1328 * 1329 * <p>In all other cases, let <i>s</i>, <i>e</i>, and <i>m</i> be three 1330 * values that can be computed from the argument: 1331 * 1332 * {@snippet lang="java" : 1333 * int s = ((bits >> 63) == 0) ? 1 : -1; 1334 * int e = (int)((bits >> 52) & 0x7ffL); 1335 * long m = (e == 0) ? 1336 * (bits & 0xfffffffffffffL) << 1 : 1337 * (bits & 0xfffffffffffffL) | 0x10000000000000L; 1338 * } 1339 * 1340 * Then the floating-point result equals the value of the mathematical 1341 * expression <i>s</i>·<i>m</i>·2<sup><i>e</i>-1075</sup>. 1342 * 1343 * <p>Note that this method may not be able to return a 1344 * {@code double} NaN with exactly same bit pattern as the 1345 * {@code long} argument. IEEE 754 distinguishes between two 1346 * kinds of NaNs, quiet NaNs and <i>signaling NaNs</i>. The 1347 * differences between the two kinds of NaN are generally not 1348 * visible in Java. Arithmetic operations on signaling NaNs turn 1349 * them into quiet NaNs with a different, but often similar, bit 1350 * pattern. However, on some processors merely copying a 1351 * signaling NaN also performs that conversion. In particular, 1352 * copying a signaling NaN to return it to the calling method 1353 * may perform this conversion. So {@code longBitsToDouble} 1354 * may not be able to return a {@code double} with a 1355 * signaling NaN bit pattern. Consequently, for some 1356 * {@code long} values, 1357 * {@code doubleToRawLongBits(longBitsToDouble(start))} may 1358 * <i>not</i> equal {@code start}. Moreover, which 1359 * particular bit patterns represent signaling NaNs is platform 1360 * dependent; although all NaN bit patterns, quiet or signaling, 1361 * must be in the NaN range identified above. 1362 * 1363 * @param bits any {@code long} integer. 1364 * @return the {@code double} floating-point value with the same 1365 * bit pattern. 1366 */ 1367 @IntrinsicCandidate 1368 public static native double longBitsToDouble(long bits); 1369 1370 /** 1371 * Compares two {@code Double} objects numerically. 1372 * 1373 * This method imposes a total order on {@code Double} objects 1374 * with two differences compared to the incomplete order defined by 1375 * the Java language numerical comparison operators ({@code <, <=, 1376 * ==, >=, >}) on {@code double} values. 1377 * 1378 * <ul><li> A NaN is <em>unordered</em> with respect to other 1379 * values and unequal to itself under the comparison 1380 * operators. This method chooses to define {@code 1381 * Double.NaN} to be equal to itself and greater than all 1382 * other {@code double} values (including {@code 1383 * Double.POSITIVE_INFINITY}). 1384 * 1385 * <li> Positive zero and negative zero compare equal 1386 * numerically, but are distinct and distinguishable values. 1387 * This method chooses to define positive zero ({@code +0.0d}), 1388 * to be greater than negative zero ({@code -0.0d}). 1389 * </ul> 1390 1391 * This ensures that the <i>natural ordering</i> of {@code Double} 1392 * objects imposed by this method is <i>consistent with 1393 * equals</i>; see <a href="#equivalenceRelation">this 1394 * discussion</a> for details of floating-point comparison and 1395 * ordering. 1396 * 1397 * @param anotherDouble the {@code Double} to be compared. 1398 * @return the value {@code 0} if {@code anotherDouble} is 1399 * numerically equal to this {@code Double}; a value 1400 * less than {@code 0} if this {@code Double} 1401 * is numerically less than {@code anotherDouble}; 1402 * and a value greater than {@code 0} if this 1403 * {@code Double} is numerically greater than 1404 * {@code anotherDouble}. 1405 * 1406 * @jls 15.20.1 Numerical Comparison Operators {@code <}, {@code <=}, {@code >}, and {@code >=} 1407 * @since 1.2 1408 */ 1409 public int compareTo(Double anotherDouble) { 1410 return Double.compare(value, anotherDouble.value); 1411 } 1412 1413 /** 1414 * Compares the two specified {@code double} values. The sign 1415 * of the integer value returned is the same as that of the 1416 * integer that would be returned by the call: 1417 * <pre> 1418 * Double.valueOf(d1).compareTo(Double.valueOf(d2)) 1419 * </pre> 1420 * 1421 * @param d1 the first {@code double} to compare 1422 * @param d2 the second {@code double} to compare 1423 * @return the value {@code 0} if {@code d1} is 1424 * numerically equal to {@code d2}; a value less than 1425 * {@code 0} if {@code d1} is numerically less than 1426 * {@code d2}; and a value greater than {@code 0} 1427 * if {@code d1} is numerically greater than 1428 * {@code d2}. 1429 * @since 1.4 1430 */ 1431 public static int compare(double d1, double d2) { 1432 if (d1 < d2) 1433 return -1; // Neither val is NaN, thisVal is smaller 1434 if (d1 > d2) 1435 return 1; // Neither val is NaN, thisVal is larger 1436 1437 // Cannot use doubleToRawLongBits because of possibility of NaNs. 1438 long thisBits = Double.doubleToLongBits(d1); 1439 long anotherBits = Double.doubleToLongBits(d2); 1440 1441 return (thisBits == anotherBits ? 0 : // Values are equal 1442 (thisBits < anotherBits ? -1 : // (-0.0, 0.0) or (!NaN, NaN) 1443 1)); // (0.0, -0.0) or (NaN, !NaN) 1444 } 1445 1446 /** 1447 * Adds two {@code double} values together as per the + operator. 1448 * 1449 * @apiNote This method corresponds to the addition operation 1450 * defined in IEEE 754. 1451 * 1452 * @param a the first operand 1453 * @param b the second operand 1454 * @return the sum of {@code a} and {@code b} 1455 * @jls 4.2.4 Floating-Point Operations 1456 * @see java.util.function.BinaryOperator 1457 * @since 1.8 1458 */ 1459 public static double sum(double a, double b) { 1460 return a + b; 1461 } 1462 1463 /** 1464 * Returns the greater of two {@code double} values 1465 * as if by calling {@link Math#max(double, double) Math.max}. 1466 * 1467 * @apiNote 1468 * This method corresponds to the maximum operation defined in 1469 * IEEE 754. 1470 * 1471 * @param a the first operand 1472 * @param b the second operand 1473 * @return the greater of {@code a} and {@code b} 1474 * @see java.util.function.BinaryOperator 1475 * @since 1.8 1476 */ 1477 public static double max(double a, double b) { 1478 return Math.max(a, b); 1479 } 1480 1481 /** 1482 * Returns the smaller of two {@code double} values 1483 * as if by calling {@link Math#min(double, double) Math.min}. 1484 * 1485 * @apiNote 1486 * This method corresponds to the minimum operation defined in 1487 * IEEE 754. 1488 * 1489 * @param a the first operand 1490 * @param b the second operand 1491 * @return the smaller of {@code a} and {@code b}. 1492 * @see java.util.function.BinaryOperator 1493 * @since 1.8 1494 */ 1495 public static double min(double a, double b) { 1496 return Math.min(a, b); 1497 } 1498 1499 /** 1500 * Returns an {@link Optional} containing the nominal descriptor for this 1501 * instance, which is the instance itself. 1502 * 1503 * @return an {@link Optional} describing the {@linkplain Double} instance 1504 * @since 12 1505 */ 1506 @Override 1507 public Optional<Double> describeConstable() { 1508 return Optional.of(this); 1509 } 1510 1511 /** 1512 * Resolves this instance as a {@link ConstantDesc}, the result of which is 1513 * the instance itself. 1514 * 1515 * @param lookup ignored 1516 * @return the {@linkplain Double} instance 1517 * @since 12 1518 */ 1519 @Override 1520 public Double resolveConstantDesc(MethodHandles.Lookup lookup) { 1521 return this; 1522 } 1523 1524 /** use serialVersionUID from JDK 1.0.2 for interoperability */ 1525 @java.io.Serial 1526 private static final long serialVersionUID = -9172774392245257468L; 1527 }