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.ValueBased 361 public final class Double extends Number 362 implements Comparable<Double>, Constable, ConstantDesc { 363 /** 364 * A constant holding the positive infinity of type 365 * {@code double}. It is equal to the value returned by 366 * {@code Double.longBitsToDouble(0x7ff0000000000000L)}. 367 */ 368 public static final double POSITIVE_INFINITY = 1.0 / 0.0; 369 370 /** 371 * A constant holding the negative infinity of type 372 * {@code double}. It is equal to the value returned by 373 * {@code Double.longBitsToDouble(0xfff0000000000000L)}. 374 */ 375 public static final double NEGATIVE_INFINITY = -1.0 / 0.0; 376 377 /** 378 * A constant holding a Not-a-Number (NaN) value of type 379 * {@code double}. It is equivalent to the value returned by 380 * {@code Double.longBitsToDouble(0x7ff8000000000000L)}. 381 */ 382 public static final double NaN = 0.0d / 0.0; 383 384 /** 385 * A constant holding the largest positive finite value of type 386 * {@code double}, 387 * (2-2<sup>-52</sup>)·2<sup>1023</sup>. It is equal to 388 * the hexadecimal floating-point literal 389 * {@code 0x1.fffffffffffffP+1023} and also equal to 390 * {@code Double.longBitsToDouble(0x7fefffffffffffffL)}. 391 */ 392 public static final double MAX_VALUE = 0x1.fffffffffffffP+1023; // 1.7976931348623157e+308 393 394 /** 395 * A constant holding the smallest positive normal value of type 396 * {@code double}, 2<sup>-1022</sup>. It is equal to the 397 * hexadecimal floating-point literal {@code 0x1.0p-1022} and also 398 * equal to {@code Double.longBitsToDouble(0x0010000000000000L)}. 399 * 400 * @since 1.6 401 */ 402 public static final double MIN_NORMAL = 0x1.0p-1022; // 2.2250738585072014E-308 403 404 /** 405 * A constant holding the smallest positive nonzero value of type 406 * {@code double}, 2<sup>-1074</sup>. It is equal to the 407 * hexadecimal floating-point literal 408 * {@code 0x0.0000000000001P-1022} and also equal to 409 * {@code Double.longBitsToDouble(0x1L)}. 410 */ 411 public static final double MIN_VALUE = 0x0.0000000000001P-1022; // 4.9e-324 412 413 /** 414 * The number of bits used to represent a {@code double} value. 415 * 416 * @since 1.5 417 */ 418 public static final int SIZE = 64; 419 420 /** 421 * The number of bits in the significand of a {@code double} value. 422 * This is the parameter N in section {@jls 4.2.3} of 423 * <cite>The Java Language Specification</cite>. 424 * 425 * @since 19 426 */ 427 public static final int PRECISION = 53; 428 429 /** 430 * Maximum exponent a finite {@code double} variable may have. 431 * It is equal to the value returned by 432 * {@code Math.getExponent(Double.MAX_VALUE)}. 433 * 434 * @since 1.6 435 */ 436 public static final int MAX_EXPONENT = (1 << (SIZE - PRECISION - 1)) - 1; // 1023 437 438 /** 439 * Minimum exponent a normalized {@code double} variable may 440 * have. It is equal to the value returned by 441 * {@code Math.getExponent(Double.MIN_NORMAL)}. 442 * 443 * @since 1.6 444 */ 445 public static final int MIN_EXPONENT = 1 - MAX_EXPONENT; // -1022 446 447 /** 448 * The number of bytes used to represent a {@code double} value. 449 * 450 * @since 1.8 451 */ 452 public static final int BYTES = SIZE / Byte.SIZE; 453 454 /** 455 * The {@code Class} instance representing the primitive type 456 * {@code double}. 457 * 458 * @since 1.1 459 */ 460 @SuppressWarnings("unchecked") 461 public static final Class<Double> TYPE = (Class<Double>) Class.getPrimitiveClass("double"); 462 463 /** 464 * Returns a string representation of the {@code double} 465 * argument. All characters mentioned below are ASCII characters. 466 * <ul> 467 * <li>If the argument is NaN, the result is the string 468 * "{@code NaN}". 469 * <li>Otherwise, the result is a string that represents the sign and 470 * magnitude (absolute value) of the argument. If the sign is negative, 471 * the first character of the result is '{@code -}' 472 * ({@code '\u005Cu002D'}); if the sign is positive, no sign character 473 * appears in the result. As for the magnitude <i>m</i>: 474 * <ul> 475 * <li>If <i>m</i> is infinity, it is represented by the characters 476 * {@code "Infinity"}; thus, positive infinity produces the result 477 * {@code "Infinity"} and negative infinity produces the result 478 * {@code "-Infinity"}. 479 * 480 * <li>If <i>m</i> is zero, it is represented by the characters 481 * {@code "0.0"}; thus, negative zero produces the result 482 * {@code "-0.0"} and positive zero produces the result 483 * {@code "0.0"}. 484 * 485 * <li> Otherwise <i>m</i> is positive and finite. 486 * It is converted to a string in two stages: 487 * <ul> 488 * <li> <em>Selection of a decimal</em>: 489 * A well-defined decimal <i>d</i><sub><i>m</i></sub> 490 * is selected to represent <i>m</i>. 491 * This decimal is (almost always) the <em>shortest</em> one that 492 * rounds to <i>m</i> according to the round to nearest 493 * rounding policy of IEEE 754 floating-point arithmetic. 494 * <li> <em>Formatting as a string</em>: 495 * The decimal <i>d</i><sub><i>m</i></sub> is formatted as a string, 496 * either in plain or in computerized scientific notation, 497 * depending on its value. 498 * </ul> 499 * </ul> 500 * </ul> 501 * 502 * <p>A <em>decimal</em> is a number of the form 503 * <i>s</i>×10<sup><i>i</i></sup> 504 * for some (unique) integers <i>s</i> > 0 and <i>i</i> such that 505 * <i>s</i> is not a multiple of 10. 506 * These integers are the <em>significand</em> and 507 * the <em>exponent</em>, respectively, of the decimal. 508 * The <em>length</em> of the decimal is the (unique) 509 * positive integer <i>n</i> meeting 510 * 10<sup><i>n</i>-1</sup> ≤ <i>s</i> < 10<sup><i>n</i></sup>. 511 * 512 * <p>The decimal <i>d</i><sub><i>m</i></sub> for a finite positive <i>m</i> 513 * is defined as follows: 514 * <ul> 515 * <li>Let <i>R</i> be the set of all decimals that round to <i>m</i> 516 * according to the usual <em>round to nearest</em> rounding policy of 517 * IEEE 754 floating-point arithmetic. 518 * <li>Let <i>p</i> be the minimal length over all decimals in <i>R</i>. 519 * <li>When <i>p</i> ≥ 2, let <i>T</i> be the set of all decimals 520 * in <i>R</i> with length <i>p</i>. 521 * Otherwise, let <i>T</i> be the set of all decimals 522 * in <i>R</i> with length 1 or 2. 523 * <li>Define <i>d</i><sub><i>m</i></sub> as the decimal in <i>T</i> 524 * that is closest to <i>m</i>. 525 * Or if there are two such decimals in <i>T</i>, 526 * select the one with the even significand. 527 * </ul> 528 * 529 * <p>The (uniquely) selected decimal <i>d</i><sub><i>m</i></sub> 530 * is then formatted. 531 * Let <i>s</i>, <i>i</i> and <i>n</i> be the significand, exponent and 532 * length of <i>d</i><sub><i>m</i></sub>, respectively. 533 * Further, let <i>e</i> = <i>n</i> + <i>i</i> - 1 and let 534 * <i>s</i><sub>1</sub>…<i>s</i><sub><i>n</i></sub> 535 * be the usual decimal expansion of <i>s</i>. 536 * Note that <i>s</i><sub>1</sub> ≠ 0 537 * and <i>s</i><sub><i>n</i></sub> ≠ 0. 538 * Below, the decimal point {@code '.'} is {@code '\u005Cu002E'} 539 * and the exponent indicator {@code 'E'} is {@code '\u005Cu0045'}. 540 * <ul> 541 * <li>Case -3 ≤ <i>e</i> < 0: 542 * <i>d</i><sub><i>m</i></sub> is formatted as 543 * <code>0.0</code>…<code>0</code><!-- 544 * --><i>s</i><sub>1</sub>…<i>s</i><sub><i>n</i></sub>, 545 * where there are exactly -(<i>n</i> + <i>i</i>) zeroes between 546 * the decimal point and <i>s</i><sub>1</sub>. 547 * For example, 123 × 10<sup>-4</sup> is formatted as 548 * {@code 0.0123}. 549 * <li>Case 0 ≤ <i>e</i> < 7: 550 * <ul> 551 * <li>Subcase <i>i</i> ≥ 0: 552 * <i>d</i><sub><i>m</i></sub> is formatted as 553 * <i>s</i><sub>1</sub>…<i>s</i><sub><i>n</i></sub><!-- 554 * --><code>0</code>…<code>0.0</code>, 555 * where there are exactly <i>i</i> zeroes 556 * between <i>s</i><sub><i>n</i></sub> and the decimal point. 557 * For example, 123 × 10<sup>2</sup> is formatted as 558 * {@code 12300.0}. 559 * <li>Subcase <i>i</i> < 0: 560 * <i>d</i><sub><i>m</i></sub> is formatted as 561 * <i>s</i><sub>1</sub>…<!-- 562 * --><i>s</i><sub><i>n</i>+<i>i</i></sub><code>.</code><!-- 563 * --><i>s</i><sub><i>n</i>+<i>i</i>+1</sub>…<!-- 564 * --><i>s</i><sub><i>n</i></sub>, 565 * where there are exactly -<i>i</i> digits to the right of 566 * the decimal point. 567 * For example, 123 × 10<sup>-1</sup> is formatted as 568 * {@code 12.3}. 569 * </ul> 570 * <li>Case <i>e</i> < -3 or <i>e</i> ≥ 7: 571 * computerized scientific notation is used to format 572 * <i>d</i><sub><i>m</i></sub>. 573 * Here <i>e</i> is formatted as by {@link Integer#toString(int)}. 574 * <ul> 575 * <li>Subcase <i>n</i> = 1: 576 * <i>d</i><sub><i>m</i></sub> is formatted as 577 * <i>s</i><sub>1</sub><code>.0E</code><i>e</i>. 578 * For example, 1 × 10<sup>23</sup> is formatted as 579 * {@code 1.0E23}. 580 * <li>Subcase <i>n</i> > 1: 581 * <i>d</i><sub><i>m</i></sub> is formatted as 582 * <i>s</i><sub>1</sub><code>.</code><i>s</i><sub>2</sub><!-- 583 * -->…<i>s</i><sub><i>n</i></sub><code>E</code><i>e</i>. 584 * For example, 123 × 10<sup>-21</sup> is formatted as 585 * {@code 1.23E-19}. 586 * </ul> 587 * </ul> 588 * 589 * <p>To create localized string representations of a floating-point 590 * value, use subclasses of {@link java.text.NumberFormat}. 591 * 592 * @param d the {@code double} to be converted. 593 * @return a string representation of the argument. 594 */ 595 public static String toString(double d) { 596 return DoubleToDecimal.toString(d); 597 } 598 599 /** 600 * Returns a hexadecimal string representation of the 601 * {@code double} argument. All characters mentioned below 602 * are ASCII characters. 603 * 604 * <ul> 605 * <li>If the argument is NaN, the result is the string 606 * "{@code NaN}". 607 * <li>Otherwise, the result is a string that represents the sign 608 * and magnitude of the argument. If the sign is negative, the 609 * first character of the result is '{@code -}' 610 * ({@code '\u005Cu002D'}); if the sign is positive, no sign 611 * character appears in the result. As for the magnitude <i>m</i>: 612 * 613 * <ul> 614 * <li>If <i>m</i> is infinity, it is represented by the string 615 * {@code "Infinity"}; thus, positive infinity produces the 616 * result {@code "Infinity"} and negative infinity produces 617 * the result {@code "-Infinity"}. 618 * 619 * <li>If <i>m</i> is zero, it is represented by the string 620 * {@code "0x0.0p0"}; thus, negative zero produces the result 621 * {@code "-0x0.0p0"} and positive zero produces the result 622 * {@code "0x0.0p0"}. 623 * 624 * <li>If <i>m</i> is a {@code double} value with a 625 * normalized representation, substrings are used to represent the 626 * significand and exponent fields. The significand is 627 * represented by the characters {@code "0x1."} 628 * followed by a lowercase hexadecimal representation of the rest 629 * of the significand as a fraction. Trailing zeros in the 630 * hexadecimal representation are removed unless all the digits 631 * are zero, in which case a single zero is used. Next, the 632 * exponent is represented by {@code "p"} followed 633 * by a decimal string of the unbiased exponent as if produced by 634 * a call to {@link Integer#toString(int) Integer.toString} on the 635 * exponent value. 636 * 637 * <li>If <i>m</i> is a {@code double} value with a subnormal 638 * representation, the significand is represented by the 639 * characters {@code "0x0."} followed by a 640 * hexadecimal representation of the rest of the significand as a 641 * fraction. Trailing zeros in the hexadecimal representation are 642 * removed. Next, the exponent is represented by 643 * {@code "p-1022"}. Note that there must be at 644 * least one nonzero digit in a subnormal significand. 645 * 646 * </ul> 647 * 648 * </ul> 649 * 650 * <table class="striped"> 651 * <caption>Examples</caption> 652 * <thead> 653 * <tr><th scope="col">Floating-point Value</th><th scope="col">Hexadecimal String</th> 654 * </thead> 655 * <tbody style="text-align:right"> 656 * <tr><th scope="row">{@code 1.0}</th> <td>{@code 0x1.0p0}</td> 657 * <tr><th scope="row">{@code -1.0}</th> <td>{@code -0x1.0p0}</td> 658 * <tr><th scope="row">{@code 2.0}</th> <td>{@code 0x1.0p1}</td> 659 * <tr><th scope="row">{@code 3.0}</th> <td>{@code 0x1.8p1}</td> 660 * <tr><th scope="row">{@code 0.5}</th> <td>{@code 0x1.0p-1}</td> 661 * <tr><th scope="row">{@code 0.25}</th> <td>{@code 0x1.0p-2}</td> 662 * <tr><th scope="row">{@code Double.MAX_VALUE}</th> 663 * <td>{@code 0x1.fffffffffffffp1023}</td> 664 * <tr><th scope="row">{@code Minimum Normal Value}</th> 665 * <td>{@code 0x1.0p-1022}</td> 666 * <tr><th scope="row">{@code Maximum Subnormal Value}</th> 667 * <td>{@code 0x0.fffffffffffffp-1022}</td> 668 * <tr><th scope="row">{@code Double.MIN_VALUE}</th> 669 * <td>{@code 0x0.0000000000001p-1022}</td> 670 * </tbody> 671 * </table> 672 * @param d the {@code double} to be converted. 673 * @return a hex string representation of the argument. 674 * @since 1.5 675 * @author Joseph D. Darcy 676 */ 677 public static String toHexString(double d) { 678 /* 679 * Modeled after the "a" conversion specifier in C99, section 680 * 7.19.6.1; however, the output of this method is more 681 * tightly specified. 682 */ 683 if (!isFinite(d) ) 684 // For infinity and NaN, use the decimal output. 685 return Double.toString(d); 686 else { 687 // Initialized to maximum size of output. 688 StringBuilder answer = new StringBuilder(24); 689 690 if (Math.copySign(1.0, d) == -1.0) // value is negative, 691 answer.append("-"); // so append sign info 692 693 answer.append("0x"); 694 695 d = Math.abs(d); 696 697 if(d == 0.0) { 698 answer.append("0.0p0"); 699 } else { 700 boolean subnormal = (d < Double.MIN_NORMAL); 701 702 // Isolate significand bits and OR in a high-order bit 703 // so that the string representation has a known 704 // length. 705 long signifBits = (Double.doubleToLongBits(d) 706 & DoubleConsts.SIGNIF_BIT_MASK) | 707 0x1000000000000000L; 708 709 // Subnormal values have a 0 implicit bit; normal 710 // values have a 1 implicit bit. 711 answer.append(subnormal ? "0." : "1."); 712 713 // Isolate the low-order 13 digits of the hex 714 // representation. If all the digits are zero, 715 // replace with a single 0; otherwise, remove all 716 // trailing zeros. 717 String signif = Long.toHexString(signifBits).substring(3,16); 718 answer.append(signif.equals("0000000000000") ? // 13 zeros 719 "0": 720 signif.replaceFirst("0{1,12}$", "")); 721 722 answer.append('p'); 723 // If the value is subnormal, use the E_min exponent 724 // value for double; otherwise, extract and report d's 725 // exponent (the representation of a subnormal uses 726 // E_min -1). 727 answer.append(subnormal ? 728 Double.MIN_EXPONENT: 729 Math.getExponent(d)); 730 } 731 return answer.toString(); 732 } 733 } 734 735 /** 736 * Returns a {@code Double} object holding the 737 * {@code double} value represented by the argument string 738 * {@code s}. 739 * 740 * <p>If {@code s} is {@code null}, then a 741 * {@code NullPointerException} is thrown. 742 * 743 * <p>Leading and trailing whitespace characters in {@code s} 744 * are ignored. Whitespace is removed as if by the {@link 745 * String#trim} method; that is, both ASCII space and control 746 * characters are removed. The rest of {@code s} should 747 * constitute a <i>FloatValue</i> as described by the lexical 748 * syntax rules: 749 * 750 * <blockquote> 751 * <dl> 752 * <dt><i>FloatValue:</i> 753 * <dd><i>Sign<sub>opt</sub></i> {@code NaN} 754 * <dd><i>Sign<sub>opt</sub></i> {@code Infinity} 755 * <dd><i>Sign<sub>opt</sub> FloatingPointLiteral</i> 756 * <dd><i>Sign<sub>opt</sub> HexFloatingPointLiteral</i> 757 * <dd><i>SignedInteger</i> 758 * </dl> 759 * 760 * <dl> 761 * <dt><i>HexFloatingPointLiteral</i>: 762 * <dd> <i>HexSignificand BinaryExponent FloatTypeSuffix<sub>opt</sub></i> 763 * </dl> 764 * 765 * <dl> 766 * <dt><i>HexSignificand:</i> 767 * <dd><i>HexNumeral</i> 768 * <dd><i>HexNumeral</i> {@code .} 769 * <dd>{@code 0x} <i>HexDigits<sub>opt</sub> 770 * </i>{@code .}<i> HexDigits</i> 771 * <dd>{@code 0X}<i> HexDigits<sub>opt</sub> 772 * </i>{@code .} <i>HexDigits</i> 773 * </dl> 774 * 775 * <dl> 776 * <dt><i>BinaryExponent:</i> 777 * <dd><i>BinaryExponentIndicator SignedInteger</i> 778 * </dl> 779 * 780 * <dl> 781 * <dt><i>BinaryExponentIndicator:</i> 782 * <dd>{@code p} 783 * <dd>{@code P} 784 * </dl> 785 * 786 * </blockquote> 787 * 788 * where <i>Sign</i>, <i>FloatingPointLiteral</i>, 789 * <i>HexNumeral</i>, <i>HexDigits</i>, <i>SignedInteger</i> and 790 * <i>FloatTypeSuffix</i> are as defined in the lexical structure 791 * sections of 792 * <cite>The Java Language Specification</cite>, 793 * except that underscores are not accepted between digits. 794 * If {@code s} does not have the form of 795 * a <i>FloatValue</i>, then a {@code NumberFormatException} 796 * is thrown. Otherwise, {@code s} is regarded as 797 * representing an exact decimal value in the usual 798 * "computerized scientific notation" or as an exact 799 * hexadecimal value; this exact numerical value is then 800 * conceptually converted to an "infinitely precise" 801 * binary value that is then rounded to type {@code double} 802 * by the usual round-to-nearest rule of IEEE 754 floating-point 803 * arithmetic, which includes preserving the sign of a zero 804 * value. 805 * 806 * Note that the round-to-nearest rule also implies overflow and 807 * underflow behaviour; if the exact value of {@code s} is large 808 * enough in magnitude (greater than or equal to ({@link 809 * #MAX_VALUE} + {@link Math#ulp(double) ulp(MAX_VALUE)}/2), 810 * rounding to {@code double} will result in an infinity and if the 811 * exact value of {@code s} is small enough in magnitude (less 812 * than or equal to {@link #MIN_VALUE}/2), rounding to float will 813 * result in a zero. 814 * 815 * Finally, after rounding a {@code Double} object representing 816 * this {@code double} value is returned. 817 * 818 * <p>Note that trailing format specifiers, specifiers that 819 * determine the type of a floating-point literal 820 * ({@code 1.0f} is a {@code float} value; 821 * {@code 1.0d} is a {@code double} value), do 822 * <em>not</em> influence the results of this method. In other 823 * words, the numerical value of the input string is converted 824 * directly to the target floating-point type. The two-step 825 * sequence of conversions, string to {@code float} followed 826 * by {@code float} to {@code double}, is <em>not</em> 827 * equivalent to converting a string directly to 828 * {@code double}. For example, the {@code float} 829 * literal {@code 0.1f} is equal to the {@code double} 830 * value {@code 0.10000000149011612}; the {@code float} 831 * literal {@code 0.1f} represents a different numerical 832 * value than the {@code double} literal 833 * {@code 0.1}. (The numerical value 0.1 cannot be exactly 834 * represented in a binary floating-point number.) 835 * 836 * <p>To avoid calling this method on an invalid string and having 837 * a {@code NumberFormatException} be thrown, the regular 838 * expression below can be used to screen the input string: 839 * 840 * {@snippet lang="java" : 841 * final String Digits = "(\\p{Digit}+)"; 842 * final String HexDigits = "(\\p{XDigit}+)"; 843 * // an exponent is 'e' or 'E' followed by an optionally 844 * // signed decimal integer. 845 * final String Exp = "[eE][+-]?"+Digits; 846 * final String fpRegex = 847 * ("[\\x00-\\x20]*"+ // Optional leading "whitespace" 848 * "[+-]?(" + // Optional sign character 849 * "NaN|" + // "NaN" string 850 * "Infinity|" + // "Infinity" string 851 * 852 * // A decimal floating-point string representing a finite positive 853 * // number without a leading sign has at most five basic pieces: 854 * // Digits . Digits ExponentPart FloatTypeSuffix 855 * // 856 * // Since this method allows integer-only strings as input 857 * // in addition to strings of floating-point literals, the 858 * // two sub-patterns below are simplifications of the grammar 859 * // productions from section 3.10.2 of 860 * // The Java Language Specification. 861 * 862 * // Digits ._opt Digits_opt ExponentPart_opt FloatTypeSuffix_opt 863 * "((("+Digits+"(\\.)?("+Digits+"?)("+Exp+")?)|"+ 864 * 865 * // . Digits ExponentPart_opt FloatTypeSuffix_opt 866 * "(\\.("+Digits+")("+Exp+")?)|"+ 867 * 868 * // Hexadecimal strings 869 * "((" + 870 * // 0[xX] HexDigits ._opt BinaryExponent FloatTypeSuffix_opt 871 * "(0[xX]" + HexDigits + "(\\.)?)|" + 872 * 873 * // 0[xX] HexDigits_opt . HexDigits BinaryExponent FloatTypeSuffix_opt 874 * "(0[xX]" + HexDigits + "?(\\.)" + HexDigits + ")" + 875 * 876 * ")[pP][+-]?" + Digits + "))" + 877 * "[fFdD]?))" + 878 * "[\\x00-\\x20]*");// Optional trailing "whitespace" 879 * // @link region substring="Pattern.matches" target ="java.util.regex.Pattern#matches" 880 * if (Pattern.matches(fpRegex, myString)) 881 * Double.valueOf(myString); // Will not throw NumberFormatException 882 * // @end 883 * else { 884 * // Perform suitable alternative action 885 * } 886 * } 887 * 888 * @apiNote To interpret localized string representations of a 889 * floating-point value, or string representations that have 890 * non-ASCII digits, use {@link java.text.NumberFormat}. For 891 * example, 892 * {@snippet lang="java" : 893 * NumberFormat.getInstance(l).parse(s).doubleValue(); 894 * } 895 * where {@code l} is the desired locale, or 896 * {@link java.util.Locale#ROOT} if locale insensitive. 897 * 898 * @param s the string to be parsed. 899 * @return a {@code Double} object holding the value 900 * represented by the {@code String} argument. 901 * @throws NumberFormatException if the string does not contain a 902 * parsable number. 903 * @see Double##decimalToBinaryConversion Decimal ↔ Binary Conversion Issues 904 */ 905 public static Double valueOf(String s) throws NumberFormatException { 906 return new Double(parseDouble(s)); 907 } 908 909 /** 910 * Returns a {@code Double} instance representing the specified 911 * {@code double} value. 912 * If a new {@code Double} instance is not required, this method 913 * should generally be used in preference to the constructor 914 * {@link #Double(double)}, as this method is likely to yield 915 * significantly better space and time performance by caching 916 * frequently requested values. 917 * 918 * @param d a double value. 919 * @return a {@code Double} instance representing {@code d}. 920 * @since 1.5 921 */ 922 @IntrinsicCandidate 923 public static Double valueOf(double d) { 924 return new Double(d); 925 } 926 927 /** 928 * Returns a new {@code double} initialized to the value 929 * represented by the specified {@code String}, as performed 930 * by the {@code valueOf} method of class 931 * {@code Double}. 932 * 933 * @param s the string to be parsed. 934 * @return the {@code double} value represented by the string 935 * argument. 936 * @throws NullPointerException if the string is null 937 * @throws NumberFormatException if the string does not contain 938 * a parsable {@code double}. 939 * @see java.lang.Double#valueOf(String) 940 * @see Double##decimalToBinaryConversion Decimal ↔ Binary Conversion Issues 941 * @since 1.2 942 */ 943 public static double parseDouble(String s) throws NumberFormatException { 944 return FloatingDecimal.parseDouble(s); 945 } 946 947 /** 948 * Returns {@code true} if the specified number is a 949 * Not-a-Number (NaN) value, {@code false} otherwise. 950 * 951 * @apiNote 952 * This method corresponds to the isNaN operation defined in IEEE 953 * 754. 954 * 955 * @param v the value to be tested. 956 * @return {@code true} if the value of the argument is NaN; 957 * {@code false} otherwise. 958 */ 959 public static boolean isNaN(double v) { 960 return (v != v); 961 } 962 963 /** 964 * Returns {@code true} if the specified number is infinitely 965 * large in magnitude, {@code false} otherwise. 966 * 967 * @apiNote 968 * This method corresponds to the isInfinite operation defined in 969 * IEEE 754. 970 * 971 * @param v the value to be tested. 972 * @return {@code true} if the value of the argument is positive 973 * infinity or negative infinity; {@code false} otherwise. 974 */ 975 @IntrinsicCandidate 976 public static boolean isInfinite(double v) { 977 return Math.abs(v) > MAX_VALUE; 978 } 979 980 /** 981 * Returns {@code true} if the argument is a finite floating-point 982 * value; returns {@code false} otherwise (for NaN and infinity 983 * arguments). 984 * 985 * @apiNote 986 * This method corresponds to the isFinite operation defined in 987 * IEEE 754. 988 * 989 * @param d the {@code double} value to be tested 990 * @return {@code true} if the argument is a finite 991 * floating-point value, {@code false} otherwise. 992 * @since 1.8 993 */ 994 @IntrinsicCandidate 995 public static boolean isFinite(double d) { 996 return Math.abs(d) <= Double.MAX_VALUE; 997 } 998 999 /** 1000 * The value of the Double. 1001 * 1002 * @serial 1003 */ 1004 private final double value; 1005 1006 /** 1007 * Constructs a newly allocated {@code Double} object that 1008 * represents the primitive {@code double} argument. 1009 * 1010 * @param value the value to be represented by the {@code Double}. 1011 * 1012 * @deprecated 1013 * It is rarely appropriate to use this constructor. The static factory 1014 * {@link #valueOf(double)} is generally a better choice, as it is 1015 * likely to yield significantly better space and time performance. 1016 */ 1017 @Deprecated(since="9", forRemoval = true) 1018 public Double(double value) { 1019 this.value = value; 1020 } 1021 1022 /** 1023 * Constructs a newly allocated {@code Double} object that 1024 * represents the floating-point value of type {@code double} 1025 * represented by the string. The string is converted to a 1026 * {@code double} value as if by the {@code valueOf} method. 1027 * 1028 * @param s a string to be converted to a {@code Double}. 1029 * @throws NumberFormatException if the string does not contain a 1030 * parsable number. 1031 * 1032 * @deprecated 1033 * It is rarely appropriate to use this constructor. 1034 * Use {@link #parseDouble(String)} to convert a string to a 1035 * {@code double} primitive, or use {@link #valueOf(String)} 1036 * to convert a string to a {@code Double} object. 1037 */ 1038 @Deprecated(since="9", forRemoval = true) 1039 public Double(String s) throws NumberFormatException { 1040 value = parseDouble(s); 1041 } 1042 1043 /** 1044 * Returns {@code true} if this {@code Double} value is 1045 * a Not-a-Number (NaN), {@code false} otherwise. 1046 * 1047 * @return {@code true} if the value represented by this object is 1048 * NaN; {@code false} otherwise. 1049 */ 1050 public boolean isNaN() { 1051 return isNaN(value); 1052 } 1053 1054 /** 1055 * Returns {@code true} if this {@code Double} value is 1056 * infinitely large in magnitude, {@code false} otherwise. 1057 * 1058 * @return {@code true} if the value represented by this object is 1059 * positive infinity or negative infinity; 1060 * {@code false} otherwise. 1061 */ 1062 public boolean isInfinite() { 1063 return isInfinite(value); 1064 } 1065 1066 /** 1067 * Returns a string representation of this {@code Double} object. 1068 * The primitive {@code double} value represented by this 1069 * object is converted to a string exactly as if by the method 1070 * {@code toString} of one argument. 1071 * 1072 * @return a {@code String} representation of this object. 1073 * @see java.lang.Double#toString(double) 1074 */ 1075 public String toString() { 1076 return toString(value); 1077 } 1078 1079 /** 1080 * Returns the value of this {@code Double} as a {@code byte} 1081 * after a narrowing primitive conversion. 1082 * 1083 * @return the {@code double} value represented by this object 1084 * converted to type {@code byte} 1085 * @jls 5.1.3 Narrowing Primitive Conversion 1086 * @since 1.1 1087 */ 1088 public byte byteValue() { 1089 return (byte)value; 1090 } 1091 1092 /** 1093 * Returns the value of this {@code Double} as a {@code short} 1094 * after a narrowing primitive conversion. 1095 * 1096 * @return the {@code double} value represented by this object 1097 * converted to type {@code short} 1098 * @jls 5.1.3 Narrowing Primitive Conversion 1099 * @since 1.1 1100 */ 1101 public short shortValue() { 1102 return (short)value; 1103 } 1104 1105 /** 1106 * Returns the value of this {@code Double} as an {@code int} 1107 * after a narrowing primitive conversion. 1108 * @jls 5.1.3 Narrowing Primitive Conversion 1109 * 1110 * @return the {@code double} value represented by this object 1111 * converted to type {@code int} 1112 */ 1113 public int intValue() { 1114 return (int)value; 1115 } 1116 1117 /** 1118 * Returns the value of this {@code Double} as a {@code long} 1119 * after a narrowing primitive conversion. 1120 * 1121 * @return the {@code double} value represented by this object 1122 * converted to type {@code long} 1123 * @jls 5.1.3 Narrowing Primitive Conversion 1124 */ 1125 public long longValue() { 1126 return (long)value; 1127 } 1128 1129 /** 1130 * Returns the value of this {@code Double} as a {@code float} 1131 * after a narrowing primitive conversion. 1132 * 1133 * @apiNote 1134 * This method corresponds to the convertFormat operation defined 1135 * in IEEE 754. 1136 * 1137 * @return the {@code double} value represented by this object 1138 * converted to type {@code float} 1139 * @jls 5.1.3 Narrowing Primitive Conversion 1140 * @since 1.0 1141 */ 1142 public float floatValue() { 1143 return (float)value; 1144 } 1145 1146 /** 1147 * Returns the {@code double} value of this {@code Double} object. 1148 * 1149 * @return the {@code double} value represented by this object 1150 */ 1151 @IntrinsicCandidate 1152 public double doubleValue() { 1153 return value; 1154 } 1155 1156 /** 1157 * Returns a hash code for this {@code Double} object. The 1158 * result is the exclusive OR of the two halves of the 1159 * {@code long} integer bit representation, exactly as 1160 * produced by the method {@link #doubleToLongBits(double)}, of 1161 * the primitive {@code double} value represented by this 1162 * {@code Double} object. That is, the hash code is the value 1163 * of the expression: 1164 * 1165 * <blockquote> 1166 * {@code (int)(v^(v>>>32))} 1167 * </blockquote> 1168 * 1169 * where {@code v} is defined by: 1170 * 1171 * <blockquote> 1172 * {@code long v = Double.doubleToLongBits(this.doubleValue());} 1173 * </blockquote> 1174 * 1175 * @return a {@code hash code} value for this object. 1176 */ 1177 @Override 1178 public int hashCode() { 1179 return Double.hashCode(value); 1180 } 1181 1182 /** 1183 * Returns a hash code for a {@code double} value; compatible with 1184 * {@code Double.hashCode()}. 1185 * 1186 * @param value the value to hash 1187 * @return a hash code value for a {@code double} value. 1188 * @since 1.8 1189 */ 1190 public static int hashCode(double value) { 1191 return Long.hashCode(doubleToLongBits(value)); 1192 } 1193 1194 /** 1195 * Compares this object against the specified object. The result 1196 * is {@code true} if and only if the argument is not 1197 * {@code null} and is a {@code Double} object that 1198 * represents a {@code double} that has the same value as the 1199 * {@code double} represented by this object. For this 1200 * purpose, two {@code double} values are considered to be 1201 * the same if and only if the method {@link 1202 * #doubleToLongBits(double)} returns the identical 1203 * {@code long} value when applied to each. 1204 * 1205 * @apiNote 1206 * This method is defined in terms of {@link 1207 * #doubleToLongBits(double)} rather than the {@code ==} operator 1208 * on {@code double} values since the {@code ==} operator does 1209 * <em>not</em> define an equivalence relation and to satisfy the 1210 * {@linkplain Object#equals equals contract} an equivalence 1211 * relation must be implemented; see <a 1212 * href="#equivalenceRelation">this discussion</a> for details of 1213 * floating-point equality and equivalence. 1214 * 1215 * @see java.lang.Double#doubleToLongBits(double) 1216 * @jls 15.21.1 Numerical Equality Operators == and != 1217 */ 1218 public boolean equals(Object obj) { 1219 return (obj instanceof Double) 1220 && (doubleToLongBits(((Double)obj).value) == 1221 doubleToLongBits(value)); 1222 } 1223 1224 /** 1225 * Returns a representation of the specified floating-point value 1226 * according to the IEEE 754 floating-point "double 1227 * format" bit layout. 1228 * 1229 * <p>Bit 63 (the bit that is selected by the mask 1230 * {@code 0x8000000000000000L}) represents the sign of the 1231 * floating-point number. Bits 1232 * 62-52 (the bits that are selected by the mask 1233 * {@code 0x7ff0000000000000L}) represent the exponent. Bits 51-0 1234 * (the bits that are selected by the mask 1235 * {@code 0x000fffffffffffffL}) represent the significand 1236 * (sometimes called the mantissa) of the floating-point number. 1237 * 1238 * <p>If the argument is positive infinity, the result is 1239 * {@code 0x7ff0000000000000L}. 1240 * 1241 * <p>If the argument is negative infinity, the result is 1242 * {@code 0xfff0000000000000L}. 1243 * 1244 * <p>If the argument is NaN, the result is 1245 * {@code 0x7ff8000000000000L}. 1246 * 1247 * <p>In all cases, the result is a {@code long} integer that, when 1248 * given to the {@link #longBitsToDouble(long)} method, will produce a 1249 * floating-point value the same as the argument to 1250 * {@code doubleToLongBits} (except all NaN values are 1251 * collapsed to a single "canonical" NaN value). 1252 * 1253 * @param value a {@code double} precision floating-point number. 1254 * @return the bits that represent the floating-point number. 1255 */ 1256 @IntrinsicCandidate 1257 public static long doubleToLongBits(double value) { 1258 if (!isNaN(value)) { 1259 return doubleToRawLongBits(value); 1260 } 1261 return 0x7ff8000000000000L; 1262 } 1263 1264 /** 1265 * Returns a representation of the specified floating-point value 1266 * according to the IEEE 754 floating-point "double 1267 * format" bit layout, preserving Not-a-Number (NaN) values. 1268 * 1269 * <p>Bit 63 (the bit that is selected by the mask 1270 * {@code 0x8000000000000000L}) represents the sign of the 1271 * floating-point number. Bits 1272 * 62-52 (the bits that are selected by the mask 1273 * {@code 0x7ff0000000000000L}) represent the exponent. Bits 51-0 1274 * (the bits that are selected by the mask 1275 * {@code 0x000fffffffffffffL}) represent the significand 1276 * (sometimes called the mantissa) of the floating-point number. 1277 * 1278 * <p>If the argument is positive infinity, the result is 1279 * {@code 0x7ff0000000000000L}. 1280 * 1281 * <p>If the argument is negative infinity, the result is 1282 * {@code 0xfff0000000000000L}. 1283 * 1284 * <p>If the argument is NaN, the result is the {@code long} 1285 * integer representing the actual NaN value. Unlike the 1286 * {@code doubleToLongBits} method, 1287 * {@code doubleToRawLongBits} does not collapse all the bit 1288 * patterns encoding a NaN to a single "canonical" NaN 1289 * value. 1290 * 1291 * <p>In all cases, the result is a {@code long} integer that, 1292 * when given to the {@link #longBitsToDouble(long)} method, will 1293 * produce a floating-point value the same as the argument to 1294 * {@code doubleToRawLongBits}. 1295 * 1296 * @param value a {@code double} precision floating-point number. 1297 * @return the bits that represent the floating-point number. 1298 * @since 1.3 1299 */ 1300 @IntrinsicCandidate 1301 public static native long doubleToRawLongBits(double value); 1302 1303 /** 1304 * Returns the {@code double} value corresponding to a given 1305 * bit representation. 1306 * The argument is considered to be a representation of a 1307 * floating-point value according to the IEEE 754 floating-point 1308 * "double format" bit layout. 1309 * 1310 * <p>If the argument is {@code 0x7ff0000000000000L}, the result 1311 * is positive infinity. 1312 * 1313 * <p>If the argument is {@code 0xfff0000000000000L}, the result 1314 * is negative infinity. 1315 * 1316 * <p>If the argument is any value in the range 1317 * {@code 0x7ff0000000000001L} through 1318 * {@code 0x7fffffffffffffffL} or in the range 1319 * {@code 0xfff0000000000001L} through 1320 * {@code 0xffffffffffffffffL}, the result is a NaN. No IEEE 1321 * 754 floating-point operation provided by Java can distinguish 1322 * between two NaN values of the same type with different bit 1323 * patterns. Distinct values of NaN are only distinguishable by 1324 * use of the {@code Double.doubleToRawLongBits} method. 1325 * 1326 * <p>In all other cases, let <i>s</i>, <i>e</i>, and <i>m</i> be three 1327 * values that can be computed from the argument: 1328 * 1329 * {@snippet lang="java" : 1330 * int s = ((bits >> 63) == 0) ? 1 : -1; 1331 * int e = (int)((bits >> 52) & 0x7ffL); 1332 * long m = (e == 0) ? 1333 * (bits & 0xfffffffffffffL) << 1 : 1334 * (bits & 0xfffffffffffffL) | 0x10000000000000L; 1335 * } 1336 * 1337 * Then the floating-point result equals the value of the mathematical 1338 * expression <i>s</i>·<i>m</i>·2<sup><i>e</i>-1075</sup>. 1339 * 1340 * <p>Note that this method may not be able to return a 1341 * {@code double} NaN with exactly same bit pattern as the 1342 * {@code long} argument. IEEE 754 distinguishes between two 1343 * kinds of NaNs, quiet NaNs and <i>signaling NaNs</i>. The 1344 * differences between the two kinds of NaN are generally not 1345 * visible in Java. Arithmetic operations on signaling NaNs turn 1346 * them into quiet NaNs with a different, but often similar, bit 1347 * pattern. However, on some processors merely copying a 1348 * signaling NaN also performs that conversion. In particular, 1349 * copying a signaling NaN to return it to the calling method 1350 * may perform this conversion. So {@code longBitsToDouble} 1351 * may not be able to return a {@code double} with a 1352 * signaling NaN bit pattern. Consequently, for some 1353 * {@code long} values, 1354 * {@code doubleToRawLongBits(longBitsToDouble(start))} may 1355 * <i>not</i> equal {@code start}. Moreover, which 1356 * particular bit patterns represent signaling NaNs is platform 1357 * dependent; although all NaN bit patterns, quiet or signaling, 1358 * must be in the NaN range identified above. 1359 * 1360 * @param bits any {@code long} integer. 1361 * @return the {@code double} floating-point value with the same 1362 * bit pattern. 1363 */ 1364 @IntrinsicCandidate 1365 public static native double longBitsToDouble(long bits); 1366 1367 /** 1368 * Compares two {@code Double} objects numerically. 1369 * 1370 * This method imposes a total order on {@code Double} objects 1371 * with two differences compared to the incomplete order defined by 1372 * the Java language numerical comparison operators ({@code <, <=, 1373 * ==, >=, >}) on {@code double} values. 1374 * 1375 * <ul><li> A NaN is <em>unordered</em> with respect to other 1376 * values and unequal to itself under the comparison 1377 * operators. This method chooses to define {@code 1378 * Double.NaN} to be equal to itself and greater than all 1379 * other {@code double} values (including {@code 1380 * Double.POSITIVE_INFINITY}). 1381 * 1382 * <li> Positive zero and negative zero compare equal 1383 * numerically, but are distinct and distinguishable values. 1384 * This method chooses to define positive zero ({@code +0.0d}), 1385 * to be greater than negative zero ({@code -0.0d}). 1386 * </ul> 1387 1388 * This ensures that the <i>natural ordering</i> of {@code Double} 1389 * objects imposed by this method is <i>consistent with 1390 * equals</i>; see <a href="#equivalenceRelation">this 1391 * discussion</a> for details of floating-point comparison and 1392 * ordering. 1393 * 1394 * @param anotherDouble the {@code Double} to be compared. 1395 * @return the value {@code 0} if {@code anotherDouble} is 1396 * numerically equal to this {@code Double}; a value 1397 * less than {@code 0} if this {@code Double} 1398 * is numerically less than {@code anotherDouble}; 1399 * and a value greater than {@code 0} if this 1400 * {@code Double} is numerically greater than 1401 * {@code anotherDouble}. 1402 * 1403 * @jls 15.20.1 Numerical Comparison Operators {@code <}, {@code <=}, {@code >}, and {@code >=} 1404 * @since 1.2 1405 */ 1406 public int compareTo(Double anotherDouble) { 1407 return Double.compare(value, anotherDouble.value); 1408 } 1409 1410 /** 1411 * Compares the two specified {@code double} values. The sign 1412 * of the integer value returned is the same as that of the 1413 * integer that would be returned by the call: 1414 * <pre> 1415 * Double.valueOf(d1).compareTo(Double.valueOf(d2)) 1416 * </pre> 1417 * 1418 * @param d1 the first {@code double} to compare 1419 * @param d2 the second {@code double} to compare 1420 * @return the value {@code 0} if {@code d1} is 1421 * numerically equal to {@code d2}; a value less than 1422 * {@code 0} if {@code d1} is numerically less than 1423 * {@code d2}; and a value greater than {@code 0} 1424 * if {@code d1} is numerically greater than 1425 * {@code d2}. 1426 * @since 1.4 1427 */ 1428 public static int compare(double d1, double d2) { 1429 if (d1 < d2) 1430 return -1; // Neither val is NaN, thisVal is smaller 1431 if (d1 > d2) 1432 return 1; // Neither val is NaN, thisVal is larger 1433 1434 // Cannot use doubleToRawLongBits because of possibility of NaNs. 1435 long thisBits = Double.doubleToLongBits(d1); 1436 long anotherBits = Double.doubleToLongBits(d2); 1437 1438 return (thisBits == anotherBits ? 0 : // Values are equal 1439 (thisBits < anotherBits ? -1 : // (-0.0, 0.0) or (!NaN, NaN) 1440 1)); // (0.0, -0.0) or (NaN, !NaN) 1441 } 1442 1443 /** 1444 * Adds two {@code double} values together as per the + operator. 1445 * 1446 * @apiNote This method corresponds to the addition operation 1447 * defined in IEEE 754. 1448 * 1449 * @param a the first operand 1450 * @param b the second operand 1451 * @return the sum of {@code a} and {@code b} 1452 * @jls 4.2.4 Floating-Point Operations 1453 * @see java.util.function.BinaryOperator 1454 * @since 1.8 1455 */ 1456 public static double sum(double a, double b) { 1457 return a + b; 1458 } 1459 1460 /** 1461 * Returns the greater of two {@code double} values 1462 * as if by calling {@link Math#max(double, double) Math.max}. 1463 * 1464 * @apiNote 1465 * This method corresponds to the maximum operation defined in 1466 * IEEE 754. 1467 * 1468 * @param a the first operand 1469 * @param b the second operand 1470 * @return the greater of {@code a} and {@code b} 1471 * @see java.util.function.BinaryOperator 1472 * @since 1.8 1473 */ 1474 public static double max(double a, double b) { 1475 return Math.max(a, b); 1476 } 1477 1478 /** 1479 * Returns the smaller of two {@code double} values 1480 * as if by calling {@link Math#min(double, double) Math.min}. 1481 * 1482 * @apiNote 1483 * This method corresponds to the minimum operation defined in 1484 * IEEE 754. 1485 * 1486 * @param a the first operand 1487 * @param b the second operand 1488 * @return the smaller of {@code a} and {@code b}. 1489 * @see java.util.function.BinaryOperator 1490 * @since 1.8 1491 */ 1492 public static double min(double a, double b) { 1493 return Math.min(a, b); 1494 } 1495 1496 /** 1497 * Returns an {@link Optional} containing the nominal descriptor for this 1498 * instance, which is the instance itself. 1499 * 1500 * @return an {@link Optional} describing the {@linkplain Double} instance 1501 * @since 12 1502 */ 1503 @Override 1504 public Optional<Double> describeConstable() { 1505 return Optional.of(this); 1506 } 1507 1508 /** 1509 * Resolves this instance as a {@link ConstantDesc}, the result of which is 1510 * the instance itself. 1511 * 1512 * @param lookup ignored 1513 * @return the {@linkplain Double} instance 1514 * @since 12 1515 */ 1516 @Override 1517 public Double resolveConstantDesc(MethodHandles.Lookup lookup) { 1518 return this; 1519 } 1520 1521 /** use serialVersionUID from JDK 1.0.2 for interoperability */ 1522 @java.io.Serial 1523 private static final long serialVersionUID = -9172774392245257468L; 1524 }