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.value.DeserializeConstructor; 37 import jdk.internal.vm.annotation.IntrinsicCandidate; 38 39 /** 40 * The {@code Double} class is the {@linkplain 41 * java.lang##wrapperClass wrapper class} for values of the primitive 42 * type {@code double}. An object of type {@code Double} contains a 43 * single field whose type is {@code double}. 44 * 45 * <p>In addition, this class provides several methods for converting a 46 * {@code double} to a {@code String} and a 47 * {@code String} to a {@code double}, as well as other 48 * constants and methods useful when dealing with a 49 * {@code double}. 50 * 51 * <p>This is a <a href="{@docRoot}/java.base/java/lang/doc-files/ValueBased.html">value-based</a> 52 * class; programmers should treat instances that are 53 * {@linkplain #equals(Object) equal} as interchangeable and should not 54 * use instances for synchronization, or unpredictable behavior may 55 * occur. For example, in a future release, synchronization may fail. 56 * 57 * <h2><a id=equivalenceRelation>Floating-point Equality, Equivalence, 58 * and Comparison</a></h2> 59 * 60 * IEEE 754 floating-point values include finite nonzero values, 61 * signed zeros ({@code +0.0} and {@code -0.0}), signed infinities 62 * ({@linkplain Double#POSITIVE_INFINITY positive infinity} and 63 * {@linkplain Double#NEGATIVE_INFINITY negative infinity}), and 64 * {@linkplain Double#NaN NaN} (not-a-number). 65 * 66 * <p>An <em>equivalence relation</em> on a set of values is a boolean 67 * relation on pairs of values that is reflexive, symmetric, and 68 * transitive. For more discussion of equivalence relations and object 69 * equality, see the {@link Object#equals Object.equals} 70 * specification. An equivalence relation partitions the values it 71 * operates over into sets called <i>equivalence classes</i>. All the 72 * members of the equivalence class are equal to each other under the 73 * relation. An equivalence class may contain only a single member. At 74 * least for some purposes, all the members of an equivalence class 75 * are substitutable for each other. In particular, in a numeric 76 * expression equivalent values can be <em>substituted</em> for one 77 * another without changing the result of the expression, meaning 78 * changing the equivalence class of the result of the expression. 79 * 80 * <p>Notably, the built-in {@code ==} operation on floating-point 81 * values is <em>not</em> an equivalence relation. Despite not 82 * defining an equivalence relation, the semantics of the IEEE 754 83 * {@code ==} operator were deliberately designed to meet other needs 84 * of numerical computation. There are two exceptions where the 85 * properties of an equivalence relation are not satisfied by {@code 86 * ==} on floating-point values: 87 * 88 * <ul> 89 * 90 * <li>If {@code v1} and {@code v2} are both NaN, then {@code v1 91 * == v2} has the value {@code false}. Therefore, for two NaN 92 * arguments the <em>reflexive</em> property of an equivalence 93 * relation is <em>not</em> satisfied by the {@code ==} operator. 94 * 95 * <li>If {@code v1} represents {@code +0.0} while {@code v2} 96 * represents {@code -0.0}, or vice versa, then {@code v1 == v2} has 97 * the value {@code true} even though {@code +0.0} and {@code -0.0} 98 * are distinguishable under various floating-point operations. For 99 * example, {@code 1.0/+0.0} evaluates to positive infinity while 100 * {@code 1.0/-0.0} evaluates to <em>negative</em> infinity and 101 * positive infinity and negative infinity are neither equal to each 102 * other nor equivalent to each other. Thus, while a signed zero input 103 * most commonly determines the sign of a zero result, because of 104 * dividing by zero, {@code +0.0} and {@code -0.0} may not be 105 * substituted for each other in general. The sign of a zero input 106 * also has a non-substitutable effect on the result of some math 107 * library methods. 108 * 109 * </ul> 110 * 111 * <p>For ordered comparisons using the built-in comparison operators 112 * ({@code <}, {@code <=}, etc.), NaN values have another anomalous 113 * situation: a NaN is neither less than, nor greater than, nor equal 114 * to any value, including itself. This means the <i>trichotomy of 115 * comparison</i> does <em>not</em> hold. 116 * 117 * <p>To provide the appropriate semantics for {@code equals} and 118 * {@code compareTo} methods, those methods cannot simply be wrappers 119 * around {@code ==} or ordered comparison operations. Instead, {@link 120 * Double#equals equals} uses {@linkplain ##repEquivalence representation 121 * equivalence}, defining NaN arguments to be equal to each other, 122 * restoring reflexivity, and defining {@code +0.0} to <em>not</em> be 123 * equal to {@code -0.0}. For comparisons, {@link Double#compareTo 124 * compareTo} defines a total order where {@code -0.0} is less than 125 * {@code +0.0} and where a NaN is equal to itself and considered 126 * greater than positive infinity. 127 * 128 * <p>The operational semantics of {@code equals} and {@code 129 * compareTo} are expressed in terms of {@linkplain #doubleToLongBits 130 * bit-wise converting} the floating-point values to integral values. 131 * 132 * <p>The <em>natural ordering</em> implemented by {@link #compareTo 133 * compareTo} is {@linkplain Comparable consistent with equals}. That 134 * is, two objects are reported as equal by {@code equals} if and only 135 * if {@code compareTo} on those objects returns zero. 136 * 137 * <p>The adjusted behaviors defined for {@code equals} and {@code 138 * compareTo} allow instances of wrapper classes to work properly with 139 * conventional data structures. For example, defining NaN 140 * values to be {@code equals} to one another allows NaN to be used as 141 * an element of a {@link java.util.HashSet HashSet} or as the key of 142 * a {@link java.util.HashMap HashMap}. Similarly, defining {@code 143 * compareTo} as a total ordering, including {@code +0.0}, {@code 144 * -0.0}, and NaN, allows instances of wrapper classes to be used as 145 * elements of a {@link java.util.SortedSet SortedSet} or as keys of a 146 * {@link java.util.SortedMap SortedMap}. 147 * 148 * <p>Comparing numerical equality to various useful equivalence 149 * relations that can be defined over floating-point values: 150 * 151 * <dl> 152 * <dt><a id=fpNumericalEq></a><dfn>{@index "numerical equality"}</dfn> ({@code ==} 153 * operator): (<em>Not</em> an equivalence relation)</dt> 154 * <dd>Two floating-point values represent the same extended real 155 * number. The extended real numbers are the real numbers augmented 156 * with positive infinity and negative infinity. Under numerical 157 * equality, {@code +0.0} and {@code -0.0} are equal since they both 158 * map to the same real value, 0. A NaN does not map to any real 159 * number and is not equal to any value, including itself. 160 * </dd> 161 * 162 * <dt><dfn>{@index "bit-wise equivalence"}</dfn>:</dt> 163 * <dd>The bits of the two floating-point values are the same. This 164 * equivalence relation for {@code double} values {@code a} and {@code 165 * b} is implemented by the expression 166 * <br>{@code Double.doubleTo}<code><b>Raw</b></code>{@code LongBits(a) == Double.doubleTo}<code><b>Raw</b></code>{@code LongBits(b)}<br> 167 * Under this relation, {@code +0.0} and {@code -0.0} are 168 * distinguished from each other and every bit pattern encoding a NaN 169 * is distinguished from every other bit pattern encoding a NaN. 170 * </dd> 171 * 172 * <dt><dfn><a id=repEquivalence></a>{@index "representation equivalence"}</dfn>:</dt> 173 * <dd>The two floating-point values represent the same IEEE 754 174 * <i>datum</i>. In particular, for {@linkplain #isFinite(double) 175 * finite} values, the sign, {@linkplain Math#getExponent(double) 176 * exponent}, and significand components of the floating-point values 177 * are the same. Under this relation: 178 * <ul> 179 * <li> {@code +0.0} and {@code -0.0} are distinguished from each other. 180 * <li> every bit pattern encoding a NaN is considered equivalent to each other 181 * <li> positive infinity is equivalent to positive infinity; negative 182 * infinity is equivalent to negative infinity. 183 * </ul> 184 * Expressions implementing this equivalence relation include: 185 * <ul> 186 * <li>{@code Double.doubleToLongBits(a) == Double.doubleToLongBits(b)} 187 * <li>{@code Double.valueOf(a).equals(Double.valueOf(b))} 188 * <li>{@code Double.compare(a, b) == 0} 189 * </ul> 190 * Note that representation equivalence is often an appropriate notion 191 * of equivalence to test the behavior of {@linkplain StrictMath math 192 * libraries}. 193 * </dd> 194 * </dl> 195 * 196 * For two binary floating-point values {@code a} and {@code b}, if 197 * neither of {@code a} and {@code b} is zero or NaN, then the three 198 * relations numerical equality, bit-wise equivalence, and 199 * representation equivalence of {@code a} and {@code b} have the same 200 * {@code true}/{@code false} value. In other words, for binary 201 * floating-point values, the three relations only differ if at least 202 * one argument is zero or NaN. 203 * 204 * <h2><a id=decimalToBinaryConversion>Decimal ↔ Binary Conversion Issues</a></h2> 205 * 206 * Many surprising results of binary floating-point arithmetic trace 207 * back to aspects of decimal to binary conversion and binary to 208 * decimal conversion. While integer values can be exactly represented 209 * in any base, which fractional values can be exactly represented in 210 * a base is a function of the base. For example, in base 10, 1/3 is a 211 * repeating fraction (0.33333....); but in base 3, 1/3 is exactly 212 * 0.1<sub>(3)</sub>, that is 1 × 3<sup>-1</sup>. 213 * Similarly, in base 10, 1/10 is exactly representable as 0.1 214 * (1 × 10<sup>-1</sup>), but in base 2, it is a 215 * repeating fraction (0.0001100110011...<sub>(2)</sub>). 216 * 217 * <p>Values of the {@code float} type have {@value Float#PRECISION} 218 * bits of precision and values of the {@code double} type have 219 * {@value Double#PRECISION} bits of precision. Therefore, since 0.1 220 * is a repeating fraction in base 2 with a four-bit repeat, {@code 221 * 0.1f} != {@code 0.1d}. In more detail, including hexadecimal 222 * floating-point literals: 223 * 224 * <ul> 225 * <li>The exact numerical value of {@code 0.1f} ({@code 0x1.99999a0000000p-4f}) is 226 * 0.100000001490116119384765625. 227 * <li>The exact numerical value of {@code 0.1d} ({@code 0x1.999999999999ap-4d}) is 228 * 0.1000000000000000055511151231257827021181583404541015625. 229 * </ul> 230 * 231 * These are the closest {@code float} and {@code double} values, 232 * respectively, to the numerical value of 0.1. These results are 233 * consistent with a {@code float} value having the equivalent of 6 to 234 * 9 digits of decimal precision and a {@code double} value having the 235 * equivalent of 15 to 17 digits of decimal precision. (The 236 * equivalent precision varies according to the different relative 237 * densities of binary and decimal values at different points along the 238 * real number line.) 239 * 240 * <p>This representation hazard of decimal fractions is one reason to 241 * use caution when storing monetary values as {@code float} or {@code 242 * double}. Alternatives include: 243 * <ul> 244 * <li>using {@link java.math.BigDecimal BigDecimal} to store decimal 245 * fractional values exactly 246 * 247 * <li>scaling up so the monetary value is an integer — for 248 * example, multiplying by 100 if the value is denominated in cents or 249 * multiplying by 1000 if the value is denominated in mills — 250 * and then storing that scaled value in an integer type 251 * 252 *</ul> 253 * 254 * <p>For each finite floating-point value and a given floating-point 255 * type, there is a contiguous region of the real number line which 256 * maps to that value. Under the default round to nearest rounding 257 * policy (JLS {@jls 15.4}), this contiguous region for a value is 258 * typically one {@linkplain Math#ulp ulp} (unit in the last place) 259 * wide and centered around the exactly representable value. (At 260 * exponent boundaries, the region is asymmetrical and larger on the 261 * side with the larger exponent.) For example, for {@code 0.1f}, the 262 * region can be computed as follows: 263 * 264 * <br>// Numeric values listed are exact values 265 * <br>oneTenthApproxAsFloat = 0.100000001490116119384765625; 266 * <br>ulpOfoneTenthApproxAsFloat = Math.ulp(0.1f) = 7.450580596923828125E-9; 267 * <br>// Numeric range that is converted to the float closest to 0.1, _excludes_ endpoints 268 * <br>(oneTenthApproxAsFloat - ½ulpOfoneTenthApproxAsFloat, oneTenthApproxAsFloat + ½ulpOfoneTenthApproxAsFloat) = 269 * <br>(0.0999999977648258209228515625, 0.1000000052154064178466796875) 270 * 271 * <p>In particular, a correctly rounded decimal to binary conversion 272 * of any string representing a number in this range, say by {@link 273 * Float#parseFloat(String)}, will be converted to the same value: 274 * 275 * {@snippet lang="java" : 276 * Float.parseFloat("0.0999999977648258209228515625000001"); // rounds up to oneTenthApproxAsFloat 277 * Float.parseFloat("0.099999998"); // rounds up to oneTenthApproxAsFloat 278 * Float.parseFloat("0.1"); // rounds up to oneTenthApproxAsFloat 279 * Float.parseFloat("0.100000001490116119384765625"); // exact conversion 280 * Float.parseFloat("0.100000005215406417846679687"); // rounds down to oneTenthApproxAsFloat 281 * Float.parseFloat("0.100000005215406417846679687499999"); // rounds down to oneTenthApproxAsFloat 282 * } 283 * 284 * <p>Similarly, an analogous range can be constructed for the {@code 285 * double} type based on the exact value of {@code double} 286 * approximation to {@code 0.1d} and the numerical value of {@code 287 * Math.ulp(0.1d)} and likewise for other particular numerical values 288 * in the {@code float} and {@code double} types. 289 * 290 * <p>As seen in the above conversions, compared to the exact 291 * numerical value the operation would have without rounding, the same 292 * floating-point value as a result can be: 293 * <ul> 294 * <li>greater than the exact result 295 * <li>equal to the exact result 296 * <li>less than the exact result 297 * </ul> 298 * 299 * A floating-point value doesn't "know" whether it was the result of 300 * rounding up, or rounding down, or an exact operation; it contains 301 * no history of how it was computed. Consequently, the sum of 302 * {@snippet lang="java" : 303 * 0.1f + 0.1f + 0.1f + 0.1f + 0.1f + 0.1f + 0.1f + 0.1f + 0.1f + 0.1f; 304 * // Numerical value of computed sum: 1.00000011920928955078125, 305 * // the next floating-point value larger than 1.0f, equal to Math.nextUp(1.0f). 306 * } 307 * or 308 * {@snippet lang="java" : 309 * 0.1d + 0.1d + 0.1d + 0.1d + 0.1d + 0.1d + 0.1d + 0.1d + 0.1d + 0.1d; 310 * // Numerical value of computed sum: 0.99999999999999988897769753748434595763683319091796875, 311 * // the next floating-point value smaller than 1.0d, equal to Math.nextDown(1.0d). 312 * } 313 * 314 * should <em>not</em> be expected to be exactly equal to 1.0, but 315 * only to be close to 1.0. Consequently, the following code is an 316 * infinite loop: 317 * 318 * {@snippet lang="java" : 319 * double d = 0.0; 320 * while (d != 1.0) { // Surprising infinite loop 321 * d += 0.1; // Sum never _exactly_ equals 1.0 322 * } 323 * } 324 * 325 * Instead, use an integer loop count for counted loops: 326 * 327 * {@snippet lang="java" : 328 * double d = 0.0; 329 * for (int i = 0; i < 10; i++) { 330 * d += 0.1; 331 * } // Value of d is equal to Math.nextDown(1.0). 332 * } 333 * 334 * or test against a floating-point limit using ordered comparisons 335 * ({@code <}, {@code <=}, {@code >}, {@code >=}): 336 * 337 * {@snippet lang="java" : 338 * double d = 0.0; 339 * while (d <= 1.0) { 340 * d += 0.1; 341 * } // Value of d approximately 1.0999999999999999 342 * } 343 * 344 * While floating-point arithmetic may have surprising results, IEEE 345 * 754 floating-point arithmetic follows a principled design and its 346 * behavior is predictable on the Java platform. 347 * 348 * @jls 4.2.3 Floating-Point Types and Values 349 * @jls 4.2.4 Floating-Point Operations 350 * @jls 15.21.1 Numerical Equality Operators == and != 351 * @jls 15.20.1 Numerical Comparison Operators {@code <}, {@code <=}, {@code >}, and {@code >=} 352 * 353 * @see <a href="https://standards.ieee.org/ieee/754/6210/"> 354 * <cite>IEEE Standard for Floating-Point Arithmetic</cite></a> 355 * 356 * @author Lee Boynton 357 * @author Arthur van Hoff 358 * @author Joseph D. Darcy 359 * @since 1.0 360 */ 361 @jdk.internal.MigratedValueClass 362 @jdk.internal.ValueBased 363 public final class Double extends Number 364 implements Comparable<Double>, Constable, ConstantDesc { 365 /** 366 * A constant holding the positive infinity of type 367 * {@code double}. It is equal to the value returned by 368 * {@code Double.longBitsToDouble(0x7ff0000000000000L)}. 369 */ 370 public static final double POSITIVE_INFINITY = 1.0 / 0.0; 371 372 /** 373 * A constant holding the negative infinity of type 374 * {@code double}. It is equal to the value returned by 375 * {@code Double.longBitsToDouble(0xfff0000000000000L)}. 376 */ 377 public static final double NEGATIVE_INFINITY = -1.0 / 0.0; 378 379 /** 380 * A constant holding a Not-a-Number (NaN) value of type 381 * {@code double}. It is equivalent to the value returned by 382 * {@code Double.longBitsToDouble(0x7ff8000000000000L)}. 383 */ 384 public static final double NaN = 0.0d / 0.0; 385 386 /** 387 * A constant holding the largest positive finite value of type 388 * {@code double}, 389 * (2-2<sup>-52</sup>)·2<sup>1023</sup>. It is equal to 390 * the hexadecimal floating-point literal 391 * {@code 0x1.fffffffffffffP+1023} and also equal to 392 * {@code Double.longBitsToDouble(0x7fefffffffffffffL)}. 393 */ 394 public static final double MAX_VALUE = 0x1.fffffffffffffP+1023; // 1.7976931348623157e+308 395 396 /** 397 * A constant holding the smallest positive normal value of type 398 * {@code double}, 2<sup>-1022</sup>. It is equal to the 399 * hexadecimal floating-point literal {@code 0x1.0p-1022} and also 400 * equal to {@code Double.longBitsToDouble(0x0010000000000000L)}. 401 * 402 * @since 1.6 403 */ 404 public static final double MIN_NORMAL = 0x1.0p-1022; // 2.2250738585072014E-308 405 406 /** 407 * A constant holding the smallest positive nonzero value of type 408 * {@code double}, 2<sup>-1074</sup>. It is equal to the 409 * hexadecimal floating-point literal 410 * {@code 0x0.0000000000001P-1022} and also equal to 411 * {@code Double.longBitsToDouble(0x1L)}. 412 */ 413 public static final double MIN_VALUE = 0x0.0000000000001P-1022; // 4.9e-324 414 415 /** 416 * The number of bits used to represent a {@code double} value, 417 * {@value}. 418 * 419 * @since 1.5 420 */ 421 public static final int SIZE = 64; 422 423 /** 424 * The number of bits in the significand of a {@code double} 425 * value, {@value}. This is the parameter N in section {@jls 426 * 4.2.3} of <cite>The Java Language Specification</cite>. 427 * 428 * @since 19 429 */ 430 public static final int PRECISION = 53; 431 432 /** 433 * Maximum exponent a finite {@code double} variable may have, 434 * {@value}. It is equal to the value returned by {@code 435 * Math.getExponent(Double.MAX_VALUE)}. 436 * 437 * @since 1.6 438 */ 439 public static final int MAX_EXPONENT = (1 << (SIZE - PRECISION - 1)) - 1; // 1023 440 441 /** 442 * Minimum exponent a normalized {@code double} variable may have, 443 * {@value}. It is equal to the value returned by {@code 444 * Math.getExponent(Double.MIN_NORMAL)}. 445 * 446 * @since 1.6 447 */ 448 public static final int MIN_EXPONENT = 1 - MAX_EXPONENT; // -1022 449 450 /** 451 * The number of bytes used to represent a {@code double} value, 452 * {@value}. 453 * 454 * @since 1.8 455 */ 456 public static final int BYTES = SIZE / Byte.SIZE; 457 458 /** 459 * The {@code Class} instance representing the primitive type 460 * {@code double}. 461 * 462 * @since 1.1 463 */ 464 public static final Class<Double> TYPE = 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 * @apiNote 596 * This method corresponds to the general functionality of the 597 * convertToDecimalCharacter operation defined in IEEE 754; 598 * however, that operation is defined in terms of specifying the 599 * number of significand digits used in the conversion. 600 * Code to do such a conversion in the Java platform includes 601 * converting the {@code double} to a {@link java.math.BigDecimal 602 * BigDecimal} exactly and then rounding the {@code BigDecimal} to 603 * the desired number of digits; sample code: 604 * {@snippet lang=java : 605 * double d = 0.1; 606 * int digits = 25; 607 * BigDecimal bd = new BigDecimal(d); 608 * String result = bd.round(new MathContext(digits, RoundingMode.HALF_UP)); 609 * // 0.1000000000000000055511151 610 * } 611 * 612 * @param d the {@code double} to be converted. 613 * @return a string representation of the argument. 614 */ 615 public static String toString(double d) { 616 return DoubleToDecimal.toString(d); 617 } 618 619 /** 620 * Returns a hexadecimal string representation of the 621 * {@code double} argument. All characters mentioned below 622 * are ASCII characters. 623 * 624 * <ul> 625 * <li>If the argument is NaN, the result is the string 626 * "{@code NaN}". 627 * <li>Otherwise, the result is a string that represents the sign 628 * and magnitude of the argument. If the sign is negative, the 629 * first character of the result is '{@code -}' 630 * ({@code '\u005Cu002D'}); if the sign is positive, no sign 631 * character appears in the result. As for the magnitude <i>m</i>: 632 * 633 * <ul> 634 * <li>If <i>m</i> is infinity, it is represented by the string 635 * {@code "Infinity"}; thus, positive infinity produces the 636 * result {@code "Infinity"} and negative infinity produces 637 * the result {@code "-Infinity"}. 638 * 639 * <li>If <i>m</i> is zero, it is represented by the string 640 * {@code "0x0.0p0"}; thus, negative zero produces the result 641 * {@code "-0x0.0p0"} and positive zero produces the result 642 * {@code "0x0.0p0"}. 643 * 644 * <li>If <i>m</i> is a {@code double} value with a 645 * normalized representation, substrings are used to represent the 646 * significand and exponent fields. The significand is 647 * represented by the characters {@code "0x1."} 648 * followed by a lowercase hexadecimal representation of the rest 649 * of the significand as a fraction. Trailing zeros in the 650 * hexadecimal representation are removed unless all the digits 651 * are zero, in which case a single zero is used. Next, the 652 * exponent is represented by {@code "p"} followed 653 * by a decimal string of the unbiased exponent as if produced by 654 * a call to {@link Integer#toString(int) Integer.toString} on the 655 * exponent value. 656 * 657 * <li>If <i>m</i> is a {@code double} value with a subnormal 658 * representation, the significand is represented by the 659 * characters {@code "0x0."} followed by a 660 * hexadecimal representation of the rest of the significand as a 661 * fraction. Trailing zeros in the hexadecimal representation are 662 * removed. Next, the exponent is represented by 663 * {@code "p-1022"}. Note that there must be at 664 * least one nonzero digit in a subnormal significand. 665 * 666 * </ul> 667 * 668 * </ul> 669 * 670 * <table class="striped"> 671 * <caption>Examples</caption> 672 * <thead> 673 * <tr><th scope="col">Floating-point Value</th><th scope="col">Hexadecimal String</th> 674 * </thead> 675 * <tbody style="text-align:right"> 676 * <tr><th scope="row">{@code 1.0}</th> <td>{@code 0x1.0p0}</td> 677 * <tr><th scope="row">{@code -1.0}</th> <td>{@code -0x1.0p0}</td> 678 * <tr><th scope="row">{@code 2.0}</th> <td>{@code 0x1.0p1}</td> 679 * <tr><th scope="row">{@code 3.0}</th> <td>{@code 0x1.8p1}</td> 680 * <tr><th scope="row">{@code 0.5}</th> <td>{@code 0x1.0p-1}</td> 681 * <tr><th scope="row">{@code 0.25}</th> <td>{@code 0x1.0p-2}</td> 682 * <tr><th scope="row">{@code Double.MAX_VALUE}</th> 683 * <td>{@code 0x1.fffffffffffffp1023}</td> 684 * <tr><th scope="row">{@code Minimum Normal Value}</th> 685 * <td>{@code 0x1.0p-1022}</td> 686 * <tr><th scope="row">{@code Maximum Subnormal Value}</th> 687 * <td>{@code 0x0.fffffffffffffp-1022}</td> 688 * <tr><th scope="row">{@code Double.MIN_VALUE}</th> 689 * <td>{@code 0x0.0000000000001p-1022}</td> 690 * </tbody> 691 * </table> 692 * 693 * @apiNote 694 * This method corresponds to the convertToHexCharacter operation 695 * defined in IEEE 754. 696 * 697 * @param d the {@code double} to be converted. 698 * @return a hex string representation of the argument. 699 * @since 1.5 700 * @author Joseph D. Darcy 701 */ 702 public static String toHexString(double d) { 703 /* 704 * Modeled after the "a" conversion specifier in C99, section 705 * 7.19.6.1; however, the output of this method is more 706 * tightly specified. 707 */ 708 if (!isFinite(d) ) 709 // For infinity and NaN, use the decimal output. 710 return Double.toString(d); 711 else { 712 // Initialized to maximum size of output. 713 StringBuilder answer = new StringBuilder(24); 714 715 if (Math.copySign(1.0, d) == -1.0) // value is negative, 716 answer.append("-"); // so append sign info 717 718 answer.append("0x"); 719 720 d = Math.abs(d); 721 722 if(d == 0.0) { 723 answer.append("0.0p0"); 724 } else { 725 boolean subnormal = (d < Double.MIN_NORMAL); 726 727 // Isolate significand bits and OR in a high-order bit 728 // so that the string representation has a known 729 // length. 730 long signifBits = (Double.doubleToLongBits(d) 731 & DoubleConsts.SIGNIF_BIT_MASK) | 732 0x1000000000000000L; 733 734 // Subnormal values have a 0 implicit bit; normal 735 // values have a 1 implicit bit. 736 answer.append(subnormal ? "0." : "1."); 737 738 // Isolate the low-order 13 digits of the hex 739 // representation. If all the digits are zero, 740 // replace with a single 0; otherwise, remove all 741 // trailing zeros. 742 String signif = Long.toHexString(signifBits).substring(3,16); 743 answer.append(signif.equals("0000000000000") ? // 13 zeros 744 "0": 745 signif.replaceFirst("0{1,12}$", "")); 746 747 answer.append('p'); 748 // If the value is subnormal, use the E_min exponent 749 // value for double; otherwise, extract and report d's 750 // exponent (the representation of a subnormal uses 751 // E_min -1). 752 answer.append(subnormal ? 753 Double.MIN_EXPONENT: 754 Math.getExponent(d)); 755 } 756 return answer.toString(); 757 } 758 } 759 760 /** 761 * Returns a {@code Double} object holding the 762 * {@code double} value represented by the argument string 763 * {@code s}. 764 * 765 * <p>If {@code s} is {@code null}, then a 766 * {@code NullPointerException} is thrown. 767 * 768 * <p>Leading and trailing whitespace characters in {@code s} 769 * are ignored. Whitespace is removed as if by the {@link 770 * String#trim} method; that is, both ASCII space and control 771 * characters are removed. The rest of {@code s} should 772 * constitute a <i>FloatValue</i> as described by the lexical 773 * syntax rules: 774 * 775 * <blockquote> 776 * <dl> 777 * <dt><i>FloatValue:</i> 778 * <dd><i>Sign<sub>opt</sub></i> {@code NaN} 779 * <dd><i>Sign<sub>opt</sub></i> {@code Infinity} 780 * <dd><i>Sign<sub>opt</sub> FloatingPointLiteral</i> 781 * <dd><i>Sign<sub>opt</sub> HexFloatingPointLiteral</i> 782 * <dd><i>SignedInteger</i> 783 * </dl> 784 * 785 * <dl> 786 * <dt><i>HexFloatingPointLiteral</i>: 787 * <dd> <i>HexSignificand BinaryExponent FloatTypeSuffix<sub>opt</sub></i> 788 * </dl> 789 * 790 * <dl> 791 * <dt><i>HexSignificand:</i> 792 * <dd><i>HexNumeral</i> 793 * <dd><i>HexNumeral</i> {@code .} 794 * <dd>{@code 0x} <i>HexDigits<sub>opt</sub> 795 * </i>{@code .}<i> HexDigits</i> 796 * <dd>{@code 0X}<i> HexDigits<sub>opt</sub> 797 * </i>{@code .} <i>HexDigits</i> 798 * </dl> 799 * 800 * <dl> 801 * <dt><i>BinaryExponent:</i> 802 * <dd><i>BinaryExponentIndicator SignedInteger</i> 803 * </dl> 804 * 805 * <dl> 806 * <dt><i>BinaryExponentIndicator:</i> 807 * <dd>{@code p} 808 * <dd>{@code P} 809 * </dl> 810 * 811 * </blockquote> 812 * 813 * where <i>Sign</i>, <i>FloatingPointLiteral</i>, 814 * <i>HexNumeral</i>, <i>HexDigits</i>, <i>SignedInteger</i> and 815 * <i>FloatTypeSuffix</i> are as defined in the lexical structure 816 * sections of 817 * <cite>The Java Language Specification</cite>, 818 * except that underscores are not accepted between digits. 819 * If {@code s} does not have the form of 820 * a <i>FloatValue</i>, then a {@code NumberFormatException} 821 * is thrown. Otherwise, {@code s} is regarded as 822 * representing an exact decimal value in the usual 823 * "computerized scientific notation" or as an exact 824 * hexadecimal value; this exact numerical value is then 825 * conceptually converted to an "infinitely precise" 826 * binary value that is then rounded to type {@code double} 827 * by the usual round-to-nearest rule of IEEE 754 floating-point 828 * arithmetic, which includes preserving the sign of a zero 829 * value. 830 * 831 * Note that the round-to-nearest rule also implies overflow and 832 * underflow behaviour; if the exact value of {@code s} is large 833 * enough in magnitude (greater than or equal to ({@link 834 * #MAX_VALUE} + {@link Math#ulp(double) ulp(MAX_VALUE)}/2), 835 * rounding to {@code double} will result in an infinity and if the 836 * exact value of {@code s} is small enough in magnitude (less 837 * than or equal to {@link #MIN_VALUE}/2), rounding to float will 838 * result in a zero. 839 * 840 * Finally, after rounding a {@code Double} object representing 841 * this {@code double} value is returned. 842 * 843 * <p>Note that trailing format specifiers, specifiers that 844 * determine the type of a floating-point literal 845 * ({@code 1.0f} is a {@code float} value; 846 * {@code 1.0d} is a {@code double} value), do 847 * <em>not</em> influence the results of this method. In other 848 * words, the numerical value of the input string is converted 849 * directly to the target floating-point type. The two-step 850 * sequence of conversions, string to {@code float} followed 851 * by {@code float} to {@code double}, is <em>not</em> 852 * equivalent to converting a string directly to 853 * {@code double}. For example, the {@code float} 854 * literal {@code 0.1f} is equal to the {@code double} 855 * value {@code 0.10000000149011612}; the {@code float} 856 * literal {@code 0.1f} represents a different numerical 857 * value than the {@code double} literal 858 * {@code 0.1}. (The numerical value 0.1 cannot be exactly 859 * represented in a binary floating-point number.) 860 * 861 * <p>To avoid calling this method on an invalid string and having 862 * a {@code NumberFormatException} be thrown, the regular 863 * expression below can be used to screen the input string: 864 * 865 * {@snippet lang="java" : 866 * final String Digits = "(\\p{Digit}+)"; 867 * final String HexDigits = "(\\p{XDigit}+)"; 868 * // an exponent is 'e' or 'E' followed by an optionally 869 * // signed decimal integer. 870 * final String Exp = "[eE][+-]?"+Digits; 871 * final String fpRegex = 872 * ("[\\x00-\\x20]*"+ // Optional leading "whitespace" 873 * "[+-]?(" + // Optional sign character 874 * "NaN|" + // "NaN" string 875 * "Infinity|" + // "Infinity" string 876 * 877 * // A decimal floating-point string representing a finite positive 878 * // number without a leading sign has at most five basic pieces: 879 * // Digits . Digits ExponentPart FloatTypeSuffix 880 * // 881 * // Since this method allows integer-only strings as input 882 * // in addition to strings of floating-point literals, the 883 * // two sub-patterns below are simplifications of the grammar 884 * // productions from section 3.10.2 of 885 * // The Java Language Specification. 886 * 887 * // Digits ._opt Digits_opt ExponentPart_opt FloatTypeSuffix_opt 888 * "((("+Digits+"(\\.)?("+Digits+"?)("+Exp+")?)|"+ 889 * 890 * // . Digits ExponentPart_opt FloatTypeSuffix_opt 891 * "(\\.("+Digits+")("+Exp+")?)|"+ 892 * 893 * // Hexadecimal strings 894 * "((" + 895 * // 0[xX] HexDigits ._opt BinaryExponent FloatTypeSuffix_opt 896 * "(0[xX]" + HexDigits + "(\\.)?)|" + 897 * 898 * // 0[xX] HexDigits_opt . HexDigits BinaryExponent FloatTypeSuffix_opt 899 * "(0[xX]" + HexDigits + "?(\\.)" + HexDigits + ")" + 900 * 901 * ")[pP][+-]?" + Digits + "))" + 902 * "[fFdD]?))" + 903 * "[\\x00-\\x20]*");// Optional trailing "whitespace" 904 * // @link region substring="Pattern.matches" target ="java.util.regex.Pattern#matches" 905 * if (Pattern.matches(fpRegex, myString)) 906 * Double.valueOf(myString); // Will not throw NumberFormatException 907 * // @end 908 * else { 909 * // Perform suitable alternative action 910 * } 911 * } 912 * 913 * @apiNote To interpret localized string representations of a 914 * floating-point value, or string representations that have 915 * non-ASCII digits, use {@link java.text.NumberFormat}. For 916 * example, 917 * {@snippet lang="java" : 918 * NumberFormat.getInstance(l).parse(s).doubleValue(); 919 * } 920 * where {@code l} is the desired locale, or 921 * {@link java.util.Locale#ROOT} if locale insensitive. 922 * 923 * @apiNote 924 * This method corresponds to the convertFromDecimalCharacter and 925 * convertFromHexCharacter operations defined in IEEE 754. 926 * 927 * @param s the string to be parsed. 928 * @return a {@code Double} object holding the value 929 * represented by the {@code String} argument. 930 * @throws NumberFormatException if the string does not contain a 931 * parsable number. 932 * @see Double##decimalToBinaryConversion Decimal ↔ Binary Conversion Issues 933 */ 934 public static Double valueOf(String s) throws NumberFormatException { 935 return new Double(parseDouble(s)); 936 } 937 938 /** 939 * Returns a {@code Double} instance representing the specified 940 * {@code double} value. 941 * If a new {@code Double} instance is not required, this method 942 * should generally be used in preference to the constructor 943 * {@link #Double(double)}, as this method is likely to yield 944 * significantly better space and time performance by caching 945 * frequently requested values. 946 * 947 * @param d a double value. 948 * @return a {@code Double} instance representing {@code d}. 949 * @since 1.5 950 */ 951 @IntrinsicCandidate 952 @DeserializeConstructor 953 public static Double valueOf(double d) { 954 return new Double(d); 955 } 956 957 /** 958 * Returns a new {@code double} initialized to the value 959 * represented by the specified {@code String}, as performed 960 * by the {@code valueOf} method of class 961 * {@code Double}. 962 * 963 * @param s the string to be parsed. 964 * @return the {@code double} value represented by the string 965 * argument. 966 * @throws NullPointerException if the string is null 967 * @throws NumberFormatException if the string does not contain 968 * a parsable {@code double}. 969 * @see java.lang.Double#valueOf(String) 970 * @see Double##decimalToBinaryConversion Decimal ↔ Binary Conversion Issues 971 * @since 1.2 972 */ 973 public static double parseDouble(String s) throws NumberFormatException { 974 return FloatingDecimal.parseDouble(s); 975 } 976 977 /** 978 * Returns {@code true} if the specified number is a 979 * Not-a-Number (NaN) value, {@code false} otherwise. 980 * 981 * @apiNote 982 * This method corresponds to the isNaN operation defined in IEEE 983 * 754. 984 * 985 * @param v the value to be tested. 986 * @return {@code true} if the value of the argument is NaN; 987 * {@code false} otherwise. 988 */ 989 public static boolean isNaN(double v) { 990 return (v != v); 991 } 992 993 /** 994 * Returns {@code true} if the specified number is infinitely 995 * large in magnitude, {@code false} otherwise. 996 * 997 * @apiNote 998 * This method corresponds to the isInfinite operation defined in 999 * IEEE 754. 1000 * 1001 * @param v the value to be tested. 1002 * @return {@code true} if the value of the argument is positive 1003 * infinity or negative infinity; {@code false} otherwise. 1004 */ 1005 @IntrinsicCandidate 1006 public static boolean isInfinite(double v) { 1007 return Math.abs(v) > MAX_VALUE; 1008 } 1009 1010 /** 1011 * Returns {@code true} if the argument is a finite floating-point 1012 * value; returns {@code false} otherwise (for NaN and infinity 1013 * arguments). 1014 * 1015 * @apiNote 1016 * This method corresponds to the isFinite operation defined in 1017 * IEEE 754. 1018 * 1019 * @param d the {@code double} value to be tested 1020 * @return {@code true} if the argument is a finite 1021 * floating-point value, {@code false} otherwise. 1022 * @since 1.8 1023 */ 1024 @IntrinsicCandidate 1025 public static boolean isFinite(double d) { 1026 return Math.abs(d) <= Double.MAX_VALUE; 1027 } 1028 1029 /** 1030 * The value of the Double. 1031 * 1032 * @serial 1033 */ 1034 private final double value; 1035 1036 /** 1037 * Constructs a newly allocated {@code Double} object that 1038 * represents the primitive {@code double} argument. 1039 * 1040 * @param value the value to be represented by the {@code Double}. 1041 * 1042 * @deprecated 1043 * It is rarely appropriate to use this constructor. The static factory 1044 * {@link #valueOf(double)} is generally a better choice, as it is 1045 * likely to yield significantly better space and time performance. 1046 */ 1047 @Deprecated(since="9", forRemoval = true) 1048 public Double(double value) { 1049 this.value = value; 1050 } 1051 1052 /** 1053 * Constructs a newly allocated {@code Double} object that 1054 * represents the floating-point value of type {@code double} 1055 * represented by the string. The string is converted to a 1056 * {@code double} value as if by the {@code valueOf} method. 1057 * 1058 * @param s a string to be converted to a {@code Double}. 1059 * @throws NumberFormatException if the string does not contain a 1060 * parsable number. 1061 * 1062 * @deprecated 1063 * It is rarely appropriate to use this constructor. 1064 * Use {@link #parseDouble(String)} to convert a string to a 1065 * {@code double} primitive, or use {@link #valueOf(String)} 1066 * to convert a string to a {@code Double} object. 1067 */ 1068 @Deprecated(since="9", forRemoval = true) 1069 public Double(String s) throws NumberFormatException { 1070 value = parseDouble(s); 1071 } 1072 1073 /** 1074 * Returns {@code true} if this {@code Double} value is 1075 * a Not-a-Number (NaN), {@code false} otherwise. 1076 * 1077 * @return {@code true} if the value represented by this object is 1078 * NaN; {@code false} otherwise. 1079 */ 1080 public boolean isNaN() { 1081 return isNaN(value); 1082 } 1083 1084 /** 1085 * Returns {@code true} if this {@code Double} value is 1086 * infinitely large in magnitude, {@code false} otherwise. 1087 * 1088 * @return {@code true} if the value represented by this object is 1089 * positive infinity or negative infinity; 1090 * {@code false} otherwise. 1091 */ 1092 public boolean isInfinite() { 1093 return isInfinite(value); 1094 } 1095 1096 /** 1097 * Returns a string representation of this {@code Double} object. 1098 * The primitive {@code double} value represented by this 1099 * object is converted to a string exactly as if by the method 1100 * {@code toString} of one argument. 1101 * 1102 * @return a {@code String} representation of this object. 1103 * @see java.lang.Double#toString(double) 1104 */ 1105 public String toString() { 1106 return toString(value); 1107 } 1108 1109 /** 1110 * Returns the value of this {@code Double} as a {@code byte} 1111 * after a narrowing primitive conversion. 1112 * 1113 * @return the {@code double} value represented by this object 1114 * converted to type {@code byte} 1115 * @jls 5.1.3 Narrowing Primitive Conversion 1116 * @since 1.1 1117 */ 1118 @Override 1119 public byte byteValue() { 1120 return (byte)value; 1121 } 1122 1123 /** 1124 * Returns the value of this {@code Double} as a {@code short} 1125 * after a narrowing primitive conversion. 1126 * 1127 * @return the {@code double} value represented by this object 1128 * converted to type {@code short} 1129 * @jls 5.1.3 Narrowing Primitive Conversion 1130 * @since 1.1 1131 */ 1132 @Override 1133 public short shortValue() { 1134 return (short)value; 1135 } 1136 1137 /** 1138 * Returns the value of this {@code Double} as an {@code int} 1139 * after a narrowing primitive conversion. 1140 * @jls 5.1.3 Narrowing Primitive Conversion 1141 * 1142 * @apiNote 1143 * This method corresponds to the convertToIntegerTowardZero 1144 * operation defined in IEEE 754. 1145 * 1146 * @return the {@code double} value represented by this object 1147 * converted to type {@code int} 1148 */ 1149 @Override 1150 public int intValue() { 1151 return (int)value; 1152 } 1153 1154 /** 1155 * Returns the value of this {@code Double} as a {@code long} 1156 * after a narrowing primitive conversion. 1157 * 1158 * @apiNote 1159 * This method corresponds to the convertToIntegerTowardZero 1160 * operation defined in IEEE 754. 1161 * 1162 * @return the {@code double} value represented by this object 1163 * converted to type {@code long} 1164 * @jls 5.1.3 Narrowing Primitive Conversion 1165 */ 1166 @Override 1167 public long longValue() { 1168 return (long)value; 1169 } 1170 1171 /** 1172 * Returns the value of this {@code Double} as a {@code float} 1173 * after a narrowing primitive conversion. 1174 * 1175 * @apiNote 1176 * This method corresponds to the convertFormat operation defined 1177 * in IEEE 754. 1178 * 1179 * @return the {@code double} value represented by this object 1180 * converted to type {@code float} 1181 * @jls 5.1.3 Narrowing Primitive Conversion 1182 * @since 1.0 1183 */ 1184 @Override 1185 public float floatValue() { 1186 return (float)value; 1187 } 1188 1189 /** 1190 * Returns the {@code double} value of this {@code Double} object. 1191 * 1192 * @return the {@code double} value represented by this object 1193 */ 1194 @Override 1195 @IntrinsicCandidate 1196 public double doubleValue() { 1197 return value; 1198 } 1199 1200 /** 1201 * Returns a hash code for this {@code Double} object. The 1202 * result is the exclusive OR of the two halves of the 1203 * {@code long} integer bit representation, exactly as 1204 * produced by the method {@link #doubleToLongBits(double)}, of 1205 * the primitive {@code double} value represented by this 1206 * {@code Double} object. That is, the hash code is the value 1207 * of the expression: 1208 * 1209 * <blockquote> 1210 * {@code (int)(v^(v>>>32))} 1211 * </blockquote> 1212 * 1213 * where {@code v} is defined by: 1214 * 1215 * <blockquote> 1216 * {@code long v = Double.doubleToLongBits(this.doubleValue());} 1217 * </blockquote> 1218 * 1219 * @return a {@code hash code} value for this object. 1220 */ 1221 @Override 1222 public int hashCode() { 1223 return Double.hashCode(value); 1224 } 1225 1226 /** 1227 * Returns a hash code for a {@code double} value; compatible with 1228 * {@code Double.hashCode()}. 1229 * 1230 * @param value the value to hash 1231 * @return a hash code value for a {@code double} value. 1232 * @since 1.8 1233 */ 1234 public static int hashCode(double value) { 1235 return Long.hashCode(doubleToLongBits(value)); 1236 } 1237 1238 /** 1239 * Compares this object against the specified object. The result 1240 * is {@code true} if and only if the argument is not 1241 * {@code null} and is a {@code Double} object that 1242 * represents a {@code double} that has the same value as the 1243 * {@code double} represented by this object. For this 1244 * purpose, two {@code double} values are considered to be 1245 * the same if and only if the method {@link 1246 * #doubleToLongBits(double)} returns the identical 1247 * {@code long} value when applied to each. 1248 * 1249 * @apiNote 1250 * This method is defined in terms of {@link 1251 * #doubleToLongBits(double)} rather than the {@code ==} operator 1252 * on {@code double} values since the {@code ==} operator does 1253 * <em>not</em> define an equivalence relation and to satisfy the 1254 * {@linkplain Object#equals equals contract} an equivalence 1255 * relation must be implemented; see {@linkplain ##equivalenceRelation 1256 * this discussion for details of floating-point equality and equivalence}. 1257 * 1258 * @see java.lang.Double#doubleToLongBits(double) 1259 * @jls 15.21.1 Numerical Equality Operators == and != 1260 */ 1261 public boolean equals(Object obj) { 1262 return (obj instanceof Double d) && 1263 (doubleToLongBits(d.value) == doubleToLongBits(value)); 1264 } 1265 1266 /** 1267 * Returns a representation of the specified floating-point value 1268 * according to the IEEE 754 floating-point "double 1269 * format" bit layout. 1270 * 1271 * <p>Bit 63 (the bit that is selected by the mask 1272 * {@code 0x8000000000000000L}) represents the sign of the 1273 * floating-point number. Bits 1274 * 62-52 (the bits that are selected by the mask 1275 * {@code 0x7ff0000000000000L}) represent the exponent. Bits 51-0 1276 * (the bits that are selected by the mask 1277 * {@code 0x000fffffffffffffL}) represent the significand 1278 * (sometimes called the mantissa) of the floating-point number. 1279 * 1280 * <p>If the argument is positive infinity, the result is 1281 * {@code 0x7ff0000000000000L}. 1282 * 1283 * <p>If the argument is negative infinity, the result is 1284 * {@code 0xfff0000000000000L}. 1285 * 1286 * <p>If the argument is NaN, the result is 1287 * {@code 0x7ff8000000000000L}. 1288 * 1289 * <p>In all cases, the result is a {@code long} integer that, when 1290 * given to the {@link #longBitsToDouble(long)} method, will produce a 1291 * floating-point value the same as the argument to 1292 * {@code doubleToLongBits} (except all NaN values are 1293 * collapsed to a single "canonical" NaN value). 1294 * 1295 * @param value a {@code double} precision floating-point number. 1296 * @return the bits that represent the floating-point number. 1297 */ 1298 @IntrinsicCandidate 1299 public static long doubleToLongBits(double value) { 1300 if (!isNaN(value)) { 1301 return doubleToRawLongBits(value); 1302 } 1303 return 0x7ff8000000000000L; 1304 } 1305 1306 /** 1307 * Returns a representation of the specified floating-point value 1308 * according to the IEEE 754 floating-point "double 1309 * format" bit layout, preserving Not-a-Number (NaN) values. 1310 * 1311 * <p>Bit 63 (the bit that is selected by the mask 1312 * {@code 0x8000000000000000L}) represents the sign of the 1313 * floating-point number. Bits 1314 * 62-52 (the bits that are selected by the mask 1315 * {@code 0x7ff0000000000000L}) represent the exponent. Bits 51-0 1316 * (the bits that are selected by the mask 1317 * {@code 0x000fffffffffffffL}) represent the significand 1318 * (sometimes called the mantissa) of the floating-point number. 1319 * 1320 * <p>If the argument is positive infinity, the result is 1321 * {@code 0x7ff0000000000000L}. 1322 * 1323 * <p>If the argument is negative infinity, the result is 1324 * {@code 0xfff0000000000000L}. 1325 * 1326 * <p>If the argument is NaN, the result is the {@code long} 1327 * integer representing the actual NaN value. Unlike the 1328 * {@code doubleToLongBits} method, 1329 * {@code doubleToRawLongBits} does not collapse all the bit 1330 * patterns encoding a NaN to a single "canonical" NaN 1331 * value. 1332 * 1333 * <p>In all cases, the result is a {@code long} integer that, 1334 * when given to the {@link #longBitsToDouble(long)} method, will 1335 * produce a floating-point value the same as the argument to 1336 * {@code doubleToRawLongBits}. 1337 * 1338 * @param value a {@code double} precision floating-point number. 1339 * @return the bits that represent the floating-point number. 1340 * @since 1.3 1341 */ 1342 @IntrinsicCandidate 1343 public static native long doubleToRawLongBits(double value); 1344 1345 /** 1346 * Returns the {@code double} value corresponding to a given 1347 * bit representation. 1348 * The argument is considered to be a representation of a 1349 * floating-point value according to the IEEE 754 floating-point 1350 * "double format" bit layout. 1351 * 1352 * <p>If the argument is {@code 0x7ff0000000000000L}, the result 1353 * is positive infinity. 1354 * 1355 * <p>If the argument is {@code 0xfff0000000000000L}, the result 1356 * is negative infinity. 1357 * 1358 * <p>If the argument is any value in the range 1359 * {@code 0x7ff0000000000001L} through 1360 * {@code 0x7fffffffffffffffL} or in the range 1361 * {@code 0xfff0000000000001L} through 1362 * {@code 0xffffffffffffffffL}, the result is a NaN. No IEEE 1363 * 754 floating-point operation provided by Java can distinguish 1364 * between two NaN values of the same type with different bit 1365 * patterns. Distinct values of NaN are only distinguishable by 1366 * use of the {@code Double.doubleToRawLongBits} method. 1367 * 1368 * <p>In all other cases, let <i>s</i>, <i>e</i>, and <i>m</i> be three 1369 * values that can be computed from the argument: 1370 * 1371 * {@snippet lang="java" : 1372 * int s = ((bits >> 63) == 0) ? 1 : -1; 1373 * int e = (int)((bits >> 52) & 0x7ffL); 1374 * long m = (e == 0) ? 1375 * (bits & 0xfffffffffffffL) << 1 : 1376 * (bits & 0xfffffffffffffL) | 0x10000000000000L; 1377 * } 1378 * 1379 * Then the floating-point result equals the value of the mathematical 1380 * expression <i>s</i>·<i>m</i>·2<sup><i>e</i>-1075</sup>. 1381 * 1382 * <p>Note that this method may not be able to return a 1383 * {@code double} NaN with exactly same bit pattern as the 1384 * {@code long} argument. IEEE 754 distinguishes between two 1385 * kinds of NaNs, quiet NaNs and <i>signaling NaNs</i>. The 1386 * differences between the two kinds of NaN are generally not 1387 * visible in Java. Arithmetic operations on signaling NaNs turn 1388 * them into quiet NaNs with a different, but often similar, bit 1389 * pattern. However, on some processors merely copying a 1390 * signaling NaN also performs that conversion. In particular, 1391 * copying a signaling NaN to return it to the calling method 1392 * may perform this conversion. So {@code longBitsToDouble} 1393 * may not be able to return a {@code double} with a 1394 * signaling NaN bit pattern. Consequently, for some 1395 * {@code long} values, 1396 * {@code doubleToRawLongBits(longBitsToDouble(start))} may 1397 * <i>not</i> equal {@code start}. Moreover, which 1398 * particular bit patterns represent signaling NaNs is platform 1399 * dependent; although all NaN bit patterns, quiet or signaling, 1400 * must be in the NaN range identified above. 1401 * 1402 * @param bits any {@code long} integer. 1403 * @return the {@code double} floating-point value with the same 1404 * bit pattern. 1405 */ 1406 @IntrinsicCandidate 1407 public static native double longBitsToDouble(long bits); 1408 1409 /** 1410 * Compares two {@code Double} objects numerically. 1411 * 1412 * This method imposes a total order on {@code Double} objects 1413 * with two differences compared to the incomplete order defined by 1414 * the Java language numerical comparison operators ({@code <, <=, 1415 * ==, >=, >}) on {@code double} values. 1416 * 1417 * <ul><li> A NaN is <em>unordered</em> with respect to other 1418 * values and unequal to itself under the comparison 1419 * operators. This method chooses to define {@code 1420 * Double.NaN} to be equal to itself and greater than all 1421 * other {@code double} values (including {@code 1422 * Double.POSITIVE_INFINITY}). 1423 * 1424 * <li> Positive zero and negative zero compare equal 1425 * numerically, but are distinct and distinguishable values. 1426 * This method chooses to define positive zero ({@code +0.0d}), 1427 * to be greater than negative zero ({@code -0.0d}). 1428 * </ul> 1429 1430 * This ensures that the <i>natural ordering</i> of {@code Double} 1431 * objects imposed by this method is <i>consistent with 1432 * equals</i>; see {@linkplain ##equivalenceRelation this 1433 * discussion for details of floating-point comparison and 1434 * ordering}. 1435 * 1436 * @param anotherDouble the {@code Double} to be compared. 1437 * @return the value {@code 0} if {@code anotherDouble} is 1438 * numerically equal to this {@code Double}; a value 1439 * less than {@code 0} if this {@code Double} 1440 * is numerically less than {@code anotherDouble}; 1441 * and a value greater than {@code 0} if this 1442 * {@code Double} is numerically greater than 1443 * {@code anotherDouble}. 1444 * 1445 * @jls 15.20.1 Numerical Comparison Operators {@code <}, {@code <=}, {@code >}, and {@code >=} 1446 * @since 1.2 1447 */ 1448 @Override 1449 public int compareTo(Double anotherDouble) { 1450 return Double.compare(value, anotherDouble.value); 1451 } 1452 1453 /** 1454 * Compares the two specified {@code double} values. The sign 1455 * of the integer value returned is the same as that of the 1456 * integer that would be returned by the call: 1457 * <pre> 1458 * Double.valueOf(d1).compareTo(Double.valueOf(d2)) 1459 * </pre> 1460 * 1461 * @param d1 the first {@code double} to compare 1462 * @param d2 the second {@code double} to compare 1463 * @return the value {@code 0} if {@code d1} is 1464 * numerically equal to {@code d2}; a value less than 1465 * {@code 0} if {@code d1} is numerically less than 1466 * {@code d2}; and a value greater than {@code 0} 1467 * if {@code d1} is numerically greater than 1468 * {@code d2}. 1469 * @since 1.4 1470 */ 1471 public static int compare(double d1, double d2) { 1472 if (d1 < d2) 1473 return -1; // Neither val is NaN, thisVal is smaller 1474 if (d1 > d2) 1475 return 1; // Neither val is NaN, thisVal is larger 1476 1477 // Cannot use doubleToRawLongBits because of possibility of NaNs. 1478 long thisBits = Double.doubleToLongBits(d1); 1479 long anotherBits = Double.doubleToLongBits(d2); 1480 1481 return (thisBits == anotherBits ? 0 : // Values are equal 1482 (thisBits < anotherBits ? -1 : // (-0.0, 0.0) or (!NaN, NaN) 1483 1)); // (0.0, -0.0) or (NaN, !NaN) 1484 } 1485 1486 /** 1487 * Adds two {@code double} values together as per the + operator. 1488 * 1489 * @apiNote This method corresponds to the addition operation 1490 * defined in IEEE 754. 1491 * 1492 * @param a the first operand 1493 * @param b the second operand 1494 * @return the sum of {@code a} and {@code b} 1495 * @jls 4.2.4 Floating-Point Operations 1496 * @see java.util.function.BinaryOperator 1497 * @since 1.8 1498 */ 1499 public static double sum(double a, double b) { 1500 return a + b; 1501 } 1502 1503 /** 1504 * Returns the greater of two {@code double} values 1505 * as if by calling {@link Math#max(double, double) Math.max}. 1506 * 1507 * @apiNote 1508 * This method corresponds to the maximum operation defined in 1509 * IEEE 754. 1510 * 1511 * @param a the first operand 1512 * @param b the second operand 1513 * @return the greater of {@code a} and {@code b} 1514 * @see java.util.function.BinaryOperator 1515 * @since 1.8 1516 */ 1517 public static double max(double a, double b) { 1518 return Math.max(a, b); 1519 } 1520 1521 /** 1522 * Returns the smaller of two {@code double} values 1523 * as if by calling {@link Math#min(double, double) Math.min}. 1524 * 1525 * @apiNote 1526 * This method corresponds to the minimum operation defined in 1527 * IEEE 754. 1528 * 1529 * @param a the first operand 1530 * @param b the second operand 1531 * @return the smaller of {@code a} and {@code b}. 1532 * @see java.util.function.BinaryOperator 1533 * @since 1.8 1534 */ 1535 public static double min(double a, double b) { 1536 return Math.min(a, b); 1537 } 1538 1539 /** 1540 * Returns an {@link Optional} containing the nominal descriptor for this 1541 * instance, which is the instance itself. 1542 * 1543 * @return an {@link Optional} describing the {@linkplain Double} instance 1544 * @since 12 1545 */ 1546 @Override 1547 public Optional<Double> describeConstable() { 1548 return Optional.of(this); 1549 } 1550 1551 /** 1552 * Resolves this instance as a {@link ConstantDesc}, the result of which is 1553 * the instance itself. 1554 * 1555 * @param lookup ignored 1556 * @return the {@linkplain Double} instance 1557 * @since 12 1558 */ 1559 @Override 1560 public Double resolveConstantDesc(MethodHandles.Lookup lookup) { 1561 return this; 1562 } 1563 1564 /** use serialVersionUID from JDK 1.0.2 for interoperability */ 1565 @java.io.Serial 1566 private static final long serialVersionUID = -9172774392245257468L; 1567 }