1 /*
2 * Copyright (c) 1994, 2025, Oracle and/or its affiliates. All rights reserved.
3 * Copyright (c) 2025, Alibaba Group Holding Limited. All Rights Reserved.
4 * DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER.
5 *
6 * This code is free software; you can redistribute it and/or modify it
7 * under the terms of the GNU General Public License version 2 only, as
8 * published by the Free Software Foundation. Oracle designates this
9 * particular file as subject to the "Classpath" exception as provided
10 * by Oracle in the LICENSE file that accompanied this code.
11 *
12 * This code is distributed in the hope that it will be useful, but WITHOUT
13 * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
14 * FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
15 * version 2 for more details (a copy is included in the LICENSE file that
16 * accompanied this code).
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25 */
26
27 package java.lang;
28
29 import java.lang.invoke.MethodHandles;
30 import java.lang.constant.Constable;
31 import java.lang.constant.ConstantDesc;
32 import java.util.Optional;
33
34 import jdk.internal.math.FloatingDecimal;
35 import jdk.internal.math.DoubleConsts;
36 import jdk.internal.math.DoubleToDecimal;
37 import jdk.internal.util.DecimalDigits;
38 import jdk.internal.value.DeserializeConstructor;
39 import jdk.internal.vm.annotation.IntrinsicCandidate;
40
41 /**
42 * The {@code Double} class is the {@linkplain
43 * java.lang##wrapperClass wrapper class} for values of the primitive
44 * type {@code double}. An object of type {@code Double} contains a
45 * single field whose type is {@code double}.
46 *
47 * <p>In addition, this class provides several methods for converting a
48 * {@code double} to a {@code String} and a
49 * {@code String} to a {@code double}, as well as other
50 * constants and methods useful when dealing with a
51 * {@code double}.
52 *
53 * <p>This is a <a href="{@docRoot}/java.base/java/lang/doc-files/ValueBased.html">value-based</a>
54 * class; programmers should treat instances that are {@linkplain #equals(Object) equal}
55 * as interchangeable and should not use instances for synchronization, mutexes, or
56 * with {@linkplain java.lang.ref.Reference object references}.
57 *
58 * <div class="preview-block">
59 * <div class="preview-comment">
60 * When preview features are enabled, {@code Double} is a {@linkplain Class#isValue value class}.
61 * Use of value class instances for synchronization, mutexes, or with
62 * {@linkplain java.lang.ref.Reference object references} result in
63 * {@link IdentityException}.
64 * </div>
65 * </div>
66 *
67 * <h2><a id=equivalenceRelation>Floating-point Equality, Equivalence,
68 * and Comparison</a></h2>
69 *
70 * IEEE 754 floating-point values include finite nonzero values,
71 * signed zeros ({@code +0.0} and {@code -0.0}), signed infinities
72 * ({@linkplain Double#POSITIVE_INFINITY positive infinity} and
73 * {@linkplain Double#NEGATIVE_INFINITY negative infinity}), and
74 * {@linkplain Double#NaN NaN} (not-a-number).
75 *
76 * <p>An <em>equivalence relation</em> on a set of values is a boolean
77 * relation on pairs of values that is reflexive, symmetric, and
78 * transitive. For more discussion of equivalence relations and object
79 * equality, see the {@link Object#equals Object.equals}
80 * specification. An equivalence relation partitions the values it
81 * operates over into sets called <i>equivalence classes</i>. All the
82 * members of the equivalence class are equal to each other under the
83 * relation. An equivalence class may contain only a single member. At
84 * least for some purposes, all the members of an equivalence class
85 * are substitutable for each other. In particular, in a numeric
86 * expression equivalent values can be <em>substituted</em> for one
87 * another without changing the result of the expression, meaning
88 * changing the equivalence class of the result of the expression.
89 *
90 * <p>Notably, the built-in {@code ==} operation on floating-point
91 * values is <em>not</em> an equivalence relation. Despite not
92 * defining an equivalence relation, the semantics of the IEEE 754
93 * {@code ==} operator were deliberately designed to meet other needs
94 * of numerical computation. There are two exceptions where the
95 * properties of an equivalence relation are not satisfied by {@code
96 * ==} on floating-point values:
97 *
98 * <ul>
99 *
100 * <li>If {@code v1} and {@code v2} are both NaN, then {@code v1
101 * == v2} has the value {@code false}. Therefore, for two NaN
102 * arguments the <em>reflexive</em> property of an equivalence
103 * relation is <em>not</em> satisfied by the {@code ==} operator.
104 *
105 * <li>If {@code v1} represents {@code +0.0} while {@code v2}
106 * represents {@code -0.0}, or vice versa, then {@code v1 == v2} has
107 * the value {@code true} even though {@code +0.0} and {@code -0.0}
108 * are distinguishable under various floating-point operations. For
109 * example, {@code 1.0/+0.0} evaluates to positive infinity while
110 * {@code 1.0/-0.0} evaluates to <em>negative</em> infinity and
111 * positive infinity and negative infinity are neither equal to each
112 * other nor equivalent to each other. Thus, while a signed zero input
113 * most commonly determines the sign of a zero result, because of
114 * dividing by zero, {@code +0.0} and {@code -0.0} may not be
115 * substituted for each other in general. The sign of a zero input
116 * also has a non-substitutable effect on the result of some math
117 * library methods.
118 *
119 * </ul>
120 *
121 * <p>For ordered comparisons using the built-in comparison operators
122 * ({@code <}, {@code <=}, etc.), NaN values have another anomalous
123 * situation: a NaN is neither less than, nor greater than, nor equal
124 * to any value, including itself. This means the <i>trichotomy of
125 * comparison</i> does <em>not</em> hold.
126 *
127 * <p>To provide the appropriate semantics for {@code equals} and
128 * {@code compareTo} methods, those methods cannot simply be wrappers
129 * around {@code ==} or ordered comparison operations. Instead, {@link
130 * Double#equals equals} uses {@linkplain ##repEquivalence representation
131 * equivalence}, defining NaN arguments to be equal to each other,
132 * restoring reflexivity, and defining {@code +0.0} to <em>not</em> be
133 * equal to {@code -0.0}. For comparisons, {@link Double#compareTo
134 * compareTo} defines a total order where {@code -0.0} is less than
135 * {@code +0.0} and where a NaN is equal to itself and considered
136 * greater than positive infinity.
137 *
138 * <p>The operational semantics of {@code equals} and {@code
139 * compareTo} are expressed in terms of {@linkplain #doubleToLongBits
140 * bit-wise converting} the floating-point values to integral values.
141 *
142 * <p>The <em>natural ordering</em> implemented by {@link #compareTo
143 * compareTo} is {@linkplain Comparable consistent with equals}. That
144 * is, two objects are reported as equal by {@code equals} if and only
145 * if {@code compareTo} on those objects returns zero.
146 *
147 * <p>The adjusted behaviors defined for {@code equals} and {@code
148 * compareTo} allow instances of wrapper classes to work properly with
149 * conventional data structures. For example, defining NaN
150 * values to be {@code equals} to one another allows NaN to be used as
151 * an element of a {@link java.util.HashSet HashSet} or as the key of
152 * a {@link java.util.HashMap HashMap}. Similarly, defining {@code
153 * compareTo} as a total ordering, including {@code +0.0}, {@code
154 * -0.0}, and NaN, allows instances of wrapper classes to be used as
155 * elements of a {@link java.util.SortedSet SortedSet} or as keys of a
156 * {@link java.util.SortedMap SortedMap}.
157 *
158 * <p>Comparing numerical equality to various useful equivalence
159 * relations that can be defined over floating-point values:
160 *
161 * <dl>
162 * <dt><a id=fpNumericalEq></a><dfn>{@index "numerical equality"}</dfn> ({@code ==}
163 * operator): (<em>Not</em> an equivalence relation)</dt>
164 * <dd>Two floating-point values represent the same extended real
165 * number. The extended real numbers are the real numbers augmented
166 * with positive infinity and negative infinity. Under numerical
167 * equality, {@code +0.0} and {@code -0.0} are equal since they both
168 * map to the same real value, 0. A NaN does not map to any real
169 * number and is not equal to any value, including itself.
170 * </dd>
171 *
172 * <dt><dfn>{@index "bit-wise equivalence"}</dfn>:</dt>
173 * <dd>The bits of the two floating-point values are the same. This
174 * equivalence relation for {@code double} values {@code a} and {@code
175 * b} is implemented by the expression
176 * <br>{@code Double.doubleTo}<code><b>Raw</b></code>{@code LongBits(a) == Double.doubleTo}<code><b>Raw</b></code>{@code LongBits(b)}<br>
177 * Under this relation, {@code +0.0} and {@code -0.0} are
178 * distinguished from each other and every bit pattern encoding a NaN
179 * is distinguished from every other bit pattern encoding a NaN.
180 * </dd>
181 *
182 * <dt><dfn><a id=repEquivalence></a>{@index "representation equivalence"}</dfn>:</dt>
183 * <dd>The two floating-point values represent the same IEEE 754
184 * <i>datum</i>. In particular, for {@linkplain #isFinite(double)
185 * finite} values, the sign, {@linkplain Math#getExponent(double)
186 * exponent}, and significand components of the floating-point values
187 * are the same. Under this relation:
188 * <ul>
189 * <li> {@code +0.0} and {@code -0.0} are distinguished from each other.
190 * <li> every bit pattern encoding a NaN is considered equivalent to each other
191 * <li> positive infinity is equivalent to positive infinity; negative
192 * infinity is equivalent to negative infinity.
193 * </ul>
194 * Expressions implementing this equivalence relation include:
195 * <ul>
196 * <li>{@code Double.doubleToLongBits(a) == Double.doubleToLongBits(b)}
197 * <li>{@code Double.valueOf(a).equals(Double.valueOf(b))}
198 * <li>{@code Double.compare(a, b) == 0}
199 * </ul>
200 * Note that representation equivalence is often an appropriate notion
201 * of equivalence to test the behavior of {@linkplain StrictMath math
202 * libraries}.
203 * </dd>
204 * </dl>
205 *
206 * For two binary floating-point values {@code a} and {@code b}, if
207 * neither of {@code a} and {@code b} is zero or NaN, then the three
208 * relations numerical equality, bit-wise equivalence, and
209 * representation equivalence of {@code a} and {@code b} have the same
210 * {@code true}/{@code false} value. In other words, for binary
211 * floating-point values, the three relations only differ if at least
212 * one argument is zero or NaN.
213 *
214 * <h2><a id=decimalToBinaryConversion>Decimal ↔ Binary Conversion Issues</a></h2>
215 *
216 * Many surprising results of binary floating-point arithmetic trace
217 * back to aspects of decimal to binary conversion and binary to
218 * decimal conversion. While integer values can be exactly represented
219 * in any base, which fractional values can be exactly represented in
220 * a base is a function of the base. For example, in base 10, 1/3 is a
221 * repeating fraction (0.33333....); but in base 3, 1/3 is exactly
222 * 0.1<sub>(3)</sub>, that is 1 × 3<sup>-1</sup>.
223 * Similarly, in base 10, 1/10 is exactly representable as 0.1
224 * (1 × 10<sup>-1</sup>), but in base 2, it is a
225 * repeating fraction (0.0001100110011...<sub>(2)</sub>).
226 *
227 * <p>Values of the {@code float} type have {@value Float#PRECISION}
228 * bits of precision and values of the {@code double} type have
229 * {@value Double#PRECISION} bits of precision. Therefore, since 0.1
230 * is a repeating fraction in base 2 with a four-bit repeat, {@code
231 * 0.1f} != {@code 0.1d}. In more detail, including hexadecimal
232 * floating-point literals:
233 *
234 * <ul>
235 * <li>The exact numerical value of {@code 0.1f} ({@code 0x1.99999a0000000p-4f}) is
236 * 0.100000001490116119384765625.
237 * <li>The exact numerical value of {@code 0.1d} ({@code 0x1.999999999999ap-4d}) is
238 * 0.1000000000000000055511151231257827021181583404541015625.
239 * </ul>
240 *
241 * These are the closest {@code float} and {@code double} values,
242 * respectively, to the numerical value of 0.1. These results are
243 * consistent with a {@code float} value having the equivalent of 6 to
244 * 9 digits of decimal precision and a {@code double} value having the
245 * equivalent of 15 to 17 digits of decimal precision. (The
246 * equivalent precision varies according to the different relative
247 * densities of binary and decimal values at different points along the
248 * real number line.)
249 *
250 * <p>This representation hazard of decimal fractions is one reason to
251 * use caution when storing monetary values as {@code float} or {@code
252 * double}. Alternatives include:
253 * <ul>
254 * <li>using {@link java.math.BigDecimal BigDecimal} to store decimal
255 * fractional values exactly
256 *
257 * <li>scaling up so the monetary value is an integer — for
258 * example, multiplying by 100 if the value is denominated in cents or
259 * multiplying by 1000 if the value is denominated in mills —
260 * and then storing that scaled value in an integer type
261 *
262 *</ul>
263 *
264 * <p>For each finite floating-point value and a given floating-point
265 * type, there is a contiguous region of the real number line which
266 * maps to that value. Under the default round to nearest rounding
267 * policy (JLS {@jls 15.4}), this contiguous region for a value is
268 * typically one {@linkplain Math#ulp ulp} (unit in the last place)
269 * wide and centered around the exactly representable value. (At
270 * exponent boundaries, the region is asymmetrical and larger on the
271 * side with the larger exponent.) For example, for {@code 0.1f}, the
272 * region can be computed as follows:
273 *
274 * <br>// Numeric values listed are exact values
275 * <br>oneTenthApproxAsFloat = 0.100000001490116119384765625;
276 * <br>ulpOfoneTenthApproxAsFloat = Math.ulp(0.1f) = 7.450580596923828125E-9;
277 * <br>// Numeric range that is converted to the float closest to 0.1, _excludes_ endpoints
278 * <br>(oneTenthApproxAsFloat - ½ulpOfoneTenthApproxAsFloat, oneTenthApproxAsFloat + ½ulpOfoneTenthApproxAsFloat) =
279 * <br>(0.0999999977648258209228515625, 0.1000000052154064178466796875)
280 *
281 * <p>In particular, a correctly rounded decimal to binary conversion
282 * of any string representing a number in this range, say by {@link
283 * Float#parseFloat(String)}, will be converted to the same value:
284 *
285 * {@snippet lang="java" :
286 * Float.parseFloat("0.0999999977648258209228515625000001"); // rounds up to oneTenthApproxAsFloat
287 * Float.parseFloat("0.099999998"); // rounds up to oneTenthApproxAsFloat
288 * Float.parseFloat("0.1"); // rounds up to oneTenthApproxAsFloat
289 * Float.parseFloat("0.100000001490116119384765625"); // exact conversion
290 * Float.parseFloat("0.100000005215406417846679687"); // rounds down to oneTenthApproxAsFloat
291 * Float.parseFloat("0.100000005215406417846679687499999"); // rounds down to oneTenthApproxAsFloat
292 * }
293 *
294 * <p>Similarly, an analogous range can be constructed for the {@code
295 * double} type based on the exact value of {@code double}
296 * approximation to {@code 0.1d} and the numerical value of {@code
297 * Math.ulp(0.1d)} and likewise for other particular numerical values
298 * in the {@code float} and {@code double} types.
299 *
300 * <p>As seen in the above conversions, compared to the exact
301 * numerical value the operation would have without rounding, the same
302 * floating-point value as a result can be:
303 * <ul>
304 * <li>greater than the exact result
305 * <li>equal to the exact result
306 * <li>less than the exact result
307 * </ul>
308 *
309 * A floating-point value doesn't "know" whether it was the result of
310 * rounding up, or rounding down, or an exact operation; it contains
311 * no history of how it was computed. Consequently, the sum of
312 * {@snippet lang="java" :
313 * 0.1f + 0.1f + 0.1f + 0.1f + 0.1f + 0.1f + 0.1f + 0.1f + 0.1f + 0.1f;
314 * // Numerical value of computed sum: 1.00000011920928955078125,
315 * // the next floating-point value larger than 1.0f, equal to Math.nextUp(1.0f).
316 * }
317 * or
318 * {@snippet lang="java" :
319 * 0.1d + 0.1d + 0.1d + 0.1d + 0.1d + 0.1d + 0.1d + 0.1d + 0.1d + 0.1d;
320 * // Numerical value of computed sum: 0.99999999999999988897769753748434595763683319091796875,
321 * // the next floating-point value smaller than 1.0d, equal to Math.nextDown(1.0d).
322 * }
323 *
324 * should <em>not</em> be expected to be exactly equal to 1.0, but
325 * only to be close to 1.0. Consequently, the following code is an
326 * infinite loop:
327 *
328 * {@snippet lang="java" :
329 * double d = 0.0;
330 * while (d != 1.0) { // Surprising infinite loop
331 * d += 0.1; // Sum never _exactly_ equals 1.0
332 * }
333 * }
334 *
335 * Instead, use an integer loop count for counted loops:
336 *
337 * {@snippet lang="java" :
338 * double d = 0.0;
339 * for (int i = 0; i < 10; i++) {
340 * d += 0.1;
341 * } // Value of d is equal to Math.nextDown(1.0).
342 * }
343 *
344 * or test against a floating-point limit using ordered comparisons
345 * ({@code <}, {@code <=}, {@code >}, {@code >=}):
346 *
347 * {@snippet lang="java" :
348 * double d = 0.0;
349 * while (d <= 1.0) {
350 * d += 0.1;
351 * } // Value of d approximately 1.0999999999999999
352 * }
353 *
354 * While floating-point arithmetic may have surprising results, IEEE
355 * 754 floating-point arithmetic follows a principled design and its
356 * behavior is predictable on the Java platform.
357 *
358 * @jls 4.2.3 Floating-Point Types and Values
359 * @jls 4.2.4 Floating-Point Operations
360 * @jls 15.21.1 Numerical Equality Operators == and !=
361 * @jls 15.20.1 Numerical Comparison Operators {@code <}, {@code <=}, {@code >}, and {@code >=}
362 *
363 * @spec https://standards.ieee.org/ieee/754/6210/
364 * IEEE Standard for Floating-Point Arithmetic
365 *
366 * @since 1.0
367 */
368 @jdk.internal.MigratedValueClass
369 @jdk.internal.ValueBased
370 public final class Double extends Number
371 implements Comparable<Double>, Constable, ConstantDesc {
372 /**
373 * A constant holding the positive infinity of type
374 * {@code double}. It is equal to the value returned by
375 * {@code Double.longBitsToDouble(0x7ff0000000000000L)}.
376 */
377 public static final double POSITIVE_INFINITY = 1.0 / 0.0;
378
379 /**
380 * A constant holding the negative infinity of type
381 * {@code double}. It is equal to the value returned by
382 * {@code Double.longBitsToDouble(0xfff0000000000000L)}.
383 */
384 public static final double NEGATIVE_INFINITY = -1.0 / 0.0;
385
386 /**
387 * A constant holding a Not-a-Number (NaN) value of type {@code double}.
388 * It is {@linkplain Double##equivalenceRelation equivalent} to the
389 * value returned by {@code Double.longBitsToDouble(0x7ff8000000000000L)}.
390 */
391 public static final double NaN = 0.0d / 0.0;
392
393 /**
394 * A constant holding the largest positive finite value of type
395 * {@code double},
396 * (2-2<sup>-52</sup>)·2<sup>1023</sup>. It is equal to
397 * the hexadecimal floating-point literal
398 * {@code 0x1.fffffffffffffP+1023} and also equal to
399 * {@code Double.longBitsToDouble(0x7fefffffffffffffL)}.
400 */
401 public static final double MAX_VALUE = 0x1.fffffffffffffP+1023; // 1.7976931348623157e+308
402
403 /**
404 * A constant holding the smallest positive normal value of type
405 * {@code double}, 2<sup>-1022</sup>. It is equal to the
406 * hexadecimal floating-point literal {@code 0x1.0p-1022} and also
407 * equal to {@code Double.longBitsToDouble(0x0010000000000000L)}.
408 *
409 * @since 1.6
410 */
411 public static final double MIN_NORMAL = 0x1.0p-1022; // 2.2250738585072014E-308
412
413 /**
414 * A constant holding the smallest positive nonzero value of type
415 * {@code double}, 2<sup>-1074</sup>. It is equal to the
416 * hexadecimal floating-point literal
417 * {@code 0x0.0000000000001P-1022} and also equal to
418 * {@code Double.longBitsToDouble(0x1L)}.
419 */
420 public static final double MIN_VALUE = 0x0.0000000000001P-1022; // 4.9e-324
421
422 /**
423 * The number of bits used to represent a {@code double} value,
424 * {@value}.
425 *
426 * @since 1.5
427 */
428 public static final int SIZE = 64;
429
430 /**
431 * The number of bits in the significand of a {@code double}
432 * value, {@value}. This is the parameter N in section {@jls
433 * 4.2.3} of <cite>The Java Language Specification</cite>.
434 *
435 * @since 19
436 */
437 public static final int PRECISION = 53;
438
439 /**
440 * Maximum exponent a finite {@code double} variable may have,
441 * {@value}. It is equal to the value returned by {@code
442 * Math.getExponent(Double.MAX_VALUE)}.
443 *
444 * @since 1.6
445 */
446 public static final int MAX_EXPONENT = (1 << (SIZE - PRECISION - 1)) - 1; // 1023
447
448 /**
449 * Minimum exponent a normalized {@code double} variable may have,
450 * {@value}. It is equal to the value returned by {@code
451 * Math.getExponent(Double.MIN_NORMAL)}.
452 *
453 * @since 1.6
454 */
455 public static final int MIN_EXPONENT = 1 - MAX_EXPONENT; // -1022
456
457 /**
458 * The number of bytes used to represent a {@code double} value,
459 * {@value}.
460 *
461 * @since 1.8
462 */
463 public static final int BYTES = SIZE / Byte.SIZE;
464
465 /**
466 * The {@code Class} instance representing the primitive type
467 * {@code double}.
468 *
469 * @since 1.1
470 */
471 public static final Class<Double> TYPE = Class.getPrimitiveClass("double");
472
473 /**
474 * Returns a string representation of the {@code double}
475 * argument. All characters mentioned below are ASCII characters.
476 * <ul>
477 * <li>If the argument is NaN, the result is the string
478 * "{@code NaN}".
479 * <li>Otherwise, the result is a string that represents the sign and
480 * magnitude (absolute value) of the argument. If the sign is negative,
481 * the first character of the result is '{@code -}'
482 * ({@code '\u005Cu002D'}); if the sign is positive, no sign character
483 * appears in the result. As for the magnitude <i>m</i>:
484 * <ul>
485 * <li>If <i>m</i> is infinity, it is represented by the characters
486 * {@code "Infinity"}; thus, positive infinity produces the result
487 * {@code "Infinity"} and negative infinity produces the result
488 * {@code "-Infinity"}.
489 *
490 * <li>If <i>m</i> is zero, it is represented by the characters
491 * {@code "0.0"}; thus, negative zero produces the result
492 * {@code "-0.0"} and positive zero produces the result
493 * {@code "0.0"}.
494 *
495 * <li> Otherwise <i>m</i> is positive and finite.
496 * It is converted to a string in two stages:
497 * <ul>
498 * <li> <em>Selection of a decimal</em>:
499 * A well-defined decimal <i>d</i><sub><i>m</i></sub>
500 * is selected to represent <i>m</i>.
501 * This decimal is (almost always) the <em>shortest</em> one that
502 * rounds to <i>m</i> according to the round to nearest
503 * rounding policy of IEEE 754 floating-point arithmetic.
504 * <li> <em>Formatting as a string</em>:
505 * The decimal <i>d</i><sub><i>m</i></sub> is formatted as a string,
506 * either in plain or in computerized scientific notation,
507 * depending on its value.
508 * </ul>
509 * </ul>
510 * </ul>
511 *
512 * <p>A <em>decimal</em> is a number of the form
513 * <i>s</i>×10<sup><i>i</i></sup>
514 * for some (unique) integers <i>s</i> > 0 and <i>i</i> such that
515 * <i>s</i> is not a multiple of 10.
516 * These integers are the <em>significand</em> and
517 * the <em>exponent</em>, respectively, of the decimal.
518 * The <em>length</em> of the decimal is the (unique)
519 * positive integer <i>n</i> meeting
520 * 10<sup><i>n</i>-1</sup> ≤ <i>s</i> < 10<sup><i>n</i></sup>.
521 *
522 * <p>The decimal <i>d</i><sub><i>m</i></sub> for a finite positive <i>m</i>
523 * is defined as follows:
524 * <ul>
525 * <li>Let <i>R</i> be the set of all decimals that round to <i>m</i>
526 * according to the usual <em>round to nearest</em> rounding policy of
527 * IEEE 754 floating-point arithmetic.
528 * <li>Let <i>p</i> be the minimal length over all decimals in <i>R</i>.
529 * <li>When <i>p</i> ≥ 2, let <i>T</i> be the set of all decimals
530 * in <i>R</i> with length <i>p</i>.
531 * Otherwise, let <i>T</i> be the set of all decimals
532 * in <i>R</i> with length 1 or 2.
533 * <li>Define <i>d</i><sub><i>m</i></sub> as the decimal in <i>T</i>
534 * that is closest to <i>m</i>.
535 * Or if there are two such decimals in <i>T</i>,
536 * select the one with the even significand.
537 * </ul>
538 *
539 * <p>The (uniquely) selected decimal <i>d</i><sub><i>m</i></sub>
540 * is then formatted.
541 * Let <i>s</i>, <i>i</i> and <i>n</i> be the significand, exponent and
542 * length of <i>d</i><sub><i>m</i></sub>, respectively.
543 * Further, let <i>e</i> = <i>n</i> + <i>i</i> - 1 and let
544 * <i>s</i><sub>1</sub>…<i>s</i><sub><i>n</i></sub>
545 * be the usual decimal expansion of <i>s</i>.
546 * Note that <i>s</i><sub>1</sub> ≠ 0
547 * and <i>s</i><sub><i>n</i></sub> ≠ 0.
548 * Below, the decimal point {@code '.'} is {@code '\u005Cu002E'}
549 * and the exponent indicator {@code 'E'} is {@code '\u005Cu0045'}.
550 * <ul>
551 * <li>Case -3 ≤ <i>e</i> < 0:
552 * <i>d</i><sub><i>m</i></sub> is formatted as
553 * <code>0.0</code>…<code>0</code><!--
554 * --><i>s</i><sub>1</sub>…<i>s</i><sub><i>n</i></sub>,
555 * where there are exactly -(<i>n</i> + <i>i</i>) zeroes between
556 * the decimal point and <i>s</i><sub>1</sub>.
557 * For example, 123 × 10<sup>-4</sup> is formatted as
558 * {@code 0.0123}.
559 * <li>Case 0 ≤ <i>e</i> < 7:
560 * <ul>
561 * <li>Subcase <i>i</i> ≥ 0:
562 * <i>d</i><sub><i>m</i></sub> is formatted as
563 * <i>s</i><sub>1</sub>…<i>s</i><sub><i>n</i></sub><!--
564 * --><code>0</code>…<code>0.0</code>,
565 * where there are exactly <i>i</i> zeroes
566 * between <i>s</i><sub><i>n</i></sub> and the decimal point.
567 * For example, 123 × 10<sup>2</sup> is formatted as
568 * {@code 12300.0}.
569 * <li>Subcase <i>i</i> < 0:
570 * <i>d</i><sub><i>m</i></sub> is formatted as
571 * <i>s</i><sub>1</sub>…<!--
572 * --><i>s</i><sub><i>n</i>+<i>i</i></sub><code>.</code><!--
573 * --><i>s</i><sub><i>n</i>+<i>i</i>+1</sub>…<!--
574 * --><i>s</i><sub><i>n</i></sub>,
575 * where there are exactly -<i>i</i> digits to the right of
576 * the decimal point.
577 * For example, 123 × 10<sup>-1</sup> is formatted as
578 * {@code 12.3}.
579 * </ul>
580 * <li>Case <i>e</i> < -3 or <i>e</i> ≥ 7:
581 * computerized scientific notation is used to format
582 * <i>d</i><sub><i>m</i></sub>.
583 * Here <i>e</i> is formatted as by {@link Integer#toString(int)}.
584 * <ul>
585 * <li>Subcase <i>n</i> = 1:
586 * <i>d</i><sub><i>m</i></sub> is formatted as
587 * <i>s</i><sub>1</sub><code>.0E</code><i>e</i>.
588 * For example, 1 × 10<sup>23</sup> is formatted as
589 * {@code 1.0E23}.
590 * <li>Subcase <i>n</i> > 1:
591 * <i>d</i><sub><i>m</i></sub> is formatted as
592 * <i>s</i><sub>1</sub><code>.</code><i>s</i><sub>2</sub><!--
593 * -->…<i>s</i><sub><i>n</i></sub><code>E</code><i>e</i>.
594 * For example, 123 × 10<sup>-21</sup> is formatted as
595 * {@code 1.23E-19}.
596 * </ul>
597 * </ul>
598 *
599 * <p>To create localized string representations of a floating-point
600 * value, use subclasses of {@link java.text.NumberFormat}.
601 *
602 * @apiNote
603 * This method corresponds to the general functionality of the
604 * convertToDecimalCharacter operation defined in IEEE 754;
605 * however, that operation is defined in terms of specifying the
606 * number of significand digits used in the conversion.
607 * Code to do such a conversion in the Java platform includes
608 * converting the {@code double} to a {@link java.math.BigDecimal
609 * BigDecimal} exactly and then rounding the {@code BigDecimal} to
610 * the desired number of digits; sample code:
611 * {@snippet lang=java :
612 * double d = 0.1;
613 * int digits = 25;
614 * BigDecimal bd = new BigDecimal(d);
615 * String result = bd.round(new MathContext(digits, RoundingMode.HALF_UP));
616 * // 0.1000000000000000055511151
617 * }
618 *
619 * @param d the {@code double} to be converted.
620 * @return a string representation of the argument.
621 */
622 public static String toString(double d) {
623 return DoubleToDecimal.toString(d);
624 }
625
626 /**
627 * Returns a hexadecimal string representation of the
628 * {@code double} argument. All characters mentioned below
629 * are ASCII characters.
630 *
631 * <ul>
632 * <li>If the argument is NaN, the result is the string
633 * "{@code NaN}".
634 * <li>Otherwise, the result is a string that represents the sign
635 * and magnitude of the argument. If the sign is negative, the
636 * first character of the result is '{@code -}'
637 * ({@code '\u005Cu002D'}); if the sign is positive, no sign
638 * character appears in the result. As for the magnitude <i>m</i>:
639 *
640 * <ul>
641 * <li>If <i>m</i> is infinity, it is represented by the string
642 * {@code "Infinity"}; thus, positive infinity produces the
643 * result {@code "Infinity"} and negative infinity produces
644 * the result {@code "-Infinity"}.
645 *
646 * <li>If <i>m</i> is zero, it is represented by the string
647 * {@code "0x0.0p0"}; thus, negative zero produces the result
648 * {@code "-0x0.0p0"} and positive zero produces the result
649 * {@code "0x0.0p0"}.
650 *
651 * <li>If <i>m</i> is a {@code double} value with a
652 * normalized representation, substrings are used to represent the
653 * significand and exponent fields. The significand is
654 * represented by the characters {@code "0x1."}
655 * followed by a lowercase hexadecimal representation of the rest
656 * of the significand as a fraction. Trailing zeros in the
657 * hexadecimal representation are removed unless all the digits
658 * are zero, in which case a single zero is used. Next, the
659 * exponent is represented by {@code "p"} followed
660 * by a decimal string of the unbiased exponent as if produced by
661 * a call to {@link Integer#toString(int) Integer.toString} on the
662 * exponent value.
663 *
664 * <li>If <i>m</i> is a {@code double} value with a subnormal
665 * representation, the significand is represented by the
666 * characters {@code "0x0."} followed by a
667 * hexadecimal representation of the rest of the significand as a
668 * fraction. Trailing zeros in the hexadecimal representation are
669 * removed. Next, the exponent is represented by
670 * {@code "p-1022"}. Note that there must be at
671 * least one nonzero digit in a subnormal significand.
672 *
673 * </ul>
674 *
675 * </ul>
676 *
677 * <table class="striped">
678 * <caption>Examples</caption>
679 * <thead>
680 * <tr><th scope="col">Floating-point Value</th><th scope="col">Hexadecimal String</th>
681 * </thead>
682 * <tbody style="text-align:right">
683 * <tr><th scope="row">{@code 1.0}</th> <td>{@code 0x1.0p0}</td>
684 * <tr><th scope="row">{@code -1.0}</th> <td>{@code -0x1.0p0}</td>
685 * <tr><th scope="row">{@code 2.0}</th> <td>{@code 0x1.0p1}</td>
686 * <tr><th scope="row">{@code 3.0}</th> <td>{@code 0x1.8p1}</td>
687 * <tr><th scope="row">{@code 0.5}</th> <td>{@code 0x1.0p-1}</td>
688 * <tr><th scope="row">{@code 0.25}</th> <td>{@code 0x1.0p-2}</td>
689 * <tr><th scope="row">{@code Double.MAX_VALUE}</th>
690 * <td>{@code 0x1.fffffffffffffp1023}</td>
691 * <tr><th scope="row">{@code Minimum Normal Value}</th>
692 * <td>{@code 0x1.0p-1022}</td>
693 * <tr><th scope="row">{@code Maximum Subnormal Value}</th>
694 * <td>{@code 0x0.fffffffffffffp-1022}</td>
695 * <tr><th scope="row">{@code Double.MIN_VALUE}</th>
696 * <td>{@code 0x0.0000000000001p-1022}</td>
697 * </tbody>
698 * </table>
699 *
700 * @apiNote
701 * This method corresponds to the convertToHexCharacter operation
702 * defined in IEEE 754.
703 *
704 * @param d the {@code double} to be converted.
705 * @return a hex string representation of the argument.
706 * @since 1.5
707 */
708 public static String toHexString(double d) {
709 /*
710 * Modeled after the "a" conversion specifier in C99, section
711 * 7.19.6.1; however, the output of this method is more
712 * tightly specified.
713 */
714 if (!isFinite(d)) {
715 // For infinity and NaN, use the decimal output.
716 return Double.toString(d);
717 }
718
719 long doubleToLongBits = Double.doubleToLongBits(d);
720 boolean negative = doubleToLongBits < 0;
721
722 if (d == 0.0) {
723 return negative ? "-0x0.0p0" : "0x0.0p0";
724 }
725 d = Math.abs(d);
726 // Check if the value is subnormal (less than the smallest normal value)
727 boolean subnormal = d < Double.MIN_NORMAL;
728
729 // Isolate significand bits and OR in a high-order bit
730 // so that the string representation has a known length.
731 // This ensures we always have 13 hex digits to work with (52 bits / 4 bits per hex digit)
732 long signifBits = doubleToLongBits & DoubleConsts.SIGNIF_BIT_MASK;
733
734 // Calculate the number of trailing zeros in the significand (in groups of 4 bits)
735 // This is used to remove trailing zeros from the hex representation
736 // We limit to 12 because we want to keep at least 1 hex digit (13 total - 12 = 1)
737 // assert 0 <= trailingZeros && trailingZeros <= 12
738 int trailingZeros = Long.numberOfTrailingZeros(signifBits | 1L << 4 * 12) >> 2;
739
740 // Determine the exponent value based on whether the number is subnormal or normal
741 // Subnormal numbers use the minimum exponent, normal numbers use the actual exponent
742 int exp = subnormal ? Double.MIN_EXPONENT : Math.getExponent(d);
743
744 // Calculate the total length of the resulting string:
745 // Sign (optional) + prefix "0x" + implicit bit + "." + hex digits + "p" + exponent
746 int charlen = (negative ? 1 : 0) // sign character
747 + 4 // "0x1." or "0x0."
748 + 13 - trailingZeros // hex digits (13 max, minus trailing zeros)
749 + 1 // "p"
750 + DecimalDigits.stringSize(exp) // exponent
751 ;
752
753 // Create a byte array to hold the result characters
754 byte[] chars = new byte[charlen];
755 int index = 0;
756
757 // Add the sign character if the number is negative
758 if (negative) { // value is negative
759 chars[index++] = '-';
760 }
761
762 // Add the prefix and the implicit bit ('1' for normal, '0' for subnormal)
763 // Subnormal values have a 0 implicit bit; normal values have a 1 implicit bit.
764 chars[index ] = '0'; // Hex prefix
765 chars[index + 1] = 'x'; // Hex prefix
766 chars[index + 2] = (byte) (subnormal ? '0' : '1'); // Implicit bit
767 chars[index + 3] = '.'; // Decimal point
768 index += 4;
769
770 // Convert significand to hex digits manually to avoid creating temporary strings
771 // Extract the 13 hex digits (52 bits) from signifBits
772 // We need to extract bits 48-51, 44-47, ..., 0-3 (13 groups of 4 bits)
773 for (int sh = 4 * 12, end = 4 * trailingZeros; sh >= end; sh -= 4) {
774 // Extract 4 bits at a time from left to right
775 // Shift right by sh positions and mask with 0xF
776 // Integer.digits maps values 0-15 to '0'-'f' characters
777 chars[index++] = Integer.digits[((int)(signifBits >> sh)) & 0xF];
778 }
779
780 // Add the exponent indicator
781 chars[index] = 'p';
782
783 // Append the exponent value to the character array
784 // This method writes the decimal representation of exp directly into the byte array
785 DecimalDigits.uncheckedGetCharsLatin1(exp, charlen, chars);
786
787 return String.newStringWithLatin1Bytes(chars);
788 }
789
790 /**
791 * Returns a {@code Double} object holding the
792 * {@code double} value represented by the argument string
793 * {@code s}.
794 *
795 * <p>If {@code s} is {@code null}, then a
796 * {@code NullPointerException} is thrown.
797 *
798 * <p>Leading and trailing whitespace characters in {@code s}
799 * are ignored. Whitespace is removed as if by the {@link
800 * String#trim} method; that is, both ASCII space and control
801 * characters are removed. The rest of {@code s} should
802 * constitute a <i>FloatValue</i> as described by the lexical
803 * syntax rules:
804 *
805 * <blockquote>
806 * <dl>
807 * <dt><i>FloatValue:</i>
808 * <dd><i>Sign<sub>opt</sub></i> {@code NaN}
809 * <dd><i>Sign<sub>opt</sub></i> {@code Infinity}
810 * <dd><i>Sign<sub>opt</sub> FloatingPointLiteral</i>
811 * <dd><i>Sign<sub>opt</sub> HexFloatingPointLiteral</i>
812 * <dd><i>SignedInteger</i>
813 * </dl>
814 *
815 * <dl>
816 * <dt><i>HexFloatingPointLiteral</i>:
817 * <dd> <i>HexSignificand BinaryExponent FloatTypeSuffix<sub>opt</sub></i>
818 * </dl>
819 *
820 * <dl>
821 * <dt><i>HexSignificand:</i>
822 * <dd><i>HexNumeral</i>
823 * <dd><i>HexNumeral</i> {@code .}
824 * <dd>{@code 0x} <i>HexDigits<sub>opt</sub>
825 * </i>{@code .}<i> HexDigits</i>
826 * <dd>{@code 0X}<i> HexDigits<sub>opt</sub>
827 * </i>{@code .} <i>HexDigits</i>
828 * </dl>
829 *
830 * <dl>
831 * <dt><i>BinaryExponent:</i>
832 * <dd><i>BinaryExponentIndicator SignedInteger</i>
833 * </dl>
834 *
835 * <dl>
836 * <dt><i>BinaryExponentIndicator:</i>
837 * <dd>{@code p}
838 * <dd>{@code P}
839 * </dl>
840 *
841 * </blockquote>
842 *
843 * where <i>Sign</i>, <i>FloatingPointLiteral</i>,
844 * <i>HexNumeral</i>, <i>HexDigits</i>, <i>SignedInteger</i> and
845 * <i>FloatTypeSuffix</i> are as defined in the lexical structure
846 * sections of
847 * <cite>The Java Language Specification</cite>,
848 * except that underscores are not accepted between digits.
849 * If {@code s} does not have the form of
850 * a <i>FloatValue</i>, then a {@code NumberFormatException}
851 * is thrown. Otherwise, {@code s} is regarded as
852 * representing an exact decimal value in the usual
853 * "computerized scientific notation" or as an exact
854 * hexadecimal value; this exact numerical value is then
855 * conceptually converted to an "infinitely precise"
856 * binary value that is then rounded to type {@code double}
857 * by the usual round-to-nearest rule of IEEE 754 floating-point
858 * arithmetic, which includes preserving the sign of a zero
859 * value.
860 *
861 * Note that the round-to-nearest rule also implies overflow and
862 * underflow behaviour; if the exact value of {@code s} is large
863 * enough in magnitude (greater than or equal to ({@link
864 * #MAX_VALUE} + {@link Math#ulp(double) ulp(MAX_VALUE)}/2),
865 * rounding to {@code double} will result in an infinity and if the
866 * exact value of {@code s} is small enough in magnitude (less
867 * than or equal to {@link #MIN_VALUE}/2), rounding to float will
868 * result in a zero.
869 *
870 * Finally, after rounding a {@code Double} object representing
871 * this {@code double} value is returned.
872 *
873 * <p>Note that trailing format specifiers, specifiers that
874 * determine the type of a floating-point literal
875 * ({@code 1.0f} is a {@code float} value;
876 * {@code 1.0d} is a {@code double} value), do
877 * <em>not</em> influence the results of this method. In other
878 * words, the numerical value of the input string is converted
879 * directly to the target floating-point type. The two-step
880 * sequence of conversions, string to {@code float} followed
881 * by {@code float} to {@code double}, is <em>not</em>
882 * equivalent to converting a string directly to
883 * {@code double}. For example, the {@code float}
884 * literal {@code 0.1f} is equal to the {@code double}
885 * value {@code 0.10000000149011612}; the {@code float}
886 * literal {@code 0.1f} represents a different numerical
887 * value than the {@code double} literal
888 * {@code 0.1}. (The numerical value 0.1 cannot be exactly
889 * represented in a binary floating-point number.)
890 *
891 * <p>To avoid calling this method on an invalid string and having
892 * a {@code NumberFormatException} be thrown, the regular
893 * expression below can be used to screen the input string:
894 *
895 * {@snippet lang="java" :
896 * final String Digits = "(\\p{Digit}+)";
897 * final String HexDigits = "(\\p{XDigit}+)";
898 * // an exponent is 'e' or 'E' followed by an optionally
899 * // signed decimal integer.
900 * final String Exp = "[eE][+-]?"+Digits;
901 * final String fpRegex =
902 * ("[\\x00-\\x20]*"+ // Optional leading "whitespace"
903 * "[+-]?(" + // Optional sign character
904 * "NaN|" + // "NaN" string
905 * "Infinity|" + // "Infinity" string
906 *
907 * // A decimal floating-point string representing a finite positive
908 * // number without a leading sign has at most five basic pieces:
909 * // Digits . Digits ExponentPart FloatTypeSuffix
910 * //
911 * // Since this method allows integer-only strings as input
912 * // in addition to strings of floating-point literals, the
913 * // two sub-patterns below are simplifications of the grammar
914 * // productions from section 3.10.2 of
915 * // The Java Language Specification.
916 *
917 * // Digits ._opt Digits_opt ExponentPart_opt FloatTypeSuffix_opt
918 * "((("+Digits+"(\\.)?("+Digits+"?)("+Exp+")?)|"+
919 *
920 * // . Digits ExponentPart_opt FloatTypeSuffix_opt
921 * "(\\.("+Digits+")("+Exp+")?)|"+
922 *
923 * // Hexadecimal strings
924 * "((" +
925 * // 0[xX] HexDigits ._opt BinaryExponent FloatTypeSuffix_opt
926 * "(0[xX]" + HexDigits + "(\\.)?)|" +
927 *
928 * // 0[xX] HexDigits_opt . HexDigits BinaryExponent FloatTypeSuffix_opt
929 * "(0[xX]" + HexDigits + "?(\\.)" + HexDigits + ")" +
930 *
931 * ")[pP][+-]?" + Digits + "))" +
932 * "[fFdD]?))" +
933 * "[\\x00-\\x20]*");// Optional trailing "whitespace"
934 * // @link region substring="Pattern.matches" target ="java.util.regex.Pattern#matches"
935 * if (Pattern.matches(fpRegex, myString))
936 * Double.valueOf(myString); // Will not throw NumberFormatException
937 * // @end
938 * else {
939 * // Perform suitable alternative action
940 * }
941 * }
942 *
943 * @apiNote To interpret localized string representations of a
944 * floating-point value, or string representations that have
945 * non-ASCII digits, use {@link java.text.NumberFormat}. For
946 * example,
947 * {@snippet lang="java" :
948 * NumberFormat.getInstance(l).parse(s).doubleValue();
949 * }
950 * where {@code l} is the desired locale, or
951 * {@link java.util.Locale#ROOT} if locale insensitive.
952 *
953 * @apiNote
954 * This method corresponds to the convertFromDecimalCharacter and
955 * convertFromHexCharacter operations defined in IEEE 754.
956 *
957 * @param s the string to be parsed.
958 * @return a {@code Double} object holding the value
959 * represented by the {@code String} argument.
960 * @throws NumberFormatException if the string does not contain a
961 * parsable number.
962 * @see Double##decimalToBinaryConversion Decimal ↔ Binary Conversion Issues
963 */
964 public static Double valueOf(String s) throws NumberFormatException {
965 return new Double(parseDouble(s));
966 }
967
968 /**
969 * Returns a {@code Double} instance representing the specified
970 * {@code double} value.
971 * If a new {@code Double} instance is not required, this method
972 * should generally be used in preference to the constructor
973 * {@link #Double(double)}, as this method is likely to yield
974 * significantly better space and time performance by caching
975 * frequently requested values.
976 *
977 * @param d a double value.
978 * @return a {@code Double} instance representing {@code d}.
979 * @since 1.5
980 */
981 @IntrinsicCandidate
982 @DeserializeConstructor
983 public static Double valueOf(double d) {
984 return new Double(d);
985 }
986
987 /**
988 * Returns a new {@code double} initialized to the value
989 * represented by the specified {@code String}, as performed
990 * by the {@code valueOf} method of class
991 * {@code Double}.
992 *
993 * @param s the string to be parsed.
994 * @return the {@code double} value represented by the string
995 * argument.
996 * @throws NullPointerException if the string is null
997 * @throws NumberFormatException if the string does not contain
998 * a parsable {@code double}.
999 * @see java.lang.Double#valueOf(String)
1000 * @see Double##decimalToBinaryConversion Decimal ↔ Binary Conversion Issues
1001 * @since 1.2
1002 */
1003 public static double parseDouble(String s) throws NumberFormatException {
1004 return FloatingDecimal.parseDouble(s);
1005 }
1006
1007 /**
1008 * Returns {@code true} if the specified number is a
1009 * Not-a-Number (NaN) value, {@code false} otherwise.
1010 *
1011 * @apiNote
1012 * This method corresponds to the isNaN operation defined in IEEE
1013 * 754.
1014 *
1015 * @param v the value to be tested.
1016 * @return {@code true} if the value of the argument is NaN;
1017 * {@code false} otherwise.
1018 */
1019 public static boolean isNaN(double v) {
1020 return (v != v);
1021 }
1022
1023 /**
1024 * Returns {@code true} if the specified number is infinitely
1025 * large in magnitude, {@code false} otherwise.
1026 *
1027 * @apiNote
1028 * This method corresponds to the isInfinite operation defined in
1029 * IEEE 754.
1030 *
1031 * @param v the value to be tested.
1032 * @return {@code true} if the value of the argument is positive
1033 * infinity or negative infinity; {@code false} otherwise.
1034 */
1035 @IntrinsicCandidate
1036 public static boolean isInfinite(double v) {
1037 return Math.abs(v) > MAX_VALUE;
1038 }
1039
1040 /**
1041 * Returns {@code true} if the argument is a finite floating-point
1042 * value; returns {@code false} otherwise (for NaN and infinity
1043 * arguments).
1044 *
1045 * @apiNote
1046 * This method corresponds to the isFinite operation defined in
1047 * IEEE 754.
1048 *
1049 * @param d the {@code double} value to be tested
1050 * @return {@code true} if the argument is a finite
1051 * floating-point value, {@code false} otherwise.
1052 * @since 1.8
1053 */
1054 @IntrinsicCandidate
1055 public static boolean isFinite(double d) {
1056 return Math.abs(d) <= Double.MAX_VALUE;
1057 }
1058
1059 /**
1060 * The value of the Double.
1061 *
1062 * @serial
1063 */
1064 private final double value;
1065
1066 /**
1067 * Constructs a newly allocated {@code Double} object that
1068 * represents the primitive {@code double} argument.
1069 *
1070 * @param value the value to be represented by the {@code Double}.
1071 *
1072 * @deprecated
1073 * It is rarely appropriate to use this constructor. The static factory
1074 * {@link #valueOf(double)} is generally a better choice, as it is
1075 * likely to yield significantly better space and time performance.
1076 */
1077 @Deprecated(since="9")
1078 public Double(double value) {
1079 this.value = value;
1080 }
1081
1082 /**
1083 * Constructs a newly allocated {@code Double} object that
1084 * represents the floating-point value of type {@code double}
1085 * represented by the string. The string is converted to a
1086 * {@code double} value as if by the {@code valueOf} method.
1087 *
1088 * @param s a string to be converted to a {@code Double}.
1089 * @throws NumberFormatException if the string does not contain a
1090 * parsable number.
1091 *
1092 * @deprecated
1093 * It is rarely appropriate to use this constructor.
1094 * Use {@link #parseDouble(String)} to convert a string to a
1095 * {@code double} primitive, or use {@link #valueOf(String)}
1096 * to convert a string to a {@code Double} object.
1097 */
1098 @Deprecated(since="9")
1099 public Double(String s) throws NumberFormatException {
1100 value = parseDouble(s);
1101 }
1102
1103 /**
1104 * Returns {@code true} if this {@code Double} value is
1105 * a Not-a-Number (NaN), {@code false} otherwise.
1106 *
1107 * @return {@code true} if the value represented by this object is
1108 * NaN; {@code false} otherwise.
1109 */
1110 public boolean isNaN() {
1111 return isNaN(value);
1112 }
1113
1114 /**
1115 * Returns {@code true} if this {@code Double} value is
1116 * infinitely large in magnitude, {@code false} otherwise.
1117 *
1118 * @return {@code true} if the value represented by this object is
1119 * positive infinity or negative infinity;
1120 * {@code false} otherwise.
1121 */
1122 public boolean isInfinite() {
1123 return isInfinite(value);
1124 }
1125
1126 /**
1127 * Returns a string representation of this {@code Double} object.
1128 * The primitive {@code double} value represented by this
1129 * object is converted to a string exactly as if by the method
1130 * {@code toString} of one argument.
1131 *
1132 * @return a {@code String} representation of this object.
1133 * @see java.lang.Double#toString(double)
1134 */
1135 public String toString() {
1136 return toString(value);
1137 }
1138
1139 /**
1140 * Returns the value of this {@code Double} as a {@code byte}
1141 * after a narrowing primitive conversion.
1142 *
1143 * @return the {@code double} value represented by this object
1144 * converted to type {@code byte}
1145 * @jls 5.1.3 Narrowing Primitive Conversion
1146 * @since 1.1
1147 */
1148 @Override
1149 public byte byteValue() {
1150 return (byte)value;
1151 }
1152
1153 /**
1154 * Returns the value of this {@code Double} as a {@code short}
1155 * after a narrowing primitive conversion.
1156 *
1157 * @return the {@code double} value represented by this object
1158 * converted to type {@code short}
1159 * @jls 5.1.3 Narrowing Primitive Conversion
1160 * @since 1.1
1161 */
1162 @Override
1163 public short shortValue() {
1164 return (short)value;
1165 }
1166
1167 /**
1168 * Returns the value of this {@code Double} as an {@code int}
1169 * after a narrowing primitive conversion.
1170 * @jls 5.1.3 Narrowing Primitive Conversion
1171 *
1172 * @apiNote
1173 * This method corresponds to the convertToIntegerTowardZero
1174 * operation defined in IEEE 754.
1175 *
1176 * @return the {@code double} value represented by this object
1177 * converted to type {@code int}
1178 */
1179 @Override
1180 public int intValue() {
1181 return (int)value;
1182 }
1183
1184 /**
1185 * Returns the value of this {@code Double} as a {@code long}
1186 * after a narrowing primitive conversion.
1187 *
1188 * @apiNote
1189 * This method corresponds to the convertToIntegerTowardZero
1190 * operation defined in IEEE 754.
1191 *
1192 * @return the {@code double} value represented by this object
1193 * converted to type {@code long}
1194 * @jls 5.1.3 Narrowing Primitive Conversion
1195 */
1196 @Override
1197 public long longValue() {
1198 return (long)value;
1199 }
1200
1201 /**
1202 * Returns the value of this {@code Double} as a {@code float}
1203 * after a narrowing primitive conversion.
1204 *
1205 * @apiNote
1206 * This method corresponds to the convertFormat operation defined
1207 * in IEEE 754.
1208 *
1209 * @return the {@code double} value represented by this object
1210 * converted to type {@code float}
1211 * @jls 5.1.3 Narrowing Primitive Conversion
1212 * @since 1.0
1213 */
1214 @Override
1215 public float floatValue() {
1216 return (float)value;
1217 }
1218
1219 /**
1220 * Returns the {@code double} value of this {@code Double} object.
1221 *
1222 * @return the {@code double} value represented by this object
1223 */
1224 @Override
1225 @IntrinsicCandidate
1226 public double doubleValue() {
1227 return value;
1228 }
1229
1230 /**
1231 * Returns a hash code for this {@code Double} object. The
1232 * result is the exclusive OR of the two halves of the
1233 * {@code long} integer bit representation, exactly as
1234 * produced by the method {@link #doubleToLongBits(double)}, of
1235 * the primitive {@code double} value represented by this
1236 * {@code Double} object. That is, the hash code is the value
1237 * of the expression:
1238 *
1239 * <blockquote>
1240 * {@code (int)(v^(v>>>32))}
1241 * </blockquote>
1242 *
1243 * where {@code v} is defined by:
1244 *
1245 * <blockquote>
1246 * {@code long v = Double.doubleToLongBits(this.doubleValue());}
1247 * </blockquote>
1248 *
1249 * @return a {@code hash code} value for this object.
1250 */
1251 @Override
1252 public int hashCode() {
1253 return Double.hashCode(value);
1254 }
1255
1256 /**
1257 * Returns a hash code for a {@code double} value; compatible with
1258 * {@code Double.hashCode()}.
1259 *
1260 * @param value the value to hash
1261 * @return a hash code value for a {@code double} value.
1262 * @since 1.8
1263 */
1264 public static int hashCode(double value) {
1265 return Long.hashCode(doubleToLongBits(value));
1266 }
1267
1268 /**
1269 * Compares this object against the specified object. The result
1270 * is {@code true} if and only if the argument is not
1271 * {@code null} and is a {@code Double} object that
1272 * represents a {@code double} that has the same value as the
1273 * {@code double} represented by this object. For this
1274 * purpose, two {@code double} values are considered to be
1275 * the same if and only if the method {@link
1276 * #doubleToLongBits(double)} returns the identical
1277 * {@code long} value when applied to each.
1278 * In other words, {@linkplain ##repEquivalence representation
1279 * equivalence} is used to compare the {@code double} values.
1280 *
1281 * @apiNote
1282 * This method is defined in terms of {@link
1283 * #doubleToLongBits(double)} rather than the {@code ==} operator
1284 * on {@code double} values since the {@code ==} operator does
1285 * <em>not</em> define an equivalence relation and to satisfy the
1286 * {@linkplain Object#equals equals contract} an equivalence
1287 * relation must be implemented; see {@linkplain ##equivalenceRelation
1288 * this discussion for details of floating-point equality and equivalence}.
1289 *
1290 * @see java.lang.Double#doubleToLongBits(double)
1291 * @jls 15.21.1 Numerical Equality Operators == and !=
1292 */
1293 public boolean equals(Object obj) {
1294 return (obj instanceof Double d) &&
1295 (doubleToLongBits(d.value) == doubleToLongBits(value));
1296 }
1297
1298 /**
1299 * Returns a representation of the specified floating-point value
1300 * according to the IEEE 754 floating-point "double
1301 * format" bit layout.
1302 *
1303 * <p>Bit 63 (the bit that is selected by the mask
1304 * {@code 0x8000000000000000L}) represents the sign of the
1305 * floating-point number. Bits
1306 * 62-52 (the bits that are selected by the mask
1307 * {@code 0x7ff0000000000000L}) represent the exponent. Bits 51-0
1308 * (the bits that are selected by the mask
1309 * {@code 0x000fffffffffffffL}) represent the significand
1310 * (sometimes called the mantissa) of the floating-point number.
1311 *
1312 * <p>If the argument is positive infinity, the result is
1313 * {@code 0x7ff0000000000000L}.
1314 *
1315 * <p>If the argument is negative infinity, the result is
1316 * {@code 0xfff0000000000000L}.
1317 *
1318 * <p>If the argument is NaN, the result is
1319 * {@code 0x7ff8000000000000L}.
1320 *
1321 * <p>In all cases, the result is a {@code long} integer that, when
1322 * given to the {@link #longBitsToDouble(long)} method, will produce a
1323 * floating-point value the same as the argument to
1324 * {@code doubleToLongBits} (except all NaN values are
1325 * collapsed to a single "canonical" NaN value).
1326 *
1327 * @param value a {@code double} precision floating-point number.
1328 * @return the bits that represent the floating-point number.
1329 */
1330 @IntrinsicCandidate
1331 public static long doubleToLongBits(double value) {
1332 if (!isNaN(value)) {
1333 return doubleToRawLongBits(value);
1334 }
1335 return 0x7ff8000000000000L;
1336 }
1337
1338 /**
1339 * Returns a representation of the specified floating-point value
1340 * according to the IEEE 754 floating-point "double
1341 * format" bit layout, preserving Not-a-Number (NaN) values.
1342 *
1343 * <p>Bit 63 (the bit that is selected by the mask
1344 * {@code 0x8000000000000000L}) represents the sign of the
1345 * floating-point number. Bits
1346 * 62-52 (the bits that are selected by the mask
1347 * {@code 0x7ff0000000000000L}) represent the exponent. Bits 51-0
1348 * (the bits that are selected by the mask
1349 * {@code 0x000fffffffffffffL}) represent the significand
1350 * (sometimes called the mantissa) of the floating-point number.
1351 *
1352 * <p>If the argument is positive infinity, the result is
1353 * {@code 0x7ff0000000000000L}.
1354 *
1355 * <p>If the argument is negative infinity, the result is
1356 * {@code 0xfff0000000000000L}.
1357 *
1358 * <p>If the argument is NaN, the result is the {@code long}
1359 * integer representing the actual NaN value. Unlike the
1360 * {@code doubleToLongBits} method,
1361 * {@code doubleToRawLongBits} does not collapse all the bit
1362 * patterns encoding a NaN to a single "canonical" NaN
1363 * value.
1364 *
1365 * <p>In all cases, the result is a {@code long} integer that,
1366 * when given to the {@link #longBitsToDouble(long)} method, will
1367 * produce a floating-point value the same as the argument to
1368 * {@code doubleToRawLongBits}.
1369 *
1370 * @param value a {@code double} precision floating-point number.
1371 * @return the bits that represent the floating-point number.
1372 * @since 1.3
1373 */
1374 @IntrinsicCandidate
1375 public static native long doubleToRawLongBits(double value);
1376
1377 /**
1378 * Returns the {@code double} value corresponding to a given
1379 * bit representation.
1380 * The argument is considered to be a representation of a
1381 * floating-point value according to the IEEE 754 floating-point
1382 * "double format" bit layout.
1383 *
1384 * <p>If the argument is {@code 0x7ff0000000000000L}, the result
1385 * is positive infinity.
1386 *
1387 * <p>If the argument is {@code 0xfff0000000000000L}, the result
1388 * is negative infinity.
1389 *
1390 * <p>If the argument is any value in the range
1391 * {@code 0x7ff0000000000001L} through
1392 * {@code 0x7fffffffffffffffL} or in the range
1393 * {@code 0xfff0000000000001L} through
1394 * {@code 0xffffffffffffffffL}, the result is a NaN. No IEEE
1395 * 754 floating-point operation provided by Java can distinguish
1396 * between two NaN values of the same type with different bit
1397 * patterns. Distinct values of NaN are only distinguishable by
1398 * use of the {@code Double.doubleToRawLongBits} method.
1399 *
1400 * <p>In all other cases, let <i>s</i>, <i>e</i>, and <i>m</i> be three
1401 * values that can be computed from the argument:
1402 *
1403 * {@snippet lang="java" :
1404 * int s = ((bits >> 63) == 0) ? 1 : -1;
1405 * int e = (int)((bits >> 52) & 0x7ffL);
1406 * long m = (e == 0) ?
1407 * (bits & 0xfffffffffffffL) << 1 :
1408 * (bits & 0xfffffffffffffL) | 0x10000000000000L;
1409 * }
1410 *
1411 * Then the floating-point result equals the value of the mathematical
1412 * expression <i>s</i>·<i>m</i>·2<sup><i>e</i>-1075</sup>.
1413 *
1414 * <p>Note that this method may not be able to return a
1415 * {@code double} NaN with exactly same bit pattern as the
1416 * {@code long} argument. IEEE 754 distinguishes between two
1417 * kinds of NaNs, quiet NaNs and <i>signaling NaNs</i>. The
1418 * differences between the two kinds of NaN are generally not
1419 * visible in Java. Arithmetic operations on signaling NaNs turn
1420 * them into quiet NaNs with a different, but often similar, bit
1421 * pattern. However, on some processors merely copying a
1422 * signaling NaN also performs that conversion. In particular,
1423 * copying a signaling NaN to return it to the calling method
1424 * may perform this conversion. So {@code longBitsToDouble}
1425 * may not be able to return a {@code double} with a
1426 * signaling NaN bit pattern. Consequently, for some
1427 * {@code long} values,
1428 * {@code doubleToRawLongBits(longBitsToDouble(start))} may
1429 * <i>not</i> equal {@code start}. Moreover, which
1430 * particular bit patterns represent signaling NaNs is platform
1431 * dependent; although all NaN bit patterns, quiet or signaling,
1432 * must be in the NaN range identified above.
1433 *
1434 * @param bits any {@code long} integer.
1435 * @return the {@code double} floating-point value with the same
1436 * bit pattern.
1437 */
1438 @IntrinsicCandidate
1439 public static native double longBitsToDouble(long bits);
1440
1441 /**
1442 * Compares two {@code Double} objects numerically.
1443 *
1444 * This method imposes a total order on {@code Double} objects
1445 * with two differences compared to the incomplete order defined by
1446 * the Java language numerical comparison operators ({@code <, <=,
1447 * ==, >=, >}) on {@code double} values.
1448 *
1449 * <ul><li> A NaN is <em>unordered</em> with respect to other
1450 * values and unequal to itself under the comparison
1451 * operators. This method chooses to define {@code
1452 * Double.NaN} to be equal to itself and greater than all
1453 * other {@code double} values (including {@code
1454 * Double.POSITIVE_INFINITY}).
1455 *
1456 * <li> Positive zero and negative zero compare equal
1457 * numerically, but are distinct and distinguishable values.
1458 * This method chooses to define positive zero ({@code +0.0d}),
1459 * to be greater than negative zero ({@code -0.0d}).
1460 * </ul>
1461 *
1462 * This ensures that the <i>natural ordering</i> of {@code Double}
1463 * objects imposed by this method is <i>consistent with
1464 * equals</i>; see {@linkplain ##equivalenceRelation this
1465 * discussion for details of floating-point comparison and
1466 * ordering}.
1467 *
1468 * @apiNote
1469 * The inclusion of a total order idiom in the Java SE API
1470 * predates the inclusion of that functionality in the IEEE 754
1471 * standard. The ordering of the totalOrder predicate chosen by
1472 * IEEE 754 differs from the total order chosen by this method.
1473 * While this method treats all NaN representations as being in
1474 * the same equivalence class, the IEEE 754 total order defines an
1475 * ordering based on the bit patterns of the NaN among the
1476 * different NaN representations. The IEEE 754 order regards
1477 * "negative" NaN representations, that is NaN representations
1478 * whose sign bit is set, to be less than any finite or infinite
1479 * value and less than any "positive" NaN. In addition, the IEEE
1480 * order regards all positive NaN values as greater than positive
1481 * infinity. See the IEEE 754 standard for full details of its
1482 * total ordering.
1483 *
1484 * @param anotherDouble the {@code Double} to be compared.
1485 * @return the value {@code 0} if {@code anotherDouble} is
1486 * numerically equal to this {@code Double}; a value
1487 * less than {@code 0} if this {@code Double}
1488 * is numerically less than {@code anotherDouble};
1489 * and a value greater than {@code 0} if this
1490 * {@code Double} is numerically greater than
1491 * {@code anotherDouble}.
1492 *
1493 * @jls 15.20.1 Numerical Comparison Operators {@code <}, {@code <=}, {@code >}, and {@code >=}
1494 * @since 1.2
1495 */
1496 @Override
1497 public int compareTo(Double anotherDouble) {
1498 return Double.compare(value, anotherDouble.value);
1499 }
1500
1501 /**
1502 * Compares the two specified {@code double} values. The sign
1503 * of the integer value returned is the same as that of the
1504 * integer that would be returned by the call:
1505 * <pre>
1506 * Double.valueOf(d1).compareTo(Double.valueOf(d2))
1507 * </pre>
1508 *
1509 * @apiNote
1510 * One idiom to implement {@linkplain ##repEquivalence
1511 * representation equivalence} on {@code double} values is
1512 * {@snippet lang="java" :
1513 * Double.compare(a, b) == 0
1514 * }
1515 * @param d1 the first {@code double} to compare
1516 * @param d2 the second {@code double} to compare
1517 * @return the value {@code 0} if {@code d1} is
1518 * numerically equal to {@code d2}; a value less than
1519 * {@code 0} if {@code d1} is numerically less than
1520 * {@code d2}; and a value greater than {@code 0}
1521 * if {@code d1} is numerically greater than
1522 * {@code d2}.
1523 * @since 1.4
1524 */
1525 public static int compare(double d1, double d2) {
1526 if (d1 < d2)
1527 return -1; // Neither val is NaN, thisVal is smaller
1528 if (d1 > d2)
1529 return 1; // Neither val is NaN, thisVal is larger
1530
1531 // Cannot use doubleToRawLongBits because of possibility of NaNs.
1532 long thisBits = Double.doubleToLongBits(d1);
1533 long anotherBits = Double.doubleToLongBits(d2);
1534
1535 return (thisBits == anotherBits ? 0 : // Values are equal
1536 (thisBits < anotherBits ? -1 : // (-0.0, 0.0) or (!NaN, NaN)
1537 1)); // (0.0, -0.0) or (NaN, !NaN)
1538 }
1539
1540 /**
1541 * Adds two {@code double} values together as per the + operator.
1542 *
1543 * @apiNote This method corresponds to the addition operation
1544 * defined in IEEE 754.
1545 *
1546 * @param a the first operand
1547 * @param b the second operand
1548 * @return the sum of {@code a} and {@code b}
1549 * @jls 4.2.4 Floating-Point Operations
1550 * @see java.util.function.BinaryOperator
1551 * @since 1.8
1552 */
1553 public static double sum(double a, double b) {
1554 return a + b;
1555 }
1556
1557 /**
1558 * Returns the greater of two {@code double} values
1559 * as if by calling {@link Math#max(double, double) Math.max}.
1560 *
1561 * @apiNote
1562 * This method corresponds to the maximum operation defined in
1563 * IEEE 754.
1564 *
1565 * @param a the first operand
1566 * @param b the second operand
1567 * @return the greater of {@code a} and {@code b}
1568 * @see java.util.function.BinaryOperator
1569 * @since 1.8
1570 */
1571 public static double max(double a, double b) {
1572 return Math.max(a, b);
1573 }
1574
1575 /**
1576 * Returns the smaller of two {@code double} values
1577 * as if by calling {@link Math#min(double, double) Math.min}.
1578 *
1579 * @apiNote
1580 * This method corresponds to the minimum operation defined in
1581 * IEEE 754.
1582 *
1583 * @param a the first operand
1584 * @param b the second operand
1585 * @return the smaller of {@code a} and {@code b}.
1586 * @see java.util.function.BinaryOperator
1587 * @since 1.8
1588 */
1589 public static double min(double a, double b) {
1590 return Math.min(a, b);
1591 }
1592
1593 /**
1594 * Returns an {@link Optional} containing the nominal descriptor for this
1595 * instance, which is the instance itself.
1596 *
1597 * @return an {@link Optional} describing the {@linkplain Double} instance
1598 * @since 12
1599 */
1600 @Override
1601 public Optional<Double> describeConstable() {
1602 return Optional.of(this);
1603 }
1604
1605 /**
1606 * Resolves this instance as a {@link ConstantDesc}, the result of which is
1607 * the instance itself.
1608 *
1609 * @param lookup ignored
1610 * @return the {@linkplain Double} instance
1611 * @since 12
1612 */
1613 @Override
1614 public Double resolveConstantDesc(MethodHandles.Lookup lookup) {
1615 return this;
1616 }
1617
1618 /** use serialVersionUID from JDK 1.0.2 for interoperability */
1619 @java.io.Serial
1620 private static final long serialVersionUID = -9172774392245257468L;
1621 }