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
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10 *
11 * This code is distributed in the hope that it will be useful, but WITHOUT
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13 * FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
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15 * accompanied this code).
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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 wraps a value of the primitive type
41 * {@code double} in an object. An object of type
42 * {@code Double} contains a single field whose type is
43 * {@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><i>numerical equality</i></a> ({@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><i>bit-wise equivalence</i>:</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><i><a id=repEquivalence>representation equivalence</a></i>:</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, Formats, 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 @SuppressWarnings("unchecked")
465 public static final Class<Double> TYPE = (Class<Double>) Class.getPrimitiveClass("double");
466
467 /**
468 * Returns a string representation of the {@code double}
469 * argument. All characters mentioned below are ASCII characters.
470 * <ul>
471 * <li>If the argument is NaN, the result is the string
472 * "{@code NaN}".
473 * <li>Otherwise, the result is a string that represents the sign and
474 * magnitude (absolute value) of the argument. If the sign is negative,
475 * the first character of the result is '{@code -}'
476 * ({@code '\u005Cu002D'}); if the sign is positive, no sign character
477 * appears in the result. As for the magnitude <i>m</i>:
478 * <ul>
479 * <li>If <i>m</i> is infinity, it is represented by the characters
480 * {@code "Infinity"}; thus, positive infinity produces the result
481 * {@code "Infinity"} and negative infinity produces the result
482 * {@code "-Infinity"}.
483 *
484 * <li>If <i>m</i> is zero, it is represented by the characters
485 * {@code "0.0"}; thus, negative zero produces the result
486 * {@code "-0.0"} and positive zero produces the result
487 * {@code "0.0"}.
488 *
489 * <li> Otherwise <i>m</i> is positive and finite.
490 * It is converted to a string in two stages:
491 * <ul>
492 * <li> <em>Selection of a decimal</em>:
493 * A well-defined decimal <i>d</i><sub><i>m</i></sub>
494 * is selected to represent <i>m</i>.
495 * This decimal is (almost always) the <em>shortest</em> one that
496 * rounds to <i>m</i> according to the round to nearest
497 * rounding policy of IEEE 754 floating-point arithmetic.
498 * <li> <em>Formatting as a string</em>:
499 * The decimal <i>d</i><sub><i>m</i></sub> is formatted as a string,
500 * either in plain or in computerized scientific notation,
501 * depending on its value.
502 * </ul>
503 * </ul>
504 * </ul>
505 *
506 * <p>A <em>decimal</em> is a number of the form
507 * <i>s</i>×10<sup><i>i</i></sup>
508 * for some (unique) integers <i>s</i> > 0 and <i>i</i> such that
509 * <i>s</i> is not a multiple of 10.
510 * These integers are the <em>significand</em> and
511 * the <em>exponent</em>, respectively, of the decimal.
512 * The <em>length</em> of the decimal is the (unique)
513 * positive integer <i>n</i> meeting
514 * 10<sup><i>n</i>-1</sup> ≤ <i>s</i> < 10<sup><i>n</i></sup>.
515 *
516 * <p>The decimal <i>d</i><sub><i>m</i></sub> for a finite positive <i>m</i>
517 * is defined as follows:
518 * <ul>
519 * <li>Let <i>R</i> be the set of all decimals that round to <i>m</i>
520 * according to the usual <em>round to nearest</em> rounding policy of
521 * IEEE 754 floating-point arithmetic.
522 * <li>Let <i>p</i> be the minimal length over all decimals in <i>R</i>.
523 * <li>When <i>p</i> ≥ 2, let <i>T</i> be the set of all decimals
524 * in <i>R</i> with length <i>p</i>.
525 * Otherwise, let <i>T</i> be the set of all decimals
526 * in <i>R</i> with length 1 or 2.
527 * <li>Define <i>d</i><sub><i>m</i></sub> as the decimal in <i>T</i>
528 * that is closest to <i>m</i>.
529 * Or if there are two such decimals in <i>T</i>,
530 * select the one with the even significand.
531 * </ul>
532 *
533 * <p>The (uniquely) selected decimal <i>d</i><sub><i>m</i></sub>
534 * is then formatted.
535 * Let <i>s</i>, <i>i</i> and <i>n</i> be the significand, exponent and
536 * length of <i>d</i><sub><i>m</i></sub>, respectively.
537 * Further, let <i>e</i> = <i>n</i> + <i>i</i> - 1 and let
538 * <i>s</i><sub>1</sub>…<i>s</i><sub><i>n</i></sub>
539 * be the usual decimal expansion of <i>s</i>.
540 * Note that <i>s</i><sub>1</sub> ≠ 0
541 * and <i>s</i><sub><i>n</i></sub> ≠ 0.
542 * Below, the decimal point {@code '.'} is {@code '\u005Cu002E'}
543 * and the exponent indicator {@code 'E'} is {@code '\u005Cu0045'}.
544 * <ul>
545 * <li>Case -3 ≤ <i>e</i> < 0:
546 * <i>d</i><sub><i>m</i></sub> is formatted as
547 * <code>0.0</code>…<code>0</code><!--
548 * --><i>s</i><sub>1</sub>…<i>s</i><sub><i>n</i></sub>,
549 * where there are exactly -(<i>n</i> + <i>i</i>) zeroes between
550 * the decimal point and <i>s</i><sub>1</sub>.
551 * For example, 123 × 10<sup>-4</sup> is formatted as
552 * {@code 0.0123}.
553 * <li>Case 0 ≤ <i>e</i> < 7:
554 * <ul>
555 * <li>Subcase <i>i</i> ≥ 0:
556 * <i>d</i><sub><i>m</i></sub> is formatted as
557 * <i>s</i><sub>1</sub>…<i>s</i><sub><i>n</i></sub><!--
558 * --><code>0</code>…<code>0.0</code>,
559 * where there are exactly <i>i</i> zeroes
560 * between <i>s</i><sub><i>n</i></sub> and the decimal point.
561 * For example, 123 × 10<sup>2</sup> is formatted as
562 * {@code 12300.0}.
563 * <li>Subcase <i>i</i> < 0:
564 * <i>d</i><sub><i>m</i></sub> is formatted as
565 * <i>s</i><sub>1</sub>…<!--
566 * --><i>s</i><sub><i>n</i>+<i>i</i></sub><code>.</code><!--
567 * --><i>s</i><sub><i>n</i>+<i>i</i>+1</sub>…<!--
568 * --><i>s</i><sub><i>n</i></sub>,
569 * where there are exactly -<i>i</i> digits to the right of
570 * the decimal point.
571 * For example, 123 × 10<sup>-1</sup> is formatted as
572 * {@code 12.3}.
573 * </ul>
574 * <li>Case <i>e</i> < -3 or <i>e</i> ≥ 7:
575 * computerized scientific notation is used to format
576 * <i>d</i><sub><i>m</i></sub>.
577 * Here <i>e</i> is formatted as by {@link Integer#toString(int)}.
578 * <ul>
579 * <li>Subcase <i>n</i> = 1:
580 * <i>d</i><sub><i>m</i></sub> is formatted as
581 * <i>s</i><sub>1</sub><code>.0E</code><i>e</i>.
582 * For example, 1 × 10<sup>23</sup> is formatted as
583 * {@code 1.0E23}.
584 * <li>Subcase <i>n</i> > 1:
585 * <i>d</i><sub><i>m</i></sub> is formatted as
586 * <i>s</i><sub>1</sub><code>.</code><i>s</i><sub>2</sub><!--
587 * -->…<i>s</i><sub><i>n</i></sub><code>E</code><i>e</i>.
588 * For example, 123 × 10<sup>-21</sup> is formatted as
589 * {@code 1.23E-19}.
590 * </ul>
591 * </ul>
592 *
593 * <p>To create localized string representations of a floating-point
594 * value, use subclasses of {@link java.text.NumberFormat}.
595 *
596 * @apiNote
597 * This method corresponds to the general functionality of the
598 * convertToDecimalCharacter operation defined in IEEE 754;
599 * however, that operation is defined in terms of specifying the
600 * number of significand digits used in the conversion.
601 * Code to do such a conversion in the Java platform includes
602 * converting the {@code double} to a {@link java.math.BigDecimal
603 * BigDecimal} exactly and then rounding the {@code BigDecimal} to
604 * the desired number of digits; sample code:
605 * {@snippet lang=java :
606 * double d = 0.1;
607 * int digits = 25;
608 * BigDecimal bd = new BigDecimal(d);
609 * String result = bd.round(new MathContext(digits, RoundingMode.HALF_UP));
610 * // 0.1000000000000000055511151
611 * }
612 *
613 * @param d the {@code double} to be converted.
614 * @return a string representation of the argument.
615 */
616 public static String toString(double d) {
617 return DoubleToDecimal.toString(d);
618 }
619
620 /**
621 * Returns a hexadecimal string representation of the
622 * {@code double} argument. All characters mentioned below
623 * are ASCII characters.
624 *
625 * <ul>
626 * <li>If the argument is NaN, the result is the string
627 * "{@code NaN}".
628 * <li>Otherwise, the result is a string that represents the sign
629 * and magnitude of the argument. If the sign is negative, the
630 * first character of the result is '{@code -}'
631 * ({@code '\u005Cu002D'}); if the sign is positive, no sign
632 * character appears in the result. As for the magnitude <i>m</i>:
633 *
634 * <ul>
635 * <li>If <i>m</i> is infinity, it is represented by the string
636 * {@code "Infinity"}; thus, positive infinity produces the
637 * result {@code "Infinity"} and negative infinity produces
638 * the result {@code "-Infinity"}.
639 *
640 * <li>If <i>m</i> is zero, it is represented by the string
641 * {@code "0x0.0p0"}; thus, negative zero produces the result
642 * {@code "-0x0.0p0"} and positive zero produces the result
643 * {@code "0x0.0p0"}.
644 *
645 * <li>If <i>m</i> is a {@code double} value with a
646 * normalized representation, substrings are used to represent the
647 * significand and exponent fields. The significand is
648 * represented by the characters {@code "0x1."}
649 * followed by a lowercase hexadecimal representation of the rest
650 * of the significand as a fraction. Trailing zeros in the
651 * hexadecimal representation are removed unless all the digits
652 * are zero, in which case a single zero is used. Next, the
653 * exponent is represented by {@code "p"} followed
654 * by a decimal string of the unbiased exponent as if produced by
655 * a call to {@link Integer#toString(int) Integer.toString} on the
656 * exponent value.
657 *
658 * <li>If <i>m</i> is a {@code double} value with a subnormal
659 * representation, the significand is represented by the
660 * characters {@code "0x0."} followed by a
661 * hexadecimal representation of the rest of the significand as a
662 * fraction. Trailing zeros in the hexadecimal representation are
663 * removed. Next, the exponent is represented by
664 * {@code "p-1022"}. Note that there must be at
665 * least one nonzero digit in a subnormal significand.
666 *
667 * </ul>
668 *
669 * </ul>
670 *
671 * <table class="striped">
672 * <caption>Examples</caption>
673 * <thead>
674 * <tr><th scope="col">Floating-point Value</th><th scope="col">Hexadecimal String</th>
675 * </thead>
676 * <tbody style="text-align:right">
677 * <tr><th scope="row">{@code 1.0}</th> <td>{@code 0x1.0p0}</td>
678 * <tr><th scope="row">{@code -1.0}</th> <td>{@code -0x1.0p0}</td>
679 * <tr><th scope="row">{@code 2.0}</th> <td>{@code 0x1.0p1}</td>
680 * <tr><th scope="row">{@code 3.0}</th> <td>{@code 0x1.8p1}</td>
681 * <tr><th scope="row">{@code 0.5}</th> <td>{@code 0x1.0p-1}</td>
682 * <tr><th scope="row">{@code 0.25}</th> <td>{@code 0x1.0p-2}</td>
683 * <tr><th scope="row">{@code Double.MAX_VALUE}</th>
684 * <td>{@code 0x1.fffffffffffffp1023}</td>
685 * <tr><th scope="row">{@code Minimum Normal Value}</th>
686 * <td>{@code 0x1.0p-1022}</td>
687 * <tr><th scope="row">{@code Maximum Subnormal Value}</th>
688 * <td>{@code 0x0.fffffffffffffp-1022}</td>
689 * <tr><th scope="row">{@code Double.MIN_VALUE}</th>
690 * <td>{@code 0x0.0000000000001p-1022}</td>
691 * </tbody>
692 * </table>
693 *
694 * @apiNote
695 * This method corresponds to the convertToHexCharacter operation
696 * defined in IEEE 754.
697 *
698 * @param d the {@code double} to be converted.
699 * @return a hex string representation of the argument.
700 * @since 1.5
701 * @author Joseph D. Darcy
702 */
703 public static String toHexString(double d) {
704 /*
705 * Modeled after the "a" conversion specifier in C99, section
706 * 7.19.6.1; however, the output of this method is more
707 * tightly specified.
708 */
709 if (!isFinite(d) )
710 // For infinity and NaN, use the decimal output.
711 return Double.toString(d);
712 else {
713 // Initialized to maximum size of output.
714 StringBuilder answer = new StringBuilder(24);
715
716 if (Math.copySign(1.0, d) == -1.0) // value is negative,
717 answer.append("-"); // so append sign info
718
719 answer.append("0x");
720
721 d = Math.abs(d);
722
723 if(d == 0.0) {
724 answer.append("0.0p0");
725 } else {
726 boolean subnormal = (d < Double.MIN_NORMAL);
727
728 // Isolate significand bits and OR in a high-order bit
729 // so that the string representation has a known
730 // length.
731 long signifBits = (Double.doubleToLongBits(d)
732 & DoubleConsts.SIGNIF_BIT_MASK) |
733 0x1000000000000000L;
734
735 // Subnormal values have a 0 implicit bit; normal
736 // values have a 1 implicit bit.
737 answer.append(subnormal ? "0." : "1.");
738
739 // Isolate the low-order 13 digits of the hex
740 // representation. If all the digits are zero,
741 // replace with a single 0; otherwise, remove all
742 // trailing zeros.
743 String signif = Long.toHexString(signifBits).substring(3,16);
744 answer.append(signif.equals("0000000000000") ? // 13 zeros
745 "0":
746 signif.replaceFirst("0{1,12}$", ""));
747
748 answer.append('p');
749 // If the value is subnormal, use the E_min exponent
750 // value for double; otherwise, extract and report d's
751 // exponent (the representation of a subnormal uses
752 // E_min -1).
753 answer.append(subnormal ?
754 Double.MIN_EXPONENT:
755 Math.getExponent(d));
756 }
757 return answer.toString();
758 }
759 }
760
761 /**
762 * Returns a {@code Double} object holding the
763 * {@code double} value represented by the argument string
764 * {@code s}.
765 *
766 * <p>If {@code s} is {@code null}, then a
767 * {@code NullPointerException} is thrown.
768 *
769 * <p>Leading and trailing whitespace characters in {@code s}
770 * are ignored. Whitespace is removed as if by the {@link
771 * String#trim} method; that is, both ASCII space and control
772 * characters are removed. The rest of {@code s} should
773 * constitute a <i>FloatValue</i> as described by the lexical
774 * syntax rules:
775 *
776 * <blockquote>
777 * <dl>
778 * <dt><i>FloatValue:</i>
779 * <dd><i>Sign<sub>opt</sub></i> {@code NaN}
780 * <dd><i>Sign<sub>opt</sub></i> {@code Infinity}
781 * <dd><i>Sign<sub>opt</sub> FloatingPointLiteral</i>
782 * <dd><i>Sign<sub>opt</sub> HexFloatingPointLiteral</i>
783 * <dd><i>SignedInteger</i>
784 * </dl>
785 *
786 * <dl>
787 * <dt><i>HexFloatingPointLiteral</i>:
788 * <dd> <i>HexSignificand BinaryExponent FloatTypeSuffix<sub>opt</sub></i>
789 * </dl>
790 *
791 * <dl>
792 * <dt><i>HexSignificand:</i>
793 * <dd><i>HexNumeral</i>
794 * <dd><i>HexNumeral</i> {@code .}
795 * <dd>{@code 0x} <i>HexDigits<sub>opt</sub>
796 * </i>{@code .}<i> HexDigits</i>
797 * <dd>{@code 0X}<i> HexDigits<sub>opt</sub>
798 * </i>{@code .} <i>HexDigits</i>
799 * </dl>
800 *
801 * <dl>
802 * <dt><i>BinaryExponent:</i>
803 * <dd><i>BinaryExponentIndicator SignedInteger</i>
804 * </dl>
805 *
806 * <dl>
807 * <dt><i>BinaryExponentIndicator:</i>
808 * <dd>{@code p}
809 * <dd>{@code P}
810 * </dl>
811 *
812 * </blockquote>
813 *
814 * where <i>Sign</i>, <i>FloatingPointLiteral</i>,
815 * <i>HexNumeral</i>, <i>HexDigits</i>, <i>SignedInteger</i> and
816 * <i>FloatTypeSuffix</i> are as defined in the lexical structure
817 * sections of
818 * <cite>The Java Language Specification</cite>,
819 * except that underscores are not accepted between digits.
820 * If {@code s} does not have the form of
821 * a <i>FloatValue</i>, then a {@code NumberFormatException}
822 * is thrown. Otherwise, {@code s} is regarded as
823 * representing an exact decimal value in the usual
824 * "computerized scientific notation" or as an exact
825 * hexadecimal value; this exact numerical value is then
826 * conceptually converted to an "infinitely precise"
827 * binary value that is then rounded to type {@code double}
828 * by the usual round-to-nearest rule of IEEE 754 floating-point
829 * arithmetic, which includes preserving the sign of a zero
830 * value.
831 *
832 * Note that the round-to-nearest rule also implies overflow and
833 * underflow behaviour; if the exact value of {@code s} is large
834 * enough in magnitude (greater than or equal to ({@link
835 * #MAX_VALUE} + {@link Math#ulp(double) ulp(MAX_VALUE)}/2),
836 * rounding to {@code double} will result in an infinity and if the
837 * exact value of {@code s} is small enough in magnitude (less
838 * than or equal to {@link #MIN_VALUE}/2), rounding to float will
839 * result in a zero.
840 *
841 * Finally, after rounding a {@code Double} object representing
842 * this {@code double} value is returned.
843 *
844 * <p>Note that trailing format specifiers, specifiers that
845 * determine the type of a floating-point literal
846 * ({@code 1.0f} is a {@code float} value;
847 * {@code 1.0d} is a {@code double} value), do
848 * <em>not</em> influence the results of this method. In other
849 * words, the numerical value of the input string is converted
850 * directly to the target floating-point type. The two-step
851 * sequence of conversions, string to {@code float} followed
852 * by {@code float} to {@code double}, is <em>not</em>
853 * equivalent to converting a string directly to
854 * {@code double}. For example, the {@code float}
855 * literal {@code 0.1f} is equal to the {@code double}
856 * value {@code 0.10000000149011612}; the {@code float}
857 * literal {@code 0.1f} represents a different numerical
858 * value than the {@code double} literal
859 * {@code 0.1}. (The numerical value 0.1 cannot be exactly
860 * represented in a binary floating-point number.)
861 *
862 * <p>To avoid calling this method on an invalid string and having
863 * a {@code NumberFormatException} be thrown, the regular
864 * expression below can be used to screen the input string:
865 *
866 * {@snippet lang="java" :
867 * final String Digits = "(\\p{Digit}+)";
868 * final String HexDigits = "(\\p{XDigit}+)";
869 * // an exponent is 'e' or 'E' followed by an optionally
870 * // signed decimal integer.
871 * final String Exp = "[eE][+-]?"+Digits;
872 * final String fpRegex =
873 * ("[\\x00-\\x20]*"+ // Optional leading "whitespace"
874 * "[+-]?(" + // Optional sign character
875 * "NaN|" + // "NaN" string
876 * "Infinity|" + // "Infinity" string
877 *
878 * // A decimal floating-point string representing a finite positive
879 * // number without a leading sign has at most five basic pieces:
880 * // Digits . Digits ExponentPart FloatTypeSuffix
881 * //
882 * // Since this method allows integer-only strings as input
883 * // in addition to strings of floating-point literals, the
884 * // two sub-patterns below are simplifications of the grammar
885 * // productions from section 3.10.2 of
886 * // The Java Language Specification.
887 *
888 * // Digits ._opt Digits_opt ExponentPart_opt FloatTypeSuffix_opt
889 * "((("+Digits+"(\\.)?("+Digits+"?)("+Exp+")?)|"+
890 *
891 * // . Digits ExponentPart_opt FloatTypeSuffix_opt
892 * "(\\.("+Digits+")("+Exp+")?)|"+
893 *
894 * // Hexadecimal strings
895 * "((" +
896 * // 0[xX] HexDigits ._opt BinaryExponent FloatTypeSuffix_opt
897 * "(0[xX]" + HexDigits + "(\\.)?)|" +
898 *
899 * // 0[xX] HexDigits_opt . HexDigits BinaryExponent FloatTypeSuffix_opt
900 * "(0[xX]" + HexDigits + "?(\\.)" + HexDigits + ")" +
901 *
902 * ")[pP][+-]?" + Digits + "))" +
903 * "[fFdD]?))" +
904 * "[\\x00-\\x20]*");// Optional trailing "whitespace"
905 * // @link region substring="Pattern.matches" target ="java.util.regex.Pattern#matches"
906 * if (Pattern.matches(fpRegex, myString))
907 * Double.valueOf(myString); // Will not throw NumberFormatException
908 * // @end
909 * else {
910 * // Perform suitable alternative action
911 * }
912 * }
913 *
914 * @apiNote To interpret localized string representations of a
915 * floating-point value, or string representations that have
916 * non-ASCII digits, use {@link java.text.NumberFormat}. For
917 * example,
918 * {@snippet lang="java" :
919 * NumberFormat.getInstance(l).parse(s).doubleValue();
920 * }
921 * where {@code l} is the desired locale, or
922 * {@link java.util.Locale#ROOT} if locale insensitive.
923 *
924 * @apiNote
925 * This method corresponds to the convertFromDecimalCharacter and
926 * convertFromHexCharacter operations defined in IEEE 754.
927 *
928 * @param s the string to be parsed.
929 * @return a {@code Double} object holding the value
930 * represented by the {@code String} argument.
931 * @throws NumberFormatException if the string does not contain a
932 * parsable number.
933 * @see Double##decimalToBinaryConversion Decimal ↔ Binary Conversion Issues
934 */
935 public static Double valueOf(String s) throws NumberFormatException {
936 return new Double(parseDouble(s));
937 }
938
939 /**
940 * Returns a {@code Double} instance representing the specified
941 * {@code double} value.
942 * If a new {@code Double} instance is not required, this method
943 * should generally be used in preference to the constructor
944 * {@link #Double(double)}, as this method is likely to yield
945 * significantly better space and time performance by caching
946 * frequently requested values.
947 *
948 * @param d a double value.
949 * @return a {@code Double} instance representing {@code d}.
950 * @since 1.5
951 */
952 @IntrinsicCandidate
953 @DeserializeConstructor
954 public static Double valueOf(double d) {
955 return new Double(d);
956 }
957
958 /**
959 * Returns a new {@code double} initialized to the value
960 * represented by the specified {@code String}, as performed
961 * by the {@code valueOf} method of class
962 * {@code Double}.
963 *
964 * @param s the string to be parsed.
965 * @return the {@code double} value represented by the string
966 * argument.
967 * @throws NullPointerException if the string is null
968 * @throws NumberFormatException if the string does not contain
969 * a parsable {@code double}.
970 * @see java.lang.Double#valueOf(String)
971 * @see Double##decimalToBinaryConversion Decimal ↔ Binary Conversion Issues
972 * @since 1.2
973 */
974 public static double parseDouble(String s) throws NumberFormatException {
975 return FloatingDecimal.parseDouble(s);
976 }
977
978 /**
979 * Returns {@code true} if the specified number is a
980 * Not-a-Number (NaN) value, {@code false} otherwise.
981 *
982 * @apiNote
983 * This method corresponds to the isNaN operation defined in IEEE
984 * 754.
985 *
986 * @param v the value to be tested.
987 * @return {@code true} if the value of the argument is NaN;
988 * {@code false} otherwise.
989 */
990 public static boolean isNaN(double v) {
991 return (v != v);
992 }
993
994 /**
995 * Returns {@code true} if the specified number is infinitely
996 * large in magnitude, {@code false} otherwise.
997 *
998 * @apiNote
999 * This method corresponds to the isInfinite operation defined in
1000 * IEEE 754.
1001 *
1002 * @param v the value to be tested.
1003 * @return {@code true} if the value of the argument is positive
1004 * infinity or negative infinity; {@code false} otherwise.
1005 */
1006 @IntrinsicCandidate
1007 public static boolean isInfinite(double v) {
1008 return Math.abs(v) > MAX_VALUE;
1009 }
1010
1011 /**
1012 * Returns {@code true} if the argument is a finite floating-point
1013 * value; returns {@code false} otherwise (for NaN and infinity
1014 * arguments).
1015 *
1016 * @apiNote
1017 * This method corresponds to the isFinite operation defined in
1018 * IEEE 754.
1019 *
1020 * @param d the {@code double} value to be tested
1021 * @return {@code true} if the argument is a finite
1022 * floating-point value, {@code false} otherwise.
1023 * @since 1.8
1024 */
1025 @IntrinsicCandidate
1026 public static boolean isFinite(double d) {
1027 return Math.abs(d) <= Double.MAX_VALUE;
1028 }
1029
1030 /**
1031 * The value of the Double.
1032 *
1033 * @serial
1034 */
1035 private final double value;
1036
1037 /**
1038 * Constructs a newly allocated {@code Double} object that
1039 * represents the primitive {@code double} argument.
1040 *
1041 * @param value the value to be represented by the {@code Double}.
1042 *
1043 * @deprecated
1044 * It is rarely appropriate to use this constructor. The static factory
1045 * {@link #valueOf(double)} is generally a better choice, as it is
1046 * likely to yield significantly better space and time performance.
1047 */
1048 @Deprecated(since="9", forRemoval = true)
1049 public Double(double value) {
1050 this.value = value;
1051 }
1052
1053 /**
1054 * Constructs a newly allocated {@code Double} object that
1055 * represents the floating-point value of type {@code double}
1056 * represented by the string. The string is converted to a
1057 * {@code double} value as if by the {@code valueOf} method.
1058 *
1059 * @param s a string to be converted to a {@code Double}.
1060 * @throws NumberFormatException if the string does not contain a
1061 * parsable number.
1062 *
1063 * @deprecated
1064 * It is rarely appropriate to use this constructor.
1065 * Use {@link #parseDouble(String)} to convert a string to a
1066 * {@code double} primitive, or use {@link #valueOf(String)}
1067 * to convert a string to a {@code Double} object.
1068 */
1069 @Deprecated(since="9", forRemoval = true)
1070 public Double(String s) throws NumberFormatException {
1071 value = parseDouble(s);
1072 }
1073
1074 /**
1075 * Returns {@code true} if this {@code Double} value is
1076 * a Not-a-Number (NaN), {@code false} otherwise.
1077 *
1078 * @return {@code true} if the value represented by this object is
1079 * NaN; {@code false} otherwise.
1080 */
1081 public boolean isNaN() {
1082 return isNaN(value);
1083 }
1084
1085 /**
1086 * Returns {@code true} if this {@code Double} value is
1087 * infinitely large in magnitude, {@code false} otherwise.
1088 *
1089 * @return {@code true} if the value represented by this object is
1090 * positive infinity or negative infinity;
1091 * {@code false} otherwise.
1092 */
1093 public boolean isInfinite() {
1094 return isInfinite(value);
1095 }
1096
1097 /**
1098 * Returns a string representation of this {@code Double} object.
1099 * The primitive {@code double} value represented by this
1100 * object is converted to a string exactly as if by the method
1101 * {@code toString} of one argument.
1102 *
1103 * @return a {@code String} representation of this object.
1104 * @see java.lang.Double#toString(double)
1105 */
1106 public String toString() {
1107 return toString(value);
1108 }
1109
1110 /**
1111 * Returns the value of this {@code Double} as a {@code byte}
1112 * after a narrowing primitive conversion.
1113 *
1114 * @return the {@code double} value represented by this object
1115 * converted to type {@code byte}
1116 * @jls 5.1.3 Narrowing Primitive Conversion
1117 * @since 1.1
1118 */
1119 @Override
1120 public byte byteValue() {
1121 return (byte)value;
1122 }
1123
1124 /**
1125 * Returns the value of this {@code Double} as a {@code short}
1126 * after a narrowing primitive conversion.
1127 *
1128 * @return the {@code double} value represented by this object
1129 * converted to type {@code short}
1130 * @jls 5.1.3 Narrowing Primitive Conversion
1131 * @since 1.1
1132 */
1133 @Override
1134 public short shortValue() {
1135 return (short)value;
1136 }
1137
1138 /**
1139 * Returns the value of this {@code Double} as an {@code int}
1140 * after a narrowing primitive conversion.
1141 * @jls 5.1.3 Narrowing Primitive Conversion
1142 *
1143 * @apiNote
1144 * This method corresponds to the convertToIntegerTowardZero
1145 * operation defined in IEEE 754.
1146 *
1147 * @return the {@code double} value represented by this object
1148 * converted to type {@code int}
1149 */
1150 @Override
1151 public int intValue() {
1152 return (int)value;
1153 }
1154
1155 /**
1156 * Returns the value of this {@code Double} as a {@code long}
1157 * after a narrowing primitive conversion.
1158 *
1159 * @apiNote
1160 * This method corresponds to the convertToIntegerTowardZero
1161 * operation defined in IEEE 754.
1162 *
1163 * @return the {@code double} value represented by this object
1164 * converted to type {@code long}
1165 * @jls 5.1.3 Narrowing Primitive Conversion
1166 */
1167 @Override
1168 public long longValue() {
1169 return (long)value;
1170 }
1171
1172 /**
1173 * Returns the value of this {@code Double} as a {@code float}
1174 * after a narrowing primitive conversion.
1175 *
1176 * @apiNote
1177 * This method corresponds to the convertFormat operation defined
1178 * in IEEE 754.
1179 *
1180 * @return the {@code double} value represented by this object
1181 * converted to type {@code float}
1182 * @jls 5.1.3 Narrowing Primitive Conversion
1183 * @since 1.0
1184 */
1185 @Override
1186 public float floatValue() {
1187 return (float)value;
1188 }
1189
1190 /**
1191 * Returns the {@code double} value of this {@code Double} object.
1192 *
1193 * @return the {@code double} value represented by this object
1194 */
1195 @Override
1196 @IntrinsicCandidate
1197 public double doubleValue() {
1198 return value;
1199 }
1200
1201 /**
1202 * Returns a hash code for this {@code Double} object. The
1203 * result is the exclusive OR of the two halves of the
1204 * {@code long} integer bit representation, exactly as
1205 * produced by the method {@link #doubleToLongBits(double)}, of
1206 * the primitive {@code double} value represented by this
1207 * {@code Double} object. That is, the hash code is the value
1208 * of the expression:
1209 *
1210 * <blockquote>
1211 * {@code (int)(v^(v>>>32))}
1212 * </blockquote>
1213 *
1214 * where {@code v} is defined by:
1215 *
1216 * <blockquote>
1217 * {@code long v = Double.doubleToLongBits(this.doubleValue());}
1218 * </blockquote>
1219 *
1220 * @return a {@code hash code} value for this object.
1221 */
1222 @Override
1223 public int hashCode() {
1224 return Double.hashCode(value);
1225 }
1226
1227 /**
1228 * Returns a hash code for a {@code double} value; compatible with
1229 * {@code Double.hashCode()}.
1230 *
1231 * @param value the value to hash
1232 * @return a hash code value for a {@code double} value.
1233 * @since 1.8
1234 */
1235 public static int hashCode(double value) {
1236 return Long.hashCode(doubleToLongBits(value));
1237 }
1238
1239 /**
1240 * Compares this object against the specified object. The result
1241 * is {@code true} if and only if the argument is not
1242 * {@code null} and is a {@code Double} object that
1243 * represents a {@code double} that has the same value as the
1244 * {@code double} represented by this object. For this
1245 * purpose, two {@code double} values are considered to be
1246 * the same if and only if the method {@link
1247 * #doubleToLongBits(double)} returns the identical
1248 * {@code long} value when applied to each.
1249 *
1250 * @apiNote
1251 * This method is defined in terms of {@link
1252 * #doubleToLongBits(double)} rather than the {@code ==} operator
1253 * on {@code double} values since the {@code ==} operator does
1254 * <em>not</em> define an equivalence relation and to satisfy the
1255 * {@linkplain Object#equals equals contract} an equivalence
1256 * relation must be implemented; see {@linkplain ##equivalenceRelation
1257 * this discussion for details of floating-point equality and equivalence}.
1258 *
1259 * @see java.lang.Double#doubleToLongBits(double)
1260 * @jls 15.21.1 Numerical Equality Operators == and !=
1261 */
1262 public boolean equals(Object obj) {
1263 return (obj instanceof Double)
1264 && (doubleToLongBits(((Double)obj).value) ==
1265 doubleToLongBits(value));
1266 }
1267
1268 /**
1269 * Returns a representation of the specified floating-point value
1270 * according to the IEEE 754 floating-point "double
1271 * format" bit layout.
1272 *
1273 * <p>Bit 63 (the bit that is selected by the mask
1274 * {@code 0x8000000000000000L}) represents the sign of the
1275 * floating-point number. Bits
1276 * 62-52 (the bits that are selected by the mask
1277 * {@code 0x7ff0000000000000L}) represent the exponent. Bits 51-0
1278 * (the bits that are selected by the mask
1279 * {@code 0x000fffffffffffffL}) represent the significand
1280 * (sometimes called the mantissa) of the floating-point number.
1281 *
1282 * <p>If the argument is positive infinity, the result is
1283 * {@code 0x7ff0000000000000L}.
1284 *
1285 * <p>If the argument is negative infinity, the result is
1286 * {@code 0xfff0000000000000L}.
1287 *
1288 * <p>If the argument is NaN, the result is
1289 * {@code 0x7ff8000000000000L}.
1290 *
1291 * <p>In all cases, the result is a {@code long} integer that, when
1292 * given to the {@link #longBitsToDouble(long)} method, will produce a
1293 * floating-point value the same as the argument to
1294 * {@code doubleToLongBits} (except all NaN values are
1295 * collapsed to a single "canonical" NaN value).
1296 *
1297 * @param value a {@code double} precision floating-point number.
1298 * @return the bits that represent the floating-point number.
1299 */
1300 @IntrinsicCandidate
1301 public static long doubleToLongBits(double value) {
1302 if (!isNaN(value)) {
1303 return doubleToRawLongBits(value);
1304 }
1305 return 0x7ff8000000000000L;
1306 }
1307
1308 /**
1309 * Returns a representation of the specified floating-point value
1310 * according to the IEEE 754 floating-point "double
1311 * format" bit layout, preserving Not-a-Number (NaN) values.
1312 *
1313 * <p>Bit 63 (the bit that is selected by the mask
1314 * {@code 0x8000000000000000L}) represents the sign of the
1315 * floating-point number. Bits
1316 * 62-52 (the bits that are selected by the mask
1317 * {@code 0x7ff0000000000000L}) represent the exponent. Bits 51-0
1318 * (the bits that are selected by the mask
1319 * {@code 0x000fffffffffffffL}) represent the significand
1320 * (sometimes called the mantissa) of the floating-point number.
1321 *
1322 * <p>If the argument is positive infinity, the result is
1323 * {@code 0x7ff0000000000000L}.
1324 *
1325 * <p>If the argument is negative infinity, the result is
1326 * {@code 0xfff0000000000000L}.
1327 *
1328 * <p>If the argument is NaN, the result is the {@code long}
1329 * integer representing the actual NaN value. Unlike the
1330 * {@code doubleToLongBits} method,
1331 * {@code doubleToRawLongBits} does not collapse all the bit
1332 * patterns encoding a NaN to a single "canonical" NaN
1333 * value.
1334 *
1335 * <p>In all cases, the result is a {@code long} integer that,
1336 * when given to the {@link #longBitsToDouble(long)} method, will
1337 * produce a floating-point value the same as the argument to
1338 * {@code doubleToRawLongBits}.
1339 *
1340 * @param value a {@code double} precision floating-point number.
1341 * @return the bits that represent the floating-point number.
1342 * @since 1.3
1343 */
1344 @IntrinsicCandidate
1345 public static native long doubleToRawLongBits(double value);
1346
1347 /**
1348 * Returns the {@code double} value corresponding to a given
1349 * bit representation.
1350 * The argument is considered to be a representation of a
1351 * floating-point value according to the IEEE 754 floating-point
1352 * "double format" bit layout.
1353 *
1354 * <p>If the argument is {@code 0x7ff0000000000000L}, the result
1355 * is positive infinity.
1356 *
1357 * <p>If the argument is {@code 0xfff0000000000000L}, the result
1358 * is negative infinity.
1359 *
1360 * <p>If the argument is any value in the range
1361 * {@code 0x7ff0000000000001L} through
1362 * {@code 0x7fffffffffffffffL} or in the range
1363 * {@code 0xfff0000000000001L} through
1364 * {@code 0xffffffffffffffffL}, the result is a NaN. No IEEE
1365 * 754 floating-point operation provided by Java can distinguish
1366 * between two NaN values of the same type with different bit
1367 * patterns. Distinct values of NaN are only distinguishable by
1368 * use of the {@code Double.doubleToRawLongBits} method.
1369 *
1370 * <p>In all other cases, let <i>s</i>, <i>e</i>, and <i>m</i> be three
1371 * values that can be computed from the argument:
1372 *
1373 * {@snippet lang="java" :
1374 * int s = ((bits >> 63) == 0) ? 1 : -1;
1375 * int e = (int)((bits >> 52) & 0x7ffL);
1376 * long m = (e == 0) ?
1377 * (bits & 0xfffffffffffffL) << 1 :
1378 * (bits & 0xfffffffffffffL) | 0x10000000000000L;
1379 * }
1380 *
1381 * Then the floating-point result equals the value of the mathematical
1382 * expression <i>s</i>·<i>m</i>·2<sup><i>e</i>-1075</sup>.
1383 *
1384 * <p>Note that this method may not be able to return a
1385 * {@code double} NaN with exactly same bit pattern as the
1386 * {@code long} argument. IEEE 754 distinguishes between two
1387 * kinds of NaNs, quiet NaNs and <i>signaling NaNs</i>. The
1388 * differences between the two kinds of NaN are generally not
1389 * visible in Java. Arithmetic operations on signaling NaNs turn
1390 * them into quiet NaNs with a different, but often similar, bit
1391 * pattern. However, on some processors merely copying a
1392 * signaling NaN also performs that conversion. In particular,
1393 * copying a signaling NaN to return it to the calling method
1394 * may perform this conversion. So {@code longBitsToDouble}
1395 * may not be able to return a {@code double} with a
1396 * signaling NaN bit pattern. Consequently, for some
1397 * {@code long} values,
1398 * {@code doubleToRawLongBits(longBitsToDouble(start))} may
1399 * <i>not</i> equal {@code start}. Moreover, which
1400 * particular bit patterns represent signaling NaNs is platform
1401 * dependent; although all NaN bit patterns, quiet or signaling,
1402 * must be in the NaN range identified above.
1403 *
1404 * @param bits any {@code long} integer.
1405 * @return the {@code double} floating-point value with the same
1406 * bit pattern.
1407 */
1408 @IntrinsicCandidate
1409 public static native double longBitsToDouble(long bits);
1410
1411 /**
1412 * Compares two {@code Double} objects numerically.
1413 *
1414 * This method imposes a total order on {@code Double} objects
1415 * with two differences compared to the incomplete order defined by
1416 * the Java language numerical comparison operators ({@code <, <=,
1417 * ==, >=, >}) on {@code double} values.
1418 *
1419 * <ul><li> A NaN is <em>unordered</em> with respect to other
1420 * values and unequal to itself under the comparison
1421 * operators. This method chooses to define {@code
1422 * Double.NaN} to be equal to itself and greater than all
1423 * other {@code double} values (including {@code
1424 * Double.POSITIVE_INFINITY}).
1425 *
1426 * <li> Positive zero and negative zero compare equal
1427 * numerically, but are distinct and distinguishable values.
1428 * This method chooses to define positive zero ({@code +0.0d}),
1429 * to be greater than negative zero ({@code -0.0d}).
1430 * </ul>
1431
1432 * This ensures that the <i>natural ordering</i> of {@code Double}
1433 * objects imposed by this method is <i>consistent with
1434 * equals</i>; see {@linkplain ##equivalenceRelation this
1435 * discussion for details of floating-point comparison and
1436 * ordering}.
1437 *
1438 * @param anotherDouble the {@code Double} to be compared.
1439 * @return the value {@code 0} if {@code anotherDouble} is
1440 * numerically equal to this {@code Double}; a value
1441 * less than {@code 0} if this {@code Double}
1442 * is numerically less than {@code anotherDouble};
1443 * and a value greater than {@code 0} if this
1444 * {@code Double} is numerically greater than
1445 * {@code anotherDouble}.
1446 *
1447 * @jls 15.20.1 Numerical Comparison Operators {@code <}, {@code <=}, {@code >}, and {@code >=}
1448 * @since 1.2
1449 */
1450 @Override
1451 public int compareTo(Double anotherDouble) {
1452 return Double.compare(value, anotherDouble.value);
1453 }
1454
1455 /**
1456 * Compares the two specified {@code double} values. The sign
1457 * of the integer value returned is the same as that of the
1458 * integer that would be returned by the call:
1459 * <pre>
1460 * Double.valueOf(d1).compareTo(Double.valueOf(d2))
1461 * </pre>
1462 *
1463 * @param d1 the first {@code double} to compare
1464 * @param d2 the second {@code double} to compare
1465 * @return the value {@code 0} if {@code d1} is
1466 * numerically equal to {@code d2}; a value less than
1467 * {@code 0} if {@code d1} is numerically less than
1468 * {@code d2}; and a value greater than {@code 0}
1469 * if {@code d1} is numerically greater than
1470 * {@code d2}.
1471 * @since 1.4
1472 */
1473 public static int compare(double d1, double d2) {
1474 if (d1 < d2)
1475 return -1; // Neither val is NaN, thisVal is smaller
1476 if (d1 > d2)
1477 return 1; // Neither val is NaN, thisVal is larger
1478
1479 // Cannot use doubleToRawLongBits because of possibility of NaNs.
1480 long thisBits = Double.doubleToLongBits(d1);
1481 long anotherBits = Double.doubleToLongBits(d2);
1482
1483 return (thisBits == anotherBits ? 0 : // Values are equal
1484 (thisBits < anotherBits ? -1 : // (-0.0, 0.0) or (!NaN, NaN)
1485 1)); // (0.0, -0.0) or (NaN, !NaN)
1486 }
1487
1488 /**
1489 * Adds two {@code double} values together as per the + operator.
1490 *
1491 * @apiNote This method corresponds to the addition operation
1492 * defined in IEEE 754.
1493 *
1494 * @param a the first operand
1495 * @param b the second operand
1496 * @return the sum of {@code a} and {@code b}
1497 * @jls 4.2.4 Floating-Point Operations
1498 * @see java.util.function.BinaryOperator
1499 * @since 1.8
1500 */
1501 public static double sum(double a, double b) {
1502 return a + b;
1503 }
1504
1505 /**
1506 * Returns the greater of two {@code double} values
1507 * as if by calling {@link Math#max(double, double) Math.max}.
1508 *
1509 * @apiNote
1510 * This method corresponds to the maximum operation defined in
1511 * IEEE 754.
1512 *
1513 * @param a the first operand
1514 * @param b the second operand
1515 * @return the greater of {@code a} and {@code b}
1516 * @see java.util.function.BinaryOperator
1517 * @since 1.8
1518 */
1519 public static double max(double a, double b) {
1520 return Math.max(a, b);
1521 }
1522
1523 /**
1524 * Returns the smaller of two {@code double} values
1525 * as if by calling {@link Math#min(double, double) Math.min}.
1526 *
1527 * @apiNote
1528 * This method corresponds to the minimum operation defined in
1529 * IEEE 754.
1530 *
1531 * @param a the first operand
1532 * @param b the second operand
1533 * @return the smaller of {@code a} and {@code b}.
1534 * @see java.util.function.BinaryOperator
1535 * @since 1.8
1536 */
1537 public static double min(double a, double b) {
1538 return Math.min(a, b);
1539 }
1540
1541 /**
1542 * Returns an {@link Optional} containing the nominal descriptor for this
1543 * instance, which is the instance itself.
1544 *
1545 * @return an {@link Optional} describing the {@linkplain Double} instance
1546 * @since 12
1547 */
1548 @Override
1549 public Optional<Double> describeConstable() {
1550 return Optional.of(this);
1551 }
1552
1553 /**
1554 * Resolves this instance as a {@link ConstantDesc}, the result of which is
1555 * the instance itself.
1556 *
1557 * @param lookup ignored
1558 * @return the {@linkplain Double} instance
1559 * @since 12
1560 */
1561 @Override
1562 public Double resolveConstantDesc(MethodHandles.Lookup lookup) {
1563 return this;
1564 }
1565
1566 /** use serialVersionUID from JDK 1.0.2 for interoperability */
1567 @java.io.Serial
1568 private static final long serialVersionUID = -9172774392245257468L;
1569 }