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