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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14 * version 2 for more details (a copy is included in the LICENSE file that
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 is the {@linkplain
41 * java.lang##wrapperClass wrapper class} for values of the primitive
42 * type {@code double}. An object of type {@code Double} contains a
43 * single field whose type is {@code double}.
44 *
45 * <p>In addition, this class provides several methods for converting a
46 * {@code double} to a {@code String} and a
47 * {@code String} to a {@code double}, as well as other
48 * constants and methods useful when dealing with a
49 * {@code double}.
50 *
51 * <p>This is a <a href="{@docRoot}/java.base/java/lang/doc-files/ValueBased.html">value-based</a>
52 * class; programmers should treat instances that are
53 * {@linkplain #equals(Object) equal} as interchangeable and should not
54 * use instances for synchronization, or unpredictable behavior may
55 * occur. For example, in a future release, synchronization may fail.
56 *
57 * <h2><a id=equivalenceRelation>Floating-point Equality, Equivalence,
58 * and Comparison</a></h2>
59 *
60 * IEEE 754 floating-point values include finite nonzero values,
61 * signed zeros ({@code +0.0} and {@code -0.0}), signed infinities
62 * ({@linkplain Double#POSITIVE_INFINITY positive infinity} and
63 * {@linkplain Double#NEGATIVE_INFINITY negative infinity}), and
64 * {@linkplain Double#NaN NaN} (not-a-number).
65 *
66 * <p>An <em>equivalence relation</em> on a set of values is a boolean
67 * relation on pairs of values that is reflexive, symmetric, and
68 * transitive. For more discussion of equivalence relations and object
69 * equality, see the {@link Object#equals Object.equals}
70 * specification. An equivalence relation partitions the values it
71 * operates over into sets called <i>equivalence classes</i>. All the
72 * members of the equivalence class are equal to each other under the
73 * relation. An equivalence class may contain only a single member. At
74 * least for some purposes, all the members of an equivalence class
75 * are substitutable for each other. In particular, in a numeric
76 * expression equivalent values can be <em>substituted</em> for one
77 * another without changing the result of the expression, meaning
78 * changing the equivalence class of the result of the expression.
79 *
80 * <p>Notably, the built-in {@code ==} operation on floating-point
81 * values is <em>not</em> an equivalence relation. Despite not
82 * defining an equivalence relation, the semantics of the IEEE 754
83 * {@code ==} operator were deliberately designed to meet other needs
84 * of numerical computation. There are two exceptions where the
85 * properties of an equivalence relation are not satisfied by {@code
86 * ==} on floating-point values:
87 *
88 * <ul>
89 *
90 * <li>If {@code v1} and {@code v2} are both NaN, then {@code v1
91 * == v2} has the value {@code false}. Therefore, for two NaN
92 * arguments the <em>reflexive</em> property of an equivalence
93 * relation is <em>not</em> satisfied by the {@code ==} operator.
94 *
95 * <li>If {@code v1} represents {@code +0.0} while {@code v2}
96 * represents {@code -0.0}, or vice versa, then {@code v1 == v2} has
97 * the value {@code true} even though {@code +0.0} and {@code -0.0}
98 * are distinguishable under various floating-point operations. For
99 * example, {@code 1.0/+0.0} evaluates to positive infinity while
100 * {@code 1.0/-0.0} evaluates to <em>negative</em> infinity and
101 * positive infinity and negative infinity are neither equal to each
102 * other nor equivalent to each other. Thus, while a signed zero input
103 * most commonly determines the sign of a zero result, because of
104 * dividing by zero, {@code +0.0} and {@code -0.0} may not be
105 * substituted for each other in general. The sign of a zero input
106 * also has a non-substitutable effect on the result of some math
107 * library methods.
108 *
109 * </ul>
110 *
111 * <p>For ordered comparisons using the built-in comparison operators
112 * ({@code <}, {@code <=}, etc.), NaN values have another anomalous
113 * situation: a NaN is neither less than, nor greater than, nor equal
114 * to any value, including itself. This means the <i>trichotomy of
115 * comparison</i> does <em>not</em> hold.
116 *
117 * <p>To provide the appropriate semantics for {@code equals} and
118 * {@code compareTo} methods, those methods cannot simply be wrappers
119 * around {@code ==} or ordered comparison operations. Instead, {@link
120 * Double#equals equals} uses {@linkplain ##repEquivalence representation
121 * equivalence}, defining NaN arguments to be equal to each other,
122 * restoring reflexivity, and defining {@code +0.0} to <em>not</em> be
123 * equal to {@code -0.0}. For comparisons, {@link Double#compareTo
124 * compareTo} defines a total order where {@code -0.0} is less than
125 * {@code +0.0} and where a NaN is equal to itself and considered
126 * greater than positive infinity.
127 *
128 * <p>The operational semantics of {@code equals} and {@code
129 * compareTo} are expressed in terms of {@linkplain #doubleToLongBits
130 * bit-wise converting} the floating-point values to integral values.
131 *
132 * <p>The <em>natural ordering</em> implemented by {@link #compareTo
133 * compareTo} is {@linkplain Comparable consistent with equals}. That
134 * is, two objects are reported as equal by {@code equals} if and only
135 * if {@code compareTo} on those objects returns zero.
136 *
137 * <p>The adjusted behaviors defined for {@code equals} and {@code
138 * compareTo} allow instances of wrapper classes to work properly with
139 * conventional data structures. For example, defining NaN
140 * values to be {@code equals} to one another allows NaN to be used as
141 * an element of a {@link java.util.HashSet HashSet} or as the key of
142 * a {@link java.util.HashMap HashMap}. Similarly, defining {@code
143 * compareTo} as a total ordering, including {@code +0.0}, {@code
144 * -0.0}, and NaN, allows instances of wrapper classes to be used as
145 * elements of a {@link java.util.SortedSet SortedSet} or as keys of a
146 * {@link java.util.SortedMap SortedMap}.
147 *
148 * <p>Comparing numerical equality to various useful equivalence
149 * relations that can be defined over floating-point values:
150 *
151 * <dl>
152 * <dt><a id=fpNumericalEq></a><dfn>{@index "numerical equality"}</dfn> ({@code ==}
153 * operator): (<em>Not</em> an equivalence relation)</dt>
154 * <dd>Two floating-point values represent the same extended real
155 * number. The extended real numbers are the real numbers augmented
156 * with positive infinity and negative infinity. Under numerical
157 * equality, {@code +0.0} and {@code -0.0} are equal since they both
158 * map to the same real value, 0. A NaN does not map to any real
159 * number and is not equal to any value, including itself.
160 * </dd>
161 *
162 * <dt><dfn>{@index "bit-wise equivalence"}</dfn>:</dt>
163 * <dd>The bits of the two floating-point values are the same. This
164 * equivalence relation for {@code double} values {@code a} and {@code
165 * b} is implemented by the expression
166 * <br>{@code Double.doubleTo}<code><b>Raw</b></code>{@code LongBits(a) == Double.doubleTo}<code><b>Raw</b></code>{@code LongBits(b)}<br>
167 * Under this relation, {@code +0.0} and {@code -0.0} are
168 * distinguished from each other and every bit pattern encoding a NaN
169 * is distinguished from every other bit pattern encoding a NaN.
170 * </dd>
171 *
172 * <dt><dfn><a id=repEquivalence></a>{@index "representation equivalence"}</dfn>:</dt>
173 * <dd>The two floating-point values represent the same IEEE 754
174 * <i>datum</i>. In particular, for {@linkplain #isFinite(double)
175 * finite} values, the sign, {@linkplain Math#getExponent(double)
176 * exponent}, and significand components of the floating-point values
177 * are the same. Under this relation:
178 * <ul>
179 * <li> {@code +0.0} and {@code -0.0} are distinguished from each other.
180 * <li> every bit pattern encoding a NaN is considered equivalent to each other
181 * <li> positive infinity is equivalent to positive infinity; negative
182 * infinity is equivalent to negative infinity.
183 * </ul>
184 * Expressions implementing this equivalence relation include:
185 * <ul>
186 * <li>{@code Double.doubleToLongBits(a) == Double.doubleToLongBits(b)}
187 * <li>{@code Double.valueOf(a).equals(Double.valueOf(b))}
188 * <li>{@code Double.compare(a, b) == 0}
189 * </ul>
190 * Note that representation equivalence is often an appropriate notion
191 * of equivalence to test the behavior of {@linkplain StrictMath math
192 * libraries}.
193 * </dd>
194 * </dl>
195 *
196 * For two binary floating-point values {@code a} and {@code b}, if
197 * neither of {@code a} and {@code b} is zero or NaN, then the three
198 * relations numerical equality, bit-wise equivalence, and
199 * representation equivalence of {@code a} and {@code b} have the same
200 * {@code true}/{@code false} value. In other words, for binary
201 * floating-point values, the three relations only differ if at least
202 * one argument is zero or NaN.
203 *
204 * <h2><a id=decimalToBinaryConversion>Decimal ↔ Binary Conversion Issues</a></h2>
205 *
206 * Many surprising results of binary floating-point arithmetic trace
207 * back to aspects of decimal to binary conversion and binary to
208 * decimal conversion. While integer values can be exactly represented
209 * in any base, which fractional values can be exactly represented in
210 * a base is a function of the base. For example, in base 10, 1/3 is a
211 * repeating fraction (0.33333....); but in base 3, 1/3 is exactly
212 * 0.1<sub>(3)</sub>, that is 1 × 3<sup>-1</sup>.
213 * Similarly, in base 10, 1/10 is exactly representable as 0.1
214 * (1 × 10<sup>-1</sup>), but in base 2, it is a
215 * repeating fraction (0.0001100110011...<sub>(2)</sub>).
216 *
217 * <p>Values of the {@code float} type have {@value Float#PRECISION}
218 * bits of precision and values of the {@code double} type have
219 * {@value Double#PRECISION} bits of precision. Therefore, since 0.1
220 * is a repeating fraction in base 2 with a four-bit repeat, {@code
221 * 0.1f} != {@code 0.1d}. In more detail, including hexadecimal
222 * floating-point literals:
223 *
224 * <ul>
225 * <li>The exact numerical value of {@code 0.1f} ({@code 0x1.99999a0000000p-4f}) is
226 * 0.100000001490116119384765625.
227 * <li>The exact numerical value of {@code 0.1d} ({@code 0x1.999999999999ap-4d}) is
228 * 0.1000000000000000055511151231257827021181583404541015625.
229 * </ul>
230 *
231 * These are the closest {@code float} and {@code double} values,
232 * respectively, to the numerical value of 0.1. These results are
233 * consistent with a {@code float} value having the equivalent of 6 to
234 * 9 digits of decimal precision and a {@code double} value having the
235 * equivalent of 15 to 17 digits of decimal precision. (The
236 * equivalent precision varies according to the different relative
237 * densities of binary and decimal values at different points along the
238 * real number line.)
239 *
240 * <p>This representation hazard of decimal fractions is one reason to
241 * use caution when storing monetary values as {@code float} or {@code
242 * double}. Alternatives include:
243 * <ul>
244 * <li>using {@link java.math.BigDecimal BigDecimal} to store decimal
245 * fractional values exactly
246 *
247 * <li>scaling up so the monetary value is an integer — for
248 * example, multiplying by 100 if the value is denominated in cents or
249 * multiplying by 1000 if the value is denominated in mills —
250 * and then storing that scaled value in an integer type
251 *
252 *</ul>
253 *
254 * <p>For each finite floating-point value and a given floating-point
255 * type, there is a contiguous region of the real number line which
256 * maps to that value. Under the default round to nearest rounding
257 * policy (JLS {@jls 15.4}), this contiguous region for a value is
258 * typically one {@linkplain Math#ulp ulp} (unit in the last place)
259 * wide and centered around the exactly representable value. (At
260 * exponent boundaries, the region is asymmetrical and larger on the
261 * side with the larger exponent.) For example, for {@code 0.1f}, the
262 * region can be computed as follows:
263 *
264 * <br>// Numeric values listed are exact values
265 * <br>oneTenthApproxAsFloat = 0.100000001490116119384765625;
266 * <br>ulpOfoneTenthApproxAsFloat = Math.ulp(0.1f) = 7.450580596923828125E-9;
267 * <br>// Numeric range that is converted to the float closest to 0.1, _excludes_ endpoints
268 * <br>(oneTenthApproxAsFloat - ½ulpOfoneTenthApproxAsFloat, oneTenthApproxAsFloat + ½ulpOfoneTenthApproxAsFloat) =
269 * <br>(0.0999999977648258209228515625, 0.1000000052154064178466796875)
270 *
271 * <p>In particular, a correctly rounded decimal to binary conversion
272 * of any string representing a number in this range, say by {@link
273 * Float#parseFloat(String)}, will be converted to the same value:
274 *
275 * {@snippet lang="java" :
276 * Float.parseFloat("0.0999999977648258209228515625000001"); // rounds up to oneTenthApproxAsFloat
277 * Float.parseFloat("0.099999998"); // rounds up to oneTenthApproxAsFloat
278 * Float.parseFloat("0.1"); // rounds up to oneTenthApproxAsFloat
279 * Float.parseFloat("0.100000001490116119384765625"); // exact conversion
280 * Float.parseFloat("0.100000005215406417846679687"); // rounds down to oneTenthApproxAsFloat
281 * Float.parseFloat("0.100000005215406417846679687499999"); // rounds down to oneTenthApproxAsFloat
282 * }
283 *
284 * <p>Similarly, an analogous range can be constructed for the {@code
285 * double} type based on the exact value of {@code double}
286 * approximation to {@code 0.1d} and the numerical value of {@code
287 * Math.ulp(0.1d)} and likewise for other particular numerical values
288 * in the {@code float} and {@code double} types.
289 *
290 * <p>As seen in the above conversions, compared to the exact
291 * numerical value the operation would have without rounding, the same
292 * floating-point value as a result can be:
293 * <ul>
294 * <li>greater than the exact result
295 * <li>equal to the exact result
296 * <li>less than the exact result
297 * </ul>
298 *
299 * A floating-point value doesn't "know" whether it was the result of
300 * rounding up, or rounding down, or an exact operation; it contains
301 * no history of how it was computed. Consequently, the sum of
302 * {@snippet lang="java" :
303 * 0.1f + 0.1f + 0.1f + 0.1f + 0.1f + 0.1f + 0.1f + 0.1f + 0.1f + 0.1f;
304 * // Numerical value of computed sum: 1.00000011920928955078125,
305 * // the next floating-point value larger than 1.0f, equal to Math.nextUp(1.0f).
306 * }
307 * or
308 * {@snippet lang="java" :
309 * 0.1d + 0.1d + 0.1d + 0.1d + 0.1d + 0.1d + 0.1d + 0.1d + 0.1d + 0.1d;
310 * // Numerical value of computed sum: 0.99999999999999988897769753748434595763683319091796875,
311 * // the next floating-point value smaller than 1.0d, equal to Math.nextDown(1.0d).
312 * }
313 *
314 * should <em>not</em> be expected to be exactly equal to 1.0, but
315 * only to be close to 1.0. Consequently, the following code is an
316 * infinite loop:
317 *
318 * {@snippet lang="java" :
319 * double d = 0.0;
320 * while (d != 1.0) { // Surprising infinite loop
321 * d += 0.1; // Sum never _exactly_ equals 1.0
322 * }
323 * }
324 *
325 * Instead, use an integer loop count for counted loops:
326 *
327 * {@snippet lang="java" :
328 * double d = 0.0;
329 * for (int i = 0; i < 10; i++) {
330 * d += 0.1;
331 * } // Value of d is equal to Math.nextDown(1.0).
332 * }
333 *
334 * or test against a floating-point limit using ordered comparisons
335 * ({@code <}, {@code <=}, {@code >}, {@code >=}):
336 *
337 * {@snippet lang="java" :
338 * double d = 0.0;
339 * while (d <= 1.0) {
340 * d += 0.1;
341 * } // Value of d approximately 1.0999999999999999
342 * }
343 *
344 * While floating-point arithmetic may have surprising results, IEEE
345 * 754 floating-point arithmetic follows a principled design and its
346 * behavior is predictable on the Java platform.
347 *
348 * @jls 4.2.3 Floating-Point Types and Values
349 * @jls 4.2.4 Floating-Point Operations
350 * @jls 15.21.1 Numerical Equality Operators == and !=
351 * @jls 15.20.1 Numerical Comparison Operators {@code <}, {@code <=}, {@code >}, and {@code >=}
352 *
353 * @see <a href="https://standards.ieee.org/ieee/754/6210/">
354 * <cite>IEEE Standard for Floating-Point Arithmetic</cite></a>
355 *
356 * @author Lee Boynton
357 * @author Arthur van Hoff
358 * @author Joseph D. Darcy
359 * @since 1.0
360 */
361 @jdk.internal.MigratedValueClass
362 @jdk.internal.ValueBased
363 public final class Double extends Number
364 implements Comparable<Double>, Constable, ConstantDesc {
365 /**
366 * A constant holding the positive infinity of type
367 * {@code double}. It is equal to the value returned by
368 * {@code Double.longBitsToDouble(0x7ff0000000000000L)}.
369 */
370 public static final double POSITIVE_INFINITY = 1.0 / 0.0;
371
372 /**
373 * A constant holding the negative infinity of type
374 * {@code double}. It is equal to the value returned by
375 * {@code Double.longBitsToDouble(0xfff0000000000000L)}.
376 */
377 public static final double NEGATIVE_INFINITY = -1.0 / 0.0;
378
379 /**
380 * A constant holding a Not-a-Number (NaN) value of type
381 * {@code double}. It is equivalent to the value returned by
382 * {@code Double.longBitsToDouble(0x7ff8000000000000L)}.
383 */
384 public static final double NaN = 0.0d / 0.0;
385
386 /**
387 * A constant holding the largest positive finite value of type
388 * {@code double},
389 * (2-2<sup>-52</sup>)·2<sup>1023</sup>. It is equal to
390 * the hexadecimal floating-point literal
391 * {@code 0x1.fffffffffffffP+1023} and also equal to
392 * {@code Double.longBitsToDouble(0x7fefffffffffffffL)}.
393 */
394 public static final double MAX_VALUE = 0x1.fffffffffffffP+1023; // 1.7976931348623157e+308
395
396 /**
397 * A constant holding the smallest positive normal value of type
398 * {@code double}, 2<sup>-1022</sup>. It is equal to the
399 * hexadecimal floating-point literal {@code 0x1.0p-1022} and also
400 * equal to {@code Double.longBitsToDouble(0x0010000000000000L)}.
401 *
402 * @since 1.6
403 */
404 public static final double MIN_NORMAL = 0x1.0p-1022; // 2.2250738585072014E-308
405
406 /**
407 * A constant holding the smallest positive nonzero value of type
408 * {@code double}, 2<sup>-1074</sup>. It is equal to the
409 * hexadecimal floating-point literal
410 * {@code 0x0.0000000000001P-1022} and also equal to
411 * {@code Double.longBitsToDouble(0x1L)}.
412 */
413 public static final double MIN_VALUE = 0x0.0000000000001P-1022; // 4.9e-324
414
415 /**
416 * The number of bits used to represent a {@code double} value,
417 * {@value}.
418 *
419 * @since 1.5
420 */
421 public static final int SIZE = 64;
422
423 /**
424 * The number of bits in the significand of a {@code double}
425 * value, {@value}. This is the parameter N in section {@jls
426 * 4.2.3} of <cite>The Java Language Specification</cite>.
427 *
428 * @since 19
429 */
430 public static final int PRECISION = 53;
431
432 /**
433 * Maximum exponent a finite {@code double} variable may have,
434 * {@value}. It is equal to the value returned by {@code
435 * Math.getExponent(Double.MAX_VALUE)}.
436 *
437 * @since 1.6
438 */
439 public static final int MAX_EXPONENT = (1 << (SIZE - PRECISION - 1)) - 1; // 1023
440
441 /**
442 * Minimum exponent a normalized {@code double} variable may have,
443 * {@value}. It is equal to the value returned by {@code
444 * Math.getExponent(Double.MIN_NORMAL)}.
445 *
446 * @since 1.6
447 */
448 public static final int MIN_EXPONENT = 1 - MAX_EXPONENT; // -1022
449
450 /**
451 * The number of bytes used to represent a {@code double} value,
452 * {@value}.
453 *
454 * @since 1.8
455 */
456 public static final int BYTES = SIZE / Byte.SIZE;
457
458 /**
459 * The {@code Class} instance representing the primitive type
460 * {@code double}.
461 *
462 * @since 1.1
463 */
464 public static final Class<Double> TYPE = Class.getPrimitiveClass("double");
465
466 /**
467 * Returns a string representation of the {@code double}
468 * argument. All characters mentioned below are ASCII characters.
469 * <ul>
470 * <li>If the argument is NaN, the result is the string
471 * "{@code NaN}".
472 * <li>Otherwise, the result is a string that represents the sign and
473 * magnitude (absolute value) of the argument. If the sign is negative,
474 * the first character of the result is '{@code -}'
475 * ({@code '\u005Cu002D'}); if the sign is positive, no sign character
476 * appears in the result. As for the magnitude <i>m</i>:
477 * <ul>
478 * <li>If <i>m</i> is infinity, it is represented by the characters
479 * {@code "Infinity"}; thus, positive infinity produces the result
480 * {@code "Infinity"} and negative infinity produces the result
481 * {@code "-Infinity"}.
482 *
483 * <li>If <i>m</i> is zero, it is represented by the characters
484 * {@code "0.0"}; thus, negative zero produces the result
485 * {@code "-0.0"} and positive zero produces the result
486 * {@code "0.0"}.
487 *
488 * <li> Otherwise <i>m</i> is positive and finite.
489 * It is converted to a string in two stages:
490 * <ul>
491 * <li> <em>Selection of a decimal</em>:
492 * A well-defined decimal <i>d</i><sub><i>m</i></sub>
493 * is selected to represent <i>m</i>.
494 * This decimal is (almost always) the <em>shortest</em> one that
495 * rounds to <i>m</i> according to the round to nearest
496 * rounding policy of IEEE 754 floating-point arithmetic.
497 * <li> <em>Formatting as a string</em>:
498 * The decimal <i>d</i><sub><i>m</i></sub> is formatted as a string,
499 * either in plain or in computerized scientific notation,
500 * depending on its value.
501 * </ul>
502 * </ul>
503 * </ul>
504 *
505 * <p>A <em>decimal</em> is a number of the form
506 * <i>s</i>×10<sup><i>i</i></sup>
507 * for some (unique) integers <i>s</i> > 0 and <i>i</i> such that
508 * <i>s</i> is not a multiple of 10.
509 * These integers are the <em>significand</em> and
510 * the <em>exponent</em>, respectively, of the decimal.
511 * The <em>length</em> of the decimal is the (unique)
512 * positive integer <i>n</i> meeting
513 * 10<sup><i>n</i>-1</sup> ≤ <i>s</i> < 10<sup><i>n</i></sup>.
514 *
515 * <p>The decimal <i>d</i><sub><i>m</i></sub> for a finite positive <i>m</i>
516 * is defined as follows:
517 * <ul>
518 * <li>Let <i>R</i> be the set of all decimals that round to <i>m</i>
519 * according to the usual <em>round to nearest</em> rounding policy of
520 * IEEE 754 floating-point arithmetic.
521 * <li>Let <i>p</i> be the minimal length over all decimals in <i>R</i>.
522 * <li>When <i>p</i> ≥ 2, let <i>T</i> be the set of all decimals
523 * in <i>R</i> with length <i>p</i>.
524 * Otherwise, let <i>T</i> be the set of all decimals
525 * in <i>R</i> with length 1 or 2.
526 * <li>Define <i>d</i><sub><i>m</i></sub> as the decimal in <i>T</i>
527 * that is closest to <i>m</i>.
528 * Or if there are two such decimals in <i>T</i>,
529 * select the one with the even significand.
530 * </ul>
531 *
532 * <p>The (uniquely) selected decimal <i>d</i><sub><i>m</i></sub>
533 * is then formatted.
534 * Let <i>s</i>, <i>i</i> and <i>n</i> be the significand, exponent and
535 * length of <i>d</i><sub><i>m</i></sub>, respectively.
536 * Further, let <i>e</i> = <i>n</i> + <i>i</i> - 1 and let
537 * <i>s</i><sub>1</sub>…<i>s</i><sub><i>n</i></sub>
538 * be the usual decimal expansion of <i>s</i>.
539 * Note that <i>s</i><sub>1</sub> ≠ 0
540 * and <i>s</i><sub><i>n</i></sub> ≠ 0.
541 * Below, the decimal point {@code '.'} is {@code '\u005Cu002E'}
542 * and the exponent indicator {@code 'E'} is {@code '\u005Cu0045'}.
543 * <ul>
544 * <li>Case -3 ≤ <i>e</i> < 0:
545 * <i>d</i><sub><i>m</i></sub> is formatted as
546 * <code>0.0</code>…<code>0</code><!--
547 * --><i>s</i><sub>1</sub>…<i>s</i><sub><i>n</i></sub>,
548 * where there are exactly -(<i>n</i> + <i>i</i>) zeroes between
549 * the decimal point and <i>s</i><sub>1</sub>.
550 * For example, 123 × 10<sup>-4</sup> is formatted as
551 * {@code 0.0123}.
552 * <li>Case 0 ≤ <i>e</i> < 7:
553 * <ul>
554 * <li>Subcase <i>i</i> ≥ 0:
555 * <i>d</i><sub><i>m</i></sub> is formatted as
556 * <i>s</i><sub>1</sub>…<i>s</i><sub><i>n</i></sub><!--
557 * --><code>0</code>…<code>0.0</code>,
558 * where there are exactly <i>i</i> zeroes
559 * between <i>s</i><sub><i>n</i></sub> and the decimal point.
560 * For example, 123 × 10<sup>2</sup> is formatted as
561 * {@code 12300.0}.
562 * <li>Subcase <i>i</i> < 0:
563 * <i>d</i><sub><i>m</i></sub> is formatted as
564 * <i>s</i><sub>1</sub>…<!--
565 * --><i>s</i><sub><i>n</i>+<i>i</i></sub><code>.</code><!--
566 * --><i>s</i><sub><i>n</i>+<i>i</i>+1</sub>…<!--
567 * --><i>s</i><sub><i>n</i></sub>,
568 * where there are exactly -<i>i</i> digits to the right of
569 * the decimal point.
570 * For example, 123 × 10<sup>-1</sup> is formatted as
571 * {@code 12.3}.
572 * </ul>
573 * <li>Case <i>e</i> < -3 or <i>e</i> ≥ 7:
574 * computerized scientific notation is used to format
575 * <i>d</i><sub><i>m</i></sub>.
576 * Here <i>e</i> is formatted as by {@link Integer#toString(int)}.
577 * <ul>
578 * <li>Subcase <i>n</i> = 1:
579 * <i>d</i><sub><i>m</i></sub> is formatted as
580 * <i>s</i><sub>1</sub><code>.0E</code><i>e</i>.
581 * For example, 1 × 10<sup>23</sup> is formatted as
582 * {@code 1.0E23}.
583 * <li>Subcase <i>n</i> > 1:
584 * <i>d</i><sub><i>m</i></sub> is formatted as
585 * <i>s</i><sub>1</sub><code>.</code><i>s</i><sub>2</sub><!--
586 * -->…<i>s</i><sub><i>n</i></sub><code>E</code><i>e</i>.
587 * For example, 123 × 10<sup>-21</sup> is formatted as
588 * {@code 1.23E-19}.
589 * </ul>
590 * </ul>
591 *
592 * <p>To create localized string representations of a floating-point
593 * value, use subclasses of {@link java.text.NumberFormat}.
594 *
595 * @apiNote
596 * This method corresponds to the general functionality of the
597 * convertToDecimalCharacter operation defined in IEEE 754;
598 * however, that operation is defined in terms of specifying the
599 * number of significand digits used in the conversion.
600 * Code to do such a conversion in the Java platform includes
601 * converting the {@code double} to a {@link java.math.BigDecimal
602 * BigDecimal} exactly and then rounding the {@code BigDecimal} to
603 * the desired number of digits; sample code:
604 * {@snippet lang=java :
605 * double d = 0.1;
606 * int digits = 25;
607 * BigDecimal bd = new BigDecimal(d);
608 * String result = bd.round(new MathContext(digits, RoundingMode.HALF_UP));
609 * // 0.1000000000000000055511151
610 * }
611 *
612 * @param d the {@code double} to be converted.
613 * @return a string representation of the argument.
614 */
615 public static String toString(double d) {
616 return DoubleToDecimal.toString(d);
617 }
618
619 /**
620 * Returns a hexadecimal string representation of the
621 * {@code double} argument. All characters mentioned below
622 * are ASCII characters.
623 *
624 * <ul>
625 * <li>If the argument is NaN, the result is the string
626 * "{@code NaN}".
627 * <li>Otherwise, the result is a string that represents the sign
628 * and magnitude of the argument. If the sign is negative, the
629 * first character of the result is '{@code -}'
630 * ({@code '\u005Cu002D'}); if the sign is positive, no sign
631 * character appears in the result. As for the magnitude <i>m</i>:
632 *
633 * <ul>
634 * <li>If <i>m</i> is infinity, it is represented by the string
635 * {@code "Infinity"}; thus, positive infinity produces the
636 * result {@code "Infinity"} and negative infinity produces
637 * the result {@code "-Infinity"}.
638 *
639 * <li>If <i>m</i> is zero, it is represented by the string
640 * {@code "0x0.0p0"}; thus, negative zero produces the result
641 * {@code "-0x0.0p0"} and positive zero produces the result
642 * {@code "0x0.0p0"}.
643 *
644 * <li>If <i>m</i> is a {@code double} value with a
645 * normalized representation, substrings are used to represent the
646 * significand and exponent fields. The significand is
647 * represented by the characters {@code "0x1."}
648 * followed by a lowercase hexadecimal representation of the rest
649 * of the significand as a fraction. Trailing zeros in the
650 * hexadecimal representation are removed unless all the digits
651 * are zero, in which case a single zero is used. Next, the
652 * exponent is represented by {@code "p"} followed
653 * by a decimal string of the unbiased exponent as if produced by
654 * a call to {@link Integer#toString(int) Integer.toString} on the
655 * exponent value.
656 *
657 * <li>If <i>m</i> is a {@code double} value with a subnormal
658 * representation, the significand is represented by the
659 * characters {@code "0x0."} followed by a
660 * hexadecimal representation of the rest of the significand as a
661 * fraction. Trailing zeros in the hexadecimal representation are
662 * removed. Next, the exponent is represented by
663 * {@code "p-1022"}. Note that there must be at
664 * least one nonzero digit in a subnormal significand.
665 *
666 * </ul>
667 *
668 * </ul>
669 *
670 * <table class="striped">
671 * <caption>Examples</caption>
672 * <thead>
673 * <tr><th scope="col">Floating-point Value</th><th scope="col">Hexadecimal String</th>
674 * </thead>
675 * <tbody style="text-align:right">
676 * <tr><th scope="row">{@code 1.0}</th> <td>{@code 0x1.0p0}</td>
677 * <tr><th scope="row">{@code -1.0}</th> <td>{@code -0x1.0p0}</td>
678 * <tr><th scope="row">{@code 2.0}</th> <td>{@code 0x1.0p1}</td>
679 * <tr><th scope="row">{@code 3.0}</th> <td>{@code 0x1.8p1}</td>
680 * <tr><th scope="row">{@code 0.5}</th> <td>{@code 0x1.0p-1}</td>
681 * <tr><th scope="row">{@code 0.25}</th> <td>{@code 0x1.0p-2}</td>
682 * <tr><th scope="row">{@code Double.MAX_VALUE}</th>
683 * <td>{@code 0x1.fffffffffffffp1023}</td>
684 * <tr><th scope="row">{@code Minimum Normal Value}</th>
685 * <td>{@code 0x1.0p-1022}</td>
686 * <tr><th scope="row">{@code Maximum Subnormal Value}</th>
687 * <td>{@code 0x0.fffffffffffffp-1022}</td>
688 * <tr><th scope="row">{@code Double.MIN_VALUE}</th>
689 * <td>{@code 0x0.0000000000001p-1022}</td>
690 * </tbody>
691 * </table>
692 *
693 * @apiNote
694 * This method corresponds to the convertToHexCharacter operation
695 * defined in IEEE 754.
696 *
697 * @param d the {@code double} to be converted.
698 * @return a hex string representation of the argument.
699 * @since 1.5
700 * @author Joseph D. Darcy
701 */
702 public static String toHexString(double d) {
703 /*
704 * Modeled after the "a" conversion specifier in C99, section
705 * 7.19.6.1; however, the output of this method is more
706 * tightly specified.
707 */
708 if (!isFinite(d) )
709 // For infinity and NaN, use the decimal output.
710 return Double.toString(d);
711 else {
712 // Initialized to maximum size of output.
713 StringBuilder answer = new StringBuilder(24);
714
715 if (Math.copySign(1.0, d) == -1.0) // value is negative,
716 answer.append("-"); // so append sign info
717
718 answer.append("0x");
719
720 d = Math.abs(d);
721
722 if(d == 0.0) {
723 answer.append("0.0p0");
724 } else {
725 boolean subnormal = (d < Double.MIN_NORMAL);
726
727 // Isolate significand bits and OR in a high-order bit
728 // so that the string representation has a known
729 // length.
730 long signifBits = (Double.doubleToLongBits(d)
731 & DoubleConsts.SIGNIF_BIT_MASK) |
732 0x1000000000000000L;
733
734 // Subnormal values have a 0 implicit bit; normal
735 // values have a 1 implicit bit.
736 answer.append(subnormal ? "0." : "1.");
737
738 // Isolate the low-order 13 digits of the hex
739 // representation. If all the digits are zero,
740 // replace with a single 0; otherwise, remove all
741 // trailing zeros.
742 String signif = Long.toHexString(signifBits).substring(3,16);
743 answer.append(signif.equals("0000000000000") ? // 13 zeros
744 "0":
745 signif.replaceFirst("0{1,12}$", ""));
746
747 answer.append('p');
748 // If the value is subnormal, use the E_min exponent
749 // value for double; otherwise, extract and report d's
750 // exponent (the representation of a subnormal uses
751 // E_min -1).
752 answer.append(subnormal ?
753 Double.MIN_EXPONENT:
754 Math.getExponent(d));
755 }
756 return answer.toString();
757 }
758 }
759
760 /**
761 * Returns a {@code Double} object holding the
762 * {@code double} value represented by the argument string
763 * {@code s}.
764 *
765 * <p>If {@code s} is {@code null}, then a
766 * {@code NullPointerException} is thrown.
767 *
768 * <p>Leading and trailing whitespace characters in {@code s}
769 * are ignored. Whitespace is removed as if by the {@link
770 * String#trim} method; that is, both ASCII space and control
771 * characters are removed. The rest of {@code s} should
772 * constitute a <i>FloatValue</i> as described by the lexical
773 * syntax rules:
774 *
775 * <blockquote>
776 * <dl>
777 * <dt><i>FloatValue:</i>
778 * <dd><i>Sign<sub>opt</sub></i> {@code NaN}
779 * <dd><i>Sign<sub>opt</sub></i> {@code Infinity}
780 * <dd><i>Sign<sub>opt</sub> FloatingPointLiteral</i>
781 * <dd><i>Sign<sub>opt</sub> HexFloatingPointLiteral</i>
782 * <dd><i>SignedInteger</i>
783 * </dl>
784 *
785 * <dl>
786 * <dt><i>HexFloatingPointLiteral</i>:
787 * <dd> <i>HexSignificand BinaryExponent FloatTypeSuffix<sub>opt</sub></i>
788 * </dl>
789 *
790 * <dl>
791 * <dt><i>HexSignificand:</i>
792 * <dd><i>HexNumeral</i>
793 * <dd><i>HexNumeral</i> {@code .}
794 * <dd>{@code 0x} <i>HexDigits<sub>opt</sub>
795 * </i>{@code .}<i> HexDigits</i>
796 * <dd>{@code 0X}<i> HexDigits<sub>opt</sub>
797 * </i>{@code .} <i>HexDigits</i>
798 * </dl>
799 *
800 * <dl>
801 * <dt><i>BinaryExponent:</i>
802 * <dd><i>BinaryExponentIndicator SignedInteger</i>
803 * </dl>
804 *
805 * <dl>
806 * <dt><i>BinaryExponentIndicator:</i>
807 * <dd>{@code p}
808 * <dd>{@code P}
809 * </dl>
810 *
811 * </blockquote>
812 *
813 * where <i>Sign</i>, <i>FloatingPointLiteral</i>,
814 * <i>HexNumeral</i>, <i>HexDigits</i>, <i>SignedInteger</i> and
815 * <i>FloatTypeSuffix</i> are as defined in the lexical structure
816 * sections of
817 * <cite>The Java Language Specification</cite>,
818 * except that underscores are not accepted between digits.
819 * If {@code s} does not have the form of
820 * a <i>FloatValue</i>, then a {@code NumberFormatException}
821 * is thrown. Otherwise, {@code s} is regarded as
822 * representing an exact decimal value in the usual
823 * "computerized scientific notation" or as an exact
824 * hexadecimal value; this exact numerical value is then
825 * conceptually converted to an "infinitely precise"
826 * binary value that is then rounded to type {@code double}
827 * by the usual round-to-nearest rule of IEEE 754 floating-point
828 * arithmetic, which includes preserving the sign of a zero
829 * value.
830 *
831 * Note that the round-to-nearest rule also implies overflow and
832 * underflow behaviour; if the exact value of {@code s} is large
833 * enough in magnitude (greater than or equal to ({@link
834 * #MAX_VALUE} + {@link Math#ulp(double) ulp(MAX_VALUE)}/2),
835 * rounding to {@code double} will result in an infinity and if the
836 * exact value of {@code s} is small enough in magnitude (less
837 * than or equal to {@link #MIN_VALUE}/2), rounding to float will
838 * result in a zero.
839 *
840 * Finally, after rounding a {@code Double} object representing
841 * this {@code double} value is returned.
842 *
843 * <p>Note that trailing format specifiers, specifiers that
844 * determine the type of a floating-point literal
845 * ({@code 1.0f} is a {@code float} value;
846 * {@code 1.0d} is a {@code double} value), do
847 * <em>not</em> influence the results of this method. In other
848 * words, the numerical value of the input string is converted
849 * directly to the target floating-point type. The two-step
850 * sequence of conversions, string to {@code float} followed
851 * by {@code float} to {@code double}, is <em>not</em>
852 * equivalent to converting a string directly to
853 * {@code double}. For example, the {@code float}
854 * literal {@code 0.1f} is equal to the {@code double}
855 * value {@code 0.10000000149011612}; the {@code float}
856 * literal {@code 0.1f} represents a different numerical
857 * value than the {@code double} literal
858 * {@code 0.1}. (The numerical value 0.1 cannot be exactly
859 * represented in a binary floating-point number.)
860 *
861 * <p>To avoid calling this method on an invalid string and having
862 * a {@code NumberFormatException} be thrown, the regular
863 * expression below can be used to screen the input string:
864 *
865 * {@snippet lang="java" :
866 * final String Digits = "(\\p{Digit}+)";
867 * final String HexDigits = "(\\p{XDigit}+)";
868 * // an exponent is 'e' or 'E' followed by an optionally
869 * // signed decimal integer.
870 * final String Exp = "[eE][+-]?"+Digits;
871 * final String fpRegex =
872 * ("[\\x00-\\x20]*"+ // Optional leading "whitespace"
873 * "[+-]?(" + // Optional sign character
874 * "NaN|" + // "NaN" string
875 * "Infinity|" + // "Infinity" string
876 *
877 * // A decimal floating-point string representing a finite positive
878 * // number without a leading sign has at most five basic pieces:
879 * // Digits . Digits ExponentPart FloatTypeSuffix
880 * //
881 * // Since this method allows integer-only strings as input
882 * // in addition to strings of floating-point literals, the
883 * // two sub-patterns below are simplifications of the grammar
884 * // productions from section 3.10.2 of
885 * // The Java Language Specification.
886 *
887 * // Digits ._opt Digits_opt ExponentPart_opt FloatTypeSuffix_opt
888 * "((("+Digits+"(\\.)?("+Digits+"?)("+Exp+")?)|"+
889 *
890 * // . Digits ExponentPart_opt FloatTypeSuffix_opt
891 * "(\\.("+Digits+")("+Exp+")?)|"+
892 *
893 * // Hexadecimal strings
894 * "((" +
895 * // 0[xX] HexDigits ._opt BinaryExponent FloatTypeSuffix_opt
896 * "(0[xX]" + HexDigits + "(\\.)?)|" +
897 *
898 * // 0[xX] HexDigits_opt . HexDigits BinaryExponent FloatTypeSuffix_opt
899 * "(0[xX]" + HexDigits + "?(\\.)" + HexDigits + ")" +
900 *
901 * ")[pP][+-]?" + Digits + "))" +
902 * "[fFdD]?))" +
903 * "[\\x00-\\x20]*");// Optional trailing "whitespace"
904 * // @link region substring="Pattern.matches" target ="java.util.regex.Pattern#matches"
905 * if (Pattern.matches(fpRegex, myString))
906 * Double.valueOf(myString); // Will not throw NumberFormatException
907 * // @end
908 * else {
909 * // Perform suitable alternative action
910 * }
911 * }
912 *
913 * @apiNote To interpret localized string representations of a
914 * floating-point value, or string representations that have
915 * non-ASCII digits, use {@link java.text.NumberFormat}. For
916 * example,
917 * {@snippet lang="java" :
918 * NumberFormat.getInstance(l).parse(s).doubleValue();
919 * }
920 * where {@code l} is the desired locale, or
921 * {@link java.util.Locale#ROOT} if locale insensitive.
922 *
923 * @apiNote
924 * This method corresponds to the convertFromDecimalCharacter and
925 * convertFromHexCharacter operations defined in IEEE 754.
926 *
927 * @param s the string to be parsed.
928 * @return a {@code Double} object holding the value
929 * represented by the {@code String} argument.
930 * @throws NumberFormatException if the string does not contain a
931 * parsable number.
932 * @see Double##decimalToBinaryConversion Decimal ↔ Binary Conversion Issues
933 */
934 public static Double valueOf(String s) throws NumberFormatException {
935 return new Double(parseDouble(s));
936 }
937
938 /**
939 * Returns a {@code Double} instance representing the specified
940 * {@code double} value.
941 * If a new {@code Double} instance is not required, this method
942 * should generally be used in preference to the constructor
943 * {@link #Double(double)}, as this method is likely to yield
944 * significantly better space and time performance by caching
945 * frequently requested values.
946 *
947 * @param d a double value.
948 * @return a {@code Double} instance representing {@code d}.
949 * @since 1.5
950 */
951 @IntrinsicCandidate
952 @DeserializeConstructor
953 public static Double valueOf(double d) {
954 return new Double(d);
955 }
956
957 /**
958 * Returns a new {@code double} initialized to the value
959 * represented by the specified {@code String}, as performed
960 * by the {@code valueOf} method of class
961 * {@code Double}.
962 *
963 * @param s the string to be parsed.
964 * @return the {@code double} value represented by the string
965 * argument.
966 * @throws NullPointerException if the string is null
967 * @throws NumberFormatException if the string does not contain
968 * a parsable {@code double}.
969 * @see java.lang.Double#valueOf(String)
970 * @see Double##decimalToBinaryConversion Decimal ↔ Binary Conversion Issues
971 * @since 1.2
972 */
973 public static double parseDouble(String s) throws NumberFormatException {
974 return FloatingDecimal.parseDouble(s);
975 }
976
977 /**
978 * Returns {@code true} if the specified number is a
979 * Not-a-Number (NaN) value, {@code false} otherwise.
980 *
981 * @apiNote
982 * This method corresponds to the isNaN operation defined in IEEE
983 * 754.
984 *
985 * @param v the value to be tested.
986 * @return {@code true} if the value of the argument is NaN;
987 * {@code false} otherwise.
988 */
989 public static boolean isNaN(double v) {
990 return (v != v);
991 }
992
993 /**
994 * Returns {@code true} if the specified number is infinitely
995 * large in magnitude, {@code false} otherwise.
996 *
997 * @apiNote
998 * This method corresponds to the isInfinite operation defined in
999 * IEEE 754.
1000 *
1001 * @param v the value to be tested.
1002 * @return {@code true} if the value of the argument is positive
1003 * infinity or negative infinity; {@code false} otherwise.
1004 */
1005 @IntrinsicCandidate
1006 public static boolean isInfinite(double v) {
1007 return Math.abs(v) > MAX_VALUE;
1008 }
1009
1010 /**
1011 * Returns {@code true} if the argument is a finite floating-point
1012 * value; returns {@code false} otherwise (for NaN and infinity
1013 * arguments).
1014 *
1015 * @apiNote
1016 * This method corresponds to the isFinite operation defined in
1017 * IEEE 754.
1018 *
1019 * @param d the {@code double} value to be tested
1020 * @return {@code true} if the argument is a finite
1021 * floating-point value, {@code false} otherwise.
1022 * @since 1.8
1023 */
1024 @IntrinsicCandidate
1025 public static boolean isFinite(double d) {
1026 return Math.abs(d) <= Double.MAX_VALUE;
1027 }
1028
1029 /**
1030 * The value of the Double.
1031 *
1032 * @serial
1033 */
1034 private final double value;
1035
1036 /**
1037 * Constructs a newly allocated {@code Double} object that
1038 * represents the primitive {@code double} argument.
1039 *
1040 * @param value the value to be represented by the {@code Double}.
1041 *
1042 * @deprecated
1043 * It is rarely appropriate to use this constructor. The static factory
1044 * {@link #valueOf(double)} is generally a better choice, as it is
1045 * likely to yield significantly better space and time performance.
1046 */
1047 @Deprecated(since="9", forRemoval = true)
1048 public Double(double value) {
1049 this.value = value;
1050 }
1051
1052 /**
1053 * Constructs a newly allocated {@code Double} object that
1054 * represents the floating-point value of type {@code double}
1055 * represented by the string. The string is converted to a
1056 * {@code double} value as if by the {@code valueOf} method.
1057 *
1058 * @param s a string to be converted to a {@code Double}.
1059 * @throws NumberFormatException if the string does not contain a
1060 * parsable number.
1061 *
1062 * @deprecated
1063 * It is rarely appropriate to use this constructor.
1064 * Use {@link #parseDouble(String)} to convert a string to a
1065 * {@code double} primitive, or use {@link #valueOf(String)}
1066 * to convert a string to a {@code Double} object.
1067 */
1068 @Deprecated(since="9", forRemoval = true)
1069 public Double(String s) throws NumberFormatException {
1070 value = parseDouble(s);
1071 }
1072
1073 /**
1074 * Returns {@code true} if this {@code Double} value is
1075 * a Not-a-Number (NaN), {@code false} otherwise.
1076 *
1077 * @return {@code true} if the value represented by this object is
1078 * NaN; {@code false} otherwise.
1079 */
1080 public boolean isNaN() {
1081 return isNaN(value);
1082 }
1083
1084 /**
1085 * Returns {@code true} if this {@code Double} value is
1086 * infinitely large in magnitude, {@code false} otherwise.
1087 *
1088 * @return {@code true} if the value represented by this object is
1089 * positive infinity or negative infinity;
1090 * {@code false} otherwise.
1091 */
1092 public boolean isInfinite() {
1093 return isInfinite(value);
1094 }
1095
1096 /**
1097 * Returns a string representation of this {@code Double} object.
1098 * The primitive {@code double} value represented by this
1099 * object is converted to a string exactly as if by the method
1100 * {@code toString} of one argument.
1101 *
1102 * @return a {@code String} representation of this object.
1103 * @see java.lang.Double#toString(double)
1104 */
1105 public String toString() {
1106 return toString(value);
1107 }
1108
1109 /**
1110 * Returns the value of this {@code Double} as a {@code byte}
1111 * after a narrowing primitive conversion.
1112 *
1113 * @return the {@code double} value represented by this object
1114 * converted to type {@code byte}
1115 * @jls 5.1.3 Narrowing Primitive Conversion
1116 * @since 1.1
1117 */
1118 @Override
1119 public byte byteValue() {
1120 return (byte)value;
1121 }
1122
1123 /**
1124 * Returns the value of this {@code Double} as a {@code short}
1125 * after a narrowing primitive conversion.
1126 *
1127 * @return the {@code double} value represented by this object
1128 * converted to type {@code short}
1129 * @jls 5.1.3 Narrowing Primitive Conversion
1130 * @since 1.1
1131 */
1132 @Override
1133 public short shortValue() {
1134 return (short)value;
1135 }
1136
1137 /**
1138 * Returns the value of this {@code Double} as an {@code int}
1139 * after a narrowing primitive conversion.
1140 * @jls 5.1.3 Narrowing Primitive Conversion
1141 *
1142 * @apiNote
1143 * This method corresponds to the convertToIntegerTowardZero
1144 * operation defined in IEEE 754.
1145 *
1146 * @return the {@code double} value represented by this object
1147 * converted to type {@code int}
1148 */
1149 @Override
1150 public int intValue() {
1151 return (int)value;
1152 }
1153
1154 /**
1155 * Returns the value of this {@code Double} as a {@code long}
1156 * after a narrowing primitive conversion.
1157 *
1158 * @apiNote
1159 * This method corresponds to the convertToIntegerTowardZero
1160 * operation defined in IEEE 754.
1161 *
1162 * @return the {@code double} value represented by this object
1163 * converted to type {@code long}
1164 * @jls 5.1.3 Narrowing Primitive Conversion
1165 */
1166 @Override
1167 public long longValue() {
1168 return (long)value;
1169 }
1170
1171 /**
1172 * Returns the value of this {@code Double} as a {@code float}
1173 * after a narrowing primitive conversion.
1174 *
1175 * @apiNote
1176 * This method corresponds to the convertFormat operation defined
1177 * in IEEE 754.
1178 *
1179 * @return the {@code double} value represented by this object
1180 * converted to type {@code float}
1181 * @jls 5.1.3 Narrowing Primitive Conversion
1182 * @since 1.0
1183 */
1184 @Override
1185 public float floatValue() {
1186 return (float)value;
1187 }
1188
1189 /**
1190 * Returns the {@code double} value of this {@code Double} object.
1191 *
1192 * @return the {@code double} value represented by this object
1193 */
1194 @Override
1195 @IntrinsicCandidate
1196 public double doubleValue() {
1197 return value;
1198 }
1199
1200 /**
1201 * Returns a hash code for this {@code Double} object. The
1202 * result is the exclusive OR of the two halves of the
1203 * {@code long} integer bit representation, exactly as
1204 * produced by the method {@link #doubleToLongBits(double)}, of
1205 * the primitive {@code double} value represented by this
1206 * {@code Double} object. That is, the hash code is the value
1207 * of the expression:
1208 *
1209 * <blockquote>
1210 * {@code (int)(v^(v>>>32))}
1211 * </blockquote>
1212 *
1213 * where {@code v} is defined by:
1214 *
1215 * <blockquote>
1216 * {@code long v = Double.doubleToLongBits(this.doubleValue());}
1217 * </blockquote>
1218 *
1219 * @return a {@code hash code} value for this object.
1220 */
1221 @Override
1222 public int hashCode() {
1223 return Double.hashCode(value);
1224 }
1225
1226 /**
1227 * Returns a hash code for a {@code double} value; compatible with
1228 * {@code Double.hashCode()}.
1229 *
1230 * @param value the value to hash
1231 * @return a hash code value for a {@code double} value.
1232 * @since 1.8
1233 */
1234 public static int hashCode(double value) {
1235 return Long.hashCode(doubleToLongBits(value));
1236 }
1237
1238 /**
1239 * Compares this object against the specified object. The result
1240 * is {@code true} if and only if the argument is not
1241 * {@code null} and is a {@code Double} object that
1242 * represents a {@code double} that has the same value as the
1243 * {@code double} represented by this object. For this
1244 * purpose, two {@code double} values are considered to be
1245 * the same if and only if the method {@link
1246 * #doubleToLongBits(double)} returns the identical
1247 * {@code long} value when applied to each.
1248 *
1249 * @apiNote
1250 * This method is defined in terms of {@link
1251 * #doubleToLongBits(double)} rather than the {@code ==} operator
1252 * on {@code double} values since the {@code ==} operator does
1253 * <em>not</em> define an equivalence relation and to satisfy the
1254 * {@linkplain Object#equals equals contract} an equivalence
1255 * relation must be implemented; see {@linkplain ##equivalenceRelation
1256 * this discussion for details of floating-point equality and equivalence}.
1257 *
1258 * @see java.lang.Double#doubleToLongBits(double)
1259 * @jls 15.21.1 Numerical Equality Operators == and !=
1260 */
1261 public boolean equals(Object obj) {
1262 return (obj instanceof Double d) &&
1263 (doubleToLongBits(d.value) == doubleToLongBits(value));
1264 }
1265
1266 /**
1267 * Returns a representation of the specified floating-point value
1268 * according to the IEEE 754 floating-point "double
1269 * format" bit layout.
1270 *
1271 * <p>Bit 63 (the bit that is selected by the mask
1272 * {@code 0x8000000000000000L}) represents the sign of the
1273 * floating-point number. Bits
1274 * 62-52 (the bits that are selected by the mask
1275 * {@code 0x7ff0000000000000L}) represent the exponent. Bits 51-0
1276 * (the bits that are selected by the mask
1277 * {@code 0x000fffffffffffffL}) represent the significand
1278 * (sometimes called the mantissa) of the floating-point number.
1279 *
1280 * <p>If the argument is positive infinity, the result is
1281 * {@code 0x7ff0000000000000L}.
1282 *
1283 * <p>If the argument is negative infinity, the result is
1284 * {@code 0xfff0000000000000L}.
1285 *
1286 * <p>If the argument is NaN, the result is
1287 * {@code 0x7ff8000000000000L}.
1288 *
1289 * <p>In all cases, the result is a {@code long} integer that, when
1290 * given to the {@link #longBitsToDouble(long)} method, will produce a
1291 * floating-point value the same as the argument to
1292 * {@code doubleToLongBits} (except all NaN values are
1293 * collapsed to a single "canonical" NaN value).
1294 *
1295 * @param value a {@code double} precision floating-point number.
1296 * @return the bits that represent the floating-point number.
1297 */
1298 @IntrinsicCandidate
1299 public static long doubleToLongBits(double value) {
1300 if (!isNaN(value)) {
1301 return doubleToRawLongBits(value);
1302 }
1303 return 0x7ff8000000000000L;
1304 }
1305
1306 /**
1307 * Returns a representation of the specified floating-point value
1308 * according to the IEEE 754 floating-point "double
1309 * format" bit layout, preserving Not-a-Number (NaN) values.
1310 *
1311 * <p>Bit 63 (the bit that is selected by the mask
1312 * {@code 0x8000000000000000L}) represents the sign of the
1313 * floating-point number. Bits
1314 * 62-52 (the bits that are selected by the mask
1315 * {@code 0x7ff0000000000000L}) represent the exponent. Bits 51-0
1316 * (the bits that are selected by the mask
1317 * {@code 0x000fffffffffffffL}) represent the significand
1318 * (sometimes called the mantissa) of the floating-point number.
1319 *
1320 * <p>If the argument is positive infinity, the result is
1321 * {@code 0x7ff0000000000000L}.
1322 *
1323 * <p>If the argument is negative infinity, the result is
1324 * {@code 0xfff0000000000000L}.
1325 *
1326 * <p>If the argument is NaN, the result is the {@code long}
1327 * integer representing the actual NaN value. Unlike the
1328 * {@code doubleToLongBits} method,
1329 * {@code doubleToRawLongBits} does not collapse all the bit
1330 * patterns encoding a NaN to a single "canonical" NaN
1331 * value.
1332 *
1333 * <p>In all cases, the result is a {@code long} integer that,
1334 * when given to the {@link #longBitsToDouble(long)} method, will
1335 * produce a floating-point value the same as the argument to
1336 * {@code doubleToRawLongBits}.
1337 *
1338 * @param value a {@code double} precision floating-point number.
1339 * @return the bits that represent the floating-point number.
1340 * @since 1.3
1341 */
1342 @IntrinsicCandidate
1343 public static native long doubleToRawLongBits(double value);
1344
1345 /**
1346 * Returns the {@code double} value corresponding to a given
1347 * bit representation.
1348 * The argument is considered to be a representation of a
1349 * floating-point value according to the IEEE 754 floating-point
1350 * "double format" bit layout.
1351 *
1352 * <p>If the argument is {@code 0x7ff0000000000000L}, the result
1353 * is positive infinity.
1354 *
1355 * <p>If the argument is {@code 0xfff0000000000000L}, the result
1356 * is negative infinity.
1357 *
1358 * <p>If the argument is any value in the range
1359 * {@code 0x7ff0000000000001L} through
1360 * {@code 0x7fffffffffffffffL} or in the range
1361 * {@code 0xfff0000000000001L} through
1362 * {@code 0xffffffffffffffffL}, the result is a NaN. No IEEE
1363 * 754 floating-point operation provided by Java can distinguish
1364 * between two NaN values of the same type with different bit
1365 * patterns. Distinct values of NaN are only distinguishable by
1366 * use of the {@code Double.doubleToRawLongBits} method.
1367 *
1368 * <p>In all other cases, let <i>s</i>, <i>e</i>, and <i>m</i> be three
1369 * values that can be computed from the argument:
1370 *
1371 * {@snippet lang="java" :
1372 * int s = ((bits >> 63) == 0) ? 1 : -1;
1373 * int e = (int)((bits >> 52) & 0x7ffL);
1374 * long m = (e == 0) ?
1375 * (bits & 0xfffffffffffffL) << 1 :
1376 * (bits & 0xfffffffffffffL) | 0x10000000000000L;
1377 * }
1378 *
1379 * Then the floating-point result equals the value of the mathematical
1380 * expression <i>s</i>·<i>m</i>·2<sup><i>e</i>-1075</sup>.
1381 *
1382 * <p>Note that this method may not be able to return a
1383 * {@code double} NaN with exactly same bit pattern as the
1384 * {@code long} argument. IEEE 754 distinguishes between two
1385 * kinds of NaNs, quiet NaNs and <i>signaling NaNs</i>. The
1386 * differences between the two kinds of NaN are generally not
1387 * visible in Java. Arithmetic operations on signaling NaNs turn
1388 * them into quiet NaNs with a different, but often similar, bit
1389 * pattern. However, on some processors merely copying a
1390 * signaling NaN also performs that conversion. In particular,
1391 * copying a signaling NaN to return it to the calling method
1392 * may perform this conversion. So {@code longBitsToDouble}
1393 * may not be able to return a {@code double} with a
1394 * signaling NaN bit pattern. Consequently, for some
1395 * {@code long} values,
1396 * {@code doubleToRawLongBits(longBitsToDouble(start))} may
1397 * <i>not</i> equal {@code start}. Moreover, which
1398 * particular bit patterns represent signaling NaNs is platform
1399 * dependent; although all NaN bit patterns, quiet or signaling,
1400 * must be in the NaN range identified above.
1401 *
1402 * @param bits any {@code long} integer.
1403 * @return the {@code double} floating-point value with the same
1404 * bit pattern.
1405 */
1406 @IntrinsicCandidate
1407 public static native double longBitsToDouble(long bits);
1408
1409 /**
1410 * Compares two {@code Double} objects numerically.
1411 *
1412 * This method imposes a total order on {@code Double} objects
1413 * with two differences compared to the incomplete order defined by
1414 * the Java language numerical comparison operators ({@code <, <=,
1415 * ==, >=, >}) on {@code double} values.
1416 *
1417 * <ul><li> A NaN is <em>unordered</em> with respect to other
1418 * values and unequal to itself under the comparison
1419 * operators. This method chooses to define {@code
1420 * Double.NaN} to be equal to itself and greater than all
1421 * other {@code double} values (including {@code
1422 * Double.POSITIVE_INFINITY}).
1423 *
1424 * <li> Positive zero and negative zero compare equal
1425 * numerically, but are distinct and distinguishable values.
1426 * This method chooses to define positive zero ({@code +0.0d}),
1427 * to be greater than negative zero ({@code -0.0d}).
1428 * </ul>
1429
1430 * This ensures that the <i>natural ordering</i> of {@code Double}
1431 * objects imposed by this method is <i>consistent with
1432 * equals</i>; see {@linkplain ##equivalenceRelation this
1433 * discussion for details of floating-point comparison and
1434 * ordering}.
1435 *
1436 * @param anotherDouble the {@code Double} to be compared.
1437 * @return the value {@code 0} if {@code anotherDouble} is
1438 * numerically equal to this {@code Double}; a value
1439 * less than {@code 0} if this {@code Double}
1440 * is numerically less than {@code anotherDouble};
1441 * and a value greater than {@code 0} if this
1442 * {@code Double} is numerically greater than
1443 * {@code anotherDouble}.
1444 *
1445 * @jls 15.20.1 Numerical Comparison Operators {@code <}, {@code <=}, {@code >}, and {@code >=}
1446 * @since 1.2
1447 */
1448 @Override
1449 public int compareTo(Double anotherDouble) {
1450 return Double.compare(value, anotherDouble.value);
1451 }
1452
1453 /**
1454 * Compares the two specified {@code double} values. The sign
1455 * of the integer value returned is the same as that of the
1456 * integer that would be returned by the call:
1457 * <pre>
1458 * Double.valueOf(d1).compareTo(Double.valueOf(d2))
1459 * </pre>
1460 *
1461 * @param d1 the first {@code double} to compare
1462 * @param d2 the second {@code double} to compare
1463 * @return the value {@code 0} if {@code d1} is
1464 * numerically equal to {@code d2}; a value less than
1465 * {@code 0} if {@code d1} is numerically less than
1466 * {@code d2}; and a value greater than {@code 0}
1467 * if {@code d1} is numerically greater than
1468 * {@code d2}.
1469 * @since 1.4
1470 */
1471 public static int compare(double d1, double d2) {
1472 if (d1 < d2)
1473 return -1; // Neither val is NaN, thisVal is smaller
1474 if (d1 > d2)
1475 return 1; // Neither val is NaN, thisVal is larger
1476
1477 // Cannot use doubleToRawLongBits because of possibility of NaNs.
1478 long thisBits = Double.doubleToLongBits(d1);
1479 long anotherBits = Double.doubleToLongBits(d2);
1480
1481 return (thisBits == anotherBits ? 0 : // Values are equal
1482 (thisBits < anotherBits ? -1 : // (-0.0, 0.0) or (!NaN, NaN)
1483 1)); // (0.0, -0.0) or (NaN, !NaN)
1484 }
1485
1486 /**
1487 * Adds two {@code double} values together as per the + operator.
1488 *
1489 * @apiNote This method corresponds to the addition operation
1490 * defined in IEEE 754.
1491 *
1492 * @param a the first operand
1493 * @param b the second operand
1494 * @return the sum of {@code a} and {@code b}
1495 * @jls 4.2.4 Floating-Point Operations
1496 * @see java.util.function.BinaryOperator
1497 * @since 1.8
1498 */
1499 public static double sum(double a, double b) {
1500 return a + b;
1501 }
1502
1503 /**
1504 * Returns the greater of two {@code double} values
1505 * as if by calling {@link Math#max(double, double) Math.max}.
1506 *
1507 * @apiNote
1508 * This method corresponds to the maximum operation defined in
1509 * IEEE 754.
1510 *
1511 * @param a the first operand
1512 * @param b the second operand
1513 * @return the greater of {@code a} and {@code b}
1514 * @see java.util.function.BinaryOperator
1515 * @since 1.8
1516 */
1517 public static double max(double a, double b) {
1518 return Math.max(a, b);
1519 }
1520
1521 /**
1522 * Returns the smaller of two {@code double} values
1523 * as if by calling {@link Math#min(double, double) Math.min}.
1524 *
1525 * @apiNote
1526 * This method corresponds to the minimum operation defined in
1527 * IEEE 754.
1528 *
1529 * @param a the first operand
1530 * @param b the second operand
1531 * @return the smaller of {@code a} and {@code b}.
1532 * @see java.util.function.BinaryOperator
1533 * @since 1.8
1534 */
1535 public static double min(double a, double b) {
1536 return Math.min(a, b);
1537 }
1538
1539 /**
1540 * Returns an {@link Optional} containing the nominal descriptor for this
1541 * instance, which is the instance itself.
1542 *
1543 * @return an {@link Optional} describing the {@linkplain Double} instance
1544 * @since 12
1545 */
1546 @Override
1547 public Optional<Double> describeConstable() {
1548 return Optional.of(this);
1549 }
1550
1551 /**
1552 * Resolves this instance as a {@link ConstantDesc}, the result of which is
1553 * the instance itself.
1554 *
1555 * @param lookup ignored
1556 * @return the {@linkplain Double} instance
1557 * @since 12
1558 */
1559 @Override
1560 public Double resolveConstantDesc(MethodHandles.Lookup lookup) {
1561 return this;
1562 }
1563
1564 /** use serialVersionUID from JDK 1.0.2 for interoperability */
1565 @java.io.Serial
1566 private static final long serialVersionUID = -9172774392245257468L;
1567 }