1 /*
2 * Copyright (c) 1994, 2025, Oracle and/or its affiliates. All rights reserved.
3 * DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER.
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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 is the {@linkplain
40 * java.lang##wrapperClass wrapper class} for values of the primitive
41 * type {@code double}. An object of type {@code Double} contains a
42 * single field whose type is {@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 {@linkplain ##repEquivalence representation
120 * equivalence}, 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></a><dfn>{@index "numerical equality"}</dfn> ({@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><dfn>{@index "bit-wise equivalence"}</dfn>:</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><dfn><a id=repEquivalence></a>{@index "representation equivalence"}</dfn>:</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 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 * @spec https://standards.ieee.org/ieee/754/6210/
353 * IEEE Standard for Floating-Point Arithmetic
354 *
355 * @since 1.0
356 */
357 @jdk.internal.ValueBased
358 public final class Double extends Number
359 implements Comparable<Double>, Constable, ConstantDesc {
360 /**
361 * A constant holding the positive infinity of type
362 * {@code double}. It is equal to the value returned by
363 * {@code Double.longBitsToDouble(0x7ff0000000000000L)}.
364 */
365 public static final double POSITIVE_INFINITY = 1.0 / 0.0;
366
367 /**
368 * A constant holding the negative infinity of type
369 * {@code double}. It is equal to the value returned by
370 * {@code Double.longBitsToDouble(0xfff0000000000000L)}.
371 */
372 public static final double NEGATIVE_INFINITY = -1.0 / 0.0;
373
374 /**
375 * A constant holding a Not-a-Number (NaN) value of type {@code double}.
376 * It is {@linkplain Double##equivalenceRelation equivalent} to the
377 * value returned by {@code Double.longBitsToDouble(0x7ff8000000000000L)}.
378 */
379 public static final double NaN = 0.0d / 0.0;
380
381 /**
382 * A constant holding the largest positive finite value of type
383 * {@code double},
384 * (2-2<sup>-52</sup>)·2<sup>1023</sup>. It is equal to
385 * the hexadecimal floating-point literal
386 * {@code 0x1.fffffffffffffP+1023} and also equal to
387 * {@code Double.longBitsToDouble(0x7fefffffffffffffL)}.
388 */
389 public static final double MAX_VALUE = 0x1.fffffffffffffP+1023; // 1.7976931348623157e+308
390
391 /**
392 * A constant holding the smallest positive normal value of type
393 * {@code double}, 2<sup>-1022</sup>. It is equal to the
394 * hexadecimal floating-point literal {@code 0x1.0p-1022} and also
395 * equal to {@code Double.longBitsToDouble(0x0010000000000000L)}.
396 *
397 * @since 1.6
398 */
399 public static final double MIN_NORMAL = 0x1.0p-1022; // 2.2250738585072014E-308
400
401 /**
402 * A constant holding the smallest positive nonzero value of type
403 * {@code double}, 2<sup>-1074</sup>. It is equal to the
404 * hexadecimal floating-point literal
405 * {@code 0x0.0000000000001P-1022} and also equal to
406 * {@code Double.longBitsToDouble(0x1L)}.
407 */
408 public static final double MIN_VALUE = 0x0.0000000000001P-1022; // 4.9e-324
409
410 /**
411 * The number of bits used to represent a {@code double} value,
412 * {@value}.
413 *
414 * @since 1.5
415 */
416 public static final int SIZE = 64;
417
418 /**
419 * The number of bits in the significand of a {@code double}
420 * value, {@value}. This is the parameter N in section {@jls
421 * 4.2.3} of <cite>The Java Language Specification</cite>.
422 *
423 * @since 19
424 */
425 public static final int PRECISION = 53;
426
427 /**
428 * Maximum exponent a finite {@code double} variable may have,
429 * {@value}. It is equal to the value returned by {@code
430 * Math.getExponent(Double.MAX_VALUE)}.
431 *
432 * @since 1.6
433 */
434 public static final int MAX_EXPONENT = (1 << (SIZE - PRECISION - 1)) - 1; // 1023
435
436 /**
437 * Minimum exponent a normalized {@code double} variable may have,
438 * {@value}. It is equal to the value returned by {@code
439 * Math.getExponent(Double.MIN_NORMAL)}.
440 *
441 * @since 1.6
442 */
443 public static final int MIN_EXPONENT = 1 - MAX_EXPONENT; // -1022
444
445 /**
446 * The number of bytes used to represent a {@code double} value,
447 * {@value}.
448 *
449 * @since 1.8
450 */
451 public static final int BYTES = SIZE / Byte.SIZE;
452
453 /**
454 * The {@code Class} instance representing the primitive type
455 * {@code double}.
456 *
457 * @since 1.1
458 */
459 public static final Class<Double> TYPE = Class.getPrimitiveClass("double");
460
461 /**
462 * Returns a string representation of the {@code double}
463 * argument. All characters mentioned below are ASCII characters.
464 * <ul>
465 * <li>If the argument is NaN, the result is the string
466 * "{@code NaN}".
467 * <li>Otherwise, the result is a string that represents the sign and
468 * magnitude (absolute value) of the argument. If the sign is negative,
469 * the first character of the result is '{@code -}'
470 * ({@code '\u005Cu002D'}); if the sign is positive, no sign character
471 * appears in the result. As for the magnitude <i>m</i>:
472 * <ul>
473 * <li>If <i>m</i> is infinity, it is represented by the characters
474 * {@code "Infinity"}; thus, positive infinity produces the result
475 * {@code "Infinity"} and negative infinity produces the result
476 * {@code "-Infinity"}.
477 *
478 * <li>If <i>m</i> is zero, it is represented by the characters
479 * {@code "0.0"}; thus, negative zero produces the result
480 * {@code "-0.0"} and positive zero produces the result
481 * {@code "0.0"}.
482 *
483 * <li> Otherwise <i>m</i> is positive and finite.
484 * It is converted to a string in two stages:
485 * <ul>
486 * <li> <em>Selection of a decimal</em>:
487 * A well-defined decimal <i>d</i><sub><i>m</i></sub>
488 * is selected to represent <i>m</i>.
489 * This decimal is (almost always) the <em>shortest</em> one that
490 * rounds to <i>m</i> according to the round to nearest
491 * rounding policy of IEEE 754 floating-point arithmetic.
492 * <li> <em>Formatting as a string</em>:
493 * The decimal <i>d</i><sub><i>m</i></sub> is formatted as a string,
494 * either in plain or in computerized scientific notation,
495 * depending on its value.
496 * </ul>
497 * </ul>
498 * </ul>
499 *
500 * <p>A <em>decimal</em> is a number of the form
501 * <i>s</i>×10<sup><i>i</i></sup>
502 * for some (unique) integers <i>s</i> > 0 and <i>i</i> such that
503 * <i>s</i> is not a multiple of 10.
504 * These integers are the <em>significand</em> and
505 * the <em>exponent</em>, respectively, of the decimal.
506 * The <em>length</em> of the decimal is the (unique)
507 * positive integer <i>n</i> meeting
508 * 10<sup><i>n</i>-1</sup> ≤ <i>s</i> < 10<sup><i>n</i></sup>.
509 *
510 * <p>The decimal <i>d</i><sub><i>m</i></sub> for a finite positive <i>m</i>
511 * is defined as follows:
512 * <ul>
513 * <li>Let <i>R</i> be the set of all decimals that round to <i>m</i>
514 * according to the usual <em>round to nearest</em> rounding policy of
515 * IEEE 754 floating-point arithmetic.
516 * <li>Let <i>p</i> be the minimal length over all decimals in <i>R</i>.
517 * <li>When <i>p</i> ≥ 2, let <i>T</i> be the set of all decimals
518 * in <i>R</i> with length <i>p</i>.
519 * Otherwise, let <i>T</i> be the set of all decimals
520 * in <i>R</i> with length 1 or 2.
521 * <li>Define <i>d</i><sub><i>m</i></sub> as the decimal in <i>T</i>
522 * that is closest to <i>m</i>.
523 * Or if there are two such decimals in <i>T</i>,
524 * select the one with the even significand.
525 * </ul>
526 *
527 * <p>The (uniquely) selected decimal <i>d</i><sub><i>m</i></sub>
528 * is then formatted.
529 * Let <i>s</i>, <i>i</i> and <i>n</i> be the significand, exponent and
530 * length of <i>d</i><sub><i>m</i></sub>, respectively.
531 * Further, let <i>e</i> = <i>n</i> + <i>i</i> - 1 and let
532 * <i>s</i><sub>1</sub>…<i>s</i><sub><i>n</i></sub>
533 * be the usual decimal expansion of <i>s</i>.
534 * Note that <i>s</i><sub>1</sub> ≠ 0
535 * and <i>s</i><sub><i>n</i></sub> ≠ 0.
536 * Below, the decimal point {@code '.'} is {@code '\u005Cu002E'}
537 * and the exponent indicator {@code 'E'} is {@code '\u005Cu0045'}.
538 * <ul>
539 * <li>Case -3 ≤ <i>e</i> < 0:
540 * <i>d</i><sub><i>m</i></sub> is formatted as
541 * <code>0.0</code>…<code>0</code><!--
542 * --><i>s</i><sub>1</sub>…<i>s</i><sub><i>n</i></sub>,
543 * where there are exactly -(<i>n</i> + <i>i</i>) zeroes between
544 * the decimal point and <i>s</i><sub>1</sub>.
545 * For example, 123 × 10<sup>-4</sup> is formatted as
546 * {@code 0.0123}.
547 * <li>Case 0 ≤ <i>e</i> < 7:
548 * <ul>
549 * <li>Subcase <i>i</i> ≥ 0:
550 * <i>d</i><sub><i>m</i></sub> is formatted as
551 * <i>s</i><sub>1</sub>…<i>s</i><sub><i>n</i></sub><!--
552 * --><code>0</code>…<code>0.0</code>,
553 * where there are exactly <i>i</i> zeroes
554 * between <i>s</i><sub><i>n</i></sub> and the decimal point.
555 * For example, 123 × 10<sup>2</sup> is formatted as
556 * {@code 12300.0}.
557 * <li>Subcase <i>i</i> < 0:
558 * <i>d</i><sub><i>m</i></sub> is formatted as
559 * <i>s</i><sub>1</sub>…<!--
560 * --><i>s</i><sub><i>n</i>+<i>i</i></sub><code>.</code><!--
561 * --><i>s</i><sub><i>n</i>+<i>i</i>+1</sub>…<!--
562 * --><i>s</i><sub><i>n</i></sub>,
563 * where there are exactly -<i>i</i> digits to the right of
564 * the decimal point.
565 * For example, 123 × 10<sup>-1</sup> is formatted as
566 * {@code 12.3}.
567 * </ul>
568 * <li>Case <i>e</i> < -3 or <i>e</i> ≥ 7:
569 * computerized scientific notation is used to format
570 * <i>d</i><sub><i>m</i></sub>.
571 * Here <i>e</i> is formatted as by {@link Integer#toString(int)}.
572 * <ul>
573 * <li>Subcase <i>n</i> = 1:
574 * <i>d</i><sub><i>m</i></sub> is formatted as
575 * <i>s</i><sub>1</sub><code>.0E</code><i>e</i>.
576 * For example, 1 × 10<sup>23</sup> is formatted as
577 * {@code 1.0E23}.
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>.</code><i>s</i><sub>2</sub><!--
581 * -->…<i>s</i><sub><i>n</i></sub><code>E</code><i>e</i>.
582 * For example, 123 × 10<sup>-21</sup> is formatted as
583 * {@code 1.23E-19}.
584 * </ul>
585 * </ul>
586 *
587 * <p>To create localized string representations of a floating-point
588 * value, use subclasses of {@link java.text.NumberFormat}.
589 *
590 * @apiNote
591 * This method corresponds to the general functionality of the
592 * convertToDecimalCharacter operation defined in IEEE 754;
593 * however, that operation is defined in terms of specifying the
594 * number of significand digits used in the conversion.
595 * Code to do such a conversion in the Java platform includes
596 * converting the {@code double} to a {@link java.math.BigDecimal
597 * BigDecimal} exactly and then rounding the {@code BigDecimal} to
598 * the desired number of digits; sample code:
599 * {@snippet lang=java :
600 * double d = 0.1;
601 * int digits = 25;
602 * BigDecimal bd = new BigDecimal(d);
603 * String result = bd.round(new MathContext(digits, RoundingMode.HALF_UP));
604 * // 0.1000000000000000055511151
605 * }
606 *
607 * @param d the {@code double} to be converted.
608 * @return a string representation of the argument.
609 */
610 public static String toString(double d) {
611 return DoubleToDecimal.toString(d);
612 }
613
614 /**
615 * Returns a hexadecimal string representation of the
616 * {@code double} argument. All characters mentioned below
617 * are ASCII characters.
618 *
619 * <ul>
620 * <li>If the argument is NaN, the result is the string
621 * "{@code NaN}".
622 * <li>Otherwise, the result is a string that represents the sign
623 * and magnitude of the argument. If the sign is negative, the
624 * first character of the result is '{@code -}'
625 * ({@code '\u005Cu002D'}); if the sign is positive, no sign
626 * character appears in the result. As for the magnitude <i>m</i>:
627 *
628 * <ul>
629 * <li>If <i>m</i> is infinity, it is represented by the string
630 * {@code "Infinity"}; thus, positive infinity produces the
631 * result {@code "Infinity"} and negative infinity produces
632 * the result {@code "-Infinity"}.
633 *
634 * <li>If <i>m</i> is zero, it is represented by the string
635 * {@code "0x0.0p0"}; thus, negative zero produces the result
636 * {@code "-0x0.0p0"} and positive zero produces the result
637 * {@code "0x0.0p0"}.
638 *
639 * <li>If <i>m</i> is a {@code double} value with a
640 * normalized representation, substrings are used to represent the
641 * significand and exponent fields. The significand is
642 * represented by the characters {@code "0x1."}
643 * followed by a lowercase hexadecimal representation of the rest
644 * of the significand as a fraction. Trailing zeros in the
645 * hexadecimal representation are removed unless all the digits
646 * are zero, in which case a single zero is used. Next, the
647 * exponent is represented by {@code "p"} followed
648 * by a decimal string of the unbiased exponent as if produced by
649 * a call to {@link Integer#toString(int) Integer.toString} on the
650 * exponent value.
651 *
652 * <li>If <i>m</i> is a {@code double} value with a subnormal
653 * representation, the significand is represented by the
654 * characters {@code "0x0."} followed by a
655 * hexadecimal representation of the rest of the significand as a
656 * fraction. Trailing zeros in the hexadecimal representation are
657 * removed. Next, the exponent is represented by
658 * {@code "p-1022"}. Note that there must be at
659 * least one nonzero digit in a subnormal significand.
660 *
661 * </ul>
662 *
663 * </ul>
664 *
665 * <table class="striped">
666 * <caption>Examples</caption>
667 * <thead>
668 * <tr><th scope="col">Floating-point Value</th><th scope="col">Hexadecimal String</th>
669 * </thead>
670 * <tbody style="text-align:right">
671 * <tr><th scope="row">{@code 1.0}</th> <td>{@code 0x1.0p0}</td>
672 * <tr><th scope="row">{@code -1.0}</th> <td>{@code -0x1.0p0}</td>
673 * <tr><th scope="row">{@code 2.0}</th> <td>{@code 0x1.0p1}</td>
674 * <tr><th scope="row">{@code 3.0}</th> <td>{@code 0x1.8p1}</td>
675 * <tr><th scope="row">{@code 0.5}</th> <td>{@code 0x1.0p-1}</td>
676 * <tr><th scope="row">{@code 0.25}</th> <td>{@code 0x1.0p-2}</td>
677 * <tr><th scope="row">{@code Double.MAX_VALUE}</th>
678 * <td>{@code 0x1.fffffffffffffp1023}</td>
679 * <tr><th scope="row">{@code Minimum Normal Value}</th>
680 * <td>{@code 0x1.0p-1022}</td>
681 * <tr><th scope="row">{@code Maximum Subnormal Value}</th>
682 * <td>{@code 0x0.fffffffffffffp-1022}</td>
683 * <tr><th scope="row">{@code Double.MIN_VALUE}</th>
684 * <td>{@code 0x0.0000000000001p-1022}</td>
685 * </tbody>
686 * </table>
687 *
688 * @apiNote
689 * This method corresponds to the convertToHexCharacter operation
690 * defined in IEEE 754.
691 *
692 * @param d the {@code double} to be converted.
693 * @return a hex string representation of the argument.
694 * @since 1.5
695 */
696 public static String toHexString(double d) {
697 /*
698 * Modeled after the "a" conversion specifier in C99, section
699 * 7.19.6.1; however, the output of this method is more
700 * tightly specified.
701 */
702 if (!isFinite(d) )
703 // For infinity and NaN, use the decimal output.
704 return Double.toString(d);
705 else {
706 // Initialized to maximum size of output.
707 StringBuilder answer = new StringBuilder(24);
708
709 if (Math.copySign(1.0, d) == -1.0) // value is negative,
710 answer.append("-"); // so append sign info
711
712 answer.append("0x");
713
714 d = Math.abs(d);
715
716 if(d == 0.0) {
717 answer.append("0.0p0");
718 } else {
719 boolean subnormal = (d < Double.MIN_NORMAL);
720
721 // Isolate significand bits and OR in a high-order bit
722 // so that the string representation has a known
723 // length.
724 long signifBits = (Double.doubleToLongBits(d)
725 & DoubleConsts.SIGNIF_BIT_MASK) |
726 0x1000000000000000L;
727
728 // Subnormal values have a 0 implicit bit; normal
729 // values have a 1 implicit bit.
730 answer.append(subnormal ? "0." : "1.");
731
732 // Isolate the low-order 13 digits of the hex
733 // representation. If all the digits are zero,
734 // replace with a single 0; otherwise, remove all
735 // trailing zeros.
736 String signif = Long.toHexString(signifBits).substring(3,16);
737 answer.append(signif.equals("0000000000000") ? // 13 zeros
738 "0":
739 signif.replaceFirst("0{1,12}$", ""));
740
741 answer.append('p');
742 // If the value is subnormal, use the E_min exponent
743 // value for double; otherwise, extract and report d's
744 // exponent (the representation of a subnormal uses
745 // E_min -1).
746 answer.append(subnormal ?
747 Double.MIN_EXPONENT:
748 Math.getExponent(d));
749 }
750 return answer.toString();
751 }
752 }
753
754 /**
755 * Returns a {@code Double} object holding the
756 * {@code double} value represented by the argument string
757 * {@code s}.
758 *
759 * <p>If {@code s} is {@code null}, then a
760 * {@code NullPointerException} is thrown.
761 *
762 * <p>Leading and trailing whitespace characters in {@code s}
763 * are ignored. Whitespace is removed as if by the {@link
764 * String#trim} method; that is, both ASCII space and control
765 * characters are removed. The rest of {@code s} should
766 * constitute a <i>FloatValue</i> as described by the lexical
767 * syntax rules:
768 *
769 * <blockquote>
770 * <dl>
771 * <dt><i>FloatValue:</i>
772 * <dd><i>Sign<sub>opt</sub></i> {@code NaN}
773 * <dd><i>Sign<sub>opt</sub></i> {@code Infinity}
774 * <dd><i>Sign<sub>opt</sub> FloatingPointLiteral</i>
775 * <dd><i>Sign<sub>opt</sub> HexFloatingPointLiteral</i>
776 * <dd><i>SignedInteger</i>
777 * </dl>
778 *
779 * <dl>
780 * <dt><i>HexFloatingPointLiteral</i>:
781 * <dd> <i>HexSignificand BinaryExponent FloatTypeSuffix<sub>opt</sub></i>
782 * </dl>
783 *
784 * <dl>
785 * <dt><i>HexSignificand:</i>
786 * <dd><i>HexNumeral</i>
787 * <dd><i>HexNumeral</i> {@code .}
788 * <dd>{@code 0x} <i>HexDigits<sub>opt</sub>
789 * </i>{@code .}<i> HexDigits</i>
790 * <dd>{@code 0X}<i> HexDigits<sub>opt</sub>
791 * </i>{@code .} <i>HexDigits</i>
792 * </dl>
793 *
794 * <dl>
795 * <dt><i>BinaryExponent:</i>
796 * <dd><i>BinaryExponentIndicator SignedInteger</i>
797 * </dl>
798 *
799 * <dl>
800 * <dt><i>BinaryExponentIndicator:</i>
801 * <dd>{@code p}
802 * <dd>{@code P}
803 * </dl>
804 *
805 * </blockquote>
806 *
807 * where <i>Sign</i>, <i>FloatingPointLiteral</i>,
808 * <i>HexNumeral</i>, <i>HexDigits</i>, <i>SignedInteger</i> and
809 * <i>FloatTypeSuffix</i> are as defined in the lexical structure
810 * sections of
811 * <cite>The Java Language Specification</cite>,
812 * except that underscores are not accepted between digits.
813 * If {@code s} does not have the form of
814 * a <i>FloatValue</i>, then a {@code NumberFormatException}
815 * is thrown. Otherwise, {@code s} is regarded as
816 * representing an exact decimal value in the usual
817 * "computerized scientific notation" or as an exact
818 * hexadecimal value; this exact numerical value is then
819 * conceptually converted to an "infinitely precise"
820 * binary value that is then rounded to type {@code double}
821 * by the usual round-to-nearest rule of IEEE 754 floating-point
822 * arithmetic, which includes preserving the sign of a zero
823 * value.
824 *
825 * Note that the round-to-nearest rule also implies overflow and
826 * underflow behaviour; if the exact value of {@code s} is large
827 * enough in magnitude (greater than or equal to ({@link
828 * #MAX_VALUE} + {@link Math#ulp(double) ulp(MAX_VALUE)}/2),
829 * rounding to {@code double} will result in an infinity and if the
830 * exact value of {@code s} is small enough in magnitude (less
831 * than or equal to {@link #MIN_VALUE}/2), rounding to float will
832 * result in a zero.
833 *
834 * Finally, after rounding a {@code Double} object representing
835 * this {@code double} value is returned.
836 *
837 * <p>Note that trailing format specifiers, specifiers that
838 * determine the type of a floating-point literal
839 * ({@code 1.0f} is a {@code float} value;
840 * {@code 1.0d} is a {@code double} value), do
841 * <em>not</em> influence the results of this method. In other
842 * words, the numerical value of the input string is converted
843 * directly to the target floating-point type. The two-step
844 * sequence of conversions, string to {@code float} followed
845 * by {@code float} to {@code double}, is <em>not</em>
846 * equivalent to converting a string directly to
847 * {@code double}. For example, the {@code float}
848 * literal {@code 0.1f} is equal to the {@code double}
849 * value {@code 0.10000000149011612}; the {@code float}
850 * literal {@code 0.1f} represents a different numerical
851 * value than the {@code double} literal
852 * {@code 0.1}. (The numerical value 0.1 cannot be exactly
853 * represented in a binary floating-point number.)
854 *
855 * <p>To avoid calling this method on an invalid string and having
856 * a {@code NumberFormatException} be thrown, the regular
857 * expression below can be used to screen the input string:
858 *
859 * {@snippet lang="java" :
860 * final String Digits = "(\\p{Digit}+)";
861 * final String HexDigits = "(\\p{XDigit}+)";
862 * // an exponent is 'e' or 'E' followed by an optionally
863 * // signed decimal integer.
864 * final String Exp = "[eE][+-]?"+Digits;
865 * final String fpRegex =
866 * ("[\\x00-\\x20]*"+ // Optional leading "whitespace"
867 * "[+-]?(" + // Optional sign character
868 * "NaN|" + // "NaN" string
869 * "Infinity|" + // "Infinity" string
870 *
871 * // A decimal floating-point string representing a finite positive
872 * // number without a leading sign has at most five basic pieces:
873 * // Digits . Digits ExponentPart FloatTypeSuffix
874 * //
875 * // Since this method allows integer-only strings as input
876 * // in addition to strings of floating-point literals, the
877 * // two sub-patterns below are simplifications of the grammar
878 * // productions from section 3.10.2 of
879 * // The Java Language Specification.
880 *
881 * // Digits ._opt Digits_opt ExponentPart_opt FloatTypeSuffix_opt
882 * "((("+Digits+"(\\.)?("+Digits+"?)("+Exp+")?)|"+
883 *
884 * // . Digits ExponentPart_opt FloatTypeSuffix_opt
885 * "(\\.("+Digits+")("+Exp+")?)|"+
886 *
887 * // Hexadecimal strings
888 * "((" +
889 * // 0[xX] HexDigits ._opt BinaryExponent FloatTypeSuffix_opt
890 * "(0[xX]" + HexDigits + "(\\.)?)|" +
891 *
892 * // 0[xX] HexDigits_opt . HexDigits BinaryExponent FloatTypeSuffix_opt
893 * "(0[xX]" + HexDigits + "?(\\.)" + HexDigits + ")" +
894 *
895 * ")[pP][+-]?" + Digits + "))" +
896 * "[fFdD]?))" +
897 * "[\\x00-\\x20]*");// Optional trailing "whitespace"
898 * // @link region substring="Pattern.matches" target ="java.util.regex.Pattern#matches"
899 * if (Pattern.matches(fpRegex, myString))
900 * Double.valueOf(myString); // Will not throw NumberFormatException
901 * // @end
902 * else {
903 * // Perform suitable alternative action
904 * }
905 * }
906 *
907 * @apiNote To interpret localized string representations of a
908 * floating-point value, or string representations that have
909 * non-ASCII digits, use {@link java.text.NumberFormat}. For
910 * example,
911 * {@snippet lang="java" :
912 * NumberFormat.getInstance(l).parse(s).doubleValue();
913 * }
914 * where {@code l} is the desired locale, or
915 * {@link java.util.Locale#ROOT} if locale insensitive.
916 *
917 * @apiNote
918 * This method corresponds to the convertFromDecimalCharacter and
919 * convertFromHexCharacter operations defined in IEEE 754.
920 *
921 * @param s the string to be parsed.
922 * @return a {@code Double} object holding the value
923 * represented by the {@code String} argument.
924 * @throws NumberFormatException if the string does not contain a
925 * parsable number.
926 * @see Double##decimalToBinaryConversion Decimal ↔ Binary Conversion Issues
927 */
928 public static Double valueOf(String s) throws NumberFormatException {
929 return new Double(parseDouble(s));
930 }
931
932 /**
933 * Returns a {@code Double} instance representing the specified
934 * {@code double} value.
935 * If a new {@code Double} instance is not required, this method
936 * should generally be used in preference to the constructor
937 * {@link #Double(double)}, as this method is likely to yield
938 * significantly better space and time performance by caching
939 * frequently requested values.
940 *
941 * @param d a double value.
942 * @return a {@code Double} instance representing {@code d}.
943 * @since 1.5
944 */
945 @IntrinsicCandidate
946 public static Double valueOf(double d) {
947 return new Double(d);
948 }
949
950 /**
951 * Returns a new {@code double} initialized to the value
952 * represented by the specified {@code String}, as performed
953 * by the {@code valueOf} method of class
954 * {@code Double}.
955 *
956 * @param s the string to be parsed.
957 * @return the {@code double} value represented by the string
958 * argument.
959 * @throws NullPointerException if the string is null
960 * @throws NumberFormatException if the string does not contain
961 * a parsable {@code double}.
962 * @see java.lang.Double#valueOf(String)
963 * @see Double##decimalToBinaryConversion Decimal ↔ Binary Conversion Issues
964 * @since 1.2
965 */
966 public static double parseDouble(String s) throws NumberFormatException {
967 return FloatingDecimal.parseDouble(s);
968 }
969
970 /**
971 * Returns {@code true} if the specified number is a
972 * Not-a-Number (NaN) value, {@code false} otherwise.
973 *
974 * @apiNote
975 * This method corresponds to the isNaN operation defined in IEEE
976 * 754.
977 *
978 * @param v the value to be tested.
979 * @return {@code true} if the value of the argument is NaN;
980 * {@code false} otherwise.
981 */
982 public static boolean isNaN(double v) {
983 return (v != v);
984 }
985
986 /**
987 * Returns {@code true} if the specified number is infinitely
988 * large in magnitude, {@code false} otherwise.
989 *
990 * @apiNote
991 * This method corresponds to the isInfinite operation defined in
992 * IEEE 754.
993 *
994 * @param v the value to be tested.
995 * @return {@code true} if the value of the argument is positive
996 * infinity or negative infinity; {@code false} otherwise.
997 */
998 @IntrinsicCandidate
999 public static boolean isInfinite(double v) {
1000 return Math.abs(v) > MAX_VALUE;
1001 }
1002
1003 /**
1004 * Returns {@code true} if the argument is a finite floating-point
1005 * value; returns {@code false} otherwise (for NaN and infinity
1006 * arguments).
1007 *
1008 * @apiNote
1009 * This method corresponds to the isFinite operation defined in
1010 * IEEE 754.
1011 *
1012 * @param d the {@code double} value to be tested
1013 * @return {@code true} if the argument is a finite
1014 * floating-point value, {@code false} otherwise.
1015 * @since 1.8
1016 */
1017 @IntrinsicCandidate
1018 public static boolean isFinite(double d) {
1019 return Math.abs(d) <= Double.MAX_VALUE;
1020 }
1021
1022 /**
1023 * The value of the Double.
1024 *
1025 * @serial
1026 */
1027 private final double value;
1028
1029 /**
1030 * Constructs a newly allocated {@code Double} object that
1031 * represents the primitive {@code double} argument.
1032 *
1033 * @param value the value to be represented by the {@code Double}.
1034 *
1035 * @deprecated
1036 * It is rarely appropriate to use this constructor. The static factory
1037 * {@link #valueOf(double)} is generally a better choice, as it is
1038 * likely to yield significantly better space and time performance.
1039 */
1040 @Deprecated(since="9")
1041 public Double(double value) {
1042 this.value = value;
1043 }
1044
1045 /**
1046 * Constructs a newly allocated {@code Double} object that
1047 * represents the floating-point value of type {@code double}
1048 * represented by the string. The string is converted to a
1049 * {@code double} value as if by the {@code valueOf} method.
1050 *
1051 * @param s a string to be converted to a {@code Double}.
1052 * @throws NumberFormatException if the string does not contain a
1053 * parsable number.
1054 *
1055 * @deprecated
1056 * It is rarely appropriate to use this constructor.
1057 * Use {@link #parseDouble(String)} to convert a string to a
1058 * {@code double} primitive, or use {@link #valueOf(String)}
1059 * to convert a string to a {@code Double} object.
1060 */
1061 @Deprecated(since="9")
1062 public Double(String s) throws NumberFormatException {
1063 value = parseDouble(s);
1064 }
1065
1066 /**
1067 * Returns {@code true} if this {@code Double} value is
1068 * a Not-a-Number (NaN), {@code false} otherwise.
1069 *
1070 * @return {@code true} if the value represented by this object is
1071 * NaN; {@code false} otherwise.
1072 */
1073 public boolean isNaN() {
1074 return isNaN(value);
1075 }
1076
1077 /**
1078 * Returns {@code true} if this {@code Double} value is
1079 * infinitely large in magnitude, {@code false} otherwise.
1080 *
1081 * @return {@code true} if the value represented by this object is
1082 * positive infinity or negative infinity;
1083 * {@code false} otherwise.
1084 */
1085 public boolean isInfinite() {
1086 return isInfinite(value);
1087 }
1088
1089 /**
1090 * Returns a string representation of this {@code Double} object.
1091 * The primitive {@code double} value represented by this
1092 * object is converted to a string exactly as if by the method
1093 * {@code toString} of one argument.
1094 *
1095 * @return a {@code String} representation of this object.
1096 * @see java.lang.Double#toString(double)
1097 */
1098 public String toString() {
1099 return toString(value);
1100 }
1101
1102 /**
1103 * Returns the value of this {@code Double} as a {@code byte}
1104 * after a narrowing primitive conversion.
1105 *
1106 * @return the {@code double} value represented by this object
1107 * converted to type {@code byte}
1108 * @jls 5.1.3 Narrowing Primitive Conversion
1109 * @since 1.1
1110 */
1111 @Override
1112 public byte byteValue() {
1113 return (byte)value;
1114 }
1115
1116 /**
1117 * Returns the value of this {@code Double} as a {@code short}
1118 * after a narrowing primitive conversion.
1119 *
1120 * @return the {@code double} value represented by this object
1121 * converted to type {@code short}
1122 * @jls 5.1.3 Narrowing Primitive Conversion
1123 * @since 1.1
1124 */
1125 @Override
1126 public short shortValue() {
1127 return (short)value;
1128 }
1129
1130 /**
1131 * Returns the value of this {@code Double} as an {@code int}
1132 * after a narrowing primitive conversion.
1133 * @jls 5.1.3 Narrowing Primitive Conversion
1134 *
1135 * @apiNote
1136 * This method corresponds to the convertToIntegerTowardZero
1137 * operation defined in IEEE 754.
1138 *
1139 * @return the {@code double} value represented by this object
1140 * converted to type {@code int}
1141 */
1142 @Override
1143 public int intValue() {
1144 return (int)value;
1145 }
1146
1147 /**
1148 * Returns the value of this {@code Double} as a {@code long}
1149 * after a narrowing primitive conversion.
1150 *
1151 * @apiNote
1152 * This method corresponds to the convertToIntegerTowardZero
1153 * operation defined in IEEE 754.
1154 *
1155 * @return the {@code double} value represented by this object
1156 * converted to type {@code long}
1157 * @jls 5.1.3 Narrowing Primitive Conversion
1158 */
1159 @Override
1160 public long longValue() {
1161 return (long)value;
1162 }
1163
1164 /**
1165 * Returns the value of this {@code Double} as a {@code float}
1166 * after a narrowing primitive conversion.
1167 *
1168 * @apiNote
1169 * This method corresponds to the convertFormat operation defined
1170 * in IEEE 754.
1171 *
1172 * @return the {@code double} value represented by this object
1173 * converted to type {@code float}
1174 * @jls 5.1.3 Narrowing Primitive Conversion
1175 * @since 1.0
1176 */
1177 @Override
1178 public float floatValue() {
1179 return (float)value;
1180 }
1181
1182 /**
1183 * Returns the {@code double} value of this {@code Double} object.
1184 *
1185 * @return the {@code double} value represented by this object
1186 */
1187 @Override
1188 @IntrinsicCandidate
1189 public double doubleValue() {
1190 return value;
1191 }
1192
1193 /**
1194 * Returns a hash code for this {@code Double} object. The
1195 * result is the exclusive OR of the two halves of the
1196 * {@code long} integer bit representation, exactly as
1197 * produced by the method {@link #doubleToLongBits(double)}, of
1198 * the primitive {@code double} value represented by this
1199 * {@code Double} object. That is, the hash code is the value
1200 * of the expression:
1201 *
1202 * <blockquote>
1203 * {@code (int)(v^(v>>>32))}
1204 * </blockquote>
1205 *
1206 * where {@code v} is defined by:
1207 *
1208 * <blockquote>
1209 * {@code long v = Double.doubleToLongBits(this.doubleValue());}
1210 * </blockquote>
1211 *
1212 * @return a {@code hash code} value for this object.
1213 */
1214 @Override
1215 public int hashCode() {
1216 return Double.hashCode(value);
1217 }
1218
1219 /**
1220 * Returns a hash code for a {@code double} value; compatible with
1221 * {@code Double.hashCode()}.
1222 *
1223 * @param value the value to hash
1224 * @return a hash code value for a {@code double} value.
1225 * @since 1.8
1226 */
1227 public static int hashCode(double value) {
1228 return Long.hashCode(doubleToLongBits(value));
1229 }
1230
1231 /**
1232 * Compares this object against the specified object. The result
1233 * is {@code true} if and only if the argument is not
1234 * {@code null} and is a {@code Double} object that
1235 * represents a {@code double} that has the same value as the
1236 * {@code double} represented by this object. For this
1237 * purpose, two {@code double} values are considered to be
1238 * the same if and only if the method {@link
1239 * #doubleToLongBits(double)} returns the identical
1240 * {@code long} value when applied to each.
1241 * In other words, {@linkplain ##repEquivalence representation
1242 * equivalence} is used to compare the {@code double} values.
1243 *
1244 * @apiNote
1245 * This method is defined in terms of {@link
1246 * #doubleToLongBits(double)} rather than the {@code ==} operator
1247 * on {@code double} values since the {@code ==} operator does
1248 * <em>not</em> define an equivalence relation and to satisfy the
1249 * {@linkplain Object#equals equals contract} an equivalence
1250 * relation must be implemented; see {@linkplain ##equivalenceRelation
1251 * this discussion for details of floating-point equality and equivalence}.
1252 *
1253 * @see java.lang.Double#doubleToLongBits(double)
1254 * @jls 15.21.1 Numerical Equality Operators == and !=
1255 */
1256 public boolean equals(Object obj) {
1257 return (obj instanceof Double d) &&
1258 (doubleToLongBits(d.value) == doubleToLongBits(value));
1259 }
1260
1261 /**
1262 * Returns a representation of the specified floating-point value
1263 * according to the IEEE 754 floating-point "double
1264 * format" bit layout.
1265 *
1266 * <p>Bit 63 (the bit that is selected by the mask
1267 * {@code 0x8000000000000000L}) represents the sign of the
1268 * floating-point number. Bits
1269 * 62-52 (the bits that are selected by the mask
1270 * {@code 0x7ff0000000000000L}) represent the exponent. Bits 51-0
1271 * (the bits that are selected by the mask
1272 * {@code 0x000fffffffffffffL}) represent the significand
1273 * (sometimes called the mantissa) of the floating-point number.
1274 *
1275 * <p>If the argument is positive infinity, the result is
1276 * {@code 0x7ff0000000000000L}.
1277 *
1278 * <p>If the argument is negative infinity, the result is
1279 * {@code 0xfff0000000000000L}.
1280 *
1281 * <p>If the argument is NaN, the result is
1282 * {@code 0x7ff8000000000000L}.
1283 *
1284 * <p>In all cases, the result is a {@code long} integer that, when
1285 * given to the {@link #longBitsToDouble(long)} method, will produce a
1286 * floating-point value the same as the argument to
1287 * {@code doubleToLongBits} (except all NaN values are
1288 * collapsed to a single "canonical" NaN value).
1289 *
1290 * @param value a {@code double} precision floating-point number.
1291 * @return the bits that represent the floating-point number.
1292 */
1293 @IntrinsicCandidate
1294 public static long doubleToLongBits(double value) {
1295 if (!isNaN(value)) {
1296 return doubleToRawLongBits(value);
1297 }
1298 return 0x7ff8000000000000L;
1299 }
1300
1301 /**
1302 * Returns a representation of the specified floating-point value
1303 * according to the IEEE 754 floating-point "double
1304 * format" bit layout, preserving Not-a-Number (NaN) values.
1305 *
1306 * <p>Bit 63 (the bit that is selected by the mask
1307 * {@code 0x8000000000000000L}) represents the sign of the
1308 * floating-point number. Bits
1309 * 62-52 (the bits that are selected by the mask
1310 * {@code 0x7ff0000000000000L}) represent the exponent. Bits 51-0
1311 * (the bits that are selected by the mask
1312 * {@code 0x000fffffffffffffL}) represent the significand
1313 * (sometimes called the mantissa) of the floating-point number.
1314 *
1315 * <p>If the argument is positive infinity, the result is
1316 * {@code 0x7ff0000000000000L}.
1317 *
1318 * <p>If the argument is negative infinity, the result is
1319 * {@code 0xfff0000000000000L}.
1320 *
1321 * <p>If the argument is NaN, the result is the {@code long}
1322 * integer representing the actual NaN value. Unlike the
1323 * {@code doubleToLongBits} method,
1324 * {@code doubleToRawLongBits} does not collapse all the bit
1325 * patterns encoding a NaN to a single "canonical" NaN
1326 * value.
1327 *
1328 * <p>In all cases, the result is a {@code long} integer that,
1329 * when given to the {@link #longBitsToDouble(long)} method, will
1330 * produce a floating-point value the same as the argument to
1331 * {@code doubleToRawLongBits}.
1332 *
1333 * @param value a {@code double} precision floating-point number.
1334 * @return the bits that represent the floating-point number.
1335 * @since 1.3
1336 */
1337 @IntrinsicCandidate
1338 public static native long doubleToRawLongBits(double value);
1339
1340 /**
1341 * Returns the {@code double} value corresponding to a given
1342 * bit representation.
1343 * The argument is considered to be a representation of a
1344 * floating-point value according to the IEEE 754 floating-point
1345 * "double format" bit layout.
1346 *
1347 * <p>If the argument is {@code 0x7ff0000000000000L}, the result
1348 * is positive infinity.
1349 *
1350 * <p>If the argument is {@code 0xfff0000000000000L}, the result
1351 * is negative infinity.
1352 *
1353 * <p>If the argument is any value in the range
1354 * {@code 0x7ff0000000000001L} through
1355 * {@code 0x7fffffffffffffffL} or in the range
1356 * {@code 0xfff0000000000001L} through
1357 * {@code 0xffffffffffffffffL}, the result is a NaN. No IEEE
1358 * 754 floating-point operation provided by Java can distinguish
1359 * between two NaN values of the same type with different bit
1360 * patterns. Distinct values of NaN are only distinguishable by
1361 * use of the {@code Double.doubleToRawLongBits} method.
1362 *
1363 * <p>In all other cases, let <i>s</i>, <i>e</i>, and <i>m</i> be three
1364 * values that can be computed from the argument:
1365 *
1366 * {@snippet lang="java" :
1367 * int s = ((bits >> 63) == 0) ? 1 : -1;
1368 * int e = (int)((bits >> 52) & 0x7ffL);
1369 * long m = (e == 0) ?
1370 * (bits & 0xfffffffffffffL) << 1 :
1371 * (bits & 0xfffffffffffffL) | 0x10000000000000L;
1372 * }
1373 *
1374 * Then the floating-point result equals the value of the mathematical
1375 * expression <i>s</i>·<i>m</i>·2<sup><i>e</i>-1075</sup>.
1376 *
1377 * <p>Note that this method may not be able to return a
1378 * {@code double} NaN with exactly same bit pattern as the
1379 * {@code long} argument. IEEE 754 distinguishes between two
1380 * kinds of NaNs, quiet NaNs and <i>signaling NaNs</i>. The
1381 * differences between the two kinds of NaN are generally not
1382 * visible in Java. Arithmetic operations on signaling NaNs turn
1383 * them into quiet NaNs with a different, but often similar, bit
1384 * pattern. However, on some processors merely copying a
1385 * signaling NaN also performs that conversion. In particular,
1386 * copying a signaling NaN to return it to the calling method
1387 * may perform this conversion. So {@code longBitsToDouble}
1388 * may not be able to return a {@code double} with a
1389 * signaling NaN bit pattern. Consequently, for some
1390 * {@code long} values,
1391 * {@code doubleToRawLongBits(longBitsToDouble(start))} may
1392 * <i>not</i> equal {@code start}. Moreover, which
1393 * particular bit patterns represent signaling NaNs is platform
1394 * dependent; although all NaN bit patterns, quiet or signaling,
1395 * must be in the NaN range identified above.
1396 *
1397 * @param bits any {@code long} integer.
1398 * @return the {@code double} floating-point value with the same
1399 * bit pattern.
1400 */
1401 @IntrinsicCandidate
1402 public static native double longBitsToDouble(long bits);
1403
1404 /**
1405 * Compares two {@code Double} objects numerically.
1406 *
1407 * This method imposes a total order on {@code Double} objects
1408 * with two differences compared to the incomplete order defined by
1409 * the Java language numerical comparison operators ({@code <, <=,
1410 * ==, >=, >}) on {@code double} values.
1411 *
1412 * <ul><li> A NaN is <em>unordered</em> with respect to other
1413 * values and unequal to itself under the comparison
1414 * operators. This method chooses to define {@code
1415 * Double.NaN} to be equal to itself and greater than all
1416 * other {@code double} values (including {@code
1417 * Double.POSITIVE_INFINITY}).
1418 *
1419 * <li> Positive zero and negative zero compare equal
1420 * numerically, but are distinct and distinguishable values.
1421 * This method chooses to define positive zero ({@code +0.0d}),
1422 * to be greater than negative zero ({@code -0.0d}).
1423 * </ul>
1424 *
1425 * This ensures that the <i>natural ordering</i> of {@code Double}
1426 * objects imposed by this method is <i>consistent with
1427 * equals</i>; see {@linkplain ##equivalenceRelation this
1428 * discussion for details of floating-point comparison and
1429 * ordering}.
1430 *
1431 * @apiNote
1432 * The inclusion of a total order idiom in the Java SE API
1433 * predates the inclusion of that functionality in the IEEE 754
1434 * standard. The ordering of the totalOrder predicate chosen by
1435 * IEEE 754 differs from the total order chosen by this method.
1436 * While this method treats all NaN representations as being in
1437 * the same equivalence class, the IEEE 754 total order defines an
1438 * ordering based on the bit patterns of the NaN among the
1439 * different NaN representations. The IEEE 754 order regards
1440 * "negative" NaN representations, that is NaN representations
1441 * whose sign bit is set, to be less than any finite or infinite
1442 * value and less than any "positive" NaN. In addition, the IEEE
1443 * order regards all positive NaN values as greater than positive
1444 * infinity. See the IEEE 754 standard for full details of its
1445 * total ordering.
1446 *
1447 * @param anotherDouble the {@code Double} to be compared.
1448 * @return the value {@code 0} if {@code anotherDouble} is
1449 * numerically equal to this {@code Double}; a value
1450 * less than {@code 0} if this {@code Double}
1451 * is numerically less than {@code anotherDouble};
1452 * and a value greater than {@code 0} if this
1453 * {@code Double} is numerically greater than
1454 * {@code anotherDouble}.
1455 *
1456 * @jls 15.20.1 Numerical Comparison Operators {@code <}, {@code <=}, {@code >}, and {@code >=}
1457 * @since 1.2
1458 */
1459 @Override
1460 public int compareTo(Double anotherDouble) {
1461 return Double.compare(value, anotherDouble.value);
1462 }
1463
1464 /**
1465 * Compares the two specified {@code double} values. The sign
1466 * of the integer value returned is the same as that of the
1467 * integer that would be returned by the call:
1468 * <pre>
1469 * Double.valueOf(d1).compareTo(Double.valueOf(d2))
1470 * </pre>
1471 *
1472 * @apiNote
1473 * One idiom to implement {@linkplain ##repEquivalence
1474 * representation equivalence} on {@code double} values is
1475 * {@snippet lang="java" :
1476 * Double.compare(a, b) == 0
1477 * }
1478 * @param d1 the first {@code double} to compare
1479 * @param d2 the second {@code double} to compare
1480 * @return the value {@code 0} if {@code d1} is
1481 * numerically equal to {@code d2}; a value less than
1482 * {@code 0} if {@code d1} is numerically less than
1483 * {@code d2}; and a value greater than {@code 0}
1484 * if {@code d1} is numerically greater than
1485 * {@code d2}.
1486 * @since 1.4
1487 */
1488 public static int compare(double d1, double d2) {
1489 if (d1 < d2)
1490 return -1; // Neither val is NaN, thisVal is smaller
1491 if (d1 > d2)
1492 return 1; // Neither val is NaN, thisVal is larger
1493
1494 // Cannot use doubleToRawLongBits because of possibility of NaNs.
1495 long thisBits = Double.doubleToLongBits(d1);
1496 long anotherBits = Double.doubleToLongBits(d2);
1497
1498 return (thisBits == anotherBits ? 0 : // Values are equal
1499 (thisBits < anotherBits ? -1 : // (-0.0, 0.0) or (!NaN, NaN)
1500 1)); // (0.0, -0.0) or (NaN, !NaN)
1501 }
1502
1503 /**
1504 * Adds two {@code double} values together as per the + operator.
1505 *
1506 * @apiNote This method corresponds to the addition operation
1507 * defined in IEEE 754.
1508 *
1509 * @param a the first operand
1510 * @param b the second operand
1511 * @return the sum of {@code a} and {@code b}
1512 * @jls 4.2.4 Floating-Point Operations
1513 * @see java.util.function.BinaryOperator
1514 * @since 1.8
1515 */
1516 public static double sum(double a, double b) {
1517 return a + b;
1518 }
1519
1520 /**
1521 * Returns the greater of two {@code double} values
1522 * as if by calling {@link Math#max(double, double) Math.max}.
1523 *
1524 * @apiNote
1525 * This method corresponds to the maximum operation defined in
1526 * IEEE 754.
1527 *
1528 * @param a the first operand
1529 * @param b the second operand
1530 * @return the greater of {@code a} and {@code b}
1531 * @see java.util.function.BinaryOperator
1532 * @since 1.8
1533 */
1534 public static double max(double a, double b) {
1535 return Math.max(a, b);
1536 }
1537
1538 /**
1539 * Returns the smaller of two {@code double} values
1540 * as if by calling {@link Math#min(double, double) Math.min}.
1541 *
1542 * @apiNote
1543 * This method corresponds to the minimum operation defined in
1544 * IEEE 754.
1545 *
1546 * @param a the first operand
1547 * @param b the second operand
1548 * @return the smaller of {@code a} and {@code b}.
1549 * @see java.util.function.BinaryOperator
1550 * @since 1.8
1551 */
1552 public static double min(double a, double b) {
1553 return Math.min(a, b);
1554 }
1555
1556 /**
1557 * Returns an {@link Optional} containing the nominal descriptor for this
1558 * instance, which is the instance itself.
1559 *
1560 * @return an {@link Optional} describing the {@linkplain Double} instance
1561 * @since 12
1562 */
1563 @Override
1564 public Optional<Double> describeConstable() {
1565 return Optional.of(this);
1566 }
1567
1568 /**
1569 * Resolves this instance as a {@link ConstantDesc}, the result of which is
1570 * the instance itself.
1571 *
1572 * @param lookup ignored
1573 * @return the {@linkplain Double} instance
1574 * @since 12
1575 */
1576 @Override
1577 public Double resolveConstantDesc(MethodHandles.Lookup lookup) {
1578 return this;
1579 }
1580
1581 /** use serialVersionUID from JDK 1.0.2 for interoperability */
1582 @java.io.Serial
1583 private static final long serialVersionUID = -9172774392245257468L;
1584 }