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
6 * under the terms of the GNU General Public License version 2 only, as
7 * published by the Free Software Foundation. Oracle designates this
8 * particular file as subject to the "Classpath" exception as provided
9 * by Oracle in the LICENSE file that accompanied this code.
10 *
11 * This code is distributed in the hope that it will be useful, but WITHOUT
12 * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
13 * FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
14 * version 2 for more details (a copy is included in the LICENSE file that
15 * accompanied this code).
16 *
17 * You should have received a copy of the GNU General Public License version
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20 *
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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.FloatConsts;
34 import jdk.internal.math.FloatingDecimal;
35 import jdk.internal.math.FloatToDecimal;
36 import jdk.internal.value.DeserializeConstructor;
37 import jdk.internal.vm.annotation.IntrinsicCandidate;
38
39 /**
40 * The {@code Float} class is the {@linkplain
41 * java.lang##wrapperClass wrapper class} for values of the primitive
42 * type {@code float}. An object of type {@code Float} contains a
43 * single field whose type is {@code float}.
44 *
45 * <p>In addition, this class provides several methods for converting a
46 * {@code float} to a {@code String} and a
47 * {@code String} to a {@code float}, as well as other
48 * constants and methods useful when dealing with a
49 * {@code float}.
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 {@linkplain #equals(Object) equal}
53 * as interchangeable and should not use instances for synchronization, mutexes, or
54 * with {@linkplain java.lang.ref.Reference object references}.
55 *
56 * <div class="preview-block">
57 * <div class="preview-comment">
58 * When preview features are enabled, {@code Float} is a {@linkplain Class#isValue value class}.
59 * Use of value class instances for synchronization, mutexes, or with
60 * {@linkplain java.lang.ref.Reference object references} result in
61 * {@link IdentityException}.
62 * </div>
63 * </div>
64 *
65 * <h2><a id=equivalenceRelation>Floating-point Equality, Equivalence,
66 * and Comparison</a></h2>
67 *
68 * The class {@code java.lang.Double} has a {@linkplain
69 * Double##equivalenceRelation discussion of equality,
70 * equivalence, and comparison of floating-point values} that is
71 * equally applicable to {@code float} values.
72 *
73 * <h2><a id=decimalToBinaryConversion>Decimal ↔ Binary Conversion Issues</a></h2>
74 *
75 * The {@linkplain Double##decimalToBinaryConversion discussion of binary to
76 * decimal conversion issues} in {@code java.lang.Double} is also
77 * applicable to {@code float} values.
78 *
79 * @see <a href="https://standards.ieee.org/ieee/754/6210/">
80 * <cite>IEEE Standard for Floating-Point Arithmetic</cite></a>
81 *
82 * @author Lee Boynton
83 * @author Arthur van Hoff
84 * @author Joseph D. Darcy
85 * @since 1.0
86 */
87 @jdk.internal.MigratedValueClass
88 @jdk.internal.ValueBased
89 public final class Float extends Number
90 implements Comparable<Float>, Constable, ConstantDesc {
91 /**
92 * A constant holding the positive infinity of type
93 * {@code float}. It is equal to the value returned by
94 * {@code Float.intBitsToFloat(0x7f800000)}.
95 */
96 public static final float POSITIVE_INFINITY = 1.0f / 0.0f;
97
98 /**
99 * A constant holding the negative infinity of type
100 * {@code float}. It is equal to the value returned by
101 * {@code Float.intBitsToFloat(0xff800000)}.
102 */
103 public static final float NEGATIVE_INFINITY = -1.0f / 0.0f;
104
105 /**
106 * A constant holding a Not-a-Number (NaN) value of type
107 * {@code float}. It is equivalent to the value returned by
108 * {@code Float.intBitsToFloat(0x7fc00000)}.
109 */
110 public static final float NaN = 0.0f / 0.0f;
111
112 /**
113 * A constant holding the largest positive finite value of type
114 * {@code float}, (2-2<sup>-23</sup>)·2<sup>127</sup>.
115 * It is equal to the hexadecimal floating-point literal
116 * {@code 0x1.fffffeP+127f} and also equal to
117 * {@code Float.intBitsToFloat(0x7f7fffff)}.
118 */
119 public static final float MAX_VALUE = 0x1.fffffeP+127f; // 3.4028235e+38f
120
121 /**
122 * A constant holding the smallest positive normal value of type
123 * {@code float}, 2<sup>-126</sup>. It is equal to the
124 * hexadecimal floating-point literal {@code 0x1.0p-126f} and also
125 * equal to {@code Float.intBitsToFloat(0x00800000)}.
126 *
127 * @since 1.6
128 */
129 public static final float MIN_NORMAL = 0x1.0p-126f; // 1.17549435E-38f
130
131 /**
132 * A constant holding the smallest positive nonzero value of type
133 * {@code float}, 2<sup>-149</sup>. It is equal to the
134 * hexadecimal floating-point literal {@code 0x0.000002P-126f}
135 * and also equal to {@code Float.intBitsToFloat(0x1)}.
136 */
137 public static final float MIN_VALUE = 0x0.000002P-126f; // 1.4e-45f
138
139 /**
140 * The number of bits used to represent a {@code float} value,
141 * {@value}.
142 *
143 * @since 1.5
144 */
145 public static final int SIZE = 32;
146
147 /**
148 * The number of bits in the significand of a {@code float} value,
149 * {@value}. This is the parameter N in section {@jls 4.2.3} of
150 * <cite>The Java Language Specification</cite>.
151 *
152 * @since 19
153 */
154 public static final int PRECISION = 24;
155
156 /**
157 * Maximum exponent a finite {@code float} variable may have,
158 * {@value}. It is equal to the value returned by {@code
159 * Math.getExponent(Float.MAX_VALUE)}.
160 *
161 * @since 1.6
162 */
163 public static final int MAX_EXPONENT = (1 << (SIZE - PRECISION - 1)) - 1; // 127
164
165 /**
166 * Minimum exponent a normalized {@code float} variable may have,
167 * {@value}. It is equal to the value returned by {@code
168 * Math.getExponent(Float.MIN_NORMAL)}.
169 *
170 * @since 1.6
171 */
172 public static final int MIN_EXPONENT = 1 - MAX_EXPONENT; // -126
173
174 /**
175 * The number of bytes used to represent a {@code float} value,
176 * {@value}.
177 *
178 * @since 1.8
179 */
180 public static final int BYTES = SIZE / Byte.SIZE;
181
182 /**
183 * The {@code Class} instance representing the primitive type
184 * {@code float}.
185 *
186 * @since 1.1
187 */
188 public static final Class<Float> TYPE = Class.getPrimitiveClass("float");
189
190 /**
191 * Returns a string representation of the {@code float}
192 * argument. All characters mentioned below are ASCII characters.
193 * <ul>
194 * <li>If the argument is NaN, the result is the string
195 * "{@code NaN}".
196 * <li>Otherwise, the result is a string that represents the sign and
197 * magnitude (absolute value) of the argument. If the sign is
198 * negative, the first character of the result is
199 * '{@code -}' ({@code '\u005Cu002D'}); if the sign is
200 * positive, no sign character appears in the result. As for
201 * the magnitude <i>m</i>:
202 * <ul>
203 * <li>If <i>m</i> is infinity, it is represented by the characters
204 * {@code "Infinity"}; thus, positive infinity produces
205 * the result {@code "Infinity"} and negative infinity
206 * produces the result {@code "-Infinity"}.
207 * <li>If <i>m</i> is zero, it is represented by the characters
208 * {@code "0.0"}; thus, negative zero produces the result
209 * {@code "-0.0"} and positive zero produces the result
210 * {@code "0.0"}.
211 *
212 * <li> Otherwise <i>m</i> is positive and finite.
213 * It is converted to a string in two stages:
214 * <ul>
215 * <li> <em>Selection of a decimal</em>:
216 * A well-defined decimal <i>d</i><sub><i>m</i></sub>
217 * is selected to represent <i>m</i>.
218 * This decimal is (almost always) the <em>shortest</em> one that
219 * rounds to <i>m</i> according to the round to nearest
220 * rounding policy of IEEE 754 floating-point arithmetic.
221 * <li> <em>Formatting as a string</em>:
222 * The decimal <i>d</i><sub><i>m</i></sub> is formatted as a string,
223 * either in plain or in computerized scientific notation,
224 * depending on its value.
225 * </ul>
226 * </ul>
227 * </ul>
228 *
229 * <p>A <em>decimal</em> is a number of the form
230 * <i>s</i>×10<sup><i>i</i></sup>
231 * for some (unique) integers <i>s</i> > 0 and <i>i</i> such that
232 * <i>s</i> is not a multiple of 10.
233 * These integers are the <em>significand</em> and
234 * the <em>exponent</em>, respectively, of the decimal.
235 * The <em>length</em> of the decimal is the (unique)
236 * positive integer <i>n</i> meeting
237 * 10<sup><i>n</i>-1</sup> ≤ <i>s</i> < 10<sup><i>n</i></sup>.
238 *
239 * <p>The decimal <i>d</i><sub><i>m</i></sub> for a finite positive <i>m</i>
240 * is defined as follows:
241 * <ul>
242 * <li>Let <i>R</i> be the set of all decimals that round to <i>m</i>
243 * according to the usual <em>round to nearest</em> rounding policy of
244 * IEEE 754 floating-point arithmetic.
245 * <li>Let <i>p</i> be the minimal length over all decimals in <i>R</i>.
246 * <li>When <i>p</i> ≥ 2, let <i>T</i> be the set of all decimals
247 * in <i>R</i> with length <i>p</i>.
248 * Otherwise, let <i>T</i> be the set of all decimals
249 * in <i>R</i> with length 1 or 2.
250 * <li>Define <i>d</i><sub><i>m</i></sub> as the decimal in <i>T</i>
251 * that is closest to <i>m</i>.
252 * Or if there are two such decimals in <i>T</i>,
253 * select the one with the even significand.
254 * </ul>
255 *
256 * <p>The (uniquely) selected decimal <i>d</i><sub><i>m</i></sub>
257 * is then formatted.
258 * Let <i>s</i>, <i>i</i> and <i>n</i> be the significand, exponent and
259 * length of <i>d</i><sub><i>m</i></sub>, respectively.
260 * Further, let <i>e</i> = <i>n</i> + <i>i</i> - 1 and let
261 * <i>s</i><sub>1</sub>…<i>s</i><sub><i>n</i></sub>
262 * be the usual decimal expansion of <i>s</i>.
263 * Note that <i>s</i><sub>1</sub> ≠ 0
264 * and <i>s</i><sub><i>n</i></sub> ≠ 0.
265 * Below, the decimal point {@code '.'} is {@code '\u005Cu002E'}
266 * and the exponent indicator {@code 'E'} is {@code '\u005Cu0045'}.
267 * <ul>
268 * <li>Case -3 ≤ <i>e</i> < 0:
269 * <i>d</i><sub><i>m</i></sub> is formatted as
270 * <code>0.0</code>…<code>0</code><!--
271 * --><i>s</i><sub>1</sub>…<i>s</i><sub><i>n</i></sub>,
272 * where there are exactly -(<i>n</i> + <i>i</i>) zeroes between
273 * the decimal point and <i>s</i><sub>1</sub>.
274 * For example, 123 × 10<sup>-4</sup> is formatted as
275 * {@code 0.0123}.
276 * <li>Case 0 ≤ <i>e</i> < 7:
277 * <ul>
278 * <li>Subcase <i>i</i> ≥ 0:
279 * <i>d</i><sub><i>m</i></sub> is formatted as
280 * <i>s</i><sub>1</sub>…<i>s</i><sub><i>n</i></sub><!--
281 * --><code>0</code>…<code>0.0</code>,
282 * where there are exactly <i>i</i> zeroes
283 * between <i>s</i><sub><i>n</i></sub> and the decimal point.
284 * For example, 123 × 10<sup>2</sup> is formatted as
285 * {@code 12300.0}.
286 * <li>Subcase <i>i</i> < 0:
287 * <i>d</i><sub><i>m</i></sub> is formatted as
288 * <i>s</i><sub>1</sub>…<!--
289 * --><i>s</i><sub><i>n</i>+<i>i</i></sub><code>.</code><!--
290 * --><i>s</i><sub><i>n</i>+<i>i</i>+1</sub>…<!--
291 * --><i>s</i><sub><i>n</i></sub>,
292 * where there are exactly -<i>i</i> digits to the right of
293 * the decimal point.
294 * For example, 123 × 10<sup>-1</sup> is formatted as
295 * {@code 12.3}.
296 * </ul>
297 * <li>Case <i>e</i> < -3 or <i>e</i> ≥ 7:
298 * computerized scientific notation is used to format
299 * <i>d</i><sub><i>m</i></sub>.
300 * Here <i>e</i> is formatted as by {@link Integer#toString(int)}.
301 * <ul>
302 * <li>Subcase <i>n</i> = 1:
303 * <i>d</i><sub><i>m</i></sub> is formatted as
304 * <i>s</i><sub>1</sub><code>.0E</code><i>e</i>.
305 * For example, 1 × 10<sup>23</sup> is formatted as
306 * {@code 1.0E23}.
307 * <li>Subcase <i>n</i> > 1:
308 * <i>d</i><sub><i>m</i></sub> is formatted as
309 * <i>s</i><sub>1</sub><code>.</code><i>s</i><sub>2</sub><!--
310 * -->…<i>s</i><sub><i>n</i></sub><code>E</code><i>e</i>.
311 * For example, 123 × 10<sup>-21</sup> is formatted as
312 * {@code 1.23E-19}.
313 * </ul>
314 * </ul>
315 *
316 * <p>To create localized string representations of a floating-point
317 * value, use subclasses of {@link java.text.NumberFormat}.
318 *
319 * @apiNote
320 * This method corresponds to the general functionality of the
321 * convertToDecimalCharacter operation defined in IEEE 754;
322 * however, that operation is defined in terms of specifying the
323 * number of significand digits used in the conversion.
324 * Code to do such a conversion in the Java platform includes
325 * converting the {@code float} to a {@link java.math.BigDecimal
326 * BigDecimal} exactly and then rounding the {@code BigDecimal} to
327 * the desired number of digits; sample code:
328 * {@snippet lang=java :
329 * floatf = 0.1f;
330 * int digits = 15;
331 * BigDecimal bd = new BigDecimal(f);
332 * String result = bd.round(new MathContext(digits, RoundingMode.HALF_UP));
333 * // 0.100000001490116
334 * }
335 *
336 * @param f the {@code float} to be converted.
337 * @return a string representation of the argument.
338 */
339 public static String toString(float f) {
340 return FloatToDecimal.toString(f);
341 }
342
343 /**
344 * Returns a hexadecimal string representation of the
345 * {@code float} argument. All characters mentioned below are
346 * ASCII characters.
347 *
348 * <ul>
349 * <li>If the argument is NaN, the result is the string
350 * "{@code NaN}".
351 * <li>Otherwise, the result is a string that represents the sign and
352 * magnitude (absolute value) of the argument. If the sign is negative,
353 * the first character of the result is '{@code -}'
354 * ({@code '\u005Cu002D'}); if the sign is positive, no sign character
355 * appears in the result. As for the magnitude <i>m</i>:
356 *
357 * <ul>
358 * <li>If <i>m</i> is infinity, it is represented by the string
359 * {@code "Infinity"}; thus, positive infinity produces the
360 * result {@code "Infinity"} and negative infinity produces
361 * the result {@code "-Infinity"}.
362 *
363 * <li>If <i>m</i> is zero, it is represented by the string
364 * {@code "0x0.0p0"}; thus, negative zero produces the result
365 * {@code "-0x0.0p0"} and positive zero produces the result
366 * {@code "0x0.0p0"}.
367 *
368 * <li>If <i>m</i> is a {@code float} value with a
369 * normalized representation, substrings are used to represent the
370 * significand and exponent fields. The significand is
371 * represented by the characters {@code "0x1."}
372 * followed by a lowercase hexadecimal representation of the rest
373 * of the significand as a fraction. Trailing zeros in the
374 * hexadecimal representation are removed unless all the digits
375 * are zero, in which case a single zero is used. Next, the
376 * exponent is represented by {@code "p"} followed
377 * by a decimal string of the unbiased exponent as if produced by
378 * a call to {@link Integer#toString(int) Integer.toString} on the
379 * exponent value.
380 *
381 * <li>If <i>m</i> is a {@code float} value with a subnormal
382 * representation, the significand is represented by the
383 * characters {@code "0x0."} followed by a
384 * hexadecimal representation of the rest of the significand as a
385 * fraction. Trailing zeros in the hexadecimal representation are
386 * removed. Next, the exponent is represented by
387 * {@code "p-126"}. Note that there must be at
388 * least one nonzero digit in a subnormal significand.
389 *
390 * </ul>
391 *
392 * </ul>
393 *
394 * <table class="striped">
395 * <caption>Examples</caption>
396 * <thead>
397 * <tr><th scope="col">Floating-point Value</th><th scope="col">Hexadecimal String</th>
398 * </thead>
399 * <tbody>
400 * <tr><th scope="row">{@code 1.0}</th> <td>{@code 0x1.0p0}</td>
401 * <tr><th scope="row">{@code -1.0}</th> <td>{@code -0x1.0p0}</td>
402 * <tr><th scope="row">{@code 2.0}</th> <td>{@code 0x1.0p1}</td>
403 * <tr><th scope="row">{@code 3.0}</th> <td>{@code 0x1.8p1}</td>
404 * <tr><th scope="row">{@code 0.5}</th> <td>{@code 0x1.0p-1}</td>
405 * <tr><th scope="row">{@code 0.25}</th> <td>{@code 0x1.0p-2}</td>
406 * <tr><th scope="row">{@code Float.MAX_VALUE}</th>
407 * <td>{@code 0x1.fffffep127}</td>
408 * <tr><th scope="row">{@code Minimum Normal Value}</th>
409 * <td>{@code 0x1.0p-126}</td>
410 * <tr><th scope="row">{@code Maximum Subnormal Value}</th>
411 * <td>{@code 0x0.fffffep-126}</td>
412 * <tr><th scope="row">{@code Float.MIN_VALUE}</th>
413 * <td>{@code 0x0.000002p-126}</td>
414 * </tbody>
415 * </table>
416 *
417 * @apiNote
418 * This method corresponds to the convertToHexCharacter operation
419 * defined in IEEE 754.
420 *
421 * @param f the {@code float} to be converted.
422 * @return a hex string representation of the argument.
423 * @since 1.5
424 * @author Joseph D. Darcy
425 */
426 public static String toHexString(float f) {
427 if (Math.abs(f) < Float.MIN_NORMAL
428 && f != 0.0f ) {// float subnormal
429 // Adjust exponent to create subnormal double, then
430 // replace subnormal double exponent with subnormal float
431 // exponent
432 String s = Double.toHexString(Math.scalb((double)f,
433 /* -1022+126 */
434 Double.MIN_EXPONENT-
435 Float.MIN_EXPONENT));
436 return s.replaceFirst("p-1022$", "p-126");
437 }
438 else // double string will be the same as float string
439 return Double.toHexString(f);
440 }
441
442 /**
443 * Returns a {@code Float} object holding the
444 * {@code float} value represented by the argument string
445 * {@code s}.
446 *
447 * <p>If {@code s} is {@code null}, then a
448 * {@code NullPointerException} is thrown.
449 *
450 * <p>Leading and trailing whitespace characters in {@code s}
451 * are ignored. Whitespace is removed as if by the {@link
452 * String#trim} method; that is, both ASCII space and control
453 * characters are removed. The rest of {@code s} should
454 * constitute a <i>FloatValue</i> as described by the lexical
455 * syntax rules:
456 *
457 * <blockquote>
458 * <dl>
459 * <dt><i>FloatValue:</i>
460 * <dd><i>Sign<sub>opt</sub></i> {@code NaN}
461 * <dd><i>Sign<sub>opt</sub></i> {@code Infinity}
462 * <dd><i>Sign<sub>opt</sub> FloatingPointLiteral</i>
463 * <dd><i>Sign<sub>opt</sub> HexFloatingPointLiteral</i>
464 * <dd><i>SignedInteger</i>
465 * </dl>
466 *
467 * <dl>
468 * <dt><i>HexFloatingPointLiteral</i>:
469 * <dd> <i>HexSignificand BinaryExponent FloatTypeSuffix<sub>opt</sub></i>
470 * </dl>
471 *
472 * <dl>
473 * <dt><i>HexSignificand:</i>
474 * <dd><i>HexNumeral</i>
475 * <dd><i>HexNumeral</i> {@code .}
476 * <dd>{@code 0x} <i>HexDigits<sub>opt</sub>
477 * </i>{@code .}<i> HexDigits</i>
478 * <dd>{@code 0X}<i> HexDigits<sub>opt</sub>
479 * </i>{@code .} <i>HexDigits</i>
480 * </dl>
481 *
482 * <dl>
483 * <dt><i>BinaryExponent:</i>
484 * <dd><i>BinaryExponentIndicator SignedInteger</i>
485 * </dl>
486 *
487 * <dl>
488 * <dt><i>BinaryExponentIndicator:</i>
489 * <dd>{@code p}
490 * <dd>{@code P}
491 * </dl>
492 *
493 * </blockquote>
494 *
495 * where <i>Sign</i>, <i>FloatingPointLiteral</i>,
496 * <i>HexNumeral</i>, <i>HexDigits</i>, <i>SignedInteger</i> and
497 * <i>FloatTypeSuffix</i> are as defined in the lexical structure
498 * sections of
499 * <cite>The Java Language Specification</cite>,
500 * except that underscores are not accepted between digits.
501 * If {@code s} does not have the form of
502 * a <i>FloatValue</i>, then a {@code NumberFormatException}
503 * is thrown. Otherwise, {@code s} is regarded as
504 * representing an exact decimal value in the usual
505 * "computerized scientific notation" or as an exact
506 * hexadecimal value; this exact numerical value is then
507 * conceptually converted to an "infinitely precise"
508 * binary value that is then rounded to type {@code float}
509 * by the usual round-to-nearest rule of IEEE 754 floating-point
510 * arithmetic, which includes preserving the sign of a zero
511 * value.
512 *
513 * Note that the round-to-nearest rule also implies overflow and
514 * underflow behaviour; if the exact value of {@code s} is large
515 * enough in magnitude (greater than or equal to ({@link
516 * #MAX_VALUE} + {@link Math#ulp(float) ulp(MAX_VALUE)}/2),
517 * rounding to {@code float} will result in an infinity and if the
518 * exact value of {@code s} is small enough in magnitude (less
519 * than or equal to {@link #MIN_VALUE}/2), rounding to float will
520 * result in a zero.
521 *
522 * Finally, after rounding a {@code Float} object representing
523 * this {@code float} value is returned.
524 *
525 * <p>Note that trailing format specifiers, specifiers that
526 * determine the type of a floating-point literal
527 * ({@code 1.0f} is a {@code float} value;
528 * {@code 1.0d} is a {@code double} value), do
529 * <em>not</em> influence the results of this method. In other
530 * words, the numerical value of the input string is converted
531 * directly to the target floating-point type. In general, the
532 * two-step sequence of conversions, string to {@code double}
533 * followed by {@code double} to {@code float}, is
534 * <em>not</em> equivalent to converting a string directly to
535 * {@code float}. For example, if first converted to an
536 * intermediate {@code double} and then to
537 * {@code float}, the string<br>
538 * {@code "1.00000017881393421514957253748434595763683319091796875001d"}<br>
539 * results in the {@code float} value
540 * {@code 1.0000002f}; if the string is converted directly to
541 * {@code float}, <code>1.000000<b>1</b>f</code> results.
542 *
543 * <p>To avoid calling this method on an invalid string and having
544 * a {@code NumberFormatException} be thrown, the documentation
545 * for {@link Double#valueOf Double.valueOf} lists a regular
546 * expression which can be used to screen the input.
547 *
548 * @apiNote To interpret localized string representations of a
549 * floating-point value, or string representations that have
550 * non-ASCII digits, use {@link java.text.NumberFormat}. For
551 * example,
552 * {@snippet lang="java" :
553 * NumberFormat.getInstance(l).parse(s).floatValue();
554 * }
555 * where {@code l} is the desired locale, or
556 * {@link java.util.Locale#ROOT} if locale insensitive.
557 *
558 * @apiNote
559 * This method corresponds to the convertFromDecimalCharacter and
560 * convertFromHexCharacter operations defined in IEEE 754.
561 *
562 * @param s the string to be parsed.
563 * @return a {@code Float} object holding the value
564 * represented by the {@code String} argument.
565 * @throws NumberFormatException if the string does not contain a
566 * parsable number.
567 * @see Double##decimalToBinaryConversion Decimal ↔ Binary Conversion Issues
568 */
569 public static Float valueOf(String s) throws NumberFormatException {
570 return new Float(parseFloat(s));
571 }
572
573 /**
574 * Returns a {@code Float} instance representing the specified
575 * {@code float} value.
576 * If a new {@code Float} instance is not required, this method
577 * should generally be used in preference to the constructor
578 * {@link #Float(float)}, as this method is likely to yield
579 * significantly better space and time performance by caching
580 * frequently requested values.
581 *
582 * @param f a float value.
583 * @return a {@code Float} instance representing {@code f}.
584 * @since 1.5
585 */
586 @IntrinsicCandidate
587 @DeserializeConstructor
588 public static Float valueOf(float f) {
589 return new Float(f);
590 }
591
592 /**
593 * Returns a new {@code float} initialized to the value
594 * represented by the specified {@code String}, as performed
595 * by the {@code valueOf} method of class {@code Float}.
596 *
597 * @param s the string to be parsed.
598 * @return the {@code float} value represented by the string
599 * argument.
600 * @throws NullPointerException if the string is null
601 * @throws NumberFormatException if the string does not contain a
602 * parsable {@code float}.
603 * @see java.lang.Float#valueOf(String)
604 * @see Double##decimalToBinaryConversion Decimal ↔ Binary Conversion Issues
605 * @since 1.2
606 */
607 public static float parseFloat(String s) throws NumberFormatException {
608 return FloatingDecimal.parseFloat(s);
609 }
610
611 /**
612 * Returns {@code true} if the specified number is a
613 * Not-a-Number (NaN) value, {@code false} otherwise.
614 *
615 * @apiNote
616 * This method corresponds to the isNaN operation defined in IEEE
617 * 754.
618 *
619 * @param v the value to be tested.
620 * @return {@code true} if the argument is NaN;
621 * {@code false} otherwise.
622 */
623 public static boolean isNaN(float v) {
624 return (v != v);
625 }
626
627 /**
628 * Returns {@code true} if the specified number is infinitely
629 * large in magnitude, {@code false} otherwise.
630 *
631 * @apiNote
632 * This method corresponds to the isInfinite operation defined in
633 * IEEE 754.
634 *
635 * @param v the value to be tested.
636 * @return {@code true} if the argument is positive infinity or
637 * negative infinity; {@code false} otherwise.
638 */
639 @IntrinsicCandidate
640 public static boolean isInfinite(float v) {
641 return Math.abs(v) > MAX_VALUE;
642 }
643
644
645 /**
646 * Returns {@code true} if the argument is a finite floating-point
647 * value; returns {@code false} otherwise (for NaN and infinity
648 * arguments).
649 *
650 * @apiNote
651 * This method corresponds to the isFinite operation defined in
652 * IEEE 754.
653 *
654 * @param f the {@code float} value to be tested
655 * @return {@code true} if the argument is a finite
656 * floating-point value, {@code false} otherwise.
657 * @since 1.8
658 */
659 @IntrinsicCandidate
660 public static boolean isFinite(float f) {
661 return Math.abs(f) <= Float.MAX_VALUE;
662 }
663
664 /**
665 * The value of the Float.
666 *
667 * @serial
668 */
669 private final float value;
670
671 /**
672 * Constructs a newly allocated {@code Float} object that
673 * represents the primitive {@code float} argument.
674 *
675 * @param value the value to be represented by the {@code Float}.
676 *
677 * @deprecated
678 * It is rarely appropriate to use this constructor. The static factory
679 * {@link #valueOf(float)} is generally a better choice, as it is
680 * likely to yield significantly better space and time performance.
681 */
682 @Deprecated(since="9", forRemoval = true)
683 public Float(float value) {
684 this.value = value;
685 }
686
687 /**
688 * Constructs a newly allocated {@code Float} object that
689 * represents the argument converted to type {@code float}.
690 *
691 * @param value the value to be represented by the {@code Float}.
692 *
693 * @deprecated
694 * It is rarely appropriate to use this constructor. Instead, use the
695 * static factory method {@link #valueOf(float)} method as follows:
696 * {@code Float.valueOf((float)value)}.
697 */
698 @Deprecated(since="9", forRemoval = true)
699 public Float(double value) {
700 this.value = (float)value;
701 }
702
703 /**
704 * Constructs a newly allocated {@code Float} object that
705 * represents the floating-point value of type {@code float}
706 * represented by the string. The string is converted to a
707 * {@code float} value as if by the {@code valueOf} method.
708 *
709 * @param s a string to be converted to a {@code Float}.
710 * @throws NumberFormatException if the string does not contain a
711 * parsable number.
712 *
713 * @deprecated
714 * It is rarely appropriate to use this constructor.
715 * Use {@link #parseFloat(String)} to convert a string to a
716 * {@code float} primitive, or use {@link #valueOf(String)}
717 * to convert a string to a {@code Float} object.
718 */
719 @Deprecated(since="9", forRemoval = true)
720 public Float(String s) throws NumberFormatException {
721 value = parseFloat(s);
722 }
723
724 /**
725 * Returns {@code true} if this {@code Float} value is a
726 * Not-a-Number (NaN), {@code false} otherwise.
727 *
728 * @return {@code true} if the value represented by this object is
729 * NaN; {@code false} otherwise.
730 */
731 public boolean isNaN() {
732 return isNaN(value);
733 }
734
735 /**
736 * Returns {@code true} if this {@code Float} value is
737 * infinitely large in magnitude, {@code false} otherwise.
738 *
739 * @return {@code true} if the value represented by this object is
740 * positive infinity or negative infinity;
741 * {@code false} otherwise.
742 */
743 public boolean isInfinite() {
744 return isInfinite(value);
745 }
746
747 /**
748 * Returns a string representation of this {@code Float} object.
749 * The primitive {@code float} value represented by this object
750 * is converted to a {@code String} exactly as if by the method
751 * {@code toString} of one argument.
752 *
753 * @return a {@code String} representation of this object.
754 * @see java.lang.Float#toString(float)
755 */
756 public String toString() {
757 return Float.toString(value);
758 }
759
760 /**
761 * Returns the value of this {@code Float} as a {@code byte} after
762 * a narrowing primitive conversion.
763 *
764 * @return the {@code float} value represented by this object
765 * converted to type {@code byte}
766 * @jls 5.1.3 Narrowing Primitive Conversion
767 */
768 @Override
769 public byte byteValue() {
770 return (byte)value;
771 }
772
773 /**
774 * Returns the value of this {@code Float} as a {@code short}
775 * after a narrowing primitive conversion.
776 *
777 * @return the {@code float} value represented by this object
778 * converted to type {@code short}
779 * @jls 5.1.3 Narrowing Primitive Conversion
780 * @since 1.1
781 */
782 @Override
783 public short shortValue() {
784 return (short)value;
785 }
786
787 /**
788 * Returns the value of this {@code Float} as an {@code int} after
789 * a narrowing primitive conversion.
790 *
791 * @apiNote
792 * This method corresponds to the convertToIntegerTowardZero
793 * operation defined in IEEE 754.
794 *
795 * @return the {@code float} value represented by this object
796 * converted to type {@code int}
797 * @jls 5.1.3 Narrowing Primitive Conversion
798 */
799 @Override
800 public int intValue() {
801 return (int)value;
802 }
803
804 /**
805 * Returns value of this {@code Float} as a {@code long} after a
806 * narrowing primitive conversion.
807 *
808 * @apiNote
809 * This method corresponds to the convertToIntegerTowardZero
810 * operation defined in IEEE 754.
811 *
812 * @return the {@code float} value represented by this object
813 * converted to type {@code long}
814 * @jls 5.1.3 Narrowing Primitive Conversion
815 */
816 @Override
817 public long longValue() {
818 return (long)value;
819 }
820
821 /**
822 * Returns the {@code float} value of this {@code Float} object.
823 *
824 * @return the {@code float} value represented by this object
825 */
826 @Override
827 @IntrinsicCandidate
828 public float floatValue() {
829 return value;
830 }
831
832 /**
833 * Returns the value of this {@code Float} as a {@code double}
834 * after a widening primitive conversion.
835 *
836 * @apiNote
837 * This method corresponds to the convertFormat operation defined
838 * in IEEE 754.
839 *
840 * @return the {@code float} value represented by this
841 * object converted to type {@code double}
842 * @jls 5.1.2 Widening Primitive Conversion
843 */
844 @Override
845 public double doubleValue() {
846 return (double)value;
847 }
848
849 /**
850 * Returns a hash code for this {@code Float} object. The
851 * result is the integer bit representation, exactly as produced
852 * by the method {@link #floatToIntBits(float)}, of the primitive
853 * {@code float} value represented by this {@code Float}
854 * object.
855 *
856 * @return a hash code value for this object.
857 */
858 @Override
859 public int hashCode() {
860 return Float.hashCode(value);
861 }
862
863 /**
864 * Returns a hash code for a {@code float} value; compatible with
865 * {@code Float.hashCode()}.
866 *
867 * @param value the value to hash
868 * @return a hash code value for a {@code float} value.
869 * @since 1.8
870 */
871 public static int hashCode(float value) {
872 return floatToIntBits(value);
873 }
874
875 /**
876 * Compares this object against the specified object. The result
877 * is {@code true} if and only if the argument is not
878 * {@code null} and is a {@code Float} object that
879 * represents a {@code float} with the same value as the
880 * {@code float} represented by this object. For this
881 * purpose, two {@code float} values are considered to be the
882 * same if and only if the method {@link #floatToIntBits(float)}
883 * returns the identical {@code int} value when applied to
884 * each.
885 *
886 * @apiNote
887 * This method is defined in terms of {@link
888 * #floatToIntBits(float)} rather than the {@code ==} operator on
889 * {@code float} values since the {@code ==} operator does
890 * <em>not</em> define an equivalence relation and to satisfy the
891 * {@linkplain Object#equals equals contract} an equivalence
892 * relation must be implemented; see {@linkplain Double##equivalenceRelation
893 * this discussion for details of floating-point equality and equivalence}.
894 *
895 * @param obj the object to be compared
896 * @return {@code true} if the objects are the same;
897 * {@code false} otherwise.
898 * @see java.lang.Float#floatToIntBits(float)
899 * @jls 15.21.1 Numerical Equality Operators == and !=
900 */
901 public boolean equals(Object obj) {
902 return (obj instanceof Float f) &&
903 (floatToIntBits(f.value) == floatToIntBits(value));
904 }
905
906 /**
907 * Returns a representation of the specified floating-point value
908 * according to the IEEE 754 floating-point "single format" bit
909 * layout.
910 *
911 * <p>Bit 31 (the bit that is selected by the mask
912 * {@code 0x80000000}) represents the sign of the floating-point
913 * number.
914 * Bits 30-23 (the bits that are selected by the mask
915 * {@code 0x7f800000}) represent the exponent.
916 * Bits 22-0 (the bits that are selected by the mask
917 * {@code 0x007fffff}) represent the significand (sometimes called
918 * the mantissa) of the floating-point number.
919 *
920 * <p>If the argument is positive infinity, the result is
921 * {@code 0x7f800000}.
922 *
923 * <p>If the argument is negative infinity, the result is
924 * {@code 0xff800000}.
925 *
926 * <p>If the argument is NaN, the result is {@code 0x7fc00000}.
927 *
928 * <p>In all cases, the result is an integer that, when given to the
929 * {@link #intBitsToFloat(int)} method, will produce a floating-point
930 * value the same as the argument to {@code floatToIntBits}
931 * (except all NaN values are collapsed to a single
932 * "canonical" NaN value).
933 *
934 * @param value a floating-point number.
935 * @return the bits that represent the floating-point number.
936 */
937 @IntrinsicCandidate
938 public static int floatToIntBits(float value) {
939 if (!isNaN(value)) {
940 return floatToRawIntBits(value);
941 }
942 return 0x7fc00000;
943 }
944
945 /**
946 * Returns a representation of the specified floating-point value
947 * according to the IEEE 754 floating-point "single format" bit
948 * layout, preserving Not-a-Number (NaN) values.
949 *
950 * <p>Bit 31 (the bit that is selected by the mask
951 * {@code 0x80000000}) represents the sign of the floating-point
952 * number.
953 * Bits 30-23 (the bits that are selected by the mask
954 * {@code 0x7f800000}) represent the exponent.
955 * Bits 22-0 (the bits that are selected by the mask
956 * {@code 0x007fffff}) represent the significand (sometimes called
957 * the mantissa) of the floating-point number.
958 *
959 * <p>If the argument is positive infinity, the result is
960 * {@code 0x7f800000}.
961 *
962 * <p>If the argument is negative infinity, the result is
963 * {@code 0xff800000}.
964 *
965 * <p>If the argument is NaN, the result is the integer representing
966 * the actual NaN value. Unlike the {@code floatToIntBits}
967 * method, {@code floatToRawIntBits} does not collapse all the
968 * bit patterns encoding a NaN to a single "canonical"
969 * NaN value.
970 *
971 * <p>In all cases, the result is an integer that, when given to the
972 * {@link #intBitsToFloat(int)} method, will produce a
973 * floating-point value the same as the argument to
974 * {@code floatToRawIntBits}.
975 *
976 * @param value a floating-point number.
977 * @return the bits that represent the floating-point number.
978 * @since 1.3
979 */
980 @IntrinsicCandidate
981 public static native int floatToRawIntBits(float value);
982
983 /**
984 * Returns the {@code float} value corresponding to a given
985 * bit representation.
986 * The argument is considered to be a representation of a
987 * floating-point value according to the IEEE 754 floating-point
988 * "single format" bit layout.
989 *
990 * <p>If the argument is {@code 0x7f800000}, the result is positive
991 * infinity.
992 *
993 * <p>If the argument is {@code 0xff800000}, the result is negative
994 * infinity.
995 *
996 * <p>If the argument is any value in the range
997 * {@code 0x7f800001} through {@code 0x7fffffff} or in
998 * the range {@code 0xff800001} through
999 * {@code 0xffffffff}, the result is a NaN. No IEEE 754
1000 * floating-point operation provided by Java can distinguish
1001 * between two NaN values of the same type with different bit
1002 * patterns. Distinct values of NaN are only distinguishable by
1003 * use of the {@code Float.floatToRawIntBits} method.
1004 *
1005 * <p>In all other cases, let <i>s</i>, <i>e</i>, and <i>m</i> be three
1006 * values that can be computed from the argument:
1007 *
1008 * {@snippet lang="java" :
1009 * int s = ((bits >> 31) == 0) ? 1 : -1;
1010 * int e = ((bits >> 23) & 0xff);
1011 * int m = (e == 0) ?
1012 * (bits & 0x7fffff) << 1 :
1013 * (bits & 0x7fffff) | 0x800000;
1014 * }
1015 *
1016 * Then the floating-point result equals the value of the mathematical
1017 * expression <i>s</i>·<i>m</i>·2<sup><i>e</i>-150</sup>.
1018 *
1019 * <p>Note that this method may not be able to return a
1020 * {@code float} NaN with exactly same bit pattern as the
1021 * {@code int} argument. IEEE 754 distinguishes between two
1022 * kinds of NaNs, quiet NaNs and <i>signaling NaNs</i>. The
1023 * differences between the two kinds of NaN are generally not
1024 * visible in Java. Arithmetic operations on signaling NaNs turn
1025 * them into quiet NaNs with a different, but often similar, bit
1026 * pattern. However, on some processors merely copying a
1027 * signaling NaN also performs that conversion. In particular,
1028 * copying a signaling NaN to return it to the calling method may
1029 * perform this conversion. So {@code intBitsToFloat} may
1030 * not be able to return a {@code float} with a signaling NaN
1031 * bit pattern. Consequently, for some {@code int} values,
1032 * {@code floatToRawIntBits(intBitsToFloat(start))} may
1033 * <i>not</i> equal {@code start}. Moreover, which
1034 * particular bit patterns represent signaling NaNs is platform
1035 * dependent; although all NaN bit patterns, quiet or signaling,
1036 * must be in the NaN range identified above.
1037 *
1038 * @param bits an integer.
1039 * @return the {@code float} floating-point value with the same bit
1040 * pattern.
1041 */
1042 @IntrinsicCandidate
1043 public static native float intBitsToFloat(int bits);
1044
1045 /**
1046 * {@return the {@code float} value closest to the numerical value
1047 * of the argument, a floating-point binary16 value encoded in a
1048 * {@code short}} The conversion is exact; all binary16 values can
1049 * be exactly represented in {@code float}.
1050 *
1051 * Special cases:
1052 * <ul>
1053 * <li> If the argument is zero, the result is a zero with the
1054 * same sign as the argument.
1055 * <li> If the argument is infinite, the result is an infinity
1056 * with the same sign as the argument.
1057 * <li> If the argument is a NaN, the result is a NaN.
1058 * </ul>
1059 *
1060 * <h4><a id=binary16Format>IEEE 754 binary16 format</a></h4>
1061 * The IEEE 754 standard defines binary16 as a 16-bit format, along
1062 * with the 32-bit binary32 format (corresponding to the {@code
1063 * float} type) and the 64-bit binary64 format (corresponding to
1064 * the {@code double} type). The binary16 format is similar to the
1065 * other IEEE 754 formats, except smaller, having all the usual
1066 * IEEE 754 values such as NaN, signed infinities, signed zeros,
1067 * and subnormals. The parameters (JLS {@jls 4.2.3}) for the
1068 * binary16 format are N = 11 precision bits, K = 5 exponent bits,
1069 * <i>E</i><sub><i>max</i></sub> = 15, and
1070 * <i>E</i><sub><i>min</i></sub> = -14.
1071 *
1072 * @apiNote
1073 * This method corresponds to the convertFormat operation defined
1074 * in IEEE 754 from the binary16 format to the binary32 format.
1075 * The operation of this method is analogous to a primitive
1076 * widening conversion (JLS {@jls 5.1.2}).
1077 *
1078 * @param floatBinary16 the binary16 value to convert to {@code float}
1079 * @since 20
1080 */
1081 @IntrinsicCandidate
1082 public static float float16ToFloat(short floatBinary16) {
1083 /*
1084 * The binary16 format has 1 sign bit, 5 exponent bits, and 10
1085 * significand bits. The exponent bias is 15.
1086 */
1087 int bin16arg = (int)floatBinary16;
1088 int bin16SignBit = 0x8000 & bin16arg;
1089 int bin16ExpBits = 0x7c00 & bin16arg;
1090 int bin16SignifBits = 0x03FF & bin16arg;
1091
1092 // Shift left difference in the number of significand bits in
1093 // the float and binary16 formats
1094 final int SIGNIF_SHIFT = (FloatConsts.SIGNIFICAND_WIDTH - 11);
1095
1096 float sign = (bin16SignBit != 0) ? -1.0f : 1.0f;
1097
1098 // Extract binary16 exponent, remove its bias, add in the bias
1099 // of a float exponent and shift to correct bit location
1100 // (significand width includes the implicit bit so shift one
1101 // less).
1102 int bin16Exp = (bin16ExpBits >> 10) - 15;
1103 if (bin16Exp == -15) {
1104 // For subnormal binary16 values and 0, the numerical
1105 // value is 2^24 * the significand as an integer (no
1106 // implicit bit).
1107 return sign * (0x1p-24f * bin16SignifBits);
1108 } else if (bin16Exp == 16) {
1109 return (bin16SignifBits == 0) ?
1110 sign * Float.POSITIVE_INFINITY :
1111 Float.intBitsToFloat((bin16SignBit << 16) |
1112 0x7f80_0000 |
1113 // Preserve NaN signif bits
1114 ( bin16SignifBits << SIGNIF_SHIFT ));
1115 }
1116
1117 assert -15 < bin16Exp && bin16Exp < 16;
1118
1119 int floatExpBits = (bin16Exp + FloatConsts.EXP_BIAS)
1120 << (FloatConsts.SIGNIFICAND_WIDTH - 1);
1121
1122 // Compute and combine result sign, exponent, and significand bits.
1123 return Float.intBitsToFloat((bin16SignBit << 16) |
1124 floatExpBits |
1125 (bin16SignifBits << SIGNIF_SHIFT));
1126 }
1127
1128 /**
1129 * {@return the floating-point binary16 value, encoded in a {@code
1130 * short}, closest in value to the argument}
1131 * The conversion is computed under the {@linkplain
1132 * java.math.RoundingMode#HALF_EVEN round to nearest even rounding
1133 * mode}.
1134 *
1135 * Special cases:
1136 * <ul>
1137 * <li> If the argument is zero, the result is a zero with the
1138 * same sign as the argument.
1139 * <li> If the argument is infinite, the result is an infinity
1140 * with the same sign as the argument.
1141 * <li> If the argument is a NaN, the result is a NaN.
1142 * </ul>
1143 *
1144 * The {@linkplain ##binary16Format binary16 format} is discussed in
1145 * more detail in the {@link #float16ToFloat} method.
1146 *
1147 * @apiNote
1148 * This method corresponds to the convertFormat operation defined
1149 * in IEEE 754 from the binary32 format to the binary16 format.
1150 * The operation of this method is analogous to a primitive
1151 * narrowing conversion (JLS {@jls 5.1.3}).
1152 *
1153 * @param f the {@code float} value to convert to binary16
1154 * @since 20
1155 */
1156 @IntrinsicCandidate
1157 public static short floatToFloat16(float f) {
1158 int doppel = Float.floatToRawIntBits(f);
1159 short sign_bit = (short)((doppel & 0x8000_0000) >> 16);
1160
1161 if (Float.isNaN(f)) {
1162 // Preserve sign and attempt to preserve significand bits
1163 return (short)(sign_bit
1164 | 0x7c00 // max exponent + 1
1165 // Preserve high order bit of float NaN in the
1166 // binary16 result NaN (tenth bit); OR in remaining
1167 // bits into lower 9 bits of binary 16 significand.
1168 | (doppel & 0x007f_e000) >> 13 // 10 bits
1169 | (doppel & 0x0000_1ff0) >> 4 // 9 bits
1170 | (doppel & 0x0000_000f)); // 4 bits
1171 }
1172
1173 float abs_f = Math.abs(f);
1174
1175 // The overflow threshold is binary16 MAX_VALUE + 1/2 ulp
1176 if (abs_f >= (0x1.ffcp15f + 0x0.002p15f) ) {
1177 return (short)(sign_bit | 0x7c00); // Positive or negative infinity
1178 }
1179
1180 // Smallest magnitude nonzero representable binary16 value
1181 // is equal to 0x1.0p-24; half-way and smaller rounds to zero.
1182 if (abs_f <= 0x1.0p-24f * 0.5f) { // Covers float zeros and subnormals.
1183 return sign_bit; // Positive or negative zero
1184 }
1185
1186 // Dealing with finite values in exponent range of binary16
1187 // (when rounding is done, could still round up)
1188 int exp = Math.getExponent(f);
1189 assert -25 <= exp && exp <= 15;
1190
1191 // For binary16 subnormals, beside forcing exp to -15, retain
1192 // the difference expdelta = E_min - exp. This is the excess
1193 // shift value, in addition to 13, to be used in the
1194 // computations below. Further the (hidden) msb with value 1
1195 // in f must be involved as well.
1196 int expdelta = 0;
1197 int msb = 0x0000_0000;
1198 if (exp < -14) {
1199 expdelta = -14 - exp;
1200 exp = -15;
1201 msb = 0x0080_0000;
1202 }
1203 int f_signif_bits = doppel & 0x007f_ffff | msb;
1204
1205 // Significand bits as if using rounding to zero (truncation).
1206 short signif_bits = (short)(f_signif_bits >> (13 + expdelta));
1207
1208 // For round to nearest even, determining whether or not to
1209 // round up (in magnitude) is a function of the least
1210 // significant bit (LSB), the next bit position (the round
1211 // position), and the sticky bit (whether there are any
1212 // nonzero bits in the exact result to the right of the round
1213 // digit). An increment occurs in three cases:
1214 //
1215 // LSB Round Sticky
1216 // 0 1 1
1217 // 1 1 0
1218 // 1 1 1
1219 // See "Computer Arithmetic Algorithms," Koren, Table 4.9
1220
1221 int lsb = f_signif_bits & (1 << 13 + expdelta);
1222 int round = f_signif_bits & (1 << 12 + expdelta);
1223 int sticky = f_signif_bits & ((1 << 12 + expdelta) - 1);
1224
1225 if (round != 0 && ((lsb | sticky) != 0 )) {
1226 signif_bits++;
1227 }
1228
1229 // No bits set in significand beyond the *first* exponent bit,
1230 // not just the significand; quantity is added to the exponent
1231 // to implement a carry out from rounding the significand.
1232 assert (0xf800 & signif_bits) == 0x0;
1233
1234 return (short)(sign_bit | ( ((exp + 15) << 10) + signif_bits ) );
1235 }
1236
1237 /**
1238 * Compares two {@code Float} objects numerically.
1239 *
1240 * This method imposes a total order on {@code Float} objects
1241 * with two differences compared to the incomplete order defined by
1242 * the Java language numerical comparison operators ({@code <, <=,
1243 * ==, >=, >}) on {@code float} values.
1244 *
1245 * <ul><li> A NaN is <em>unordered</em> with respect to other
1246 * values and unequal to itself under the comparison
1247 * operators. This method chooses to define {@code
1248 * Float.NaN} to be equal to itself and greater than all
1249 * other {@code double} values (including {@code
1250 * Float.POSITIVE_INFINITY}).
1251 *
1252 * <li> Positive zero and negative zero compare equal
1253 * numerically, but are distinct and distinguishable values.
1254 * This method chooses to define positive zero ({@code +0.0f}),
1255 * to be greater than negative zero ({@code -0.0f}).
1256 * </ul>
1257 *
1258 * This ensures that the <i>natural ordering</i> of {@code Float}
1259 * objects imposed by this method is <i>consistent with
1260 * equals</i>; see {@linkplain Double##equivalenceRelation this
1261 * discussion for details of floating-point comparison and
1262 * ordering}.
1263 *
1264 *
1265 * @param anotherFloat the {@code Float} to be compared.
1266 * @return the value {@code 0} if {@code anotherFloat} is
1267 * numerically equal to this {@code Float}; a value
1268 * less than {@code 0} if this {@code Float}
1269 * is numerically less than {@code anotherFloat};
1270 * and a value greater than {@code 0} if this
1271 * {@code Float} is numerically greater than
1272 * {@code anotherFloat}.
1273 *
1274 * @jls 15.20.1 Numerical Comparison Operators {@code <}, {@code <=}, {@code >}, and {@code >=}
1275 * @since 1.2
1276 */
1277 @Override
1278 public int compareTo(Float anotherFloat) {
1279 return Float.compare(value, anotherFloat.value);
1280 }
1281
1282 /**
1283 * Compares the two specified {@code float} values. The sign
1284 * of the integer value returned is the same as that of the
1285 * integer that would be returned by the call:
1286 * <pre>
1287 * Float.valueOf(f1).compareTo(Float.valueOf(f2))
1288 * </pre>
1289 *
1290 * @param f1 the first {@code float} to compare.
1291 * @param f2 the second {@code float} to compare.
1292 * @return the value {@code 0} if {@code f1} is
1293 * numerically equal to {@code f2}; a value less than
1294 * {@code 0} if {@code f1} is numerically less than
1295 * {@code f2}; and a value greater than {@code 0}
1296 * if {@code f1} is numerically greater than
1297 * {@code f2}.
1298 * @since 1.4
1299 */
1300 public static int compare(float f1, float f2) {
1301 if (f1 < f2)
1302 return -1; // Neither val is NaN, thisVal is smaller
1303 if (f1 > f2)
1304 return 1; // Neither val is NaN, thisVal is larger
1305
1306 // Cannot use floatToRawIntBits because of possibility of NaNs.
1307 int thisBits = Float.floatToIntBits(f1);
1308 int anotherBits = Float.floatToIntBits(f2);
1309
1310 return (thisBits == anotherBits ? 0 : // Values are equal
1311 (thisBits < anotherBits ? -1 : // (-0.0, 0.0) or (!NaN, NaN)
1312 1)); // (0.0, -0.0) or (NaN, !NaN)
1313 }
1314
1315 /**
1316 * Adds two {@code float} values together as per the + operator.
1317 *
1318 * @apiNote This method corresponds to the addition operation
1319 * defined in IEEE 754.
1320 *
1321 * @param a the first operand
1322 * @param b the second operand
1323 * @return the sum of {@code a} and {@code b}
1324 * @jls 4.2.4 Floating-Point Operations
1325 * @see java.util.function.BinaryOperator
1326 * @since 1.8
1327 */
1328 public static float sum(float a, float b) {
1329 return a + b;
1330 }
1331
1332 /**
1333 * Returns the greater of two {@code float} values
1334 * as if by calling {@link Math#max(float, float) Math.max}.
1335 *
1336 * @apiNote
1337 * This method corresponds to the maximum operation defined in
1338 * IEEE 754.
1339 *
1340 * @param a the first operand
1341 * @param b the second operand
1342 * @return the greater of {@code a} and {@code b}
1343 * @see java.util.function.BinaryOperator
1344 * @since 1.8
1345 */
1346 public static float max(float a, float b) {
1347 return Math.max(a, b);
1348 }
1349
1350 /**
1351 * Returns the smaller of two {@code float} values
1352 * as if by calling {@link Math#min(float, float) Math.min}.
1353 *
1354 * @apiNote
1355 * This method corresponds to the minimum operation defined in
1356 * IEEE 754.
1357 *
1358 * @param a the first operand
1359 * @param b the second operand
1360 * @return the smaller of {@code a} and {@code b}
1361 * @see java.util.function.BinaryOperator
1362 * @since 1.8
1363 */
1364 public static float min(float a, float b) {
1365 return Math.min(a, b);
1366 }
1367
1368 /**
1369 * Returns an {@link Optional} containing the nominal descriptor for this
1370 * instance, which is the instance itself.
1371 *
1372 * @return an {@link Optional} describing the {@linkplain Float} instance
1373 * @since 12
1374 */
1375 @Override
1376 public Optional<Float> describeConstable() {
1377 return Optional.of(this);
1378 }
1379
1380 /**
1381 * Resolves this instance as a {@link ConstantDesc}, the result of which is
1382 * the instance itself.
1383 *
1384 * @param lookup ignored
1385 * @return the {@linkplain Float} instance
1386 * @since 12
1387 */
1388 @Override
1389 public Float resolveConstantDesc(MethodHandles.Lookup lookup) {
1390 return this;
1391 }
1392
1393 /** use serialVersionUID from JDK 1.0.2 for interoperability */
1394 @java.io.Serial
1395 private static final long serialVersionUID = -2671257302660747028L;
1396 }