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
18 * 2 along with this work; if not, write to the Free Software Foundation,
19 * Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA.
20 *
21 * Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA
22 * or visit www.oracle.com if you need additional information or have any
23 * questions.
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 wraps a value of primitive type
41 * {@code float} in an object. An object of type
42 * {@code Float} contains a single field whose type is
43 * {@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
53 * {@linkplain #equals(Object) equal} as interchangeable and should not
54 * use instances for synchronization, or unpredictable behavior may
55 * occur. For example, in a future release, synchronization may fail.
56 *
57 * <h2><a id=equivalenceRelation>Floating-point Equality, Equivalence,
58 * and Comparison</a></h2>
59 *
60 * The class {@code java.lang.Double} has a {@linkplain
61 * Double##equivalenceRelation discussion of equality,
62 * equivalence, and comparison of floating-point values} that is
63 * equally applicable to {@code float} values.
64 *
65 * <h2><a id=decimalToBinaryConversion>Decimal ↔ Binary Conversion Issues</a></h2>
66 *
67 * The {@linkplain Double##decimalToBinaryConversion discussion of binary to
68 * decimal conversion issues} in {@code java.lang.Double} is also
69 * applicable to {@code float} values.
70 *
71 * @see <a href="https://standards.ieee.org/ieee/754/6210/">
72 * <cite>IEEE Standard for Floating-Point Arithmetic</cite></a>
73 *
74 * @author Lee Boynton
75 * @author Arthur van Hoff
76 * @author Joseph D. Darcy
77 * @since 1.0
78 */
79 @jdk.internal.MigratedValueClass
80 @jdk.internal.ValueBased
81 public final class Float extends Number
82 implements Comparable<Float>, Constable, ConstantDesc {
83 /**
84 * A constant holding the positive infinity of type
85 * {@code float}. It is equal to the value returned by
86 * {@code Float.intBitsToFloat(0x7f800000)}.
87 */
88 public static final float POSITIVE_INFINITY = 1.0f / 0.0f;
89
90 /**
91 * A constant holding the negative infinity of type
92 * {@code float}. It is equal to the value returned by
93 * {@code Float.intBitsToFloat(0xff800000)}.
94 */
95 public static final float NEGATIVE_INFINITY = -1.0f / 0.0f;
96
97 /**
98 * A constant holding a Not-a-Number (NaN) value of type
99 * {@code float}. It is equivalent to the value returned by
100 * {@code Float.intBitsToFloat(0x7fc00000)}.
101 */
102 public static final float NaN = 0.0f / 0.0f;
103
104 /**
105 * A constant holding the largest positive finite value of type
106 * {@code float}, (2-2<sup>-23</sup>)·2<sup>127</sup>.
107 * It is equal to the hexadecimal floating-point literal
108 * {@code 0x1.fffffeP+127f} and also equal to
109 * {@code Float.intBitsToFloat(0x7f7fffff)}.
110 */
111 public static final float MAX_VALUE = 0x1.fffffeP+127f; // 3.4028235e+38f
112
113 /**
114 * A constant holding the smallest positive normal value of type
115 * {@code float}, 2<sup>-126</sup>. It is equal to the
116 * hexadecimal floating-point literal {@code 0x1.0p-126f} and also
117 * equal to {@code Float.intBitsToFloat(0x00800000)}.
118 *
119 * @since 1.6
120 */
121 public static final float MIN_NORMAL = 0x1.0p-126f; // 1.17549435E-38f
122
123 /**
124 * A constant holding the smallest positive nonzero value of type
125 * {@code float}, 2<sup>-149</sup>. It is equal to the
126 * hexadecimal floating-point literal {@code 0x0.000002P-126f}
127 * and also equal to {@code Float.intBitsToFloat(0x1)}.
128 */
129 public static final float MIN_VALUE = 0x0.000002P-126f; // 1.4e-45f
130
131 /**
132 * The number of bits used to represent a {@code float} value,
133 * {@value}.
134 *
135 * @since 1.5
136 */
137 public static final int SIZE = 32;
138
139 /**
140 * The number of bits in the significand of a {@code float} value,
141 * {@value}. This is the parameter N in section {@jls 4.2.3} of
142 * <cite>The Java Language Specification</cite>.
143 *
144 * @since 19
145 */
146 public static final int PRECISION = 24;
147
148 /**
149 * Maximum exponent a finite {@code float} variable may have,
150 * {@value}. It is equal to the value returned by {@code
151 * Math.getExponent(Float.MAX_VALUE)}.
152 *
153 * @since 1.6
154 */
155 public static final int MAX_EXPONENT = (1 << (SIZE - PRECISION - 1)) - 1; // 127
156
157 /**
158 * Minimum exponent a normalized {@code float} variable may have,
159 * {@value}. It is equal to the value returned by {@code
160 * Math.getExponent(Float.MIN_NORMAL)}.
161 *
162 * @since 1.6
163 */
164 public static final int MIN_EXPONENT = 1 - MAX_EXPONENT; // -126
165
166 /**
167 * The number of bytes used to represent a {@code float} value,
168 * {@value}.
169 *
170 * @since 1.8
171 */
172 public static final int BYTES = SIZE / Byte.SIZE;
173
174 /**
175 * The {@code Class} instance representing the primitive type
176 * {@code float}.
177 *
178 * @since 1.1
179 */
180 @SuppressWarnings("unchecked")
181 public static final Class<Float> TYPE = (Class<Float>) Class.getPrimitiveClass("float");
182
183 /**
184 * Returns a string representation of the {@code float}
185 * argument. All characters mentioned below are ASCII characters.
186 * <ul>
187 * <li>If the argument is NaN, the result is the string
188 * "{@code NaN}".
189 * <li>Otherwise, the result is a string that represents the sign and
190 * magnitude (absolute value) of the argument. If the sign is
191 * negative, the first character of the result is
192 * '{@code -}' ({@code '\u005Cu002D'}); if the sign is
193 * positive, no sign character appears in the result. As for
194 * the magnitude <i>m</i>:
195 * <ul>
196 * <li>If <i>m</i> is infinity, it is represented by the characters
197 * {@code "Infinity"}; thus, positive infinity produces
198 * the result {@code "Infinity"} and negative infinity
199 * produces the result {@code "-Infinity"}.
200 * <li>If <i>m</i> is zero, it is represented by the characters
201 * {@code "0.0"}; thus, negative zero produces the result
202 * {@code "-0.0"} and positive zero produces the result
203 * {@code "0.0"}.
204 *
205 * <li> Otherwise <i>m</i> is positive and finite.
206 * It is converted to a string in two stages:
207 * <ul>
208 * <li> <em>Selection of a decimal</em>:
209 * A well-defined decimal <i>d</i><sub><i>m</i></sub>
210 * is selected to represent <i>m</i>.
211 * This decimal is (almost always) the <em>shortest</em> one that
212 * rounds to <i>m</i> according to the round to nearest
213 * rounding policy of IEEE 754 floating-point arithmetic.
214 * <li> <em>Formatting as a string</em>:
215 * The decimal <i>d</i><sub><i>m</i></sub> is formatted as a string,
216 * either in plain or in computerized scientific notation,
217 * depending on its value.
218 * </ul>
219 * </ul>
220 * </ul>
221 *
222 * <p>A <em>decimal</em> is a number of the form
223 * <i>s</i>×10<sup><i>i</i></sup>
224 * for some (unique) integers <i>s</i> > 0 and <i>i</i> such that
225 * <i>s</i> is not a multiple of 10.
226 * These integers are the <em>significand</em> and
227 * the <em>exponent</em>, respectively, of the decimal.
228 * The <em>length</em> of the decimal is the (unique)
229 * positive integer <i>n</i> meeting
230 * 10<sup><i>n</i>-1</sup> ≤ <i>s</i> < 10<sup><i>n</i></sup>.
231 *
232 * <p>The decimal <i>d</i><sub><i>m</i></sub> for a finite positive <i>m</i>
233 * is defined as follows:
234 * <ul>
235 * <li>Let <i>R</i> be the set of all decimals that round to <i>m</i>
236 * according to the usual <em>round to nearest</em> rounding policy of
237 * IEEE 754 floating-point arithmetic.
238 * <li>Let <i>p</i> be the minimal length over all decimals in <i>R</i>.
239 * <li>When <i>p</i> ≥ 2, let <i>T</i> be the set of all decimals
240 * in <i>R</i> with length <i>p</i>.
241 * Otherwise, let <i>T</i> be the set of all decimals
242 * in <i>R</i> with length 1 or 2.
243 * <li>Define <i>d</i><sub><i>m</i></sub> as the decimal in <i>T</i>
244 * that is closest to <i>m</i>.
245 * Or if there are two such decimals in <i>T</i>,
246 * select the one with the even significand.
247 * </ul>
248 *
249 * <p>The (uniquely) selected decimal <i>d</i><sub><i>m</i></sub>
250 * is then formatted.
251 * Let <i>s</i>, <i>i</i> and <i>n</i> be the significand, exponent and
252 * length of <i>d</i><sub><i>m</i></sub>, respectively.
253 * Further, let <i>e</i> = <i>n</i> + <i>i</i> - 1 and let
254 * <i>s</i><sub>1</sub>…<i>s</i><sub><i>n</i></sub>
255 * be the usual decimal expansion of <i>s</i>.
256 * Note that <i>s</i><sub>1</sub> ≠ 0
257 * and <i>s</i><sub><i>n</i></sub> ≠ 0.
258 * Below, the decimal point {@code '.'} is {@code '\u005Cu002E'}
259 * and the exponent indicator {@code 'E'} is {@code '\u005Cu0045'}.
260 * <ul>
261 * <li>Case -3 ≤ <i>e</i> < 0:
262 * <i>d</i><sub><i>m</i></sub> is formatted as
263 * <code>0.0</code>…<code>0</code><!--
264 * --><i>s</i><sub>1</sub>…<i>s</i><sub><i>n</i></sub>,
265 * where there are exactly -(<i>n</i> + <i>i</i>) zeroes between
266 * the decimal point and <i>s</i><sub>1</sub>.
267 * For example, 123 × 10<sup>-4</sup> is formatted as
268 * {@code 0.0123}.
269 * <li>Case 0 ≤ <i>e</i> < 7:
270 * <ul>
271 * <li>Subcase <i>i</i> ≥ 0:
272 * <i>d</i><sub><i>m</i></sub> is formatted as
273 * <i>s</i><sub>1</sub>…<i>s</i><sub><i>n</i></sub><!--
274 * --><code>0</code>…<code>0.0</code>,
275 * where there are exactly <i>i</i> zeroes
276 * between <i>s</i><sub><i>n</i></sub> and the decimal point.
277 * For example, 123 × 10<sup>2</sup> is formatted as
278 * {@code 12300.0}.
279 * <li>Subcase <i>i</i> < 0:
280 * <i>d</i><sub><i>m</i></sub> is formatted as
281 * <i>s</i><sub>1</sub>…<!--
282 * --><i>s</i><sub><i>n</i>+<i>i</i></sub><code>.</code><!--
283 * --><i>s</i><sub><i>n</i>+<i>i</i>+1</sub>…<!--
284 * --><i>s</i><sub><i>n</i></sub>,
285 * where there are exactly -<i>i</i> digits to the right of
286 * the decimal point.
287 * For example, 123 × 10<sup>-1</sup> is formatted as
288 * {@code 12.3}.
289 * </ul>
290 * <li>Case <i>e</i> < -3 or <i>e</i> ≥ 7:
291 * computerized scientific notation is used to format
292 * <i>d</i><sub><i>m</i></sub>.
293 * Here <i>e</i> is formatted as by {@link Integer#toString(int)}.
294 * <ul>
295 * <li>Subcase <i>n</i> = 1:
296 * <i>d</i><sub><i>m</i></sub> is formatted as
297 * <i>s</i><sub>1</sub><code>.0E</code><i>e</i>.
298 * For example, 1 × 10<sup>23</sup> is formatted as
299 * {@code 1.0E23}.
300 * <li>Subcase <i>n</i> > 1:
301 * <i>d</i><sub><i>m</i></sub> is formatted as
302 * <i>s</i><sub>1</sub><code>.</code><i>s</i><sub>2</sub><!--
303 * -->…<i>s</i><sub><i>n</i></sub><code>E</code><i>e</i>.
304 * For example, 123 × 10<sup>-21</sup> is formatted as
305 * {@code 1.23E-19}.
306 * </ul>
307 * </ul>
308 *
309 * <p>To create localized string representations of a floating-point
310 * value, use subclasses of {@link java.text.NumberFormat}.
311 *
312 * @apiNote
313 * This method corresponds to the general functionality of the
314 * convertToDecimalCharacter operation defined in IEEE 754;
315 * however, that operation is defined in terms of specifying the
316 * number of significand digits used in the conversion.
317 * Code to do such a conversion in the Java platform includes
318 * converting the {@code float} to a {@link java.math.BigDecimal
319 * BigDecimal} exactly and then rounding the {@code BigDecimal} to
320 * the desired number of digits; sample code:
321 * {@snippet lang=java :
322 * floatf = 0.1f;
323 * int digits = 15;
324 * BigDecimal bd = new BigDecimal(f);
325 * String result = bd.round(new MathContext(digits, RoundingMode.HALF_UP));
326 * // 0.100000001490116
327 * }
328 *
329 * @param f the {@code float} to be converted.
330 * @return a string representation of the argument.
331 */
332 public static String toString(float f) {
333 return FloatToDecimal.toString(f);
334 }
335
336 /**
337 * Returns a hexadecimal string representation of the
338 * {@code float} argument. All characters mentioned below are
339 * ASCII characters.
340 *
341 * <ul>
342 * <li>If the argument is NaN, the result is the string
343 * "{@code NaN}".
344 * <li>Otherwise, the result is a string that represents the sign and
345 * magnitude (absolute value) of the argument. If the sign is negative,
346 * the first character of the result is '{@code -}'
347 * ({@code '\u005Cu002D'}); if the sign is positive, no sign character
348 * appears in the result. As for the magnitude <i>m</i>:
349 *
350 * <ul>
351 * <li>If <i>m</i> is infinity, it is represented by the string
352 * {@code "Infinity"}; thus, positive infinity produces the
353 * result {@code "Infinity"} and negative infinity produces
354 * the result {@code "-Infinity"}.
355 *
356 * <li>If <i>m</i> is zero, it is represented by the string
357 * {@code "0x0.0p0"}; thus, negative zero produces the result
358 * {@code "-0x0.0p0"} and positive zero produces the result
359 * {@code "0x0.0p0"}.
360 *
361 * <li>If <i>m</i> is a {@code float} value with a
362 * normalized representation, substrings are used to represent the
363 * significand and exponent fields. The significand is
364 * represented by the characters {@code "0x1."}
365 * followed by a lowercase hexadecimal representation of the rest
366 * of the significand as a fraction. Trailing zeros in the
367 * hexadecimal representation are removed unless all the digits
368 * are zero, in which case a single zero is used. Next, the
369 * exponent is represented by {@code "p"} followed
370 * by a decimal string of the unbiased exponent as if produced by
371 * a call to {@link Integer#toString(int) Integer.toString} on the
372 * exponent value.
373 *
374 * <li>If <i>m</i> is a {@code float} value with a subnormal
375 * representation, the significand is represented by the
376 * characters {@code "0x0."} followed by a
377 * hexadecimal representation of the rest of the significand as a
378 * fraction. Trailing zeros in the hexadecimal representation are
379 * removed. Next, the exponent is represented by
380 * {@code "p-126"}. Note that there must be at
381 * least one nonzero digit in a subnormal significand.
382 *
383 * </ul>
384 *
385 * </ul>
386 *
387 * <table class="striped">
388 * <caption>Examples</caption>
389 * <thead>
390 * <tr><th scope="col">Floating-point Value</th><th scope="col">Hexadecimal String</th>
391 * </thead>
392 * <tbody>
393 * <tr><th scope="row">{@code 1.0}</th> <td>{@code 0x1.0p0}</td>
394 * <tr><th scope="row">{@code -1.0}</th> <td>{@code -0x1.0p0}</td>
395 * <tr><th scope="row">{@code 2.0}</th> <td>{@code 0x1.0p1}</td>
396 * <tr><th scope="row">{@code 3.0}</th> <td>{@code 0x1.8p1}</td>
397 * <tr><th scope="row">{@code 0.5}</th> <td>{@code 0x1.0p-1}</td>
398 * <tr><th scope="row">{@code 0.25}</th> <td>{@code 0x1.0p-2}</td>
399 * <tr><th scope="row">{@code Float.MAX_VALUE}</th>
400 * <td>{@code 0x1.fffffep127}</td>
401 * <tr><th scope="row">{@code Minimum Normal Value}</th>
402 * <td>{@code 0x1.0p-126}</td>
403 * <tr><th scope="row">{@code Maximum Subnormal Value}</th>
404 * <td>{@code 0x0.fffffep-126}</td>
405 * <tr><th scope="row">{@code Float.MIN_VALUE}</th>
406 * <td>{@code 0x0.000002p-126}</td>
407 * </tbody>
408 * </table>
409 *
410 * @apiNote
411 * This method corresponds to the convertToHexCharacter operation
412 * defined in IEEE 754.
413 *
414 * @param f the {@code float} to be converted.
415 * @return a hex string representation of the argument.
416 * @since 1.5
417 * @author Joseph D. Darcy
418 */
419 public static String toHexString(float f) {
420 if (Math.abs(f) < Float.MIN_NORMAL
421 && f != 0.0f ) {// float subnormal
422 // Adjust exponent to create subnormal double, then
423 // replace subnormal double exponent with subnormal float
424 // exponent
425 String s = Double.toHexString(Math.scalb((double)f,
426 /* -1022+126 */
427 Double.MIN_EXPONENT-
428 Float.MIN_EXPONENT));
429 return s.replaceFirst("p-1022$", "p-126");
430 }
431 else // double string will be the same as float string
432 return Double.toHexString(f);
433 }
434
435 /**
436 * Returns a {@code Float} object holding the
437 * {@code float} value represented by the argument string
438 * {@code s}.
439 *
440 * <p>If {@code s} is {@code null}, then a
441 * {@code NullPointerException} is thrown.
442 *
443 * <p>Leading and trailing whitespace characters in {@code s}
444 * are ignored. Whitespace is removed as if by the {@link
445 * String#trim} method; that is, both ASCII space and control
446 * characters are removed. The rest of {@code s} should
447 * constitute a <i>FloatValue</i> as described by the lexical
448 * syntax rules:
449 *
450 * <blockquote>
451 * <dl>
452 * <dt><i>FloatValue:</i>
453 * <dd><i>Sign<sub>opt</sub></i> {@code NaN}
454 * <dd><i>Sign<sub>opt</sub></i> {@code Infinity}
455 * <dd><i>Sign<sub>opt</sub> FloatingPointLiteral</i>
456 * <dd><i>Sign<sub>opt</sub> HexFloatingPointLiteral</i>
457 * <dd><i>SignedInteger</i>
458 * </dl>
459 *
460 * <dl>
461 * <dt><i>HexFloatingPointLiteral</i>:
462 * <dd> <i>HexSignificand BinaryExponent FloatTypeSuffix<sub>opt</sub></i>
463 * </dl>
464 *
465 * <dl>
466 * <dt><i>HexSignificand:</i>
467 * <dd><i>HexNumeral</i>
468 * <dd><i>HexNumeral</i> {@code .}
469 * <dd>{@code 0x} <i>HexDigits<sub>opt</sub>
470 * </i>{@code .}<i> HexDigits</i>
471 * <dd>{@code 0X}<i> HexDigits<sub>opt</sub>
472 * </i>{@code .} <i>HexDigits</i>
473 * </dl>
474 *
475 * <dl>
476 * <dt><i>BinaryExponent:</i>
477 * <dd><i>BinaryExponentIndicator SignedInteger</i>
478 * </dl>
479 *
480 * <dl>
481 * <dt><i>BinaryExponentIndicator:</i>
482 * <dd>{@code p}
483 * <dd>{@code P}
484 * </dl>
485 *
486 * </blockquote>
487 *
488 * where <i>Sign</i>, <i>FloatingPointLiteral</i>,
489 * <i>HexNumeral</i>, <i>HexDigits</i>, <i>SignedInteger</i> and
490 * <i>FloatTypeSuffix</i> are as defined in the lexical structure
491 * sections of
492 * <cite>The Java Language Specification</cite>,
493 * except that underscores are not accepted between digits.
494 * If {@code s} does not have the form of
495 * a <i>FloatValue</i>, then a {@code NumberFormatException}
496 * is thrown. Otherwise, {@code s} is regarded as
497 * representing an exact decimal value in the usual
498 * "computerized scientific notation" or as an exact
499 * hexadecimal value; this exact numerical value is then
500 * conceptually converted to an "infinitely precise"
501 * binary value that is then rounded to type {@code float}
502 * by the usual round-to-nearest rule of IEEE 754 floating-point
503 * arithmetic, which includes preserving the sign of a zero
504 * value.
505 *
506 * Note that the round-to-nearest rule also implies overflow and
507 * underflow behaviour; if the exact value of {@code s} is large
508 * enough in magnitude (greater than or equal to ({@link
509 * #MAX_VALUE} + {@link Math#ulp(float) ulp(MAX_VALUE)}/2),
510 * rounding to {@code float} will result in an infinity and if the
511 * exact value of {@code s} is small enough in magnitude (less
512 * than or equal to {@link #MIN_VALUE}/2), rounding to float will
513 * result in a zero.
514 *
515 * Finally, after rounding a {@code Float} object representing
516 * this {@code float} value is returned.
517 *
518 * <p>Note that trailing format specifiers, specifiers that
519 * determine the type of a floating-point literal
520 * ({@code 1.0f} is a {@code float} value;
521 * {@code 1.0d} is a {@code double} value), do
522 * <em>not</em> influence the results of this method. In other
523 * words, the numerical value of the input string is converted
524 * directly to the target floating-point type. In general, the
525 * two-step sequence of conversions, string to {@code double}
526 * followed by {@code double} to {@code float}, is
527 * <em>not</em> equivalent to converting a string directly to
528 * {@code float}. For example, if first converted to an
529 * intermediate {@code double} and then to
530 * {@code float}, the string<br>
531 * {@code "1.00000017881393421514957253748434595763683319091796875001d"}<br>
532 * results in the {@code float} value
533 * {@code 1.0000002f}; if the string is converted directly to
534 * {@code float}, <code>1.000000<b>1</b>f</code> results.
535 *
536 * <p>To avoid calling this method on an invalid string and having
537 * a {@code NumberFormatException} be thrown, the documentation
538 * for {@link Double#valueOf Double.valueOf} lists a regular
539 * expression which can be used to screen the input.
540 *
541 * @apiNote To interpret localized string representations of a
542 * floating-point value, or string representations that have
543 * non-ASCII digits, use {@link java.text.NumberFormat}. For
544 * example,
545 * {@snippet lang="java" :
546 * NumberFormat.getInstance(l).parse(s).floatValue();
547 * }
548 * where {@code l} is the desired locale, or
549 * {@link java.util.Locale#ROOT} if locale insensitive.
550 *
551 * @apiNote
552 * This method corresponds to the convertFromDecimalCharacter and
553 * convertFromHexCharacter operations defined in IEEE 754.
554 *
555 * @param s the string to be parsed.
556 * @return a {@code Float} object holding the value
557 * represented by the {@code String} argument.
558 * @throws NumberFormatException if the string does not contain a
559 * parsable number.
560 * @see Double##decimalToBinaryConversion Decimal ↔ Binary Conversion Issues
561 */
562 public static Float valueOf(String s) throws NumberFormatException {
563 return new Float(parseFloat(s));
564 }
565
566 /**
567 * Returns a {@code Float} instance representing the specified
568 * {@code float} value.
569 * If a new {@code Float} instance is not required, this method
570 * should generally be used in preference to the constructor
571 * {@link #Float(float)}, as this method is likely to yield
572 * significantly better space and time performance by caching
573 * frequently requested values.
574 *
575 * @param f a float value.
576 * @return a {@code Float} instance representing {@code f}.
577 * @since 1.5
578 */
579 @IntrinsicCandidate
580 @DeserializeConstructor
581 public static Float valueOf(float f) {
582 return new Float(f);
583 }
584
585 /**
586 * Returns a new {@code float} initialized to the value
587 * represented by the specified {@code String}, as performed
588 * by the {@code valueOf} method of class {@code Float}.
589 *
590 * @param s the string to be parsed.
591 * @return the {@code float} value represented by the string
592 * argument.
593 * @throws NullPointerException if the string is null
594 * @throws NumberFormatException if the string does not contain a
595 * parsable {@code float}.
596 * @see java.lang.Float#valueOf(String)
597 * @see Double##decimalToBinaryConversion Decimal ↔ Binary Conversion Issues
598 * @since 1.2
599 */
600 public static float parseFloat(String s) throws NumberFormatException {
601 return FloatingDecimal.parseFloat(s);
602 }
603
604 /**
605 * Returns {@code true} if the specified number is a
606 * Not-a-Number (NaN) value, {@code false} otherwise.
607 *
608 * @apiNote
609 * This method corresponds to the isNaN operation defined in IEEE
610 * 754.
611 *
612 * @param v the value to be tested.
613 * @return {@code true} if the argument is NaN;
614 * {@code false} otherwise.
615 */
616 public static boolean isNaN(float v) {
617 return (v != v);
618 }
619
620 /**
621 * Returns {@code true} if the specified number is infinitely
622 * large in magnitude, {@code false} otherwise.
623 *
624 * @apiNote
625 * This method corresponds to the isInfinite operation defined in
626 * IEEE 754.
627 *
628 * @param v the value to be tested.
629 * @return {@code true} if the argument is positive infinity or
630 * negative infinity; {@code false} otherwise.
631 */
632 @IntrinsicCandidate
633 public static boolean isInfinite(float v) {
634 return Math.abs(v) > MAX_VALUE;
635 }
636
637
638 /**
639 * Returns {@code true} if the argument is a finite floating-point
640 * value; returns {@code false} otherwise (for NaN and infinity
641 * arguments).
642 *
643 * @apiNote
644 * This method corresponds to the isFinite operation defined in
645 * IEEE 754.
646 *
647 * @param f the {@code float} value to be tested
648 * @return {@code true} if the argument is a finite
649 * floating-point value, {@code false} otherwise.
650 * @since 1.8
651 */
652 @IntrinsicCandidate
653 public static boolean isFinite(float f) {
654 return Math.abs(f) <= Float.MAX_VALUE;
655 }
656
657 /**
658 * The value of the Float.
659 *
660 * @serial
661 */
662 private final float value;
663
664 /**
665 * Constructs a newly allocated {@code Float} object that
666 * represents the primitive {@code float} argument.
667 *
668 * @param value the value to be represented by the {@code Float}.
669 *
670 * @deprecated
671 * It is rarely appropriate to use this constructor. The static factory
672 * {@link #valueOf(float)} is generally a better choice, as it is
673 * likely to yield significantly better space and time performance.
674 */
675 @Deprecated(since="9", forRemoval = true)
676 public Float(float value) {
677 this.value = value;
678 }
679
680 /**
681 * Constructs a newly allocated {@code Float} object that
682 * represents the argument converted to type {@code float}.
683 *
684 * @param value the value to be represented by the {@code Float}.
685 *
686 * @deprecated
687 * It is rarely appropriate to use this constructor. Instead, use the
688 * static factory method {@link #valueOf(float)} method as follows:
689 * {@code Float.valueOf((float)value)}.
690 */
691 @Deprecated(since="9", forRemoval = true)
692 public Float(double value) {
693 this.value = (float)value;
694 }
695
696 /**
697 * Constructs a newly allocated {@code Float} object that
698 * represents the floating-point value of type {@code float}
699 * represented by the string. The string is converted to a
700 * {@code float} value as if by the {@code valueOf} method.
701 *
702 * @param s a string to be converted to a {@code Float}.
703 * @throws NumberFormatException if the string does not contain a
704 * parsable number.
705 *
706 * @deprecated
707 * It is rarely appropriate to use this constructor.
708 * Use {@link #parseFloat(String)} to convert a string to a
709 * {@code float} primitive, or use {@link #valueOf(String)}
710 * to convert a string to a {@code Float} object.
711 */
712 @Deprecated(since="9", forRemoval = true)
713 public Float(String s) throws NumberFormatException {
714 value = parseFloat(s);
715 }
716
717 /**
718 * Returns {@code true} if this {@code Float} value is a
719 * Not-a-Number (NaN), {@code false} otherwise.
720 *
721 * @return {@code true} if the value represented by this object is
722 * NaN; {@code false} otherwise.
723 */
724 public boolean isNaN() {
725 return isNaN(value);
726 }
727
728 /**
729 * Returns {@code true} if this {@code Float} value is
730 * infinitely large in magnitude, {@code false} otherwise.
731 *
732 * @return {@code true} if the value represented by this object is
733 * positive infinity or negative infinity;
734 * {@code false} otherwise.
735 */
736 public boolean isInfinite() {
737 return isInfinite(value);
738 }
739
740 /**
741 * Returns a string representation of this {@code Float} object.
742 * The primitive {@code float} value represented by this object
743 * is converted to a {@code String} exactly as if by the method
744 * {@code toString} of one argument.
745 *
746 * @return a {@code String} representation of this object.
747 * @see java.lang.Float#toString(float)
748 */
749 public String toString() {
750 return Float.toString(value);
751 }
752
753 /**
754 * Returns the value of this {@code Float} as a {@code byte} after
755 * a narrowing primitive conversion.
756 *
757 * @return the {@code float} value represented by this object
758 * converted to type {@code byte}
759 * @jls 5.1.3 Narrowing Primitive Conversion
760 */
761 @Override
762 public byte byteValue() {
763 return (byte)value;
764 }
765
766 /**
767 * Returns the value of this {@code Float} as a {@code short}
768 * after a narrowing primitive conversion.
769 *
770 * @return the {@code float} value represented by this object
771 * converted to type {@code short}
772 * @jls 5.1.3 Narrowing Primitive Conversion
773 * @since 1.1
774 */
775 @Override
776 public short shortValue() {
777 return (short)value;
778 }
779
780 /**
781 * Returns the value of this {@code Float} as an {@code int} after
782 * a narrowing primitive conversion.
783 *
784 * @apiNote
785 * This method corresponds to the convertToIntegerTowardZero
786 * operation defined in IEEE 754.
787 *
788 * @return the {@code float} value represented by this object
789 * converted to type {@code int}
790 * @jls 5.1.3 Narrowing Primitive Conversion
791 */
792 @Override
793 public int intValue() {
794 return (int)value;
795 }
796
797 /**
798 * Returns value of this {@code Float} as a {@code long} after a
799 * narrowing primitive conversion.
800 *
801 * @apiNote
802 * This method corresponds to the convertToIntegerTowardZero
803 * operation defined in IEEE 754.
804 *
805 * @return the {@code float} value represented by this object
806 * converted to type {@code long}
807 * @jls 5.1.3 Narrowing Primitive Conversion
808 */
809 @Override
810 public long longValue() {
811 return (long)value;
812 }
813
814 /**
815 * Returns the {@code float} value of this {@code Float} object.
816 *
817 * @return the {@code float} value represented by this object
818 */
819 @Override
820 @IntrinsicCandidate
821 public float floatValue() {
822 return value;
823 }
824
825 /**
826 * Returns the value of this {@code Float} as a {@code double}
827 * after a widening primitive conversion.
828 *
829 * @apiNote
830 * This method corresponds to the convertFormat operation defined
831 * in IEEE 754.
832 *
833 * @return the {@code float} value represented by this
834 * object converted to type {@code double}
835 * @jls 5.1.2 Widening Primitive Conversion
836 */
837 @Override
838 public double doubleValue() {
839 return (double)value;
840 }
841
842 /**
843 * Returns a hash code for this {@code Float} object. The
844 * result is the integer bit representation, exactly as produced
845 * by the method {@link #floatToIntBits(float)}, of the primitive
846 * {@code float} value represented by this {@code Float}
847 * object.
848 *
849 * @return a hash code value for this object.
850 */
851 @Override
852 public int hashCode() {
853 return Float.hashCode(value);
854 }
855
856 /**
857 * Returns a hash code for a {@code float} value; compatible with
858 * {@code Float.hashCode()}.
859 *
860 * @param value the value to hash
861 * @return a hash code value for a {@code float} value.
862 * @since 1.8
863 */
864 public static int hashCode(float value) {
865 return floatToIntBits(value);
866 }
867
868 /**
869 * Compares this object against the specified object. The result
870 * is {@code true} if and only if the argument is not
871 * {@code null} and is a {@code Float} object that
872 * represents a {@code float} with the same value as the
873 * {@code float} represented by this object. For this
874 * purpose, two {@code float} values are considered to be the
875 * same if and only if the method {@link #floatToIntBits(float)}
876 * returns the identical {@code int} value when applied to
877 * each.
878 *
879 * @apiNote
880 * This method is defined in terms of {@link
881 * #floatToIntBits(float)} rather than the {@code ==} operator on
882 * {@code float} values since the {@code ==} operator does
883 * <em>not</em> define an equivalence relation and to satisfy the
884 * {@linkplain Object#equals equals contract} an equivalence
885 * relation must be implemented; see {@linkplain Double##equivalenceRelation
886 * this discussion for details of floating-point equality and equivalence}.
887 *
888 * @param obj the object to be compared
889 * @return {@code true} if the objects are the same;
890 * {@code false} otherwise.
891 * @see java.lang.Float#floatToIntBits(float)
892 * @jls 15.21.1 Numerical Equality Operators == and !=
893 */
894 public boolean equals(Object obj) {
895 return (obj instanceof Float)
896 && (floatToIntBits(((Float)obj).value) == floatToIntBits(value));
897 }
898
899 /**
900 * Returns a representation of the specified floating-point value
901 * according to the IEEE 754 floating-point "single format" bit
902 * layout.
903 *
904 * <p>Bit 31 (the bit that is selected by the mask
905 * {@code 0x80000000}) represents the sign of the floating-point
906 * number.
907 * Bits 30-23 (the bits that are selected by the mask
908 * {@code 0x7f800000}) represent the exponent.
909 * Bits 22-0 (the bits that are selected by the mask
910 * {@code 0x007fffff}) represent the significand (sometimes called
911 * the mantissa) of the floating-point number.
912 *
913 * <p>If the argument is positive infinity, the result is
914 * {@code 0x7f800000}.
915 *
916 * <p>If the argument is negative infinity, the result is
917 * {@code 0xff800000}.
918 *
919 * <p>If the argument is NaN, the result is {@code 0x7fc00000}.
920 *
921 * <p>In all cases, the result is an integer that, when given to the
922 * {@link #intBitsToFloat(int)} method, will produce a floating-point
923 * value the same as the argument to {@code floatToIntBits}
924 * (except all NaN values are collapsed to a single
925 * "canonical" NaN value).
926 *
927 * @param value a floating-point number.
928 * @return the bits that represent the floating-point number.
929 */
930 @IntrinsicCandidate
931 public static int floatToIntBits(float value) {
932 if (!isNaN(value)) {
933 return floatToRawIntBits(value);
934 }
935 return 0x7fc00000;
936 }
937
938 /**
939 * Returns a representation of the specified floating-point value
940 * according to the IEEE 754 floating-point "single format" bit
941 * layout, preserving Not-a-Number (NaN) values.
942 *
943 * <p>Bit 31 (the bit that is selected by the mask
944 * {@code 0x80000000}) represents the sign of the floating-point
945 * number.
946 * Bits 30-23 (the bits that are selected by the mask
947 * {@code 0x7f800000}) represent the exponent.
948 * Bits 22-0 (the bits that are selected by the mask
949 * {@code 0x007fffff}) represent the significand (sometimes called
950 * the mantissa) of the floating-point number.
951 *
952 * <p>If the argument is positive infinity, the result is
953 * {@code 0x7f800000}.
954 *
955 * <p>If the argument is negative infinity, the result is
956 * {@code 0xff800000}.
957 *
958 * <p>If the argument is NaN, the result is the integer representing
959 * the actual NaN value. Unlike the {@code floatToIntBits}
960 * method, {@code floatToRawIntBits} does not collapse all the
961 * bit patterns encoding a NaN to a single "canonical"
962 * NaN value.
963 *
964 * <p>In all cases, the result is an integer that, when given to the
965 * {@link #intBitsToFloat(int)} method, will produce a
966 * floating-point value the same as the argument to
967 * {@code floatToRawIntBits}.
968 *
969 * @param value a floating-point number.
970 * @return the bits that represent the floating-point number.
971 * @since 1.3
972 */
973 @IntrinsicCandidate
974 public static native int floatToRawIntBits(float value);
975
976 /**
977 * Returns the {@code float} value corresponding to a given
978 * bit representation.
979 * The argument is considered to be a representation of a
980 * floating-point value according to the IEEE 754 floating-point
981 * "single format" bit layout.
982 *
983 * <p>If the argument is {@code 0x7f800000}, the result is positive
984 * infinity.
985 *
986 * <p>If the argument is {@code 0xff800000}, the result is negative
987 * infinity.
988 *
989 * <p>If the argument is any value in the range
990 * {@code 0x7f800001} through {@code 0x7fffffff} or in
991 * the range {@code 0xff800001} through
992 * {@code 0xffffffff}, the result is a NaN. No IEEE 754
993 * floating-point operation provided by Java can distinguish
994 * between two NaN values of the same type with different bit
995 * patterns. Distinct values of NaN are only distinguishable by
996 * use of the {@code Float.floatToRawIntBits} method.
997 *
998 * <p>In all other cases, let <i>s</i>, <i>e</i>, and <i>m</i> be three
999 * values that can be computed from the argument:
1000 *
1001 * {@snippet lang="java" :
1002 * int s = ((bits >> 31) == 0) ? 1 : -1;
1003 * int e = ((bits >> 23) & 0xff);
1004 * int m = (e == 0) ?
1005 * (bits & 0x7fffff) << 1 :
1006 * (bits & 0x7fffff) | 0x800000;
1007 * }
1008 *
1009 * Then the floating-point result equals the value of the mathematical
1010 * expression <i>s</i>·<i>m</i>·2<sup><i>e</i>-150</sup>.
1011 *
1012 * <p>Note that this method may not be able to return a
1013 * {@code float} NaN with exactly same bit pattern as the
1014 * {@code int} argument. IEEE 754 distinguishes between two
1015 * kinds of NaNs, quiet NaNs and <i>signaling NaNs</i>. The
1016 * differences between the two kinds of NaN are generally not
1017 * visible in Java. Arithmetic operations on signaling NaNs turn
1018 * them into quiet NaNs with a different, but often similar, bit
1019 * pattern. However, on some processors merely copying a
1020 * signaling NaN also performs that conversion. In particular,
1021 * copying a signaling NaN to return it to the calling method may
1022 * perform this conversion. So {@code intBitsToFloat} may
1023 * not be able to return a {@code float} with a signaling NaN
1024 * bit pattern. Consequently, for some {@code int} values,
1025 * {@code floatToRawIntBits(intBitsToFloat(start))} may
1026 * <i>not</i> equal {@code start}. Moreover, which
1027 * particular bit patterns represent signaling NaNs is platform
1028 * dependent; although all NaN bit patterns, quiet or signaling,
1029 * must be in the NaN range identified above.
1030 *
1031 * @param bits an integer.
1032 * @return the {@code float} floating-point value with the same bit
1033 * pattern.
1034 */
1035 @IntrinsicCandidate
1036 public static native float intBitsToFloat(int bits);
1037
1038 /**
1039 * {@return the {@code float} value closest to the numerical value
1040 * of the argument, a floating-point binary16 value encoded in a
1041 * {@code short}} The conversion is exact; all binary16 values can
1042 * be exactly represented in {@code float}.
1043 *
1044 * Special cases:
1045 * <ul>
1046 * <li> If the argument is zero, the result is a zero with the
1047 * same sign as the argument.
1048 * <li> If the argument is infinite, the result is an infinity
1049 * with the same sign as the argument.
1050 * <li> If the argument is a NaN, the result is a NaN.
1051 * </ul>
1052 *
1053 * <h4><a id=binary16Format>IEEE 754 binary16 format</a></h4>
1054 * The IEEE 754 standard defines binary16 as a 16-bit format, along
1055 * with the 32-bit binary32 format (corresponding to the {@code
1056 * float} type) and the 64-bit binary64 format (corresponding to
1057 * the {@code double} type). The binary16 format is similar to the
1058 * other IEEE 754 formats, except smaller, having all the usual
1059 * IEEE 754 values such as NaN, signed infinities, signed zeros,
1060 * and subnormals. The parameters (JLS {@jls 4.2.3}) for the
1061 * binary16 format are N = 11 precision bits, K = 5 exponent bits,
1062 * <i>E</i><sub><i>max</i></sub> = 15, and
1063 * <i>E</i><sub><i>min</i></sub> = -14.
1064 *
1065 * @apiNote
1066 * This method corresponds to the convertFormat operation defined
1067 * in IEEE 754 from the binary16 format to the binary32 format.
1068 * The operation of this method is analogous to a primitive
1069 * widening conversion (JLS {@jls 5.1.2}).
1070 *
1071 * @param floatBinary16 the binary16 value to convert to {@code float}
1072 * @since 20
1073 */
1074 @IntrinsicCandidate
1075 public static float float16ToFloat(short floatBinary16) {
1076 /*
1077 * The binary16 format has 1 sign bit, 5 exponent bits, and 10
1078 * significand bits. The exponent bias is 15.
1079 */
1080 int bin16arg = (int)floatBinary16;
1081 int bin16SignBit = 0x8000 & bin16arg;
1082 int bin16ExpBits = 0x7c00 & bin16arg;
1083 int bin16SignifBits = 0x03FF & bin16arg;
1084
1085 // Shift left difference in the number of significand bits in
1086 // the float and binary16 formats
1087 final int SIGNIF_SHIFT = (FloatConsts.SIGNIFICAND_WIDTH - 11);
1088
1089 float sign = (bin16SignBit != 0) ? -1.0f : 1.0f;
1090
1091 // Extract binary16 exponent, remove its bias, add in the bias
1092 // of a float exponent and shift to correct bit location
1093 // (significand width includes the implicit bit so shift one
1094 // less).
1095 int bin16Exp = (bin16ExpBits >> 10) - 15;
1096 if (bin16Exp == -15) {
1097 // For subnormal binary16 values and 0, the numerical
1098 // value is 2^24 * the significand as an integer (no
1099 // implicit bit).
1100 return sign * (0x1p-24f * bin16SignifBits);
1101 } else if (bin16Exp == 16) {
1102 return (bin16SignifBits == 0) ?
1103 sign * Float.POSITIVE_INFINITY :
1104 Float.intBitsToFloat((bin16SignBit << 16) |
1105 0x7f80_0000 |
1106 // Preserve NaN signif bits
1107 ( bin16SignifBits << SIGNIF_SHIFT ));
1108 }
1109
1110 assert -15 < bin16Exp && bin16Exp < 16;
1111
1112 int floatExpBits = (bin16Exp + FloatConsts.EXP_BIAS)
1113 << (FloatConsts.SIGNIFICAND_WIDTH - 1);
1114
1115 // Compute and combine result sign, exponent, and significand bits.
1116 return Float.intBitsToFloat((bin16SignBit << 16) |
1117 floatExpBits |
1118 (bin16SignifBits << SIGNIF_SHIFT));
1119 }
1120
1121 /**
1122 * {@return the floating-point binary16 value, encoded in a {@code
1123 * short}, closest in value to the argument}
1124 * The conversion is computed under the {@linkplain
1125 * java.math.RoundingMode#HALF_EVEN round to nearest even rounding
1126 * mode}.
1127 *
1128 * Special cases:
1129 * <ul>
1130 * <li> If the argument is zero, the result is a zero with the
1131 * same sign as the argument.
1132 * <li> If the argument is infinite, the result is an infinity
1133 * with the same sign as the argument.
1134 * <li> If the argument is a NaN, the result is a NaN.
1135 * </ul>
1136 *
1137 * The {@linkplain ##binary16Format binary16 format} is discussed in
1138 * more detail in the {@link #float16ToFloat} method.
1139 *
1140 * @apiNote
1141 * This method corresponds to the convertFormat operation defined
1142 * in IEEE 754 from the binary32 format to the binary16 format.
1143 * The operation of this method is analogous to a primitive
1144 * narrowing conversion (JLS {@jls 5.1.3}).
1145 *
1146 * @param f the {@code float} value to convert to binary16
1147 * @since 20
1148 */
1149 @IntrinsicCandidate
1150 public static short floatToFloat16(float f) {
1151 int doppel = Float.floatToRawIntBits(f);
1152 short sign_bit = (short)((doppel & 0x8000_0000) >> 16);
1153
1154 if (Float.isNaN(f)) {
1155 // Preserve sign and attempt to preserve significand bits
1156 return (short)(sign_bit
1157 | 0x7c00 // max exponent + 1
1158 // Preserve high order bit of float NaN in the
1159 // binary16 result NaN (tenth bit); OR in remaining
1160 // bits into lower 9 bits of binary 16 significand.
1161 | (doppel & 0x007f_e000) >> 13 // 10 bits
1162 | (doppel & 0x0000_1ff0) >> 4 // 9 bits
1163 | (doppel & 0x0000_000f)); // 4 bits
1164 }
1165
1166 float abs_f = Math.abs(f);
1167
1168 // The overflow threshold is binary16 MAX_VALUE + 1/2 ulp
1169 if (abs_f >= (0x1.ffcp15f + 0x0.002p15f) ) {
1170 return (short)(sign_bit | 0x7c00); // Positive or negative infinity
1171 }
1172
1173 // Smallest magnitude nonzero representable binary16 value
1174 // is equal to 0x1.0p-24; half-way and smaller rounds to zero.
1175 if (abs_f <= 0x1.0p-24f * 0.5f) { // Covers float zeros and subnormals.
1176 return sign_bit; // Positive or negative zero
1177 }
1178
1179 // Dealing with finite values in exponent range of binary16
1180 // (when rounding is done, could still round up)
1181 int exp = Math.getExponent(f);
1182 assert -25 <= exp && exp <= 15;
1183
1184 // For binary16 subnormals, beside forcing exp to -15, retain
1185 // the difference expdelta = E_min - exp. This is the excess
1186 // shift value, in addition to 13, to be used in the
1187 // computations below. Further the (hidden) msb with value 1
1188 // in f must be involved as well.
1189 int expdelta = 0;
1190 int msb = 0x0000_0000;
1191 if (exp < -14) {
1192 expdelta = -14 - exp;
1193 exp = -15;
1194 msb = 0x0080_0000;
1195 }
1196 int f_signif_bits = doppel & 0x007f_ffff | msb;
1197
1198 // Significand bits as if using rounding to zero (truncation).
1199 short signif_bits = (short)(f_signif_bits >> (13 + expdelta));
1200
1201 // For round to nearest even, determining whether or not to
1202 // round up (in magnitude) is a function of the least
1203 // significant bit (LSB), the next bit position (the round
1204 // position), and the sticky bit (whether there are any
1205 // nonzero bits in the exact result to the right of the round
1206 // digit). An increment occurs in three cases:
1207 //
1208 // LSB Round Sticky
1209 // 0 1 1
1210 // 1 1 0
1211 // 1 1 1
1212 // See "Computer Arithmetic Algorithms," Koren, Table 4.9
1213
1214 int lsb = f_signif_bits & (1 << 13 + expdelta);
1215 int round = f_signif_bits & (1 << 12 + expdelta);
1216 int sticky = f_signif_bits & ((1 << 12 + expdelta) - 1);
1217
1218 if (round != 0 && ((lsb | sticky) != 0 )) {
1219 signif_bits++;
1220 }
1221
1222 // No bits set in significand beyond the *first* exponent bit,
1223 // not just the significand; quantity is added to the exponent
1224 // to implement a carry out from rounding the significand.
1225 assert (0xf800 & signif_bits) == 0x0;
1226
1227 return (short)(sign_bit | ( ((exp + 15) << 10) + signif_bits ) );
1228 }
1229
1230 /**
1231 * Compares two {@code Float} objects numerically.
1232 *
1233 * This method imposes a total order on {@code Float} objects
1234 * with two differences compared to the incomplete order defined by
1235 * the Java language numerical comparison operators ({@code <, <=,
1236 * ==, >=, >}) on {@code float} values.
1237 *
1238 * <ul><li> A NaN is <em>unordered</em> with respect to other
1239 * values and unequal to itself under the comparison
1240 * operators. This method chooses to define {@code
1241 * Float.NaN} to be equal to itself and greater than all
1242 * other {@code double} values (including {@code
1243 * Float.POSITIVE_INFINITY}).
1244 *
1245 * <li> Positive zero and negative zero compare equal
1246 * numerically, but are distinct and distinguishable values.
1247 * This method chooses to define positive zero ({@code +0.0f}),
1248 * to be greater than negative zero ({@code -0.0f}).
1249 * </ul>
1250 *
1251 * This ensures that the <i>natural ordering</i> of {@code Float}
1252 * objects imposed by this method is <i>consistent with
1253 * equals</i>; see {@linkplain Double##equivalenceRelation this
1254 * discussion for details of floating-point comparison and
1255 * ordering}.
1256 *
1257 *
1258 * @param anotherFloat the {@code Float} to be compared.
1259 * @return the value {@code 0} if {@code anotherFloat} is
1260 * numerically equal to this {@code Float}; a value
1261 * less than {@code 0} if this {@code Float}
1262 * is numerically less than {@code anotherFloat};
1263 * and a value greater than {@code 0} if this
1264 * {@code Float} is numerically greater than
1265 * {@code anotherFloat}.
1266 *
1267 * @jls 15.20.1 Numerical Comparison Operators {@code <}, {@code <=}, {@code >}, and {@code >=}
1268 * @since 1.2
1269 */
1270 @Override
1271 public int compareTo(Float anotherFloat) {
1272 return Float.compare(value, anotherFloat.value);
1273 }
1274
1275 /**
1276 * Compares the two specified {@code float} values. The sign
1277 * of the integer value returned is the same as that of the
1278 * integer that would be returned by the call:
1279 * <pre>
1280 * Float.valueOf(f1).compareTo(Float.valueOf(f2))
1281 * </pre>
1282 *
1283 * @param f1 the first {@code float} to compare.
1284 * @param f2 the second {@code float} to compare.
1285 * @return the value {@code 0} if {@code f1} is
1286 * numerically equal to {@code f2}; a value less than
1287 * {@code 0} if {@code f1} is numerically less than
1288 * {@code f2}; and a value greater than {@code 0}
1289 * if {@code f1} is numerically greater than
1290 * {@code f2}.
1291 * @since 1.4
1292 */
1293 public static int compare(float f1, float f2) {
1294 if (f1 < f2)
1295 return -1; // Neither val is NaN, thisVal is smaller
1296 if (f1 > f2)
1297 return 1; // Neither val is NaN, thisVal is larger
1298
1299 // Cannot use floatToRawIntBits because of possibility of NaNs.
1300 int thisBits = Float.floatToIntBits(f1);
1301 int anotherBits = Float.floatToIntBits(f2);
1302
1303 return (thisBits == anotherBits ? 0 : // Values are equal
1304 (thisBits < anotherBits ? -1 : // (-0.0, 0.0) or (!NaN, NaN)
1305 1)); // (0.0, -0.0) or (NaN, !NaN)
1306 }
1307
1308 /**
1309 * Adds two {@code float} values together as per the + operator.
1310 *
1311 * @apiNote This method corresponds to the addition operation
1312 * defined in IEEE 754.
1313 *
1314 * @param a the first operand
1315 * @param b the second operand
1316 * @return the sum of {@code a} and {@code b}
1317 * @jls 4.2.4 Floating-Point Operations
1318 * @see java.util.function.BinaryOperator
1319 * @since 1.8
1320 */
1321 public static float sum(float a, float b) {
1322 return a + b;
1323 }
1324
1325 /**
1326 * Returns the greater of two {@code float} values
1327 * as if by calling {@link Math#max(float, float) Math.max}.
1328 *
1329 * @apiNote
1330 * This method corresponds to the maximum operation defined in
1331 * IEEE 754.
1332 *
1333 * @param a the first operand
1334 * @param b the second operand
1335 * @return the greater of {@code a} and {@code b}
1336 * @see java.util.function.BinaryOperator
1337 * @since 1.8
1338 */
1339 public static float max(float a, float b) {
1340 return Math.max(a, b);
1341 }
1342
1343 /**
1344 * Returns the smaller of two {@code float} values
1345 * as if by calling {@link Math#min(float, float) Math.min}.
1346 *
1347 * @apiNote
1348 * This method corresponds to the minimum operation defined in
1349 * IEEE 754.
1350 *
1351 * @param a the first operand
1352 * @param b the second operand
1353 * @return the smaller of {@code a} and {@code b}
1354 * @see java.util.function.BinaryOperator
1355 * @since 1.8
1356 */
1357 public static float min(float a, float b) {
1358 return Math.min(a, b);
1359 }
1360
1361 /**
1362 * Returns an {@link Optional} containing the nominal descriptor for this
1363 * instance, which is the instance itself.
1364 *
1365 * @return an {@link Optional} describing the {@linkplain Float} instance
1366 * @since 12
1367 */
1368 @Override
1369 public Optional<Float> describeConstable() {
1370 return Optional.of(this);
1371 }
1372
1373 /**
1374 * Resolves this instance as a {@link ConstantDesc}, the result of which is
1375 * the instance itself.
1376 *
1377 * @param lookup ignored
1378 * @return the {@linkplain Float} instance
1379 * @since 12
1380 */
1381 @Override
1382 public Float resolveConstantDesc(MethodHandles.Lookup lookup) {
1383 return this;
1384 }
1385
1386 /** use serialVersionUID from JDK 1.0.2 for interoperability */
1387 @java.io.Serial
1388 private static final long serialVersionUID = -2671257302660747028L;
1389 }