1 /*
2 * Copyright (c) 1994, 2024, Oracle and/or its affiliates. All rights reserved.
3 * DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER.
4 *
5 * This code is free software; you can redistribute it and/or modify it
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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.vm.annotation.IntrinsicCandidate;
37
38 /**
39 * The {@code Float} class is the {@linkplain
40 * java.lang##wrapperClass wrapper class} for values of the primitive
41 * type {@code float}. An object of type {@code Float} contains a
42 * single field whose type is {@code float}.
43 *
44 * <p>In addition, this class provides several methods for converting a
45 * {@code float} to a {@code String} and a
46 * {@code String} to a {@code float}, as well as other
47 * constants and methods useful when dealing with a
48 * {@code float}.
49 *
50 * <p>This is a <a href="{@docRoot}/java.base/java/lang/doc-files/ValueBased.html">value-based</a>
51 * class; programmers should treat instances that are
52 * {@linkplain #equals(Object) equal} as interchangeable and should not
53 * use instances for synchronization, or unpredictable behavior may
54 * occur. For example, in a future release, synchronization may fail.
55 *
56 * <h2><a id=equivalenceRelation>Floating-point Equality, Equivalence,
57 * and Comparison</a></h2>
58 *
59 * The class {@code java.lang.Double} has a {@linkplain
60 * Double##equivalenceRelation discussion of equality,
61 * equivalence, and comparison of floating-point values} that is
62 * equally applicable to {@code float} values.
63 *
64 * <h2><a id=decimalToBinaryConversion>Decimal ↔ Binary Conversion Issues</a></h2>
65 *
66 * The {@linkplain Double##decimalToBinaryConversion discussion of binary to
67 * decimal conversion issues} in {@code java.lang.Double} is also
68 * applicable to {@code float} values.
69 *
70 * @see <a href="https://standards.ieee.org/ieee/754/6210/">
71 * <cite>IEEE Standard for Floating-Point Arithmetic</cite></a>
72 *
73 * @author Lee Boynton
74 * @author Arthur van Hoff
75 * @author Joseph D. Darcy
76 * @since 1.0
77 */
78 @jdk.internal.ValueBased
79 public final class Float extends Number
80 implements Comparable<Float>, Constable, ConstantDesc {
81 /**
82 * A constant holding the positive infinity of type
83 * {@code float}. It is equal to the value returned by
84 * {@code Float.intBitsToFloat(0x7f800000)}.
85 */
86 public static final float POSITIVE_INFINITY = 1.0f / 0.0f;
87
88 /**
89 * A constant holding the negative infinity of type
90 * {@code float}. It is equal to the value returned by
91 * {@code Float.intBitsToFloat(0xff800000)}.
92 */
93 public static final float NEGATIVE_INFINITY = -1.0f / 0.0f;
94
95 /**
96 * A constant holding a Not-a-Number (NaN) value of type
97 * {@code float}. It is equivalent to the value returned by
98 * {@code Float.intBitsToFloat(0x7fc00000)}.
99 */
100 public static final float NaN = 0.0f / 0.0f;
101
102 /**
103 * A constant holding the largest positive finite value of type
104 * {@code float}, (2-2<sup>-23</sup>)·2<sup>127</sup>.
105 * It is equal to the hexadecimal floating-point literal
106 * {@code 0x1.fffffeP+127f} and also equal to
107 * {@code Float.intBitsToFloat(0x7f7fffff)}.
108 */
109 public static final float MAX_VALUE = 0x1.fffffeP+127f; // 3.4028235e+38f
110
111 /**
112 * A constant holding the smallest positive normal value of type
113 * {@code float}, 2<sup>-126</sup>. It is equal to the
114 * hexadecimal floating-point literal {@code 0x1.0p-126f} and also
115 * equal to {@code Float.intBitsToFloat(0x00800000)}.
116 *
117 * @since 1.6
118 */
119 public static final float MIN_NORMAL = 0x1.0p-126f; // 1.17549435E-38f
120
121 /**
122 * A constant holding the smallest positive nonzero value of type
123 * {@code float}, 2<sup>-149</sup>. It is equal to the
124 * hexadecimal floating-point literal {@code 0x0.000002P-126f}
125 * and also equal to {@code Float.intBitsToFloat(0x1)}.
126 */
127 public static final float MIN_VALUE = 0x0.000002P-126f; // 1.4e-45f
128
129 /**
130 * The number of bits used to represent a {@code float} value,
131 * {@value}.
132 *
133 * @since 1.5
134 */
135 public static final int SIZE = 32;
136
137 /**
138 * The number of bits in the significand of a {@code float} value,
139 * {@value}. This is the parameter N in section {@jls 4.2.3} of
140 * <cite>The Java Language Specification</cite>.
141 *
142 * @since 19
143 */
144 public static final int PRECISION = 24;
145
146 /**
147 * Maximum exponent a finite {@code float} variable may have,
148 * {@value}. It is equal to the value returned by {@code
149 * Math.getExponent(Float.MAX_VALUE)}.
150 *
151 * @since 1.6
152 */
153 public static final int MAX_EXPONENT = (1 << (SIZE - PRECISION - 1)) - 1; // 127
154
155 /**
156 * Minimum exponent a normalized {@code float} variable may have,
157 * {@value}. It is equal to the value returned by {@code
158 * Math.getExponent(Float.MIN_NORMAL)}.
159 *
160 * @since 1.6
161 */
162 public static final int MIN_EXPONENT = 1 - MAX_EXPONENT; // -126
163
164 /**
165 * The number of bytes used to represent a {@code float} value,
166 * {@value}.
167 *
168 * @since 1.8
169 */
170 public static final int BYTES = SIZE / Byte.SIZE;
171
172 /**
173 * The {@code Class} instance representing the primitive type
174 * {@code float}.
175 *
176 * @since 1.1
177 */
178 public static final Class<Float> TYPE = Class.getPrimitiveClass("float");
179
180 /**
181 * Returns a string representation of the {@code float}
182 * argument. All characters mentioned below are ASCII characters.
183 * <ul>
184 * <li>If the argument is NaN, the result is the string
185 * "{@code NaN}".
186 * <li>Otherwise, the result is a string that represents the sign and
187 * magnitude (absolute value) of the argument. If the sign is
188 * negative, the first character of the result is
189 * '{@code -}' ({@code '\u005Cu002D'}); if the sign is
190 * positive, no sign character appears in the result. As for
191 * the magnitude <i>m</i>:
192 * <ul>
193 * <li>If <i>m</i> is infinity, it is represented by the characters
194 * {@code "Infinity"}; thus, positive infinity produces
195 * the result {@code "Infinity"} and negative infinity
196 * produces the result {@code "-Infinity"}.
197 * <li>If <i>m</i> is zero, it is represented by the characters
198 * {@code "0.0"}; thus, negative zero produces the result
199 * {@code "-0.0"} and positive zero produces the result
200 * {@code "0.0"}.
201 *
202 * <li> Otherwise <i>m</i> is positive and finite.
203 * It is converted to a string in two stages:
204 * <ul>
205 * <li> <em>Selection of a decimal</em>:
206 * A well-defined decimal <i>d</i><sub><i>m</i></sub>
207 * is selected to represent <i>m</i>.
208 * This decimal is (almost always) the <em>shortest</em> one that
209 * rounds to <i>m</i> according to the round to nearest
210 * rounding policy of IEEE 754 floating-point arithmetic.
211 * <li> <em>Formatting as a string</em>:
212 * The decimal <i>d</i><sub><i>m</i></sub> is formatted as a string,
213 * either in plain or in computerized scientific notation,
214 * depending on its value.
215 * </ul>
216 * </ul>
217 * </ul>
218 *
219 * <p>A <em>decimal</em> is a number of the form
220 * <i>s</i>×10<sup><i>i</i></sup>
221 * for some (unique) integers <i>s</i> > 0 and <i>i</i> such that
222 * <i>s</i> is not a multiple of 10.
223 * These integers are the <em>significand</em> and
224 * the <em>exponent</em>, respectively, of the decimal.
225 * The <em>length</em> of the decimal is the (unique)
226 * positive integer <i>n</i> meeting
227 * 10<sup><i>n</i>-1</sup> ≤ <i>s</i> < 10<sup><i>n</i></sup>.
228 *
229 * <p>The decimal <i>d</i><sub><i>m</i></sub> for a finite positive <i>m</i>
230 * is defined as follows:
231 * <ul>
232 * <li>Let <i>R</i> be the set of all decimals that round to <i>m</i>
233 * according to the usual <em>round to nearest</em> rounding policy of
234 * IEEE 754 floating-point arithmetic.
235 * <li>Let <i>p</i> be the minimal length over all decimals in <i>R</i>.
236 * <li>When <i>p</i> ≥ 2, let <i>T</i> be the set of all decimals
237 * in <i>R</i> with length <i>p</i>.
238 * Otherwise, let <i>T</i> be the set of all decimals
239 * in <i>R</i> with length 1 or 2.
240 * <li>Define <i>d</i><sub><i>m</i></sub> as the decimal in <i>T</i>
241 * that is closest to <i>m</i>.
242 * Or if there are two such decimals in <i>T</i>,
243 * select the one with the even significand.
244 * </ul>
245 *
246 * <p>The (uniquely) selected decimal <i>d</i><sub><i>m</i></sub>
247 * is then formatted.
248 * Let <i>s</i>, <i>i</i> and <i>n</i> be the significand, exponent and
249 * length of <i>d</i><sub><i>m</i></sub>, respectively.
250 * Further, let <i>e</i> = <i>n</i> + <i>i</i> - 1 and let
251 * <i>s</i><sub>1</sub>…<i>s</i><sub><i>n</i></sub>
252 * be the usual decimal expansion of <i>s</i>.
253 * Note that <i>s</i><sub>1</sub> ≠ 0
254 * and <i>s</i><sub><i>n</i></sub> ≠ 0.
255 * Below, the decimal point {@code '.'} is {@code '\u005Cu002E'}
256 * and the exponent indicator {@code 'E'} is {@code '\u005Cu0045'}.
257 * <ul>
258 * <li>Case -3 ≤ <i>e</i> < 0:
259 * <i>d</i><sub><i>m</i></sub> is formatted as
260 * <code>0.0</code>…<code>0</code><!--
261 * --><i>s</i><sub>1</sub>…<i>s</i><sub><i>n</i></sub>,
262 * where there are exactly -(<i>n</i> + <i>i</i>) zeroes between
263 * the decimal point and <i>s</i><sub>1</sub>.
264 * For example, 123 × 10<sup>-4</sup> is formatted as
265 * {@code 0.0123}.
266 * <li>Case 0 ≤ <i>e</i> < 7:
267 * <ul>
268 * <li>Subcase <i>i</i> ≥ 0:
269 * <i>d</i><sub><i>m</i></sub> is formatted as
270 * <i>s</i><sub>1</sub>…<i>s</i><sub><i>n</i></sub><!--
271 * --><code>0</code>…<code>0.0</code>,
272 * where there are exactly <i>i</i> zeroes
273 * between <i>s</i><sub><i>n</i></sub> and the decimal point.
274 * For example, 123 × 10<sup>2</sup> is formatted as
275 * {@code 12300.0}.
276 * <li>Subcase <i>i</i> < 0:
277 * <i>d</i><sub><i>m</i></sub> is formatted as
278 * <i>s</i><sub>1</sub>…<!--
279 * --><i>s</i><sub><i>n</i>+<i>i</i></sub><code>.</code><!--
280 * --><i>s</i><sub><i>n</i>+<i>i</i>+1</sub>…<!--
281 * --><i>s</i><sub><i>n</i></sub>,
282 * where there are exactly -<i>i</i> digits to the right of
283 * the decimal point.
284 * For example, 123 × 10<sup>-1</sup> is formatted as
285 * {@code 12.3}.
286 * </ul>
287 * <li>Case <i>e</i> < -3 or <i>e</i> ≥ 7:
288 * computerized scientific notation is used to format
289 * <i>d</i><sub><i>m</i></sub>.
290 * Here <i>e</i> is formatted as by {@link Integer#toString(int)}.
291 * <ul>
292 * <li>Subcase <i>n</i> = 1:
293 * <i>d</i><sub><i>m</i></sub> is formatted as
294 * <i>s</i><sub>1</sub><code>.0E</code><i>e</i>.
295 * For example, 1 × 10<sup>23</sup> is formatted as
296 * {@code 1.0E23}.
297 * <li>Subcase <i>n</i> > 1:
298 * <i>d</i><sub><i>m</i></sub> is formatted as
299 * <i>s</i><sub>1</sub><code>.</code><i>s</i><sub>2</sub><!--
300 * -->…<i>s</i><sub><i>n</i></sub><code>E</code><i>e</i>.
301 * For example, 123 × 10<sup>-21</sup> is formatted as
302 * {@code 1.23E-19}.
303 * </ul>
304 * </ul>
305 *
306 * <p>To create localized string representations of a floating-point
307 * value, use subclasses of {@link java.text.NumberFormat}.
308 *
309 * @apiNote
310 * This method corresponds to the general functionality of the
311 * convertToDecimalCharacter operation defined in IEEE 754;
312 * however, that operation is defined in terms of specifying the
313 * number of significand digits used in the conversion.
314 * Code to do such a conversion in the Java platform includes
315 * converting the {@code float} to a {@link java.math.BigDecimal
316 * BigDecimal} exactly and then rounding the {@code BigDecimal} to
317 * the desired number of digits; sample code:
318 * {@snippet lang=java :
319 * floatf = 0.1f;
320 * int digits = 15;
321 * BigDecimal bd = new BigDecimal(f);
322 * String result = bd.round(new MathContext(digits, RoundingMode.HALF_UP));
323 * // 0.100000001490116
324 * }
325 *
326 * @param f the {@code float} to be converted.
327 * @return a string representation of the argument.
328 */
329 public static String toString(float f) {
330 return FloatToDecimal.toString(f);
331 }
332
333 /**
334 * Returns a hexadecimal string representation of the
335 * {@code float} argument. All characters mentioned below are
336 * ASCII characters.
337 *
338 * <ul>
339 * <li>If the argument is NaN, the result is the string
340 * "{@code NaN}".
341 * <li>Otherwise, the result is a string that represents the sign and
342 * magnitude (absolute value) of the argument. If the sign is negative,
343 * the first character of the result is '{@code -}'
344 * ({@code '\u005Cu002D'}); if the sign is positive, no sign character
345 * appears in the result. As for the magnitude <i>m</i>:
346 *
347 * <ul>
348 * <li>If <i>m</i> is infinity, it is represented by the string
349 * {@code "Infinity"}; thus, positive infinity produces the
350 * result {@code "Infinity"} and negative infinity produces
351 * the result {@code "-Infinity"}.
352 *
353 * <li>If <i>m</i> is zero, it is represented by the string
354 * {@code "0x0.0p0"}; thus, negative zero produces the result
355 * {@code "-0x0.0p0"} and positive zero produces the result
356 * {@code "0x0.0p0"}.
357 *
358 * <li>If <i>m</i> is a {@code float} value with a
359 * normalized representation, substrings are used to represent the
360 * significand and exponent fields. The significand is
361 * represented by the characters {@code "0x1."}
362 * followed by a lowercase hexadecimal representation of the rest
363 * of the significand as a fraction. Trailing zeros in the
364 * hexadecimal representation are removed unless all the digits
365 * are zero, in which case a single zero is used. Next, the
366 * exponent is represented by {@code "p"} followed
367 * by a decimal string of the unbiased exponent as if produced by
368 * a call to {@link Integer#toString(int) Integer.toString} on the
369 * exponent value.
370 *
371 * <li>If <i>m</i> is a {@code float} value with a subnormal
372 * representation, the significand is represented by the
373 * characters {@code "0x0."} followed by a
374 * hexadecimal representation of the rest of the significand as a
375 * fraction. Trailing zeros in the hexadecimal representation are
376 * removed. Next, the exponent is represented by
377 * {@code "p-126"}. Note that there must be at
378 * least one nonzero digit in a subnormal significand.
379 *
380 * </ul>
381 *
382 * </ul>
383 *
384 * <table class="striped">
385 * <caption>Examples</caption>
386 * <thead>
387 * <tr><th scope="col">Floating-point Value</th><th scope="col">Hexadecimal String</th>
388 * </thead>
389 * <tbody>
390 * <tr><th scope="row">{@code 1.0}</th> <td>{@code 0x1.0p0}</td>
391 * <tr><th scope="row">{@code -1.0}</th> <td>{@code -0x1.0p0}</td>
392 * <tr><th scope="row">{@code 2.0}</th> <td>{@code 0x1.0p1}</td>
393 * <tr><th scope="row">{@code 3.0}</th> <td>{@code 0x1.8p1}</td>
394 * <tr><th scope="row">{@code 0.5}</th> <td>{@code 0x1.0p-1}</td>
395 * <tr><th scope="row">{@code 0.25}</th> <td>{@code 0x1.0p-2}</td>
396 * <tr><th scope="row">{@code Float.MAX_VALUE}</th>
397 * <td>{@code 0x1.fffffep127}</td>
398 * <tr><th scope="row">{@code Minimum Normal Value}</th>
399 * <td>{@code 0x1.0p-126}</td>
400 * <tr><th scope="row">{@code Maximum Subnormal Value}</th>
401 * <td>{@code 0x0.fffffep-126}</td>
402 * <tr><th scope="row">{@code Float.MIN_VALUE}</th>
403 * <td>{@code 0x0.000002p-126}</td>
404 * </tbody>
405 * </table>
406 *
407 * @apiNote
408 * This method corresponds to the convertToHexCharacter operation
409 * defined in IEEE 754.
410 *
411 * @param f the {@code float} to be converted.
412 * @return a hex string representation of the argument.
413 * @since 1.5
414 * @author Joseph D. Darcy
415 */
416 public static String toHexString(float f) {
417 if (Math.abs(f) < Float.MIN_NORMAL
418 && f != 0.0f ) {// float subnormal
419 // Adjust exponent to create subnormal double, then
420 // replace subnormal double exponent with subnormal float
421 // exponent
422 String s = Double.toHexString(Math.scalb((double)f,
423 /* -1022+126 */
424 Double.MIN_EXPONENT-
425 Float.MIN_EXPONENT));
426 return s.replaceFirst("p-1022$", "p-126");
427 }
428 else // double string will be the same as float string
429 return Double.toHexString(f);
430 }
431
432 /**
433 * Returns a {@code Float} object holding the
434 * {@code float} value represented by the argument string
435 * {@code s}.
436 *
437 * <p>If {@code s} is {@code null}, then a
438 * {@code NullPointerException} is thrown.
439 *
440 * <p>Leading and trailing whitespace characters in {@code s}
441 * are ignored. Whitespace is removed as if by the {@link
442 * String#trim} method; that is, both ASCII space and control
443 * characters are removed. The rest of {@code s} should
444 * constitute a <i>FloatValue</i> as described by the lexical
445 * syntax rules:
446 *
447 * <blockquote>
448 * <dl>
449 * <dt><i>FloatValue:</i>
450 * <dd><i>Sign<sub>opt</sub></i> {@code NaN}
451 * <dd><i>Sign<sub>opt</sub></i> {@code Infinity}
452 * <dd><i>Sign<sub>opt</sub> FloatingPointLiteral</i>
453 * <dd><i>Sign<sub>opt</sub> HexFloatingPointLiteral</i>
454 * <dd><i>SignedInteger</i>
455 * </dl>
456 *
457 * <dl>
458 * <dt><i>HexFloatingPointLiteral</i>:
459 * <dd> <i>HexSignificand BinaryExponent FloatTypeSuffix<sub>opt</sub></i>
460 * </dl>
461 *
462 * <dl>
463 * <dt><i>HexSignificand:</i>
464 * <dd><i>HexNumeral</i>
465 * <dd><i>HexNumeral</i> {@code .}
466 * <dd>{@code 0x} <i>HexDigits<sub>opt</sub>
467 * </i>{@code .}<i> HexDigits</i>
468 * <dd>{@code 0X}<i> HexDigits<sub>opt</sub>
469 * </i>{@code .} <i>HexDigits</i>
470 * </dl>
471 *
472 * <dl>
473 * <dt><i>BinaryExponent:</i>
474 * <dd><i>BinaryExponentIndicator SignedInteger</i>
475 * </dl>
476 *
477 * <dl>
478 * <dt><i>BinaryExponentIndicator:</i>
479 * <dd>{@code p}
480 * <dd>{@code P}
481 * </dl>
482 *
483 * </blockquote>
484 *
485 * where <i>Sign</i>, <i>FloatingPointLiteral</i>,
486 * <i>HexNumeral</i>, <i>HexDigits</i>, <i>SignedInteger</i> and
487 * <i>FloatTypeSuffix</i> are as defined in the lexical structure
488 * sections of
489 * <cite>The Java Language Specification</cite>,
490 * except that underscores are not accepted between digits.
491 * If {@code s} does not have the form of
492 * a <i>FloatValue</i>, then a {@code NumberFormatException}
493 * is thrown. Otherwise, {@code s} is regarded as
494 * representing an exact decimal value in the usual
495 * "computerized scientific notation" or as an exact
496 * hexadecimal value; this exact numerical value is then
497 * conceptually converted to an "infinitely precise"
498 * binary value that is then rounded to type {@code float}
499 * by the usual round-to-nearest rule of IEEE 754 floating-point
500 * arithmetic, which includes preserving the sign of a zero
501 * value.
502 *
503 * Note that the round-to-nearest rule also implies overflow and
504 * underflow behaviour; if the exact value of {@code s} is large
505 * enough in magnitude (greater than or equal to ({@link
506 * #MAX_VALUE} + {@link Math#ulp(float) ulp(MAX_VALUE)}/2),
507 * rounding to {@code float} will result in an infinity and if the
508 * exact value of {@code s} is small enough in magnitude (less
509 * than or equal to {@link #MIN_VALUE}/2), rounding to float will
510 * result in a zero.
511 *
512 * Finally, after rounding a {@code Float} object representing
513 * this {@code float} value is returned.
514 *
515 * <p>Note that trailing format specifiers, specifiers that
516 * determine the type of a floating-point literal
517 * ({@code 1.0f} is a {@code float} value;
518 * {@code 1.0d} is a {@code double} value), do
519 * <em>not</em> influence the results of this method. In other
520 * words, the numerical value of the input string is converted
521 * directly to the target floating-point type. In general, the
522 * two-step sequence of conversions, string to {@code double}
523 * followed by {@code double} to {@code float}, is
524 * <em>not</em> equivalent to converting a string directly to
525 * {@code float}. For example, if first converted to an
526 * intermediate {@code double} and then to
527 * {@code float}, the string<br>
528 * {@code "1.00000017881393421514957253748434595763683319091796875001d"}<br>
529 * results in the {@code float} value
530 * {@code 1.0000002f}; if the string is converted directly to
531 * {@code float}, <code>1.000000<b>1</b>f</code> results.
532 *
533 * <p>To avoid calling this method on an invalid string and having
534 * a {@code NumberFormatException} be thrown, the documentation
535 * for {@link Double#valueOf Double.valueOf} lists a regular
536 * expression which can be used to screen the input.
537 *
538 * @apiNote To interpret localized string representations of a
539 * floating-point value, or string representations that have
540 * non-ASCII digits, use {@link java.text.NumberFormat}. For
541 * example,
542 * {@snippet lang="java" :
543 * NumberFormat.getInstance(l).parse(s).floatValue();
544 * }
545 * where {@code l} is the desired locale, or
546 * {@link java.util.Locale#ROOT} if locale insensitive.
547 *
548 * @apiNote
549 * This method corresponds to the convertFromDecimalCharacter and
550 * convertFromHexCharacter operations defined in IEEE 754.
551 *
552 * @param s the string to be parsed.
553 * @return a {@code Float} object holding the value
554 * represented by the {@code String} argument.
555 * @throws NumberFormatException if the string does not contain a
556 * parsable number.
557 * @see Double##decimalToBinaryConversion Decimal ↔ Binary Conversion Issues
558 */
559 public static Float valueOf(String s) throws NumberFormatException {
560 return new Float(parseFloat(s));
561 }
562
563 /**
564 * Returns a {@code Float} instance representing the specified
565 * {@code float} value.
566 * If a new {@code Float} instance is not required, this method
567 * should generally be used in preference to the constructor
568 * {@link #Float(float)}, as this method is likely to yield
569 * significantly better space and time performance by caching
570 * frequently requested values.
571 *
572 * @param f a float value.
573 * @return a {@code Float} instance representing {@code f}.
574 * @since 1.5
575 */
576 @IntrinsicCandidate
577 public static Float valueOf(float f) {
578 return new Float(f);
579 }
580
581 /**
582 * Returns a new {@code float} initialized to the value
583 * represented by the specified {@code String}, as performed
584 * by the {@code valueOf} method of class {@code Float}.
585 *
586 * @param s the string to be parsed.
587 * @return the {@code float} value represented by the string
588 * argument.
589 * @throws NullPointerException if the string is null
590 * @throws NumberFormatException if the string does not contain a
591 * parsable {@code float}.
592 * @see java.lang.Float#valueOf(String)
593 * @see Double##decimalToBinaryConversion Decimal ↔ Binary Conversion Issues
594 * @since 1.2
595 */
596 public static float parseFloat(String s) throws NumberFormatException {
597 return FloatingDecimal.parseFloat(s);
598 }
599
600 /**
601 * Returns {@code true} if the specified number is a
602 * Not-a-Number (NaN) value, {@code false} otherwise.
603 *
604 * @apiNote
605 * This method corresponds to the isNaN operation defined in IEEE
606 * 754.
607 *
608 * @param v the value to be tested.
609 * @return {@code true} if the argument is NaN;
610 * {@code false} otherwise.
611 */
612 public static boolean isNaN(float v) {
613 return (v != v);
614 }
615
616 /**
617 * Returns {@code true} if the specified number is infinitely
618 * large in magnitude, {@code false} otherwise.
619 *
620 * @apiNote
621 * This method corresponds to the isInfinite operation defined in
622 * IEEE 754.
623 *
624 * @param v the value to be tested.
625 * @return {@code true} if the argument is positive infinity or
626 * negative infinity; {@code false} otherwise.
627 */
628 @IntrinsicCandidate
629 public static boolean isInfinite(float v) {
630 return Math.abs(v) > MAX_VALUE;
631 }
632
633
634 /**
635 * Returns {@code true} if the argument is a finite floating-point
636 * value; returns {@code false} otherwise (for NaN and infinity
637 * arguments).
638 *
639 * @apiNote
640 * This method corresponds to the isFinite operation defined in
641 * IEEE 754.
642 *
643 * @param f the {@code float} value to be tested
644 * @return {@code true} if the argument is a finite
645 * floating-point value, {@code false} otherwise.
646 * @since 1.8
647 */
648 @IntrinsicCandidate
649 public static boolean isFinite(float f) {
650 return Math.abs(f) <= Float.MAX_VALUE;
651 }
652
653 /**
654 * The value of the Float.
655 *
656 * @serial
657 */
658 private final float value;
659
660 /**
661 * Constructs a newly allocated {@code Float} object that
662 * represents the primitive {@code float} argument.
663 *
664 * @param value the value to be represented by the {@code Float}.
665 *
666 * @deprecated
667 * It is rarely appropriate to use this constructor. The static factory
668 * {@link #valueOf(float)} is generally a better choice, as it is
669 * likely to yield significantly better space and time performance.
670 */
671 @Deprecated(since="9", forRemoval = true)
672 public Float(float value) {
673 this.value = value;
674 }
675
676 /**
677 * Constructs a newly allocated {@code Float} object that
678 * represents the argument converted to type {@code float}.
679 *
680 * @param value the value to be represented by the {@code Float}.
681 *
682 * @deprecated
683 * It is rarely appropriate to use this constructor. Instead, use the
684 * static factory method {@link #valueOf(float)} method as follows:
685 * {@code Float.valueOf((float)value)}.
686 */
687 @Deprecated(since="9", forRemoval = true)
688 public Float(double value) {
689 this.value = (float)value;
690 }
691
692 /**
693 * Constructs a newly allocated {@code Float} object that
694 * represents the floating-point value of type {@code float}
695 * represented by the string. The string is converted to a
696 * {@code float} value as if by the {@code valueOf} method.
697 *
698 * @param s a string to be converted to a {@code Float}.
699 * @throws NumberFormatException if the string does not contain a
700 * parsable number.
701 *
702 * @deprecated
703 * It is rarely appropriate to use this constructor.
704 * Use {@link #parseFloat(String)} to convert a string to a
705 * {@code float} primitive, or use {@link #valueOf(String)}
706 * to convert a string to a {@code Float} object.
707 */
708 @Deprecated(since="9", forRemoval = true)
709 public Float(String s) throws NumberFormatException {
710 value = parseFloat(s);
711 }
712
713 /**
714 * Returns {@code true} if this {@code Float} value is a
715 * Not-a-Number (NaN), {@code false} otherwise.
716 *
717 * @return {@code true} if the value represented by this object is
718 * NaN; {@code false} otherwise.
719 */
720 public boolean isNaN() {
721 return isNaN(value);
722 }
723
724 /**
725 * Returns {@code true} if this {@code Float} value is
726 * infinitely large in magnitude, {@code false} otherwise.
727 *
728 * @return {@code true} if the value represented by this object is
729 * positive infinity or negative infinity;
730 * {@code false} otherwise.
731 */
732 public boolean isInfinite() {
733 return isInfinite(value);
734 }
735
736 /**
737 * Returns a string representation of this {@code Float} object.
738 * The primitive {@code float} value represented by this object
739 * is converted to a {@code String} exactly as if by the method
740 * {@code toString} of one argument.
741 *
742 * @return a {@code String} representation of this object.
743 * @see java.lang.Float#toString(float)
744 */
745 public String toString() {
746 return Float.toString(value);
747 }
748
749 /**
750 * Returns the value of this {@code Float} as a {@code byte} after
751 * a narrowing primitive conversion.
752 *
753 * @return the {@code float} value represented by this object
754 * converted to type {@code byte}
755 * @jls 5.1.3 Narrowing Primitive Conversion
756 */
757 @Override
758 public byte byteValue() {
759 return (byte)value;
760 }
761
762 /**
763 * Returns the value of this {@code Float} as a {@code short}
764 * after a narrowing primitive conversion.
765 *
766 * @return the {@code float} value represented by this object
767 * converted to type {@code short}
768 * @jls 5.1.3 Narrowing Primitive Conversion
769 * @since 1.1
770 */
771 @Override
772 public short shortValue() {
773 return (short)value;
774 }
775
776 /**
777 * Returns the value of this {@code Float} as an {@code int} after
778 * a narrowing primitive conversion.
779 *
780 * @apiNote
781 * This method corresponds to the convertToIntegerTowardZero
782 * operation defined in IEEE 754.
783 *
784 * @return the {@code float} value represented by this object
785 * converted to type {@code int}
786 * @jls 5.1.3 Narrowing Primitive Conversion
787 */
788 @Override
789 public int intValue() {
790 return (int)value;
791 }
792
793 /**
794 * Returns value of this {@code Float} as a {@code long} after a
795 * narrowing primitive conversion.
796 *
797 * @apiNote
798 * This method corresponds to the convertToIntegerTowardZero
799 * operation defined in IEEE 754.
800 *
801 * @return the {@code float} value represented by this object
802 * converted to type {@code long}
803 * @jls 5.1.3 Narrowing Primitive Conversion
804 */
805 @Override
806 public long longValue() {
807 return (long)value;
808 }
809
810 /**
811 * Returns the {@code float} value of this {@code Float} object.
812 *
813 * @return the {@code float} value represented by this object
814 */
815 @Override
816 @IntrinsicCandidate
817 public float floatValue() {
818 return value;
819 }
820
821 /**
822 * Returns the value of this {@code Float} as a {@code double}
823 * after a widening primitive conversion.
824 *
825 * @apiNote
826 * This method corresponds to the convertFormat operation defined
827 * in IEEE 754.
828 *
829 * @return the {@code float} value represented by this
830 * object converted to type {@code double}
831 * @jls 5.1.2 Widening Primitive Conversion
832 */
833 @Override
834 public double doubleValue() {
835 return (double)value;
836 }
837
838 /**
839 * Returns a hash code for this {@code Float} object. The
840 * result is the integer bit representation, exactly as produced
841 * by the method {@link #floatToIntBits(float)}, of the primitive
842 * {@code float} value represented by this {@code Float}
843 * object.
844 *
845 * @return a hash code value for this object.
846 */
847 @Override
848 public int hashCode() {
849 return Float.hashCode(value);
850 }
851
852 /**
853 * Returns a hash code for a {@code float} value; compatible with
854 * {@code Float.hashCode()}.
855 *
856 * @param value the value to hash
857 * @return a hash code value for a {@code float} value.
858 * @since 1.8
859 */
860 public static int hashCode(float value) {
861 return floatToIntBits(value);
862 }
863
864 /**
865 * Compares this object against the specified object. The result
866 * is {@code true} if and only if the argument is not
867 * {@code null} and is a {@code Float} object that
868 * represents a {@code float} with the same value as the
869 * {@code float} represented by this object. For this
870 * purpose, two {@code float} values are considered to be the
871 * same if and only if the method {@link #floatToIntBits(float)}
872 * returns the identical {@code int} value when applied to
873 * each.
874 *
875 * @apiNote
876 * This method is defined in terms of {@link
877 * #floatToIntBits(float)} rather than the {@code ==} operator on
878 * {@code float} values since the {@code ==} operator does
879 * <em>not</em> define an equivalence relation and to satisfy the
880 * {@linkplain Object#equals equals contract} an equivalence
881 * relation must be implemented; see {@linkplain Double##equivalenceRelation
882 * this discussion for details of floating-point equality and equivalence}.
883 *
884 * @param obj the object to be compared
885 * @return {@code true} if the objects are the same;
886 * {@code false} otherwise.
887 * @see java.lang.Float#floatToIntBits(float)
888 * @jls 15.21.1 Numerical Equality Operators == and !=
889 */
890 public boolean equals(Object obj) {
891 return (obj instanceof Float f) &&
892 (floatToIntBits(f.value) == floatToIntBits(value));
893 }
894
895 /**
896 * Returns a representation of the specified floating-point value
897 * according to the IEEE 754 floating-point "single format" bit
898 * layout.
899 *
900 * <p>Bit 31 (the bit that is selected by the mask
901 * {@code 0x80000000}) represents the sign of the floating-point
902 * number.
903 * Bits 30-23 (the bits that are selected by the mask
904 * {@code 0x7f800000}) represent the exponent.
905 * Bits 22-0 (the bits that are selected by the mask
906 * {@code 0x007fffff}) represent the significand (sometimes called
907 * the mantissa) of the floating-point number.
908 *
909 * <p>If the argument is positive infinity, the result is
910 * {@code 0x7f800000}.
911 *
912 * <p>If the argument is negative infinity, the result is
913 * {@code 0xff800000}.
914 *
915 * <p>If the argument is NaN, the result is {@code 0x7fc00000}.
916 *
917 * <p>In all cases, the result is an integer that, when given to the
918 * {@link #intBitsToFloat(int)} method, will produce a floating-point
919 * value the same as the argument to {@code floatToIntBits}
920 * (except all NaN values are collapsed to a single
921 * "canonical" NaN value).
922 *
923 * @param value a floating-point number.
924 * @return the bits that represent the floating-point number.
925 */
926 @IntrinsicCandidate
927 public static int floatToIntBits(float value) {
928 if (!isNaN(value)) {
929 return floatToRawIntBits(value);
930 }
931 return 0x7fc00000;
932 }
933
934 /**
935 * Returns a representation of the specified floating-point value
936 * according to the IEEE 754 floating-point "single format" bit
937 * layout, preserving Not-a-Number (NaN) values.
938 *
939 * <p>Bit 31 (the bit that is selected by the mask
940 * {@code 0x80000000}) represents the sign of the floating-point
941 * number.
942 * Bits 30-23 (the bits that are selected by the mask
943 * {@code 0x7f800000}) represent the exponent.
944 * Bits 22-0 (the bits that are selected by the mask
945 * {@code 0x007fffff}) represent the significand (sometimes called
946 * the mantissa) of the floating-point number.
947 *
948 * <p>If the argument is positive infinity, the result is
949 * {@code 0x7f800000}.
950 *
951 * <p>If the argument is negative infinity, the result is
952 * {@code 0xff800000}.
953 *
954 * <p>If the argument is NaN, the result is the integer representing
955 * the actual NaN value. Unlike the {@code floatToIntBits}
956 * method, {@code floatToRawIntBits} does not collapse all the
957 * bit patterns encoding a NaN to a single "canonical"
958 * NaN value.
959 *
960 * <p>In all cases, the result is an integer that, when given to the
961 * {@link #intBitsToFloat(int)} method, will produce a
962 * floating-point value the same as the argument to
963 * {@code floatToRawIntBits}.
964 *
965 * @param value a floating-point number.
966 * @return the bits that represent the floating-point number.
967 * @since 1.3
968 */
969 @IntrinsicCandidate
970 public static native int floatToRawIntBits(float value);
971
972 /**
973 * Returns the {@code float} value corresponding to a given
974 * bit representation.
975 * The argument is considered to be a representation of a
976 * floating-point value according to the IEEE 754 floating-point
977 * "single format" bit layout.
978 *
979 * <p>If the argument is {@code 0x7f800000}, the result is positive
980 * infinity.
981 *
982 * <p>If the argument is {@code 0xff800000}, the result is negative
983 * infinity.
984 *
985 * <p>If the argument is any value in the range
986 * {@code 0x7f800001} through {@code 0x7fffffff} or in
987 * the range {@code 0xff800001} through
988 * {@code 0xffffffff}, the result is a NaN. No IEEE 754
989 * floating-point operation provided by Java can distinguish
990 * between two NaN values of the same type with different bit
991 * patterns. Distinct values of NaN are only distinguishable by
992 * use of the {@code Float.floatToRawIntBits} method.
993 *
994 * <p>In all other cases, let <i>s</i>, <i>e</i>, and <i>m</i> be three
995 * values that can be computed from the argument:
996 *
997 * {@snippet lang="java" :
998 * int s = ((bits >> 31) == 0) ? 1 : -1;
999 * int e = ((bits >> 23) & 0xff);
1000 * int m = (e == 0) ?
1001 * (bits & 0x7fffff) << 1 :
1002 * (bits & 0x7fffff) | 0x800000;
1003 * }
1004 *
1005 * Then the floating-point result equals the value of the mathematical
1006 * expression <i>s</i>·<i>m</i>·2<sup><i>e</i>-150</sup>.
1007 *
1008 * <p>Note that this method may not be able to return a
1009 * {@code float} NaN with exactly same bit pattern as the
1010 * {@code int} argument. IEEE 754 distinguishes between two
1011 * kinds of NaNs, quiet NaNs and <i>signaling NaNs</i>. The
1012 * differences between the two kinds of NaN are generally not
1013 * visible in Java. Arithmetic operations on signaling NaNs turn
1014 * them into quiet NaNs with a different, but often similar, bit
1015 * pattern. However, on some processors merely copying a
1016 * signaling NaN also performs that conversion. In particular,
1017 * copying a signaling NaN to return it to the calling method may
1018 * perform this conversion. So {@code intBitsToFloat} may
1019 * not be able to return a {@code float} with a signaling NaN
1020 * bit pattern. Consequently, for some {@code int} values,
1021 * {@code floatToRawIntBits(intBitsToFloat(start))} may
1022 * <i>not</i> equal {@code start}. Moreover, which
1023 * particular bit patterns represent signaling NaNs is platform
1024 * dependent; although all NaN bit patterns, quiet or signaling,
1025 * must be in the NaN range identified above.
1026 *
1027 * @param bits an integer.
1028 * @return the {@code float} floating-point value with the same bit
1029 * pattern.
1030 */
1031 @IntrinsicCandidate
1032 public static native float intBitsToFloat(int bits);
1033
1034 /**
1035 * {@return the {@code float} value closest to the numerical value
1036 * of the argument, a floating-point binary16 value encoded in a
1037 * {@code short}} The conversion is exact; all binary16 values can
1038 * be exactly represented in {@code float}.
1039 *
1040 * Special cases:
1041 * <ul>
1042 * <li> If the argument is zero, the result is a zero with the
1043 * same sign as the argument.
1044 * <li> If the argument is infinite, the result is an infinity
1045 * with the same sign as the argument.
1046 * <li> If the argument is a NaN, the result is a NaN.
1047 * </ul>
1048 *
1049 * <h4><a id=binary16Format>IEEE 754 binary16 format</a></h4>
1050 * The IEEE 754 standard defines binary16 as a 16-bit format, along
1051 * with the 32-bit binary32 format (corresponding to the {@code
1052 * float} type) and the 64-bit binary64 format (corresponding to
1053 * the {@code double} type). The binary16 format is similar to the
1054 * other IEEE 754 formats, except smaller, having all the usual
1055 * IEEE 754 values such as NaN, signed infinities, signed zeros,
1056 * and subnormals. The parameters (JLS {@jls 4.2.3}) for the
1057 * binary16 format are N = 11 precision bits, K = 5 exponent bits,
1058 * <i>E</i><sub><i>max</i></sub> = 15, and
1059 * <i>E</i><sub><i>min</i></sub> = -14.
1060 *
1061 * @apiNote
1062 * This method corresponds to the convertFormat operation defined
1063 * in IEEE 754 from the binary16 format to the binary32 format.
1064 * The operation of this method is analogous to a primitive
1065 * widening conversion (JLS {@jls 5.1.2}).
1066 *
1067 * @param floatBinary16 the binary16 value to convert to {@code float}
1068 * @since 20
1069 */
1070 @IntrinsicCandidate
1071 public static float float16ToFloat(short floatBinary16) {
1072 /*
1073 * The binary16 format has 1 sign bit, 5 exponent bits, and 10
1074 * significand bits. The exponent bias is 15.
1075 */
1076 int bin16arg = (int)floatBinary16;
1077 int bin16SignBit = 0x8000 & bin16arg;
1078 int bin16ExpBits = 0x7c00 & bin16arg;
1079 int bin16SignifBits = 0x03FF & bin16arg;
1080
1081 // Shift left difference in the number of significand bits in
1082 // the float and binary16 formats
1083 final int SIGNIF_SHIFT = (FloatConsts.SIGNIFICAND_WIDTH - 11);
1084
1085 float sign = (bin16SignBit != 0) ? -1.0f : 1.0f;
1086
1087 // Extract binary16 exponent, remove its bias, add in the bias
1088 // of a float exponent and shift to correct bit location
1089 // (significand width includes the implicit bit so shift one
1090 // less).
1091 int bin16Exp = (bin16ExpBits >> 10) - 15;
1092 if (bin16Exp == -15) {
1093 // For subnormal binary16 values and 0, the numerical
1094 // value is 2^24 * the significand as an integer (no
1095 // implicit bit).
1096 return sign * (0x1p-24f * bin16SignifBits);
1097 } else if (bin16Exp == 16) {
1098 return (bin16SignifBits == 0) ?
1099 sign * Float.POSITIVE_INFINITY :
1100 Float.intBitsToFloat((bin16SignBit << 16) |
1101 0x7f80_0000 |
1102 // Preserve NaN signif bits
1103 ( bin16SignifBits << SIGNIF_SHIFT ));
1104 }
1105
1106 assert -15 < bin16Exp && bin16Exp < 16;
1107
1108 int floatExpBits = (bin16Exp + FloatConsts.EXP_BIAS)
1109 << (FloatConsts.SIGNIFICAND_WIDTH - 1);
1110
1111 // Compute and combine result sign, exponent, and significand bits.
1112 return Float.intBitsToFloat((bin16SignBit << 16) |
1113 floatExpBits |
1114 (bin16SignifBits << SIGNIF_SHIFT));
1115 }
1116
1117 /**
1118 * {@return the floating-point binary16 value, encoded in a {@code
1119 * short}, closest in value to the argument}
1120 * The conversion is computed under the {@linkplain
1121 * java.math.RoundingMode#HALF_EVEN round to nearest even rounding
1122 * mode}.
1123 *
1124 * Special cases:
1125 * <ul>
1126 * <li> If the argument is zero, the result is a zero with the
1127 * same sign as the argument.
1128 * <li> If the argument is infinite, the result is an infinity
1129 * with the same sign as the argument.
1130 * <li> If the argument is a NaN, the result is a NaN.
1131 * </ul>
1132 *
1133 * The {@linkplain ##binary16Format binary16 format} is discussed in
1134 * more detail in the {@link #float16ToFloat} method.
1135 *
1136 * @apiNote
1137 * This method corresponds to the convertFormat operation defined
1138 * in IEEE 754 from the binary32 format to the binary16 format.
1139 * The operation of this method is analogous to a primitive
1140 * narrowing conversion (JLS {@jls 5.1.3}).
1141 *
1142 * @param f the {@code float} value to convert to binary16
1143 * @since 20
1144 */
1145 @IntrinsicCandidate
1146 public static short floatToFloat16(float f) {
1147 int doppel = Float.floatToRawIntBits(f);
1148 short sign_bit = (short)((doppel & 0x8000_0000) >> 16);
1149
1150 if (Float.isNaN(f)) {
1151 // Preserve sign and attempt to preserve significand bits
1152 return (short)(sign_bit
1153 | 0x7c00 // max exponent + 1
1154 // Preserve high order bit of float NaN in the
1155 // binary16 result NaN (tenth bit); OR in remaining
1156 // bits into lower 9 bits of binary 16 significand.
1157 | (doppel & 0x007f_e000) >> 13 // 10 bits
1158 | (doppel & 0x0000_1ff0) >> 4 // 9 bits
1159 | (doppel & 0x0000_000f)); // 4 bits
1160 }
1161
1162 float abs_f = Math.abs(f);
1163
1164 // The overflow threshold is binary16 MAX_VALUE + 1/2 ulp
1165 if (abs_f >= (0x1.ffcp15f + 0x0.002p15f) ) {
1166 return (short)(sign_bit | 0x7c00); // Positive or negative infinity
1167 }
1168
1169 // Smallest magnitude nonzero representable binary16 value
1170 // is equal to 0x1.0p-24; half-way and smaller rounds to zero.
1171 if (abs_f <= 0x1.0p-24f * 0.5f) { // Covers float zeros and subnormals.
1172 return sign_bit; // Positive or negative zero
1173 }
1174
1175 // Dealing with finite values in exponent range of binary16
1176 // (when rounding is done, could still round up)
1177 int exp = Math.getExponent(f);
1178 assert -25 <= exp && exp <= 15;
1179
1180 // For binary16 subnormals, beside forcing exp to -15, retain
1181 // the difference expdelta = E_min - exp. This is the excess
1182 // shift value, in addition to 13, to be used in the
1183 // computations below. Further the (hidden) msb with value 1
1184 // in f must be involved as well.
1185 int expdelta = 0;
1186 int msb = 0x0000_0000;
1187 if (exp < -14) {
1188 expdelta = -14 - exp;
1189 exp = -15;
1190 msb = 0x0080_0000;
1191 }
1192 int f_signif_bits = doppel & 0x007f_ffff | msb;
1193
1194 // Significand bits as if using rounding to zero (truncation).
1195 short signif_bits = (short)(f_signif_bits >> (13 + expdelta));
1196
1197 // For round to nearest even, determining whether or not to
1198 // round up (in magnitude) is a function of the least
1199 // significant bit (LSB), the next bit position (the round
1200 // position), and the sticky bit (whether there are any
1201 // nonzero bits in the exact result to the right of the round
1202 // digit). An increment occurs in three cases:
1203 //
1204 // LSB Round Sticky
1205 // 0 1 1
1206 // 1 1 0
1207 // 1 1 1
1208 // See "Computer Arithmetic Algorithms," Koren, Table 4.9
1209
1210 int lsb = f_signif_bits & (1 << 13 + expdelta);
1211 int round = f_signif_bits & (1 << 12 + expdelta);
1212 int sticky = f_signif_bits & ((1 << 12 + expdelta) - 1);
1213
1214 if (round != 0 && ((lsb | sticky) != 0 )) {
1215 signif_bits++;
1216 }
1217
1218 // No bits set in significand beyond the *first* exponent bit,
1219 // not just the significand; quantity is added to the exponent
1220 // to implement a carry out from rounding the significand.
1221 assert (0xf800 & signif_bits) == 0x0;
1222
1223 return (short)(sign_bit | ( ((exp + 15) << 10) + signif_bits ) );
1224 }
1225
1226 /**
1227 * Compares two {@code Float} objects numerically.
1228 *
1229 * This method imposes a total order on {@code Float} objects
1230 * with two differences compared to the incomplete order defined by
1231 * the Java language numerical comparison operators ({@code <, <=,
1232 * ==, >=, >}) on {@code float} values.
1233 *
1234 * <ul><li> A NaN is <em>unordered</em> with respect to other
1235 * values and unequal to itself under the comparison
1236 * operators. This method chooses to define {@code
1237 * Float.NaN} to be equal to itself and greater than all
1238 * other {@code double} values (including {@code
1239 * Float.POSITIVE_INFINITY}).
1240 *
1241 * <li> Positive zero and negative zero compare equal
1242 * numerically, but are distinct and distinguishable values.
1243 * This method chooses to define positive zero ({@code +0.0f}),
1244 * to be greater than negative zero ({@code -0.0f}).
1245 * </ul>
1246 *
1247 * This ensures that the <i>natural ordering</i> of {@code Float}
1248 * objects imposed by this method is <i>consistent with
1249 * equals</i>; see {@linkplain Double##equivalenceRelation this
1250 * discussion for details of floating-point comparison and
1251 * ordering}.
1252 *
1253 *
1254 * @param anotherFloat the {@code Float} to be compared.
1255 * @return the value {@code 0} if {@code anotherFloat} is
1256 * numerically equal to this {@code Float}; a value
1257 * less than {@code 0} if this {@code Float}
1258 * is numerically less than {@code anotherFloat};
1259 * and a value greater than {@code 0} if this
1260 * {@code Float} is numerically greater than
1261 * {@code anotherFloat}.
1262 *
1263 * @jls 15.20.1 Numerical Comparison Operators {@code <}, {@code <=}, {@code >}, and {@code >=}
1264 * @since 1.2
1265 */
1266 @Override
1267 public int compareTo(Float anotherFloat) {
1268 return Float.compare(value, anotherFloat.value);
1269 }
1270
1271 /**
1272 * Compares the two specified {@code float} values. The sign
1273 * of the integer value returned is the same as that of the
1274 * integer that would be returned by the call:
1275 * <pre>
1276 * Float.valueOf(f1).compareTo(Float.valueOf(f2))
1277 * </pre>
1278 *
1279 * @param f1 the first {@code float} to compare.
1280 * @param f2 the second {@code float} to compare.
1281 * @return the value {@code 0} if {@code f1} is
1282 * numerically equal to {@code f2}; a value less than
1283 * {@code 0} if {@code f1} is numerically less than
1284 * {@code f2}; and a value greater than {@code 0}
1285 * if {@code f1} is numerically greater than
1286 * {@code f2}.
1287 * @since 1.4
1288 */
1289 public static int compare(float f1, float f2) {
1290 if (f1 < f2)
1291 return -1; // Neither val is NaN, thisVal is smaller
1292 if (f1 > f2)
1293 return 1; // Neither val is NaN, thisVal is larger
1294
1295 // Cannot use floatToRawIntBits because of possibility of NaNs.
1296 int thisBits = Float.floatToIntBits(f1);
1297 int anotherBits = Float.floatToIntBits(f2);
1298
1299 return (thisBits == anotherBits ? 0 : // Values are equal
1300 (thisBits < anotherBits ? -1 : // (-0.0, 0.0) or (!NaN, NaN)
1301 1)); // (0.0, -0.0) or (NaN, !NaN)
1302 }
1303
1304 /**
1305 * Adds two {@code float} values together as per the + operator.
1306 *
1307 * @apiNote This method corresponds to the addition operation
1308 * defined in IEEE 754.
1309 *
1310 * @param a the first operand
1311 * @param b the second operand
1312 * @return the sum of {@code a} and {@code b}
1313 * @jls 4.2.4 Floating-Point Operations
1314 * @see java.util.function.BinaryOperator
1315 * @since 1.8
1316 */
1317 public static float sum(float a, float b) {
1318 return a + b;
1319 }
1320
1321 /**
1322 * Returns the greater of two {@code float} values
1323 * as if by calling {@link Math#max(float, float) Math.max}.
1324 *
1325 * @apiNote
1326 * This method corresponds to the maximum operation defined in
1327 * IEEE 754.
1328 *
1329 * @param a the first operand
1330 * @param b the second operand
1331 * @return the greater of {@code a} and {@code b}
1332 * @see java.util.function.BinaryOperator
1333 * @since 1.8
1334 */
1335 public static float max(float a, float b) {
1336 return Math.max(a, b);
1337 }
1338
1339 /**
1340 * Returns the smaller of two {@code float} values
1341 * as if by calling {@link Math#min(float, float) Math.min}.
1342 *
1343 * @apiNote
1344 * This method corresponds to the minimum operation defined in
1345 * IEEE 754.
1346 *
1347 * @param a the first operand
1348 * @param b the second operand
1349 * @return the smaller of {@code a} and {@code b}
1350 * @see java.util.function.BinaryOperator
1351 * @since 1.8
1352 */
1353 public static float min(float a, float b) {
1354 return Math.min(a, b);
1355 }
1356
1357 /**
1358 * Returns an {@link Optional} containing the nominal descriptor for this
1359 * instance, which is the instance itself.
1360 *
1361 * @return an {@link Optional} describing the {@linkplain Float} instance
1362 * @since 12
1363 */
1364 @Override
1365 public Optional<Float> describeConstable() {
1366 return Optional.of(this);
1367 }
1368
1369 /**
1370 * Resolves this instance as a {@link ConstantDesc}, the result of which is
1371 * the instance itself.
1372 *
1373 * @param lookup ignored
1374 * @return the {@linkplain Float} instance
1375 * @since 12
1376 */
1377 @Override
1378 public Float resolveConstantDesc(MethodHandles.Lookup lookup) {
1379 return this;
1380 }
1381
1382 /** use serialVersionUID from JDK 1.0.2 for interoperability */
1383 @java.io.Serial
1384 private static final long serialVersionUID = -2671257302660747028L;
1385 }