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