1 /*
2 * Copyright (c) 1994, 2024, Oracle and/or its affiliates. All rights reserved.
3 * DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER.
4 *
5 * This code is free software; you can redistribute it and/or modify it
6 * under the terms of the GNU General Public License version 2 only, as
7 * published by the Free Software Foundation. Oracle designates this
8 * particular file as subject to the "Classpath" exception as provided
9 * by Oracle in the LICENSE file that accompanied this code.
10 *
11 * This code is distributed in the hope that it will be useful, but WITHOUT
12 * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
13 * FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
14 * version 2 for more details (a copy is included in the LICENSE file that
15 * accompanied this code).
16 *
17 * You should have received a copy of the GNU General Public License version
18 * 2 along with this work; if not, write to the Free Software Foundation,
19 * Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA.
20 *
21 * Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA
22 * or visit www.oracle.com if you need additional information or have any
23 * questions.
24 */
25
26 package java.lang;
27
28 import java.lang.invoke.MethodHandles;
29 import java.lang.constant.Constable;
30 import java.lang.constant.ConstantDesc;
31 import java.util.Optional;
32
33 import jdk.internal.math.FloatConsts;
34 import jdk.internal.math.FloatingDecimal;
35 import jdk.internal.math.FloatToDecimal;
36 import jdk.internal.value.DeserializeConstructor;
37 import jdk.internal.vm.annotation.IntrinsicCandidate;
38
39 /**
40 * The {@code Float} class is the {@linkplain
41 * java.lang##wrapperClass wrapper class} for values of the primitive
42 * type {@code float}. An object of type {@code Float} contains a
43 * single field whose type is {@code float}.
44 *
45 * <p>In addition, this class provides several methods for converting a
46 * {@code float} to a {@code String} and a
47 * {@code String} to a {@code float}, as well as other
48 * constants and methods useful when dealing with a
49 * {@code float}.
50 *
51 * <p>This is a <a href="{@docRoot}/java.base/java/lang/doc-files/ValueBased.html">value-based</a>
52 * class; programmers should treat instances that are
53 * {@linkplain #equals(Object) equal} as interchangeable and should not
54 * use instances for synchronization, or unpredictable behavior may
55 * occur. For example, in a future release, synchronization may fail.
56 *
57 * <h2><a id=equivalenceRelation>Floating-point Equality, Equivalence,
58 * and Comparison</a></h2>
59 *
60 * The class {@code java.lang.Double} has a {@linkplain
61 * Double##equivalenceRelation discussion of equality,
62 * equivalence, and comparison of floating-point values} that is
63 * equally applicable to {@code float} values.
64 *
65 * <h2><a id=decimalToBinaryConversion>Decimal ↔ Binary Conversion Issues</a></h2>
66 *
67 * The {@linkplain Double##decimalToBinaryConversion discussion of binary to
68 * decimal conversion issues} in {@code java.lang.Double} is also
69 * applicable to {@code float} values.
70 *
71 * @see <a href="https://standards.ieee.org/ieee/754/6210/">
72 * <cite>IEEE Standard for Floating-Point Arithmetic</cite></a>
73 *
74 * @author Lee Boynton
75 * @author Arthur van Hoff
76 * @author Joseph D. Darcy
77 * @since 1.0
78 */
79 @jdk.internal.MigratedValueClass
80 @jdk.internal.ValueBased
81 public final class Float extends Number
82 implements Comparable<Float>, Constable, ConstantDesc {
83 /**
84 * A constant holding the positive infinity of type
85 * {@code float}. It is equal to the value returned by
86 * {@code Float.intBitsToFloat(0x7f800000)}.
87 */
88 public static final float POSITIVE_INFINITY = 1.0f / 0.0f;
89
90 /**
91 * A constant holding the negative infinity of type
92 * {@code float}. It is equal to the value returned by
93 * {@code Float.intBitsToFloat(0xff800000)}.
94 */
95 public static final float NEGATIVE_INFINITY = -1.0f / 0.0f;
96
97 /**
98 * A constant holding a Not-a-Number (NaN) value of type
99 * {@code float}. It is equivalent to the value returned by
100 * {@code Float.intBitsToFloat(0x7fc00000)}.
101 */
102 public static final float NaN = 0.0f / 0.0f;
103
104 /**
105 * A constant holding the largest positive finite value of type
106 * {@code float}, (2-2<sup>-23</sup>)·2<sup>127</sup>.
107 * It is equal to the hexadecimal floating-point literal
108 * {@code 0x1.fffffeP+127f} and also equal to
109 * {@code Float.intBitsToFloat(0x7f7fffff)}.
110 */
111 public static final float MAX_VALUE = 0x1.fffffeP+127f; // 3.4028235e+38f
112
113 /**
114 * A constant holding the smallest positive normal value of type
115 * {@code float}, 2<sup>-126</sup>. It is equal to the
116 * hexadecimal floating-point literal {@code 0x1.0p-126f} and also
117 * equal to {@code Float.intBitsToFloat(0x00800000)}.
118 *
119 * @since 1.6
120 */
121 public static final float MIN_NORMAL = 0x1.0p-126f; // 1.17549435E-38f
122
123 /**
124 * A constant holding the smallest positive nonzero value of type
125 * {@code float}, 2<sup>-149</sup>. It is equal to the
126 * hexadecimal floating-point literal {@code 0x0.000002P-126f}
127 * and also equal to {@code Float.intBitsToFloat(0x1)}.
128 */
129 public static final float MIN_VALUE = 0x0.000002P-126f; // 1.4e-45f
130
131 /**
132 * The number of bits used to represent a {@code float} value,
133 * {@value}.
134 *
135 * @since 1.5
136 */
137 public static final int SIZE = 32;
138
139 /**
140 * The number of bits in the significand of a {@code float} value,
141 * {@value}. This is the parameter N in section {@jls 4.2.3} of
142 * <cite>The Java Language Specification</cite>.
143 *
144 * @since 19
145 */
146 public static final int PRECISION = 24;
147
148 /**
149 * Maximum exponent a finite {@code float} variable may have,
150 * {@value}. It is equal to the value returned by {@code
151 * Math.getExponent(Float.MAX_VALUE)}.
152 *
153 * @since 1.6
154 */
155 public static final int MAX_EXPONENT = (1 << (SIZE - PRECISION - 1)) - 1; // 127
156
157 /**
158 * Minimum exponent a normalized {@code float} variable may have,
159 * {@value}. It is equal to the value returned by {@code
160 * Math.getExponent(Float.MIN_NORMAL)}.
161 *
162 * @since 1.6
163 */
164 public static final int MIN_EXPONENT = 1 - MAX_EXPONENT; // -126
165
166 /**
167 * The number of bytes used to represent a {@code float} value,
168 * {@value}.
169 *
170 * @since 1.8
171 */
172 public static final int BYTES = SIZE / Byte.SIZE;
173
174 /**
175 * The {@code Class} instance representing the primitive type
176 * {@code float}.
177 *
178 * @since 1.1
179 */
180 public static final Class<Float> TYPE = Class.getPrimitiveClass("float");
181
182 /**
183 * Returns a string representation of the {@code float}
184 * argument. All characters mentioned below are ASCII characters.
185 * <ul>
186 * <li>If the argument is NaN, the result is the string
187 * "{@code NaN}".
188 * <li>Otherwise, the result is a string that represents the sign and
189 * magnitude (absolute value) of the argument. If the sign is
190 * negative, the first character of the result is
191 * '{@code -}' ({@code '\u005Cu002D'}); if the sign is
192 * positive, no sign character appears in the result. As for
193 * the magnitude <i>m</i>:
194 * <ul>
195 * <li>If <i>m</i> is infinity, it is represented by the characters
196 * {@code "Infinity"}; thus, positive infinity produces
197 * the result {@code "Infinity"} and negative infinity
198 * produces the result {@code "-Infinity"}.
199 * <li>If <i>m</i> is zero, it is represented by the characters
200 * {@code "0.0"}; thus, negative zero produces the result
201 * {@code "-0.0"} and positive zero produces the result
202 * {@code "0.0"}.
203 *
204 * <li> Otherwise <i>m</i> is positive and finite.
205 * It is converted to a string in two stages:
206 * <ul>
207 * <li> <em>Selection of a decimal</em>:
208 * A well-defined decimal <i>d</i><sub><i>m</i></sub>
209 * is selected to represent <i>m</i>.
210 * This decimal is (almost always) the <em>shortest</em> one that
211 * rounds to <i>m</i> according to the round to nearest
212 * rounding policy of IEEE 754 floating-point arithmetic.
213 * <li> <em>Formatting as a string</em>:
214 * The decimal <i>d</i><sub><i>m</i></sub> is formatted as a string,
215 * either in plain or in computerized scientific notation,
216 * depending on its value.
217 * </ul>
218 * </ul>
219 * </ul>
220 *
221 * <p>A <em>decimal</em> is a number of the form
222 * <i>s</i>×10<sup><i>i</i></sup>
223 * for some (unique) integers <i>s</i> > 0 and <i>i</i> such that
224 * <i>s</i> is not a multiple of 10.
225 * These integers are the <em>significand</em> and
226 * the <em>exponent</em>, respectively, of the decimal.
227 * The <em>length</em> of the decimal is the (unique)
228 * positive integer <i>n</i> meeting
229 * 10<sup><i>n</i>-1</sup> ≤ <i>s</i> < 10<sup><i>n</i></sup>.
230 *
231 * <p>The decimal <i>d</i><sub><i>m</i></sub> for a finite positive <i>m</i>
232 * is defined as follows:
233 * <ul>
234 * <li>Let <i>R</i> be the set of all decimals that round to <i>m</i>
235 * according to the usual <em>round to nearest</em> rounding policy of
236 * IEEE 754 floating-point arithmetic.
237 * <li>Let <i>p</i> be the minimal length over all decimals in <i>R</i>.
238 * <li>When <i>p</i> ≥ 2, let <i>T</i> be the set of all decimals
239 * in <i>R</i> with length <i>p</i>.
240 * Otherwise, let <i>T</i> be the set of all decimals
241 * in <i>R</i> with length 1 or 2.
242 * <li>Define <i>d</i><sub><i>m</i></sub> as the decimal in <i>T</i>
243 * that is closest to <i>m</i>.
244 * Or if there are two such decimals in <i>T</i>,
245 * select the one with the even significand.
246 * </ul>
247 *
248 * <p>The (uniquely) selected decimal <i>d</i><sub><i>m</i></sub>
249 * is then formatted.
250 * Let <i>s</i>, <i>i</i> and <i>n</i> be the significand, exponent and
251 * length of <i>d</i><sub><i>m</i></sub>, respectively.
252 * Further, let <i>e</i> = <i>n</i> + <i>i</i> - 1 and let
253 * <i>s</i><sub>1</sub>…<i>s</i><sub><i>n</i></sub>
254 * be the usual decimal expansion of <i>s</i>.
255 * Note that <i>s</i><sub>1</sub> ≠ 0
256 * and <i>s</i><sub><i>n</i></sub> ≠ 0.
257 * Below, the decimal point {@code '.'} is {@code '\u005Cu002E'}
258 * and the exponent indicator {@code 'E'} is {@code '\u005Cu0045'}.
259 * <ul>
260 * <li>Case -3 ≤ <i>e</i> < 0:
261 * <i>d</i><sub><i>m</i></sub> is formatted as
262 * <code>0.0</code>…<code>0</code><!--
263 * --><i>s</i><sub>1</sub>…<i>s</i><sub><i>n</i></sub>,
264 * where there are exactly -(<i>n</i> + <i>i</i>) zeroes between
265 * the decimal point and <i>s</i><sub>1</sub>.
266 * For example, 123 × 10<sup>-4</sup> is formatted as
267 * {@code 0.0123}.
268 * <li>Case 0 ≤ <i>e</i> < 7:
269 * <ul>
270 * <li>Subcase <i>i</i> ≥ 0:
271 * <i>d</i><sub><i>m</i></sub> is formatted as
272 * <i>s</i><sub>1</sub>…<i>s</i><sub><i>n</i></sub><!--
273 * --><code>0</code>…<code>0.0</code>,
274 * where there are exactly <i>i</i> zeroes
275 * between <i>s</i><sub><i>n</i></sub> and the decimal point.
276 * For example, 123 × 10<sup>2</sup> is formatted as
277 * {@code 12300.0}.
278 * <li>Subcase <i>i</i> < 0:
279 * <i>d</i><sub><i>m</i></sub> is formatted as
280 * <i>s</i><sub>1</sub>…<!--
281 * --><i>s</i><sub><i>n</i>+<i>i</i></sub><code>.</code><!--
282 * --><i>s</i><sub><i>n</i>+<i>i</i>+1</sub>…<!--
283 * --><i>s</i><sub><i>n</i></sub>,
284 * where there are exactly -<i>i</i> digits to the right of
285 * the decimal point.
286 * For example, 123 × 10<sup>-1</sup> is formatted as
287 * {@code 12.3}.
288 * </ul>
289 * <li>Case <i>e</i> < -3 or <i>e</i> ≥ 7:
290 * computerized scientific notation is used to format
291 * <i>d</i><sub><i>m</i></sub>.
292 * Here <i>e</i> is formatted as by {@link Integer#toString(int)}.
293 * <ul>
294 * <li>Subcase <i>n</i> = 1:
295 * <i>d</i><sub><i>m</i></sub> is formatted as
296 * <i>s</i><sub>1</sub><code>.0E</code><i>e</i>.
297 * For example, 1 × 10<sup>23</sup> is formatted as
298 * {@code 1.0E23}.
299 * <li>Subcase <i>n</i> > 1:
300 * <i>d</i><sub><i>m</i></sub> is formatted as
301 * <i>s</i><sub>1</sub><code>.</code><i>s</i><sub>2</sub><!--
302 * -->…<i>s</i><sub><i>n</i></sub><code>E</code><i>e</i>.
303 * For example, 123 × 10<sup>-21</sup> is formatted as
304 * {@code 1.23E-19}.
305 * </ul>
306 * </ul>
307 *
308 * <p>To create localized string representations of a floating-point
309 * value, use subclasses of {@link java.text.NumberFormat}.
310 *
311 * @apiNote
312 * This method corresponds to the general functionality of the
313 * convertToDecimalCharacter operation defined in IEEE 754;
314 * however, that operation is defined in terms of specifying the
315 * number of significand digits used in the conversion.
316 * Code to do such a conversion in the Java platform includes
317 * converting the {@code float} to a {@link java.math.BigDecimal
318 * BigDecimal} exactly and then rounding the {@code BigDecimal} to
319 * the desired number of digits; sample code:
320 * {@snippet lang=java :
321 * floatf = 0.1f;
322 * int digits = 15;
323 * BigDecimal bd = new BigDecimal(f);
324 * String result = bd.round(new MathContext(digits, RoundingMode.HALF_UP));
325 * // 0.100000001490116
326 * }
327 *
328 * @param f the {@code float} to be converted.
329 * @return a string representation of the argument.
330 */
331 public static String toString(float f) {
332 return FloatToDecimal.toString(f);
333 }
334
335 /**
336 * Returns a hexadecimal string representation of the
337 * {@code float} argument. All characters mentioned below are
338 * ASCII characters.
339 *
340 * <ul>
341 * <li>If the argument is NaN, the result is the string
342 * "{@code NaN}".
343 * <li>Otherwise, the result is a string that represents the sign and
344 * magnitude (absolute value) of the argument. If the sign is negative,
345 * the first character of the result is '{@code -}'
346 * ({@code '\u005Cu002D'}); if the sign is positive, no sign character
347 * appears in the result. As for the magnitude <i>m</i>:
348 *
349 * <ul>
350 * <li>If <i>m</i> is infinity, it is represented by the string
351 * {@code "Infinity"}; thus, positive infinity produces the
352 * result {@code "Infinity"} and negative infinity produces
353 * the result {@code "-Infinity"}.
354 *
355 * <li>If <i>m</i> is zero, it is represented by the string
356 * {@code "0x0.0p0"}; thus, negative zero produces the result
357 * {@code "-0x0.0p0"} and positive zero produces the result
358 * {@code "0x0.0p0"}.
359 *
360 * <li>If <i>m</i> is a {@code float} value with a
361 * normalized representation, substrings are used to represent the
362 * significand and exponent fields. The significand is
363 * represented by the characters {@code "0x1."}
364 * followed by a lowercase hexadecimal representation of the rest
365 * of the significand as a fraction. Trailing zeros in the
366 * hexadecimal representation are removed unless all the digits
367 * are zero, in which case a single zero is used. Next, the
368 * exponent is represented by {@code "p"} followed
369 * by a decimal string of the unbiased exponent as if produced by
370 * a call to {@link Integer#toString(int) Integer.toString} on the
371 * exponent value.
372 *
373 * <li>If <i>m</i> is a {@code float} value with a subnormal
374 * representation, the significand is represented by the
375 * characters {@code "0x0."} followed by a
376 * hexadecimal representation of the rest of the significand as a
377 * fraction. Trailing zeros in the hexadecimal representation are
378 * removed. Next, the exponent is represented by
379 * {@code "p-126"}. Note that there must be at
380 * least one nonzero digit in a subnormal significand.
381 *
382 * </ul>
383 *
384 * </ul>
385 *
386 * <table class="striped">
387 * <caption>Examples</caption>
388 * <thead>
389 * <tr><th scope="col">Floating-point Value</th><th scope="col">Hexadecimal String</th>
390 * </thead>
391 * <tbody>
392 * <tr><th scope="row">{@code 1.0}</th> <td>{@code 0x1.0p0}</td>
393 * <tr><th scope="row">{@code -1.0}</th> <td>{@code -0x1.0p0}</td>
394 * <tr><th scope="row">{@code 2.0}</th> <td>{@code 0x1.0p1}</td>
395 * <tr><th scope="row">{@code 3.0}</th> <td>{@code 0x1.8p1}</td>
396 * <tr><th scope="row">{@code 0.5}</th> <td>{@code 0x1.0p-1}</td>
397 * <tr><th scope="row">{@code 0.25}</th> <td>{@code 0x1.0p-2}</td>
398 * <tr><th scope="row">{@code Float.MAX_VALUE}</th>
399 * <td>{@code 0x1.fffffep127}</td>
400 * <tr><th scope="row">{@code Minimum Normal Value}</th>
401 * <td>{@code 0x1.0p-126}</td>
402 * <tr><th scope="row">{@code Maximum Subnormal Value}</th>
403 * <td>{@code 0x0.fffffep-126}</td>
404 * <tr><th scope="row">{@code Float.MIN_VALUE}</th>
405 * <td>{@code 0x0.000002p-126}</td>
406 * </tbody>
407 * </table>
408 *
409 * @apiNote
410 * This method corresponds to the convertToHexCharacter operation
411 * defined in IEEE 754.
412 *
413 * @param f the {@code float} to be converted.
414 * @return a hex string representation of the argument.
415 * @since 1.5
416 * @author Joseph D. Darcy
417 */
418 public static String toHexString(float f) {
419 if (Math.abs(f) < Float.MIN_NORMAL
420 && f != 0.0f ) {// float subnormal
421 // Adjust exponent to create subnormal double, then
422 // replace subnormal double exponent with subnormal float
423 // exponent
424 String s = Double.toHexString(Math.scalb((double)f,
425 /* -1022+126 */
426 Double.MIN_EXPONENT-
427 Float.MIN_EXPONENT));
428 return s.replaceFirst("p-1022$", "p-126");
429 }
430 else // double string will be the same as float string
431 return Double.toHexString(f);
432 }
433
434 /**
435 * Returns a {@code Float} object holding the
436 * {@code float} value represented by the argument string
437 * {@code s}.
438 *
439 * <p>If {@code s} is {@code null}, then a
440 * {@code NullPointerException} is thrown.
441 *
442 * <p>Leading and trailing whitespace characters in {@code s}
443 * are ignored. Whitespace is removed as if by the {@link
444 * String#trim} method; that is, both ASCII space and control
445 * characters are removed. The rest of {@code s} should
446 * constitute a <i>FloatValue</i> as described by the lexical
447 * syntax rules:
448 *
449 * <blockquote>
450 * <dl>
451 * <dt><i>FloatValue:</i>
452 * <dd><i>Sign<sub>opt</sub></i> {@code NaN}
453 * <dd><i>Sign<sub>opt</sub></i> {@code Infinity}
454 * <dd><i>Sign<sub>opt</sub> FloatingPointLiteral</i>
455 * <dd><i>Sign<sub>opt</sub> HexFloatingPointLiteral</i>
456 * <dd><i>SignedInteger</i>
457 * </dl>
458 *
459 * <dl>
460 * <dt><i>HexFloatingPointLiteral</i>:
461 * <dd> <i>HexSignificand BinaryExponent FloatTypeSuffix<sub>opt</sub></i>
462 * </dl>
463 *
464 * <dl>
465 * <dt><i>HexSignificand:</i>
466 * <dd><i>HexNumeral</i>
467 * <dd><i>HexNumeral</i> {@code .}
468 * <dd>{@code 0x} <i>HexDigits<sub>opt</sub>
469 * </i>{@code .}<i> HexDigits</i>
470 * <dd>{@code 0X}<i> HexDigits<sub>opt</sub>
471 * </i>{@code .} <i>HexDigits</i>
472 * </dl>
473 *
474 * <dl>
475 * <dt><i>BinaryExponent:</i>
476 * <dd><i>BinaryExponentIndicator SignedInteger</i>
477 * </dl>
478 *
479 * <dl>
480 * <dt><i>BinaryExponentIndicator:</i>
481 * <dd>{@code p}
482 * <dd>{@code P}
483 * </dl>
484 *
485 * </blockquote>
486 *
487 * where <i>Sign</i>, <i>FloatingPointLiteral</i>,
488 * <i>HexNumeral</i>, <i>HexDigits</i>, <i>SignedInteger</i> and
489 * <i>FloatTypeSuffix</i> are as defined in the lexical structure
490 * sections of
491 * <cite>The Java Language Specification</cite>,
492 * except that underscores are not accepted between digits.
493 * If {@code s} does not have the form of
494 * a <i>FloatValue</i>, then a {@code NumberFormatException}
495 * is thrown. Otherwise, {@code s} is regarded as
496 * representing an exact decimal value in the usual
497 * "computerized scientific notation" or as an exact
498 * hexadecimal value; this exact numerical value is then
499 * conceptually converted to an "infinitely precise"
500 * binary value that is then rounded to type {@code float}
501 * by the usual round-to-nearest rule of IEEE 754 floating-point
502 * arithmetic, which includes preserving the sign of a zero
503 * value.
504 *
505 * Note that the round-to-nearest rule also implies overflow and
506 * underflow behaviour; if the exact value of {@code s} is large
507 * enough in magnitude (greater than or equal to ({@link
508 * #MAX_VALUE} + {@link Math#ulp(float) ulp(MAX_VALUE)}/2),
509 * rounding to {@code float} will result in an infinity and if the
510 * exact value of {@code s} is small enough in magnitude (less
511 * than or equal to {@link #MIN_VALUE}/2), rounding to float will
512 * result in a zero.
513 *
514 * Finally, after rounding a {@code Float} object representing
515 * this {@code float} value is returned.
516 *
517 * <p>Note that trailing format specifiers, specifiers that
518 * determine the type of a floating-point literal
519 * ({@code 1.0f} is a {@code float} value;
520 * {@code 1.0d} is a {@code double} value), do
521 * <em>not</em> influence the results of this method. In other
522 * words, the numerical value of the input string is converted
523 * directly to the target floating-point type. In general, the
524 * two-step sequence of conversions, string to {@code double}
525 * followed by {@code double} to {@code float}, is
526 * <em>not</em> equivalent to converting a string directly to
527 * {@code float}. For example, if first converted to an
528 * intermediate {@code double} and then to
529 * {@code float}, the string<br>
530 * {@code "1.00000017881393421514957253748434595763683319091796875001d"}<br>
531 * results in the {@code float} value
532 * {@code 1.0000002f}; if the string is converted directly to
533 * {@code float}, <code>1.000000<b>1</b>f</code> results.
534 *
535 * <p>To avoid calling this method on an invalid string and having
536 * a {@code NumberFormatException} be thrown, the documentation
537 * for {@link Double#valueOf Double.valueOf} lists a regular
538 * expression which can be used to screen the input.
539 *
540 * @apiNote To interpret localized string representations of a
541 * floating-point value, or string representations that have
542 * non-ASCII digits, use {@link java.text.NumberFormat}. For
543 * example,
544 * {@snippet lang="java" :
545 * NumberFormat.getInstance(l).parse(s).floatValue();
546 * }
547 * where {@code l} is the desired locale, or
548 * {@link java.util.Locale#ROOT} if locale insensitive.
549 *
550 * @apiNote
551 * This method corresponds to the convertFromDecimalCharacter and
552 * convertFromHexCharacter operations defined in IEEE 754.
553 *
554 * @param s the string to be parsed.
555 * @return a {@code Float} object holding the value
556 * represented by the {@code String} argument.
557 * @throws NumberFormatException if the string does not contain a
558 * parsable number.
559 * @see Double##decimalToBinaryConversion Decimal ↔ Binary Conversion Issues
560 */
561 public static Float valueOf(String s) throws NumberFormatException {
562 return new Float(parseFloat(s));
563 }
564
565 /**
566 * Returns a {@code Float} instance representing the specified
567 * {@code float} value.
568 * If a new {@code Float} instance is not required, this method
569 * should generally be used in preference to the constructor
570 * {@link #Float(float)}, as this method is likely to yield
571 * significantly better space and time performance by caching
572 * frequently requested values.
573 *
574 * @param f a float value.
575 * @return a {@code Float} instance representing {@code f}.
576 * @since 1.5
577 */
578 @IntrinsicCandidate
579 @DeserializeConstructor
580 public static Float valueOf(float f) {
581 return new Float(f);
582 }
583
584 /**
585 * Returns a new {@code float} initialized to the value
586 * represented by the specified {@code String}, as performed
587 * by the {@code valueOf} method of class {@code Float}.
588 *
589 * @param s the string to be parsed.
590 * @return the {@code float} value represented by the string
591 * argument.
592 * @throws NullPointerException if the string is null
593 * @throws NumberFormatException if the string does not contain a
594 * parsable {@code float}.
595 * @see java.lang.Float#valueOf(String)
596 * @see Double##decimalToBinaryConversion Decimal ↔ Binary Conversion Issues
597 * @since 1.2
598 */
599 public static float parseFloat(String s) throws NumberFormatException {
600 return FloatingDecimal.parseFloat(s);
601 }
602
603 /**
604 * Returns {@code true} if the specified number is a
605 * Not-a-Number (NaN) value, {@code false} otherwise.
606 *
607 * @apiNote
608 * This method corresponds to the isNaN operation defined in IEEE
609 * 754.
610 *
611 * @param v the value to be tested.
612 * @return {@code true} if the argument is NaN;
613 * {@code false} otherwise.
614 */
615 public static boolean isNaN(float v) {
616 return (v != v);
617 }
618
619 /**
620 * Returns {@code true} if the specified number is infinitely
621 * large in magnitude, {@code false} otherwise.
622 *
623 * @apiNote
624 * This method corresponds to the isInfinite operation defined in
625 * IEEE 754.
626 *
627 * @param v the value to be tested.
628 * @return {@code true} if the argument is positive infinity or
629 * negative infinity; {@code false} otherwise.
630 */
631 @IntrinsicCandidate
632 public static boolean isInfinite(float v) {
633 return Math.abs(v) > MAX_VALUE;
634 }
635
636
637 /**
638 * Returns {@code true} if the argument is a finite floating-point
639 * value; returns {@code false} otherwise (for NaN and infinity
640 * arguments).
641 *
642 * @apiNote
643 * This method corresponds to the isFinite operation defined in
644 * IEEE 754.
645 *
646 * @param f the {@code float} value to be tested
647 * @return {@code true} if the argument is a finite
648 * floating-point value, {@code false} otherwise.
649 * @since 1.8
650 */
651 @IntrinsicCandidate
652 public static boolean isFinite(float f) {
653 return Math.abs(f) <= Float.MAX_VALUE;
654 }
655
656 /**
657 * The value of the Float.
658 *
659 * @serial
660 */
661 private final float value;
662
663 /**
664 * Constructs a newly allocated {@code Float} object that
665 * represents the primitive {@code float} argument.
666 *
667 * @param value the value to be represented by the {@code Float}.
668 *
669 * @deprecated
670 * It is rarely appropriate to use this constructor. The static factory
671 * {@link #valueOf(float)} is generally a better choice, as it is
672 * likely to yield significantly better space and time performance.
673 */
674 @Deprecated(since="9", forRemoval = true)
675 public Float(float value) {
676 this.value = value;
677 }
678
679 /**
680 * Constructs a newly allocated {@code Float} object that
681 * represents the argument converted to type {@code float}.
682 *
683 * @param value the value to be represented by the {@code Float}.
684 *
685 * @deprecated
686 * It is rarely appropriate to use this constructor. Instead, use the
687 * static factory method {@link #valueOf(float)} method as follows:
688 * {@code Float.valueOf((float)value)}.
689 */
690 @Deprecated(since="9", forRemoval = true)
691 public Float(double value) {
692 this.value = (float)value;
693 }
694
695 /**
696 * Constructs a newly allocated {@code Float} object that
697 * represents the floating-point value of type {@code float}
698 * represented by the string. The string is converted to a
699 * {@code float} value as if by the {@code valueOf} method.
700 *
701 * @param s a string to be converted to a {@code Float}.
702 * @throws NumberFormatException if the string does not contain a
703 * parsable number.
704 *
705 * @deprecated
706 * It is rarely appropriate to use this constructor.
707 * Use {@link #parseFloat(String)} to convert a string to a
708 * {@code float} primitive, or use {@link #valueOf(String)}
709 * to convert a string to a {@code Float} object.
710 */
711 @Deprecated(since="9", forRemoval = true)
712 public Float(String s) throws NumberFormatException {
713 value = parseFloat(s);
714 }
715
716 /**
717 * Returns {@code true} if this {@code Float} value is a
718 * Not-a-Number (NaN), {@code false} otherwise.
719 *
720 * @return {@code true} if the value represented by this object is
721 * NaN; {@code false} otherwise.
722 */
723 public boolean isNaN() {
724 return isNaN(value);
725 }
726
727 /**
728 * Returns {@code true} if this {@code Float} value is
729 * infinitely large in magnitude, {@code false} otherwise.
730 *
731 * @return {@code true} if the value represented by this object is
732 * positive infinity or negative infinity;
733 * {@code false} otherwise.
734 */
735 public boolean isInfinite() {
736 return isInfinite(value);
737 }
738
739 /**
740 * Returns a string representation of this {@code Float} object.
741 * The primitive {@code float} value represented by this object
742 * is converted to a {@code String} exactly as if by the method
743 * {@code toString} of one argument.
744 *
745 * @return a {@code String} representation of this object.
746 * @see java.lang.Float#toString(float)
747 */
748 public String toString() {
749 return Float.toString(value);
750 }
751
752 /**
753 * Returns the value of this {@code Float} as a {@code byte} after
754 * a narrowing primitive conversion.
755 *
756 * @return the {@code float} value represented by this object
757 * converted to type {@code byte}
758 * @jls 5.1.3 Narrowing Primitive Conversion
759 */
760 @Override
761 public byte byteValue() {
762 return (byte)value;
763 }
764
765 /**
766 * Returns the value of this {@code Float} as a {@code short}
767 * after a narrowing primitive conversion.
768 *
769 * @return the {@code float} value represented by this object
770 * converted to type {@code short}
771 * @jls 5.1.3 Narrowing Primitive Conversion
772 * @since 1.1
773 */
774 @Override
775 public short shortValue() {
776 return (short)value;
777 }
778
779 /**
780 * Returns the value of this {@code Float} as an {@code int} after
781 * a narrowing primitive conversion.
782 *
783 * @apiNote
784 * This method corresponds to the convertToIntegerTowardZero
785 * operation defined in IEEE 754.
786 *
787 * @return the {@code float} value represented by this object
788 * converted to type {@code int}
789 * @jls 5.1.3 Narrowing Primitive Conversion
790 */
791 @Override
792 public int intValue() {
793 return (int)value;
794 }
795
796 /**
797 * Returns value of this {@code Float} as a {@code long} after a
798 * narrowing primitive conversion.
799 *
800 * @apiNote
801 * This method corresponds to the convertToIntegerTowardZero
802 * operation defined in IEEE 754.
803 *
804 * @return the {@code float} value represented by this object
805 * converted to type {@code long}
806 * @jls 5.1.3 Narrowing Primitive Conversion
807 */
808 @Override
809 public long longValue() {
810 return (long)value;
811 }
812
813 /**
814 * Returns the {@code float} value of this {@code Float} object.
815 *
816 * @return the {@code float} value represented by this object
817 */
818 @Override
819 @IntrinsicCandidate
820 public float floatValue() {
821 return value;
822 }
823
824 /**
825 * Returns the value of this {@code Float} as a {@code double}
826 * after a widening primitive conversion.
827 *
828 * @apiNote
829 * This method corresponds to the convertFormat operation defined
830 * in IEEE 754.
831 *
832 * @return the {@code float} value represented by this
833 * object converted to type {@code double}
834 * @jls 5.1.2 Widening Primitive Conversion
835 */
836 @Override
837 public double doubleValue() {
838 return (double)value;
839 }
840
841 /**
842 * Returns a hash code for this {@code Float} object. The
843 * result is the integer bit representation, exactly as produced
844 * by the method {@link #floatToIntBits(float)}, of the primitive
845 * {@code float} value represented by this {@code Float}
846 * object.
847 *
848 * @return a hash code value for this object.
849 */
850 @Override
851 public int hashCode() {
852 return Float.hashCode(value);
853 }
854
855 /**
856 * Returns a hash code for a {@code float} value; compatible with
857 * {@code Float.hashCode()}.
858 *
859 * @param value the value to hash
860 * @return a hash code value for a {@code float} value.
861 * @since 1.8
862 */
863 public static int hashCode(float value) {
864 return floatToIntBits(value);
865 }
866
867 /**
868 * Compares this object against the specified object. The result
869 * is {@code true} if and only if the argument is not
870 * {@code null} and is a {@code Float} object that
871 * represents a {@code float} with the same value as the
872 * {@code float} represented by this object. For this
873 * purpose, two {@code float} values are considered to be the
874 * same if and only if the method {@link #floatToIntBits(float)}
875 * returns the identical {@code int} value when applied to
876 * each.
877 *
878 * @apiNote
879 * This method is defined in terms of {@link
880 * #floatToIntBits(float)} rather than the {@code ==} operator on
881 * {@code float} values since the {@code ==} operator does
882 * <em>not</em> define an equivalence relation and to satisfy the
883 * {@linkplain Object#equals equals contract} an equivalence
884 * relation must be implemented; see {@linkplain Double##equivalenceRelation
885 * this discussion for details of floating-point equality and equivalence}.
886 *
887 * @param obj the object to be compared
888 * @return {@code true} if the objects are the same;
889 * {@code false} otherwise.
890 * @see java.lang.Float#floatToIntBits(float)
891 * @jls 15.21.1 Numerical Equality Operators == and !=
892 */
893 public boolean equals(Object obj) {
894 return (obj instanceof Float f) &&
895 (floatToIntBits(f.value) == floatToIntBits(value));
896 }
897
898 /**
899 * Returns a representation of the specified floating-point value
900 * according to the IEEE 754 floating-point "single format" bit
901 * layout.
902 *
903 * <p>Bit 31 (the bit that is selected by the mask
904 * {@code 0x80000000}) represents the sign of the floating-point
905 * number.
906 * Bits 30-23 (the bits that are selected by the mask
907 * {@code 0x7f800000}) represent the exponent.
908 * Bits 22-0 (the bits that are selected by the mask
909 * {@code 0x007fffff}) represent the significand (sometimes called
910 * the mantissa) of the floating-point number.
911 *
912 * <p>If the argument is positive infinity, the result is
913 * {@code 0x7f800000}.
914 *
915 * <p>If the argument is negative infinity, the result is
916 * {@code 0xff800000}.
917 *
918 * <p>If the argument is NaN, the result is {@code 0x7fc00000}.
919 *
920 * <p>In all cases, the result is an integer that, when given to the
921 * {@link #intBitsToFloat(int)} method, will produce a floating-point
922 * value the same as the argument to {@code floatToIntBits}
923 * (except all NaN values are collapsed to a single
924 * "canonical" NaN value).
925 *
926 * @param value a floating-point number.
927 * @return the bits that represent the floating-point number.
928 */
929 @IntrinsicCandidate
930 public static int floatToIntBits(float value) {
931 if (!isNaN(value)) {
932 return floatToRawIntBits(value);
933 }
934 return 0x7fc00000;
935 }
936
937 /**
938 * Returns a representation of the specified floating-point value
939 * according to the IEEE 754 floating-point "single format" bit
940 * layout, preserving Not-a-Number (NaN) values.
941 *
942 * <p>Bit 31 (the bit that is selected by the mask
943 * {@code 0x80000000}) represents the sign of the floating-point
944 * number.
945 * Bits 30-23 (the bits that are selected by the mask
946 * {@code 0x7f800000}) represent the exponent.
947 * Bits 22-0 (the bits that are selected by the mask
948 * {@code 0x007fffff}) represent the significand (sometimes called
949 * the mantissa) of the floating-point number.
950 *
951 * <p>If the argument is positive infinity, the result is
952 * {@code 0x7f800000}.
953 *
954 * <p>If the argument is negative infinity, the result is
955 * {@code 0xff800000}.
956 *
957 * <p>If the argument is NaN, the result is the integer representing
958 * the actual NaN value. Unlike the {@code floatToIntBits}
959 * method, {@code floatToRawIntBits} does not collapse all the
960 * bit patterns encoding a NaN to a single "canonical"
961 * NaN value.
962 *
963 * <p>In all cases, the result is an integer that, when given to the
964 * {@link #intBitsToFloat(int)} method, will produce a
965 * floating-point value the same as the argument to
966 * {@code floatToRawIntBits}.
967 *
968 * @param value a floating-point number.
969 * @return the bits that represent the floating-point number.
970 * @since 1.3
971 */
972 @IntrinsicCandidate
973 public static native int floatToRawIntBits(float value);
974
975 /**
976 * Returns the {@code float} value corresponding to a given
977 * bit representation.
978 * The argument is considered to be a representation of a
979 * floating-point value according to the IEEE 754 floating-point
980 * "single format" bit layout.
981 *
982 * <p>If the argument is {@code 0x7f800000}, the result is positive
983 * infinity.
984 *
985 * <p>If the argument is {@code 0xff800000}, the result is negative
986 * infinity.
987 *
988 * <p>If the argument is any value in the range
989 * {@code 0x7f800001} through {@code 0x7fffffff} or in
990 * the range {@code 0xff800001} through
991 * {@code 0xffffffff}, the result is a NaN. No IEEE 754
992 * floating-point operation provided by Java can distinguish
993 * between two NaN values of the same type with different bit
994 * patterns. Distinct values of NaN are only distinguishable by
995 * use of the {@code Float.floatToRawIntBits} method.
996 *
997 * <p>In all other cases, let <i>s</i>, <i>e</i>, and <i>m</i> be three
998 * values that can be computed from the argument:
999 *
1000 * {@snippet lang="java" :
1001 * int s = ((bits >> 31) == 0) ? 1 : -1;
1002 * int e = ((bits >> 23) & 0xff);
1003 * int m = (e == 0) ?
1004 * (bits & 0x7fffff) << 1 :
1005 * (bits & 0x7fffff) | 0x800000;
1006 * }
1007 *
1008 * Then the floating-point result equals the value of the mathematical
1009 * expression <i>s</i>·<i>m</i>·2<sup><i>e</i>-150</sup>.
1010 *
1011 * <p>Note that this method may not be able to return a
1012 * {@code float} NaN with exactly same bit pattern as the
1013 * {@code int} argument. IEEE 754 distinguishes between two
1014 * kinds of NaNs, quiet NaNs and <i>signaling NaNs</i>. The
1015 * differences between the two kinds of NaN are generally not
1016 * visible in Java. Arithmetic operations on signaling NaNs turn
1017 * them into quiet NaNs with a different, but often similar, bit
1018 * pattern. However, on some processors merely copying a
1019 * signaling NaN also performs that conversion. In particular,
1020 * copying a signaling NaN to return it to the calling method may
1021 * perform this conversion. So {@code intBitsToFloat} may
1022 * not be able to return a {@code float} with a signaling NaN
1023 * bit pattern. Consequently, for some {@code int} values,
1024 * {@code floatToRawIntBits(intBitsToFloat(start))} may
1025 * <i>not</i> equal {@code start}. Moreover, which
1026 * particular bit patterns represent signaling NaNs is platform
1027 * dependent; although all NaN bit patterns, quiet or signaling,
1028 * must be in the NaN range identified above.
1029 *
1030 * @param bits an integer.
1031 * @return the {@code float} floating-point value with the same bit
1032 * pattern.
1033 */
1034 @IntrinsicCandidate
1035 public static native float intBitsToFloat(int bits);
1036
1037 /**
1038 * {@return the {@code float} value closest to the numerical value
1039 * of the argument, a floating-point binary16 value encoded in a
1040 * {@code short}} The conversion is exact; all binary16 values can
1041 * be exactly represented in {@code float}.
1042 *
1043 * Special cases:
1044 * <ul>
1045 * <li> If the argument is zero, the result is a zero with the
1046 * same sign as the argument.
1047 * <li> If the argument is infinite, the result is an infinity
1048 * with the same sign as the argument.
1049 * <li> If the argument is a NaN, the result is a NaN.
1050 * </ul>
1051 *
1052 * <h4><a id=binary16Format>IEEE 754 binary16 format</a></h4>
1053 * The IEEE 754 standard defines binary16 as a 16-bit format, along
1054 * with the 32-bit binary32 format (corresponding to the {@code
1055 * float} type) and the 64-bit binary64 format (corresponding to
1056 * the {@code double} type). The binary16 format is similar to the
1057 * other IEEE 754 formats, except smaller, having all the usual
1058 * IEEE 754 values such as NaN, signed infinities, signed zeros,
1059 * and subnormals. The parameters (JLS {@jls 4.2.3}) for the
1060 * binary16 format are N = 11 precision bits, K = 5 exponent bits,
1061 * <i>E</i><sub><i>max</i></sub> = 15, and
1062 * <i>E</i><sub><i>min</i></sub> = -14.
1063 *
1064 * @apiNote
1065 * This method corresponds to the convertFormat operation defined
1066 * in IEEE 754 from the binary16 format to the binary32 format.
1067 * The operation of this method is analogous to a primitive
1068 * widening conversion (JLS {@jls 5.1.2}).
1069 *
1070 * @param floatBinary16 the binary16 value to convert to {@code float}
1071 * @since 20
1072 */
1073 @IntrinsicCandidate
1074 public static float float16ToFloat(short floatBinary16) {
1075 /*
1076 * The binary16 format has 1 sign bit, 5 exponent bits, and 10
1077 * significand bits. The exponent bias is 15.
1078 */
1079 int bin16arg = (int)floatBinary16;
1080 int bin16SignBit = 0x8000 & bin16arg;
1081 int bin16ExpBits = 0x7c00 & bin16arg;
1082 int bin16SignifBits = 0x03FF & bin16arg;
1083
1084 // Shift left difference in the number of significand bits in
1085 // the float and binary16 formats
1086 final int SIGNIF_SHIFT = (FloatConsts.SIGNIFICAND_WIDTH - 11);
1087
1088 float sign = (bin16SignBit != 0) ? -1.0f : 1.0f;
1089
1090 // Extract binary16 exponent, remove its bias, add in the bias
1091 // of a float exponent and shift to correct bit location
1092 // (significand width includes the implicit bit so shift one
1093 // less).
1094 int bin16Exp = (bin16ExpBits >> 10) - 15;
1095 if (bin16Exp == -15) {
1096 // For subnormal binary16 values and 0, the numerical
1097 // value is 2^24 * the significand as an integer (no
1098 // implicit bit).
1099 return sign * (0x1p-24f * bin16SignifBits);
1100 } else if (bin16Exp == 16) {
1101 return (bin16SignifBits == 0) ?
1102 sign * Float.POSITIVE_INFINITY :
1103 Float.intBitsToFloat((bin16SignBit << 16) |
1104 0x7f80_0000 |
1105 // Preserve NaN signif bits
1106 ( bin16SignifBits << SIGNIF_SHIFT ));
1107 }
1108
1109 assert -15 < bin16Exp && bin16Exp < 16;
1110
1111 int floatExpBits = (bin16Exp + FloatConsts.EXP_BIAS)
1112 << (FloatConsts.SIGNIFICAND_WIDTH - 1);
1113
1114 // Compute and combine result sign, exponent, and significand bits.
1115 return Float.intBitsToFloat((bin16SignBit << 16) |
1116 floatExpBits |
1117 (bin16SignifBits << SIGNIF_SHIFT));
1118 }
1119
1120 /**
1121 * {@return the floating-point binary16 value, encoded in a {@code
1122 * short}, closest in value to the argument}
1123 * The conversion is computed under the {@linkplain
1124 * java.math.RoundingMode#HALF_EVEN round to nearest even rounding
1125 * mode}.
1126 *
1127 * Special cases:
1128 * <ul>
1129 * <li> If the argument is zero, the result is a zero with the
1130 * same sign as the argument.
1131 * <li> If the argument is infinite, the result is an infinity
1132 * with the same sign as the argument.
1133 * <li> If the argument is a NaN, the result is a NaN.
1134 * </ul>
1135 *
1136 * The {@linkplain ##binary16Format binary16 format} is discussed in
1137 * more detail in the {@link #float16ToFloat} method.
1138 *
1139 * @apiNote
1140 * This method corresponds to the convertFormat operation defined
1141 * in IEEE 754 from the binary32 format to the binary16 format.
1142 * The operation of this method is analogous to a primitive
1143 * narrowing conversion (JLS {@jls 5.1.3}).
1144 *
1145 * @param f the {@code float} value to convert to binary16
1146 * @since 20
1147 */
1148 @IntrinsicCandidate
1149 public static short floatToFloat16(float f) {
1150 int doppel = Float.floatToRawIntBits(f);
1151 short sign_bit = (short)((doppel & 0x8000_0000) >> 16);
1152
1153 if (Float.isNaN(f)) {
1154 // Preserve sign and attempt to preserve significand bits
1155 return (short)(sign_bit
1156 | 0x7c00 // max exponent + 1
1157 // Preserve high order bit of float NaN in the
1158 // binary16 result NaN (tenth bit); OR in remaining
1159 // bits into lower 9 bits of binary 16 significand.
1160 | (doppel & 0x007f_e000) >> 13 // 10 bits
1161 | (doppel & 0x0000_1ff0) >> 4 // 9 bits
1162 | (doppel & 0x0000_000f)); // 4 bits
1163 }
1164
1165 float abs_f = Math.abs(f);
1166
1167 // The overflow threshold is binary16 MAX_VALUE + 1/2 ulp
1168 if (abs_f >= (0x1.ffcp15f + 0x0.002p15f) ) {
1169 return (short)(sign_bit | 0x7c00); // Positive or negative infinity
1170 }
1171
1172 // Smallest magnitude nonzero representable binary16 value
1173 // is equal to 0x1.0p-24; half-way and smaller rounds to zero.
1174 if (abs_f <= 0x1.0p-24f * 0.5f) { // Covers float zeros and subnormals.
1175 return sign_bit; // Positive or negative zero
1176 }
1177
1178 // Dealing with finite values in exponent range of binary16
1179 // (when rounding is done, could still round up)
1180 int exp = Math.getExponent(f);
1181 assert -25 <= exp && exp <= 15;
1182
1183 // For binary16 subnormals, beside forcing exp to -15, retain
1184 // the difference expdelta = E_min - exp. This is the excess
1185 // shift value, in addition to 13, to be used in the
1186 // computations below. Further the (hidden) msb with value 1
1187 // in f must be involved as well.
1188 int expdelta = 0;
1189 int msb = 0x0000_0000;
1190 if (exp < -14) {
1191 expdelta = -14 - exp;
1192 exp = -15;
1193 msb = 0x0080_0000;
1194 }
1195 int f_signif_bits = doppel & 0x007f_ffff | msb;
1196
1197 // Significand bits as if using rounding to zero (truncation).
1198 short signif_bits = (short)(f_signif_bits >> (13 + expdelta));
1199
1200 // For round to nearest even, determining whether or not to
1201 // round up (in magnitude) is a function of the least
1202 // significant bit (LSB), the next bit position (the round
1203 // position), and the sticky bit (whether there are any
1204 // nonzero bits in the exact result to the right of the round
1205 // digit). An increment occurs in three cases:
1206 //
1207 // LSB Round Sticky
1208 // 0 1 1
1209 // 1 1 0
1210 // 1 1 1
1211 // See "Computer Arithmetic Algorithms," Koren, Table 4.9
1212
1213 int lsb = f_signif_bits & (1 << 13 + expdelta);
1214 int round = f_signif_bits & (1 << 12 + expdelta);
1215 int sticky = f_signif_bits & ((1 << 12 + expdelta) - 1);
1216
1217 if (round != 0 && ((lsb | sticky) != 0 )) {
1218 signif_bits++;
1219 }
1220
1221 // No bits set in significand beyond the *first* exponent bit,
1222 // not just the significand; quantity is added to the exponent
1223 // to implement a carry out from rounding the significand.
1224 assert (0xf800 & signif_bits) == 0x0;
1225
1226 return (short)(sign_bit | ( ((exp + 15) << 10) + signif_bits ) );
1227 }
1228
1229 /**
1230 * Compares two {@code Float} objects numerically.
1231 *
1232 * This method imposes a total order on {@code Float} objects
1233 * with two differences compared to the incomplete order defined by
1234 * the Java language numerical comparison operators ({@code <, <=,
1235 * ==, >=, >}) on {@code float} values.
1236 *
1237 * <ul><li> A NaN is <em>unordered</em> with respect to other
1238 * values and unequal to itself under the comparison
1239 * operators. This method chooses to define {@code
1240 * Float.NaN} to be equal to itself and greater than all
1241 * other {@code double} values (including {@code
1242 * Float.POSITIVE_INFINITY}).
1243 *
1244 * <li> Positive zero and negative zero compare equal
1245 * numerically, but are distinct and distinguishable values.
1246 * This method chooses to define positive zero ({@code +0.0f}),
1247 * to be greater than negative zero ({@code -0.0f}).
1248 * </ul>
1249 *
1250 * This ensures that the <i>natural ordering</i> of {@code Float}
1251 * objects imposed by this method is <i>consistent with
1252 * equals</i>; see {@linkplain Double##equivalenceRelation this
1253 * discussion for details of floating-point comparison and
1254 * ordering}.
1255 *
1256 *
1257 * @param anotherFloat the {@code Float} to be compared.
1258 * @return the value {@code 0} if {@code anotherFloat} is
1259 * numerically equal to this {@code Float}; a value
1260 * less than {@code 0} if this {@code Float}
1261 * is numerically less than {@code anotherFloat};
1262 * and a value greater than {@code 0} if this
1263 * {@code Float} is numerically greater than
1264 * {@code anotherFloat}.
1265 *
1266 * @jls 15.20.1 Numerical Comparison Operators {@code <}, {@code <=}, {@code >}, and {@code >=}
1267 * @since 1.2
1268 */
1269 @Override
1270 public int compareTo(Float anotherFloat) {
1271 return Float.compare(value, anotherFloat.value);
1272 }
1273
1274 /**
1275 * Compares the two specified {@code float} values. The sign
1276 * of the integer value returned is the same as that of the
1277 * integer that would be returned by the call:
1278 * <pre>
1279 * Float.valueOf(f1).compareTo(Float.valueOf(f2))
1280 * </pre>
1281 *
1282 * @param f1 the first {@code float} to compare.
1283 * @param f2 the second {@code float} to compare.
1284 * @return the value {@code 0} if {@code f1} is
1285 * numerically equal to {@code f2}; a value less than
1286 * {@code 0} if {@code f1} is numerically less than
1287 * {@code f2}; and a value greater than {@code 0}
1288 * if {@code f1} is numerically greater than
1289 * {@code f2}.
1290 * @since 1.4
1291 */
1292 public static int compare(float f1, float f2) {
1293 if (f1 < f2)
1294 return -1; // Neither val is NaN, thisVal is smaller
1295 if (f1 > f2)
1296 return 1; // Neither val is NaN, thisVal is larger
1297
1298 // Cannot use floatToRawIntBits because of possibility of NaNs.
1299 int thisBits = Float.floatToIntBits(f1);
1300 int anotherBits = Float.floatToIntBits(f2);
1301
1302 return (thisBits == anotherBits ? 0 : // Values are equal
1303 (thisBits < anotherBits ? -1 : // (-0.0, 0.0) or (!NaN, NaN)
1304 1)); // (0.0, -0.0) or (NaN, !NaN)
1305 }
1306
1307 /**
1308 * Adds two {@code float} values together as per the + operator.
1309 *
1310 * @apiNote This method corresponds to the addition operation
1311 * defined in IEEE 754.
1312 *
1313 * @param a the first operand
1314 * @param b the second operand
1315 * @return the sum of {@code a} and {@code b}
1316 * @jls 4.2.4 Floating-Point Operations
1317 * @see java.util.function.BinaryOperator
1318 * @since 1.8
1319 */
1320 public static float sum(float a, float b) {
1321 return a + b;
1322 }
1323
1324 /**
1325 * Returns the greater of two {@code float} values
1326 * as if by calling {@link Math#max(float, float) Math.max}.
1327 *
1328 * @apiNote
1329 * This method corresponds to the maximum operation defined in
1330 * IEEE 754.
1331 *
1332 * @param a the first operand
1333 * @param b the second operand
1334 * @return the greater of {@code a} and {@code b}
1335 * @see java.util.function.BinaryOperator
1336 * @since 1.8
1337 */
1338 public static float max(float a, float b) {
1339 return Math.max(a, b);
1340 }
1341
1342 /**
1343 * Returns the smaller of two {@code float} values
1344 * as if by calling {@link Math#min(float, float) Math.min}.
1345 *
1346 * @apiNote
1347 * This method corresponds to the minimum operation defined in
1348 * IEEE 754.
1349 *
1350 * @param a the first operand
1351 * @param b the second operand
1352 * @return the smaller of {@code a} and {@code b}
1353 * @see java.util.function.BinaryOperator
1354 * @since 1.8
1355 */
1356 public static float min(float a, float b) {
1357 return Math.min(a, b);
1358 }
1359
1360 /**
1361 * Returns an {@link Optional} containing the nominal descriptor for this
1362 * instance, which is the instance itself.
1363 *
1364 * @return an {@link Optional} describing the {@linkplain Float} instance
1365 * @since 12
1366 */
1367 @Override
1368 public Optional<Float> describeConstable() {
1369 return Optional.of(this);
1370 }
1371
1372 /**
1373 * Resolves this instance as a {@link ConstantDesc}, the result of which is
1374 * the instance itself.
1375 *
1376 * @param lookup ignored
1377 * @return the {@linkplain Float} instance
1378 * @since 12
1379 */
1380 @Override
1381 public Float resolveConstantDesc(MethodHandles.Lookup lookup) {
1382 return this;
1383 }
1384
1385 /** use serialVersionUID from JDK 1.0.2 for interoperability */
1386 @java.io.Serial
1387 private static final long serialVersionUID = -2671257302660747028L;
1388 }