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