| /* | |
| * Copyright (c) 1994, 2025, Oracle and/or its affiliates. All rights reserved. | |
| * DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER. | |
| * | |
| * This code is free software; you can redistribute it and/or modify it | |
| * under the terms of the GNU General Public License version 2 only, as | |
| * published by the Free Software Foundation. Oracle designates this | |
| * particular file as subject to the "Classpath" exception as provided | |
| * by Oracle in the LICENSE file that accompanied this code. | |
| * | |
| * This code is distributed in the hope that it will be useful, but WITHOUT | |
| * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or | |
| * FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License | |
| * version 2 for more details (a copy is included in the LICENSE file that | |
| * accompanied this code). | |
| * | |
| * You should have received a copy of the GNU General Public License version | |
| * 2 along with this work; if not, write to the Free Software Foundation, | |
| * Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA. | |
| * | |
| * Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA | |
| * or visit www.oracle.com if you need additional information or have any | |
| * questions. | |
| */ | |
| package java.lang; | |
| import java.lang.invoke.MethodHandles; | |
| import java.lang.constant.Constable; | |
| import java.lang.constant.ConstantDesc; | |
| import java.util.Optional; | |
| import jdk.internal.math.FloatConsts; | |
| import jdk.internal.math.FloatingDecimal; | |
| import jdk.internal.math.FloatToDecimal; | |
| import jdk.internal.vm.annotation.IntrinsicCandidate; | |
| /** | |
| * The {@code Float} class is the {@linkplain | |
| * java.lang##wrapperClass wrapper class} for values of the primitive | |
| * type {@code float}. An object of type {@code Float} contains a | |
| * single field whose type is {@code float}. | |
| * | |
| * <p>In addition, this class provides several methods for converting a | |
| * {@code float} to a {@code String} and a | |
| * {@code String} to a {@code float}, as well as other | |
| * constants and methods useful when dealing with a | |
| * {@code float}. | |
| * | |
| * <p>This is a <a href="{@docRoot}/java.base/java/lang/doc-files/ValueBased.html">value-based</a> | |
| * class; programmers should treat instances that are | |
| * {@linkplain #equals(Object) equal} as interchangeable and should not | |
| * use instances for synchronization, or unpredictable behavior may | |
| * occur. For example, in a future release, synchronization may fail. | |
| * | |
| * <h2><a id=equivalenceRelation>Floating-point Equality, Equivalence, | |
| * and Comparison</a></h2> | |
| * | |
| * The class {@code java.lang.Double} has a {@linkplain | |
| * Double##equivalenceRelation discussion of equality, | |
| * equivalence, and comparison of floating-point values} that is | |
| * equally applicable to {@code float} values. | |
| * | |
| * <h2><a id=decimalToBinaryConversion>Decimal ↔ Binary Conversion Issues</a></h2> | |
| * | |
| * The {@linkplain Double##decimalToBinaryConversion discussion of binary to | |
| * decimal conversion issues} in {@code java.lang.Double} is also | |
| * applicable to {@code float} values. | |
| * | |
| * @spec https://standards.ieee.org/ieee/754/6210/ | |
| * IEEE Standard for Floating-Point Arithmetic | |
| * | |
| * @author Lee Boynton | |
| * @author Arthur van Hoff | |
| * @author Joseph D. Darcy | |
| * @since 1.0 | |
| */ | |
| @jdk.internal.ValueBased | |
| public final class Float extends Number | |
| implements Comparable<Float>, Constable, ConstantDesc { | |
| /** | |
| * A constant holding the positive infinity of type | |
| * {@code float}. It is equal to the value returned by | |
| * {@code Float.intBitsToFloat(0x7f800000)}. | |
| */ | |
| public static final float POSITIVE_INFINITY = 1.0f / 0.0f; | |
| /** | |
| * A constant holding the negative infinity of type | |
| * {@code float}. It is equal to the value returned by | |
| * {@code Float.intBitsToFloat(0xff800000)}. | |
| */ | |
| public static final float NEGATIVE_INFINITY = -1.0f / 0.0f; | |
| /** | |
| * A constant holding a Not-a-Number (NaN) value of type {@code float}. | |
| * It is {@linkplain Double##equivalenceRelation equivalent} | |
| * to the value returned by{@code Float.intBitsToFloat(0x7fc00000)}. | |
| */ | |
| public static final float NaN = 0.0f / 0.0f; | |
| /** | |
| * A constant holding the largest positive finite value of type | |
| * {@code float}, (2-2<sup>-23</sup>)·2<sup>127</sup>. | |
| * It is equal to the hexadecimal floating-point literal | |
| * {@code 0x1.fffffeP+127f} and also equal to | |
| * {@code Float.intBitsToFloat(0x7f7fffff)}. | |
| */ | |
| public static final float MAX_VALUE = 0x1.fffffeP+127f; // 3.4028235e+38f | |
| /** | |
| * A constant holding the smallest positive normal value of type | |
| * {@code float}, 2<sup>-126</sup>. It is equal to the | |
| * hexadecimal floating-point literal {@code 0x1.0p-126f} and also | |
| * equal to {@code Float.intBitsToFloat(0x00800000)}. | |
| * | |
| * @since 1.6 | |
| */ | |
| public static final float MIN_NORMAL = 0x1.0p-126f; // 1.17549435E-38f | |
| /** | |
| * A constant holding the smallest positive nonzero value of type | |
| * {@code float}, 2<sup>-149</sup>. It is equal to the | |
| * hexadecimal floating-point literal {@code 0x0.000002P-126f} | |
| * and also equal to {@code Float.intBitsToFloat(0x1)}. | |
| */ | |
| public static final float MIN_VALUE = 0x0.000002P-126f; // 1.4e-45f | |
| /** | |
| * The number of bits used to represent a {@code float} value, | |
| * {@value}. | |
| * | |
| * @since 1.5 | |
| */ | |
| public static final int SIZE = 32; | |
| /** | |
| * The number of bits in the significand of a {@code float} value, | |
| * {@value}. This is the parameter N in section {@jls 4.2.3} of | |
| * <cite>The Java Language Specification</cite>. | |
| * | |
| * @since 19 | |
| */ | |
| public static final int PRECISION = 24; | |
| /** | |
| * Maximum exponent a finite {@code float} variable may have, | |
| * {@value}. It is equal to the value returned by {@code | |
| * Math.getExponent(Float.MAX_VALUE)}. | |
| * | |
| * @since 1.6 | |
| */ | |
| public static final int MAX_EXPONENT = (1 << (SIZE - PRECISION - 1)) - 1; // 127 | |
| /** | |
| * Minimum exponent a normalized {@code float} variable may have, | |
| * {@value}. It is equal to the value returned by {@code | |
| * Math.getExponent(Float.MIN_NORMAL)}. | |
| * | |
| * @since 1.6 | |
| */ | |
| public static final int MIN_EXPONENT = 1 - MAX_EXPONENT; // -126 | |
| /** | |
| * The number of bytes used to represent a {@code float} value, | |
| * {@value}. | |
| * | |
| * @since 1.8 | |
| */ | |
| public static final int BYTES = SIZE / Byte.SIZE; | |
| /** | |
| * The {@code Class} instance representing the primitive type | |
| * {@code float}. | |
| * | |
| * @since 1.1 | |
| */ | |
| public static final Class<Float> TYPE = Class.getPrimitiveClass("float"); | |
| /** | |
| * Returns a string representation of the {@code float} | |
| * argument. All characters mentioned below are ASCII characters. | |
| * <ul> | |
| * <li>If the argument is NaN, the result is the string | |
| * "{@code NaN}". | |
| * <li>Otherwise, the result is a string that represents the sign and | |
| * magnitude (absolute value) of the argument. If the sign is | |
| * negative, the first character of the result is | |
| * '{@code -}' ({@code '\u005Cu002D'}); if the sign is | |
| * positive, no sign character appears in the result. As for | |
| * the magnitude <i>m</i>: | |
| * <ul> | |
| * <li>If <i>m</i> is infinity, it is represented by the characters | |
| * {@code "Infinity"}; thus, positive infinity produces | |
| * the result {@code "Infinity"} and negative infinity | |
| * produces the result {@code "-Infinity"}. | |
| * <li>If <i>m</i> is zero, it is represented by the characters | |
| * {@code "0.0"}; thus, negative zero produces the result | |
| * {@code "-0.0"} and positive zero produces the result | |
| * {@code "0.0"}. | |
| * | |
| * <li> Otherwise <i>m</i> is positive and finite. | |
| * It is converted to a string in two stages: | |
| * <ul> | |
| * <li> <em>Selection of a decimal</em>: | |
| * A well-defined decimal <i>d</i><sub><i>m</i></sub> | |
| * is selected to represent <i>m</i>. | |
| * This decimal is (almost always) the <em>shortest</em> one that | |
| * rounds to <i>m</i> according to the round to nearest | |
| * rounding policy of IEEE 754 floating-point arithmetic. | |
| * <li> <em>Formatting as a string</em>: | |
| * The decimal <i>d</i><sub><i>m</i></sub> is formatted as a string, | |
| * either in plain or in computerized scientific notation, | |
| * depending on its value. | |
| * </ul> | |
| * </ul> | |
| * </ul> | |
| * | |
| * <p>A <em>decimal</em> is a number of the form | |
| * <i>s</i>×10<sup><i>i</i></sup> | |
| * for some (unique) integers <i>s</i> > 0 and <i>i</i> such that | |
| * <i>s</i> is not a multiple of 10. | |
| * These integers are the <em>significand</em> and | |
| * the <em>exponent</em>, respectively, of the decimal. | |
| * The <em>length</em> of the decimal is the (unique) | |
| * positive integer <i>n</i> meeting | |
| * 10<sup><i>n</i>-1</sup> ≤ <i>s</i> < 10<sup><i>n</i></sup>. | |
| * | |
| * <p>The decimal <i>d</i><sub><i>m</i></sub> for a finite positive <i>m</i> | |
| * is defined as follows: | |
| * <ul> | |
| * <li>Let <i>R</i> be the set of all decimals that round to <i>m</i> | |
| * according to the usual <em>round to nearest</em> rounding policy of | |
| * IEEE 754 floating-point arithmetic. | |
| * <li>Let <i>p</i> be the minimal length over all decimals in <i>R</i>. | |
| * <li>When <i>p</i> ≥ 2, let <i>T</i> be the set of all decimals | |
| * in <i>R</i> with length <i>p</i>. | |
| * Otherwise, let <i>T</i> be the set of all decimals | |
| * in <i>R</i> with length 1 or 2. | |
| * <li>Define <i>d</i><sub><i>m</i></sub> as the decimal in <i>T</i> | |
| * that is closest to <i>m</i>. | |
| * Or if there are two such decimals in <i>T</i>, | |
| * select the one with the even significand. | |
| * </ul> | |
| * | |
| * <p>The (uniquely) selected decimal <i>d</i><sub><i>m</i></sub> | |
| * is then formatted. | |
| * Let <i>s</i>, <i>i</i> and <i>n</i> be the significand, exponent and | |
| * length of <i>d</i><sub><i>m</i></sub>, respectively. | |
| * Further, let <i>e</i> = <i>n</i> + <i>i</i> - 1 and let | |
| * <i>s</i><sub>1</sub>…<i>s</i><sub><i>n</i></sub> | |
| * be the usual decimal expansion of <i>s</i>. | |
| * Note that <i>s</i><sub>1</sub> ≠ 0 | |
| * and <i>s</i><sub><i>n</i></sub> ≠ 0. | |
| * Below, the decimal point {@code '.'} is {@code '\u005Cu002E'} | |
| * and the exponent indicator {@code 'E'} is {@code '\u005Cu0045'}. | |
| * <ul> | |
| * <li>Case -3 ≤ <i>e</i> < 0: | |
| * <i>d</i><sub><i>m</i></sub> is formatted as | |
| * <code>0.0</code>…<code>0</code><!-- | |
| * --><i>s</i><sub>1</sub>…<i>s</i><sub><i>n</i></sub>, | |
| * where there are exactly -(<i>n</i> + <i>i</i>) zeroes between | |
| * the decimal point and <i>s</i><sub>1</sub>. | |
| * For example, 123 × 10<sup>-4</sup> is formatted as | |
| * {@code 0.0123}. | |
| * <li>Case 0 ≤ <i>e</i> < 7: | |
| * <ul> | |
| * <li>Subcase <i>i</i> ≥ 0: | |
| * <i>d</i><sub><i>m</i></sub> is formatted as | |
| * <i>s</i><sub>1</sub>…<i>s</i><sub><i>n</i></sub><!-- | |
| * --><code>0</code>…<code>0.0</code>, | |
| * where there are exactly <i>i</i> zeroes | |
| * between <i>s</i><sub><i>n</i></sub> and the decimal point. | |
| * For example, 123 × 10<sup>2</sup> is formatted as | |
| * {@code 12300.0}. | |
| * <li>Subcase <i>i</i> < 0: | |
| * <i>d</i><sub><i>m</i></sub> is formatted as | |
| * <i>s</i><sub>1</sub>…<!-- | |
| * --><i>s</i><sub><i>n</i>+<i>i</i></sub><code>.</code><!-- | |
| * --><i>s</i><sub><i>n</i>+<i>i</i>+1</sub>…<!-- | |
| * --><i>s</i><sub><i>n</i></sub>, | |
| * where there are exactly -<i>i</i> digits to the right of | |
| * the decimal point. | |
| * For example, 123 × 10<sup>-1</sup> is formatted as | |
| * {@code 12.3}. | |
| * </ul> | |
| * <li>Case <i>e</i> < -3 or <i>e</i> ≥ 7: | |
| * computerized scientific notation is used to format | |
| * <i>d</i><sub><i>m</i></sub>. | |
| * Here <i>e</i> is formatted as by {@link Integer#toString(int)}. | |
| * <ul> | |
| * <li>Subcase <i>n</i> = 1: | |
| * <i>d</i><sub><i>m</i></sub> is formatted as | |
| * <i>s</i><sub>1</sub><code>.0E</code><i>e</i>. | |
| * For example, 1 × 10<sup>23</sup> is formatted as | |
| * {@code 1.0E23}. | |
| * <li>Subcase <i>n</i> > 1: | |
| * <i>d</i><sub><i>m</i></sub> is formatted as | |
| * <i>s</i><sub>1</sub><code>.</code><i>s</i><sub>2</sub><!-- | |
| * -->…<i>s</i><sub><i>n</i></sub><code>E</code><i>e</i>. | |
| * For example, 123 × 10<sup>-21</sup> is formatted as | |
| * {@code 1.23E-19}. | |
| * </ul> | |
| * </ul> | |
| * | |
| * <p>To create localized string representations of a floating-point | |
| * value, use subclasses of {@link java.text.NumberFormat}. | |
| * | |
| * @apiNote | |
| * This method corresponds to the general functionality of the | |
| * convertToDecimalCharacter operation defined in IEEE 754; | |
| * however, that operation is defined in terms of specifying the | |
| * number of significand digits used in the conversion. | |
| * Code to do such a conversion in the Java platform includes | |
| * converting the {@code float} to a {@link java.math.BigDecimal | |
| * BigDecimal} exactly and then rounding the {@code BigDecimal} to | |
| * the desired number of digits; sample code: | |
| * {@snippet lang=java : | |
| * floatf = 0.1f; | |
| * int digits = 15; | |
| * BigDecimal bd = new BigDecimal(f); | |
| * String result = bd.round(new MathContext(digits, RoundingMode.HALF_UP)); | |
| * // 0.100000001490116 | |
| * } | |
| * | |
| * @param f the {@code float} to be converted. | |
| * @return a string representation of the argument. | |
| */ | |
| public static String toString(float f) { | |
| return FloatToDecimal.toString(f); | |
| } | |
| /** | |
| * Returns a hexadecimal string representation of the | |
| * {@code float} argument. All characters mentioned below are | |
| * ASCII characters. | |
| * | |
| * <ul> | |
| * <li>If the argument is NaN, the result is the string | |
| * "{@code NaN}". | |
| * <li>Otherwise, the result is a string that represents the sign and | |
| * magnitude (absolute value) of the argument. If the sign is negative, | |
| * the first character of the result is '{@code -}' | |
| * ({@code '\u005Cu002D'}); if the sign is positive, no sign character | |
| * appears in the result. As for the magnitude <i>m</i>: | |
| * | |
| * <ul> | |
| * <li>If <i>m</i> is infinity, it is represented by the string | |
| * {@code "Infinity"}; thus, positive infinity produces the | |
| * result {@code "Infinity"} and negative infinity produces | |
| * the result {@code "-Infinity"}. | |
| * | |
| * <li>If <i>m</i> is zero, it is represented by the string | |
| * {@code "0x0.0p0"}; thus, negative zero produces the result | |
| * {@code "-0x0.0p0"} and positive zero produces the result | |
| * {@code "0x0.0p0"}. | |
| * | |
| * <li>If <i>m</i> is a {@code float} value with a | |
| * normalized representation, substrings are used to represent the | |
| * significand and exponent fields. The significand is | |
| * represented by the characters {@code "0x1."} | |
| * followed by a lowercase hexadecimal representation of the rest | |
| * of the significand as a fraction. Trailing zeros in the | |
| * hexadecimal representation are removed unless all the digits | |
| * are zero, in which case a single zero is used. Next, the | |
| * exponent is represented by {@code "p"} followed | |
| * by a decimal string of the unbiased exponent as if produced by | |
| * a call to {@link Integer#toString(int) Integer.toString} on the | |
| * exponent value. | |
| * | |
| * <li>If <i>m</i> is a {@code float} value with a subnormal | |
| * representation, the significand is represented by the | |
| * characters {@code "0x0."} followed by a | |
| * hexadecimal representation of the rest of the significand as a | |
| * fraction. Trailing zeros in the hexadecimal representation are | |
| * removed. Next, the exponent is represented by | |
| * {@code "p-126"}. Note that there must be at | |
| * least one nonzero digit in a subnormal significand. | |
| * | |
| * </ul> | |
| * | |
| * </ul> | |
| * | |
| * <table class="striped"> | |
| * <caption>Examples</caption> | |
| * <thead> | |
| * <tr><th scope="col">Floating-point Value</th><th scope="col">Hexadecimal String</th> | |
| * </thead> | |
| * <tbody> | |
| * <tr><th scope="row">{@code 1.0}</th> <td>{@code 0x1.0p0}</td> | |
| * <tr><th scope="row">{@code -1.0}</th> <td>{@code -0x1.0p0}</td> | |
| * <tr><th scope="row">{@code 2.0}</th> <td>{@code 0x1.0p1}</td> | |
| * <tr><th scope="row">{@code 3.0}</th> <td>{@code 0x1.8p1}</td> | |
| * <tr><th scope="row">{@code 0.5}</th> <td>{@code 0x1.0p-1}</td> | |
| * <tr><th scope="row">{@code 0.25}</th> <td>{@code 0x1.0p-2}</td> | |
| * <tr><th scope="row">{@code Float.MAX_VALUE}</th> | |
| * <td>{@code 0x1.fffffep127}</td> | |
| * <tr><th scope="row">{@code Minimum Normal Value}</th> | |
| * <td>{@code 0x1.0p-126}</td> | |
| * <tr><th scope="row">{@code Maximum Subnormal Value}</th> | |
| * <td>{@code 0x0.fffffep-126}</td> | |
| * <tr><th scope="row">{@code Float.MIN_VALUE}</th> | |
| * <td>{@code 0x0.000002p-126}</td> | |
| * </tbody> | |
| * </table> | |
| * | |
| * @apiNote | |
| * This method corresponds to the convertToHexCharacter operation | |
| * defined in IEEE 754. | |
| * | |
| * @param f the {@code float} to be converted. | |
| * @return a hex string representation of the argument. | |
| * @since 1.5 | |
| * @author Joseph D. Darcy | |
| */ | |
| public static String toHexString(float f) { | |
| if (Math.abs(f) < Float.MIN_NORMAL | |
| && f != 0.0f ) {// float subnormal | |
| // Adjust exponent to create subnormal double, then | |
| // replace subnormal double exponent with subnormal float | |
| // exponent | |
| String s = Double.toHexString(Math.scalb((double)f, | |
| /* -1022+126 */ | |
| Double.MIN_EXPONENT- | |
| Float.MIN_EXPONENT)); | |
| return s.replaceFirst("p-1022$", "p-126"); | |
| } | |
| else // double string will be the same as float string | |
| return Double.toHexString(f); | |
| } | |
| /** | |
| * Returns a {@code Float} object holding the | |
| * {@code float} value represented by the argument string | |
| * {@code s}. | |
| * | |
| * <p>If {@code s} is {@code null}, then a | |
| * {@code NullPointerException} is thrown. | |
| * | |
| * <p>Leading and trailing whitespace characters in {@code s} | |
| * are ignored. Whitespace is removed as if by the {@link | |
| * String#trim} method; that is, both ASCII space and control | |
| * characters are removed. The rest of {@code s} should | |
| * constitute a <i>FloatValue</i> as described by the lexical | |
| * syntax rules: | |
| * | |
| * <blockquote> | |
| * <dl> | |
| * <dt><i>FloatValue:</i> | |
| * <dd><i>Sign<sub>opt</sub></i> {@code NaN} | |
| * <dd><i>Sign<sub>opt</sub></i> {@code Infinity} | |
| * <dd><i>Sign<sub>opt</sub> FloatingPointLiteral</i> | |
| * <dd><i>Sign<sub>opt</sub> HexFloatingPointLiteral</i> | |
| * <dd><i>SignedInteger</i> | |
| * </dl> | |
| * | |
| * <dl> | |
| * <dt><i>HexFloatingPointLiteral</i>: | |
| * <dd> <i>HexSignificand BinaryExponent FloatTypeSuffix<sub>opt</sub></i> | |
| * </dl> | |
| * | |
| * <dl> | |
| * <dt><i>HexSignificand:</i> | |
| * <dd><i>HexNumeral</i> | |
| * <dd><i>HexNumeral</i> {@code .} | |
| * <dd>{@code 0x} <i>HexDigits<sub>opt</sub> | |
| * </i>{@code .}<i> HexDigits</i> | |
| * <dd>{@code 0X}<i> HexDigits<sub>opt</sub> | |
| * </i>{@code .} <i>HexDigits</i> | |
| * </dl> | |
| * | |
| * <dl> | |
| * <dt><i>BinaryExponent:</i> | |
| * <dd><i>BinaryExponentIndicator SignedInteger</i> | |
| * </dl> | |
| * | |
| * <dl> | |
| * <dt><i>BinaryExponentIndicator:</i> | |
| * <dd>{@code p} | |
| * <dd>{@code P} | |
| * </dl> | |
| * | |
| * </blockquote> | |
| * | |
| * where <i>Sign</i>, <i>FloatingPointLiteral</i>, | |
| * <i>HexNumeral</i>, <i>HexDigits</i>, <i>SignedInteger</i> and | |
| * <i>FloatTypeSuffix</i> are as defined in the lexical structure | |
| * sections of | |
| * <cite>The Java Language Specification</cite>, | |
| * except that underscores are not accepted between digits. | |
| * If {@code s} does not have the form of | |
| * a <i>FloatValue</i>, then a {@code NumberFormatException} | |
| * is thrown. Otherwise, {@code s} is regarded as | |
| * representing an exact decimal value in the usual | |
| * "computerized scientific notation" or as an exact | |
| * hexadecimal value; this exact numerical value is then | |
| * conceptually converted to an "infinitely precise" | |
| * binary value that is then rounded to type {@code float} | |
| * by the usual round-to-nearest rule of IEEE 754 floating-point | |
| * arithmetic, which includes preserving the sign of a zero | |
| * value. | |
| * | |
| * Note that the round-to-nearest rule also implies overflow and | |
| * underflow behaviour; if the exact value of {@code s} is large | |
| * enough in magnitude (greater than or equal to ({@link | |
| * #MAX_VALUE} + {@link Math#ulp(float) ulp(MAX_VALUE)}/2), | |
| * rounding to {@code float} will result in an infinity and if the | |
| * exact value of {@code s} is small enough in magnitude (less | |
| * than or equal to {@link #MIN_VALUE}/2), rounding to float will | |
| * result in a zero. | |
| * | |
| * Finally, after rounding a {@code Float} object representing | |
| * this {@code float} value is returned. | |
| * | |
| * <p>Note that trailing format specifiers, specifiers that | |
| * determine the type of a floating-point literal | |
| * ({@code 1.0f} is a {@code float} value; | |
| * {@code 1.0d} is a {@code double} value), do | |
| * <em>not</em> influence the results of this method. In other | |
| * words, the numerical value of the input string is converted | |
| * directly to the target floating-point type. In general, the | |
| * two-step sequence of conversions, string to {@code double} | |
| * followed by {@code double} to {@code float}, is | |
| * <em>not</em> equivalent to converting a string directly to | |
| * {@code float}. For example, if first converted to an | |
| * intermediate {@code double} and then to | |
| * {@code float}, the string<br> | |
| * {@code "1.00000017881393421514957253748434595763683319091796875001d"}<br> | |
| * results in the {@code float} value | |
| * {@code 1.0000002f}; if the string is converted directly to | |
| * {@code float}, <code>1.000000<b>1</b>f</code> results. | |
| * | |
| * <p>To avoid calling this method on an invalid string and having | |
| * a {@code NumberFormatException} be thrown, the documentation | |
| * for {@link Double#valueOf Double.valueOf} lists a regular | |
| * expression which can be used to screen the input. | |
| * | |
| * @apiNote To interpret localized string representations of a | |
| * floating-point value, or string representations that have | |
| * non-ASCII digits, use {@link java.text.NumberFormat}. For | |
| * example, | |
| * {@snippet lang="java" : | |
| * NumberFormat.getInstance(l).parse(s).floatValue(); | |
| * } | |
| * where {@code l} is the desired locale, or | |
| * {@link java.util.Locale#ROOT} if locale insensitive. | |
| * | |
| * @apiNote | |
| * This method corresponds to the convertFromDecimalCharacter and | |
| * convertFromHexCharacter operations defined in IEEE 754. | |
| * | |
| * @param s the string to be parsed. | |
| * @return a {@code Float} object holding the value | |
| * represented by the {@code String} argument. | |
| * @throws NumberFormatException if the string does not contain a | |
| * parsable number. | |
| * @see Double##decimalToBinaryConversion Decimal ↔ Binary Conversion Issues | |
| */ | |
| public static Float valueOf(String s) throws NumberFormatException { | |
| return new Float(parseFloat(s)); | |
| } | |
| /** | |
| * Returns a {@code Float} instance representing the specified | |
| * {@code float} value. | |
| * If a new {@code Float} instance is not required, this method | |
| * should generally be used in preference to the constructor | |
| * {@link #Float(float)}, as this method is likely to yield | |
| * significantly better space and time performance by caching | |
| * frequently requested values. | |
| * | |
| * @param f a float value. | |
| * @return a {@code Float} instance representing {@code f}. | |
| * @since 1.5 | |
| */ | |
| @IntrinsicCandidate | |
| public static Float valueOf(float f) { | |
| return new Float(f); | |
| } | |
| /** | |
| * Returns a new {@code float} initialized to the value | |
| * represented by the specified {@code String}, as performed | |
| * by the {@code valueOf} method of class {@code Float}. | |
| * | |
| * @param s the string to be parsed. | |
| * @return the {@code float} value represented by the string | |
| * argument. | |
| * @throws NullPointerException if the string is null | |
| * @throws NumberFormatException if the string does not contain a | |
| * parsable {@code float}. | |
| * @see java.lang.Float#valueOf(String) | |
| * @see Double##decimalToBinaryConversion Decimal ↔ Binary Conversion Issues | |
| * @since 1.2 | |
| */ | |
| public static float parseFloat(String s) throws NumberFormatException { | |
| return FloatingDecimal.parseFloat(s); | |
| } | |
| /** | |
| * Returns {@code true} if the specified number is a | |
| * Not-a-Number (NaN) value, {@code false} otherwise. | |
| * | |
| * @apiNote | |
| * This method corresponds to the isNaN operation defined in IEEE | |
| * 754. | |
| * | |
| * @param v the value to be tested. | |
| * @return {@code true} if the argument is NaN; | |
| * {@code false} otherwise. | |
| */ | |
| public static boolean isNaN(float v) { | |
| return (v != v); | |
| } | |
| /** | |
| * Returns {@code true} if the specified number is infinitely | |
| * large in magnitude, {@code false} otherwise. | |
| * | |
| * @apiNote | |
| * This method corresponds to the isInfinite operation defined in | |
| * IEEE 754. | |
| * | |
| * @param v the value to be tested. | |
| * @return {@code true} if the argument is positive infinity or | |
| * negative infinity; {@code false} otherwise. | |
| */ | |
| @IntrinsicCandidate | |
| public static boolean isInfinite(float v) { | |
| return Math.abs(v) > MAX_VALUE; | |
| } | |
| /** | |
| * Returns {@code true} if the argument is a finite floating-point | |
| * value; returns {@code false} otherwise (for NaN and infinity | |
| * arguments). | |
| * | |
| * @apiNote | |
| * This method corresponds to the isFinite operation defined in | |
| * IEEE 754. | |
| * | |
| * @param f the {@code float} value to be tested | |
| * @return {@code true} if the argument is a finite | |
| * floating-point value, {@code false} otherwise. | |
| * @since 1.8 | |
| */ | |
| @IntrinsicCandidate | |
| public static boolean isFinite(float f) { | |
| return Math.abs(f) <= Float.MAX_VALUE; | |
| } | |
| /** | |
| * The value of the Float. | |
| * | |
| * @serial | |
| */ | |
| private final float value; | |
| /** | |
| * Constructs a newly allocated {@code Float} object that | |
| * represents the primitive {@code float} argument. | |
| * | |
| * @param value the value to be represented by the {@code Float}. | |
| * | |
| * @deprecated | |
| * It is rarely appropriate to use this constructor. The static factory | |
| * {@link #valueOf(float)} is generally a better choice, as it is | |
| * likely to yield significantly better space and time performance. | |
| */ | |
| @Deprecated(since="9") | |
| public Float(float value) { | |
| this.value = value; | |
| } | |
| /** | |
| * Constructs a newly allocated {@code Float} object that | |
| * represents the argument converted to type {@code float}. | |
| * | |
| * @param value the value to be represented by the {@code Float}. | |
| * | |
| * @deprecated | |
| * It is rarely appropriate to use this constructor. Instead, use the | |
| * static factory method {@link #valueOf(float)} method as follows: | |
| * {@code Float.valueOf((float)value)}. | |
| */ | |
| @Deprecated(since="9") | |
| public Float(double value) { | |
| this.value = (float)value; | |
| } | |
| /** | |
| * Constructs a newly allocated {@code Float} object that | |
| * represents the floating-point value of type {@code float} | |
| * represented by the string. The string is converted to a | |
| * {@code float} value as if by the {@code valueOf} method. | |
| * | |
| * @param s a string to be converted to a {@code Float}. | |
| * @throws NumberFormatException if the string does not contain a | |
| * parsable number. | |
| * | |
| * @deprecated | |
| * It is rarely appropriate to use this constructor. | |
| * Use {@link #parseFloat(String)} to convert a string to a | |
| * {@code float} primitive, or use {@link #valueOf(String)} | |
| * to convert a string to a {@code Float} object. | |
| */ | |
| @Deprecated(since="9") | |
| public Float(String s) throws NumberFormatException { | |
| value = parseFloat(s); | |
| } | |
| /** | |
| * Returns {@code true} if this {@code Float} value is a | |
| * Not-a-Number (NaN), {@code false} otherwise. | |
| * | |
| * @return {@code true} if the value represented by this object is | |
| * NaN; {@code false} otherwise. | |
| */ | |
| public boolean isNaN() { | |
| return isNaN(value); | |
| } | |
| /** | |
| * Returns {@code true} if this {@code Float} value is | |
| * infinitely large in magnitude, {@code false} otherwise. | |
| * | |
| * @return {@code true} if the value represented by this object is | |
| * positive infinity or negative infinity; | |
| * {@code false} otherwise. | |
| */ | |
| public boolean isInfinite() { | |
| return isInfinite(value); | |
| } | |
| /** | |
| * Returns a string representation of this {@code Float} object. | |
| * The primitive {@code float} value represented by this object | |
| * is converted to a {@code String} exactly as if by the method | |
| * {@code toString} of one argument. | |
| * | |
| * @return a {@code String} representation of this object. | |
| * @see java.lang.Float#toString(float) | |
| */ | |
| public String toString() { | |
| return Float.toString(value); | |
| } | |
| /** | |
| * Returns the value of this {@code Float} as a {@code byte} after | |
| * a narrowing primitive conversion. | |
| * | |
| * @return the {@code float} value represented by this object | |
| * converted to type {@code byte} | |
| * @jls 5.1.3 Narrowing Primitive Conversion | |
| */ | |
| @Override | |
| public byte byteValue() { | |
| return (byte)value; | |
| } | |
| /** | |
| * Returns the value of this {@code Float} as a {@code short} | |
| * after a narrowing primitive conversion. | |
| * | |
| * @return the {@code float} value represented by this object | |
| * converted to type {@code short} | |
| * @jls 5.1.3 Narrowing Primitive Conversion | |
| * @since 1.1 | |
| */ | |
| @Override | |
| public short shortValue() { | |
| return (short)value; | |
| } | |
| /** | |
| * Returns the value of this {@code Float} as an {@code int} after | |
| * a narrowing primitive conversion. | |
| * | |
| * @apiNote | |
| * This method corresponds to the convertToIntegerTowardZero | |
| * operation defined in IEEE 754. | |
| * | |
| * @return the {@code float} value represented by this object | |
| * converted to type {@code int} | |
| * @jls 5.1.3 Narrowing Primitive Conversion | |
| */ | |
| @Override | |
| public int intValue() { | |
| return (int)value; | |
| } | |
| /** | |
| * Returns value of this {@code Float} as a {@code long} after a | |
| * narrowing primitive conversion. | |
| * | |
| * @apiNote | |
| * This method corresponds to the convertToIntegerTowardZero | |
| * operation defined in IEEE 754. | |
| * | |
| * @return the {@code float} value represented by this object | |
| * converted to type {@code long} | |
| * @jls 5.1.3 Narrowing Primitive Conversion | |
| */ | |
| @Override | |
| public long longValue() { | |
| return (long)value; | |
| } | |
| /** | |
| * Returns the {@code float} value of this {@code Float} object. | |
| * | |
| * @return the {@code float} value represented by this object | |
| */ | |
| @Override | |
| @IntrinsicCandidate | |
| public float floatValue() { | |
| return value; | |
| } | |
| /** | |
| * Returns the value of this {@code Float} as a {@code double} | |
| * after a widening primitive conversion. | |
| * | |
| * @apiNote | |
| * This method corresponds to the convertFormat operation defined | |
| * in IEEE 754. | |
| * | |
| * @return the {@code float} value represented by this | |
| * object converted to type {@code double} | |
| * @jls 5.1.2 Widening Primitive Conversion | |
| */ | |
| @Override | |
| public double doubleValue() { | |
| return (double)value; | |
| } | |
| /** | |
| * Returns a hash code for this {@code Float} object. The | |
| * result is the integer bit representation, exactly as produced | |
| * by the method {@link #floatToIntBits(float)}, of the primitive | |
| * {@code float} value represented by this {@code Float} | |
| * object. | |
| * | |
| * @return a hash code value for this object. | |
| */ | |
| @Override | |
| public int hashCode() { | |
| return Float.hashCode(value); | |
| } | |
| /** | |
| * Returns a hash code for a {@code float} value; compatible with | |
| * {@code Float.hashCode()}. | |
| * | |
| * @param value the value to hash | |
| * @return a hash code value for a {@code float} value. | |
| * @since 1.8 | |
| */ | |
| public static int hashCode(float value) { | |
| return floatToIntBits(value); | |
| } | |
| /** | |
| * Compares this object against the specified object. The result | |
| * is {@code true} if and only if the argument is not | |
| * {@code null} and is a {@code Float} object that | |
| * represents a {@code float} with the same value as the | |
| * {@code float} represented by this object. For this | |
| * purpose, two {@code float} values are considered to be the | |
| * same if and only if the method {@link #floatToIntBits(float)} | |
| * returns the identical {@code int} value when applied to | |
| * each. | |
| * | |
| * @apiNote | |
| * This method is defined in terms of {@link | |
| * #floatToIntBits(float)} rather than the {@code ==} operator on | |
| * {@code float} values since the {@code ==} operator does | |
| * <em>not</em> define an equivalence relation and to satisfy the | |
| * {@linkplain Object#equals equals contract} an equivalence | |
| * relation must be implemented; see {@linkplain Double##equivalenceRelation | |
| * this discussion for details of floating-point equality and equivalence}. | |
| * | |
| * @param obj the object to be compared | |
| * @return {@code true} if the objects are the same; | |
| * {@code false} otherwise. | |
| * @see java.lang.Float#floatToIntBits(float) | |
| * @jls 15.21.1 Numerical Equality Operators == and != | |
| */ | |
| public boolean equals(Object obj) { | |
| return (obj instanceof Float f) && | |
| (floatToIntBits(f.value) == floatToIntBits(value)); | |
| } | |
| /** | |
| * Returns a representation of the specified floating-point value | |
| * according to the IEEE 754 floating-point "single format" bit | |
| * layout. | |
| * | |
| * <p>Bit 31 (the bit that is selected by the mask | |
| * {@code 0x80000000}) represents the sign of the floating-point | |
| * number. | |
| * Bits 30-23 (the bits that are selected by the mask | |
| * {@code 0x7f800000}) represent the exponent. | |
| * Bits 22-0 (the bits that are selected by the mask | |
| * {@code 0x007fffff}) represent the significand (sometimes called | |
| * the mantissa) of the floating-point number. | |
| * | |
| * <p>If the argument is positive infinity, the result is | |
| * {@code 0x7f800000}. | |
| * | |
| * <p>If the argument is negative infinity, the result is | |
| * {@code 0xff800000}. | |
| * | |
| * <p>If the argument is NaN, the result is {@code 0x7fc00000}. | |
| * | |
| * <p>In all cases, the result is an integer that, when given to the | |
| * {@link #intBitsToFloat(int)} method, will produce a floating-point | |
| * value the same as the argument to {@code floatToIntBits} | |
| * (except all NaN values are collapsed to a single | |
| * "canonical" NaN value). | |
| * | |
| * @param value a floating-point number. | |
| * @return the bits that represent the floating-point number. | |
| */ | |
| @IntrinsicCandidate | |
| public static int floatToIntBits(float value) { | |
| if (!isNaN(value)) { | |
| return floatToRawIntBits(value); | |
| } | |
| return 0x7fc00000; | |
| } | |
| /** | |
| * Returns a representation of the specified floating-point value | |
| * according to the IEEE 754 floating-point "single format" bit | |
| * layout, preserving Not-a-Number (NaN) values. | |
| * | |
| * <p>Bit 31 (the bit that is selected by the mask | |
| * {@code 0x80000000}) represents the sign of the floating-point | |
| * number. | |
| * Bits 30-23 (the bits that are selected by the mask | |
| * {@code 0x7f800000}) represent the exponent. | |
| * Bits 22-0 (the bits that are selected by the mask | |
| * {@code 0x007fffff}) represent the significand (sometimes called | |
| * the mantissa) of the floating-point number. | |
| * | |
| * <p>If the argument is positive infinity, the result is | |
| * {@code 0x7f800000}. | |
| * | |
| * <p>If the argument is negative infinity, the result is | |
| * {@code 0xff800000}. | |
| * | |
| * <p>If the argument is NaN, the result is the integer representing | |
| * the actual NaN value. Unlike the {@code floatToIntBits} | |
| * method, {@code floatToRawIntBits} does not collapse all the | |
| * bit patterns encoding a NaN to a single "canonical" | |
| * NaN value. | |
| * | |
| * <p>In all cases, the result is an integer that, when given to the | |
| * {@link #intBitsToFloat(int)} method, will produce a | |
| * floating-point value the same as the argument to | |
| * {@code floatToRawIntBits}. | |
| * | |
| * @param value a floating-point number. | |
| * @return the bits that represent the floating-point number. | |
| * @since 1.3 | |
| */ | |
| @IntrinsicCandidate | |
| public static native int floatToRawIntBits(float value); | |
| /** | |
| * Returns the {@code float} value corresponding to a given | |
| * bit representation. | |
| * The argument is considered to be a representation of a | |
| * floating-point value according to the IEEE 754 floating-point | |
| * "single format" bit layout. | |
| * | |
| * <p>If the argument is {@code 0x7f800000}, the result is positive | |
| * infinity. | |
| * | |
| * <p>If the argument is {@code 0xff800000}, the result is negative | |
| * infinity. | |
| * | |
| * <p>If the argument is any value in the range | |
| * {@code 0x7f800001} through {@code 0x7fffffff} or in | |
| * the range {@code 0xff800001} through | |
| * {@code 0xffffffff}, the result is a NaN. No IEEE 754 | |
| * floating-point operation provided by Java can distinguish | |
| * between two NaN values of the same type with different bit | |
| * patterns. Distinct values of NaN are only distinguishable by | |
| * use of the {@code Float.floatToRawIntBits} method. | |
| * | |
| * <p>In all other cases, let <i>s</i>, <i>e</i>, and <i>m</i> be three | |
| * values that can be computed from the argument: | |
| * | |
| * {@snippet lang="java" : | |
| * int s = ((bits >> 31) == 0) ? 1 : -1; | |
| * int e = ((bits >> 23) & 0xff); | |
| * int m = (e == 0) ? | |
| * (bits & 0x7fffff) << 1 : | |
| * (bits & 0x7fffff) | 0x800000; | |
| * } | |
| * | |
| * Then the floating-point result equals the value of the mathematical | |
| * expression <i>s</i>·<i>m</i>·2<sup><i>e</i>-150</sup>. | |
| * | |
| * <p>Note that this method may not be able to return a | |
| * {@code float} NaN with exactly same bit pattern as the | |
| * {@code int} argument. IEEE 754 distinguishes between two | |
| * kinds of NaNs, quiet NaNs and <i>signaling NaNs</i>. The | |
| * differences between the two kinds of NaN are generally not | |
| * visible in Java. Arithmetic operations on signaling NaNs turn | |
| * them into quiet NaNs with a different, but often similar, bit | |
| * pattern. However, on some processors merely copying a | |
| * signaling NaN also performs that conversion. In particular, | |
| * copying a signaling NaN to return it to the calling method may | |
| * perform this conversion. So {@code intBitsToFloat} may | |
| * not be able to return a {@code float} with a signaling NaN | |
| * bit pattern. Consequently, for some {@code int} values, | |
| * {@code floatToRawIntBits(intBitsToFloat(start))} may | |
| * <i>not</i> equal {@code start}. Moreover, which | |
| * particular bit patterns represent signaling NaNs is platform | |
| * dependent; although all NaN bit patterns, quiet or signaling, | |
| * must be in the NaN range identified above. | |
| * | |
| * @param bits an integer. | |
| * @return the {@code float} floating-point value with the same bit | |
| * pattern. | |
| */ | |
| @IntrinsicCandidate | |
| public static native float intBitsToFloat(int bits); | |
| /** | |
| * {@return the {@code float} value closest to the numerical value | |
| * of the argument, a floating-point binary16 value encoded in a | |
| * {@code short}} The conversion is exact; all binary16 values can | |
| * be exactly represented in {@code float}. | |
| * | |
| * Special cases: | |
| * <ul> | |
| * <li> If the argument is zero, the result is a zero with the | |
| * same sign as the argument. | |
| * <li> If the argument is infinite, the result is an infinity | |
| * with the same sign as the argument. | |
| * <li> If the argument is a NaN, the result is a NaN. | |
| * </ul> | |
| * | |
| * <h4><a id=binary16Format>IEEE 754 binary16 format</a></h4> | |
| * The IEEE 754 standard defines binary16 as a 16-bit format, along | |
| * with the 32-bit binary32 format (corresponding to the {@code | |
| * float} type) and the 64-bit binary64 format (corresponding to | |
| * the {@code double} type). The binary16 format is similar to the | |
| * other IEEE 754 formats, except smaller, having all the usual | |
| * IEEE 754 values such as NaN, signed infinities, signed zeros, | |
| * and subnormals. The parameters (JLS {@jls 4.2.3}) for the | |
| * binary16 format are N = 11 precision bits, K = 5 exponent bits, | |
| * <i>E</i><sub><i>max</i></sub> = 15, and | |
| * <i>E</i><sub><i>min</i></sub> = -14. | |
| * | |
| * @apiNote | |
| * This method corresponds to the convertFormat operation defined | |
| * in IEEE 754 from the binary16 format to the binary32 format. | |
| * The operation of this method is analogous to a primitive | |
| * widening conversion (JLS {@jls 5.1.2}). | |
| * | |
| * @param floatBinary16 the binary16 value to convert to {@code float} | |
| * @since 20 | |
| */ | |
| @IntrinsicCandidate | |
| public static float float16ToFloat(short floatBinary16) { | |
| /* | |
| * The binary16 format has 1 sign bit, 5 exponent bits, and 10 | |
| * significand bits. The exponent bias is 15. | |
| */ | |
| int bin16arg = (int)floatBinary16; | |
| int bin16SignBit = 0x8000 & bin16arg; | |
| int bin16ExpBits = 0x7c00 & bin16arg; | |
| int bin16SignifBits = 0x03FF & bin16arg; | |
| // Shift left difference in the number of significand bits in | |
| // the float and binary16 formats | |
| final int SIGNIF_SHIFT = (FloatConsts.SIGNIFICAND_WIDTH - 11); | |
| float sign = (bin16SignBit != 0) ? -1.0f : 1.0f; | |
| // Extract binary16 exponent, remove its bias, add in the bias | |
| // of a float exponent and shift to correct bit location | |
| // (significand width includes the implicit bit so shift one | |
| // less). | |
| int bin16Exp = (bin16ExpBits >> 10) - 15; | |
| if (bin16Exp == -15) { | |
| // For subnormal binary16 values and 0, the numerical | |
| // value is 2^24 * the significand as an integer (no | |
| // implicit bit). | |
| return sign * (0x1p-24f * bin16SignifBits); | |
| } else if (bin16Exp == 16) { | |
| return (bin16SignifBits == 0) ? | |
| sign * Float.POSITIVE_INFINITY : | |
| Float.intBitsToFloat((bin16SignBit << 16) | | |
| 0x7f80_0000 | | |
| // Preserve NaN signif bits | |
| ( bin16SignifBits << SIGNIF_SHIFT )); | |
| } | |
| assert -15 < bin16Exp && bin16Exp < 16; | |
| int floatExpBits = (bin16Exp + FloatConsts.EXP_BIAS) | |
| << (FloatConsts.SIGNIFICAND_WIDTH - 1); | |
| // Compute and combine result sign, exponent, and significand bits. | |
| return Float.intBitsToFloat((bin16SignBit << 16) | | |
| floatExpBits | | |
| (bin16SignifBits << SIGNIF_SHIFT)); | |
| } | |
| /** | |
| * {@return the floating-point binary16 value, encoded in a {@code | |
| * short}, closest in value to the argument} | |
| * The conversion is computed under the {@linkplain | |
| * java.math.RoundingMode#HALF_EVEN round to nearest even rounding | |
| * mode}. | |
| * | |
| * Special cases: | |
| * <ul> | |
| * <li> If the argument is zero, the result is a zero with the | |
| * same sign as the argument. | |
| * <li> If the argument is infinite, the result is an infinity | |
| * with the same sign as the argument. | |
| * <li> If the argument is a NaN, the result is a NaN. | |
| * </ul> | |
| * | |
| * The {@linkplain ##binary16Format binary16 format} is discussed in | |
| * more detail in the {@link #float16ToFloat} method. | |
| * | |
| * @apiNote | |
| * This method corresponds to the convertFormat operation defined | |
| * in IEEE 754 from the binary32 format to the binary16 format. | |
| * The operation of this method is analogous to a primitive | |
| * narrowing conversion (JLS {@jls 5.1.3}). | |
| * | |
| * @param f the {@code float} value to convert to binary16 | |
| * @since 20 | |
| */ | |
| @IntrinsicCandidate | |
| public static short floatToFloat16(float f) { | |
| int doppel = Float.floatToRawIntBits(f); | |
| short sign_bit = (short)((doppel & 0x8000_0000) >> 16); | |
| if (Float.isNaN(f)) { | |
| // Preserve sign and attempt to preserve significand bits | |
| return (short)(sign_bit | |
| | 0x7c00 // max exponent + 1 | |
| // Preserve high order bit of float NaN in the | |
| // binary16 result NaN (tenth bit); OR in remaining | |
| // bits into lower 9 bits of binary 16 significand. | |
| | (doppel & 0x007f_e000) >> 13 // 10 bits | |
| | (doppel & 0x0000_1ff0) >> 4 // 9 bits | |
| | (doppel & 0x0000_000f)); // 4 bits | |
| } | |
| float abs_f = Math.abs(f); | |
| // The overflow threshold is binary16 MAX_VALUE + 1/2 ulp | |
| if (abs_f >= (0x1.ffcp15f + 0x0.002p15f) ) { | |
| return (short)(sign_bit | 0x7c00); // Positive or negative infinity | |
| } | |
| // Smallest magnitude nonzero representable binary16 value | |
| // is equal to 0x1.0p-24; half-way and smaller rounds to zero. | |
| if (abs_f <= 0x1.0p-24f * 0.5f) { // Covers float zeros and subnormals. | |
| return sign_bit; // Positive or negative zero | |
| } | |
| // Dealing with finite values in exponent range of binary16 | |
| // (when rounding is done, could still round up) | |
| int exp = Math.getExponent(f); | |
| assert -25 <= exp && exp <= 15; | |
| // For binary16 subnormals, beside forcing exp to -15, retain | |
| // the difference expdelta = E_min - exp. This is the excess | |
| // shift value, in addition to 13, to be used in the | |
| // computations below. Further the (hidden) msb with value 1 | |
| // in f must be involved as well. | |
| int expdelta = 0; | |
| int msb = 0x0000_0000; | |
| if (exp < -14) { | |
| expdelta = -14 - exp; | |
| exp = -15; | |
| msb = 0x0080_0000; | |
| } | |
| int f_signif_bits = doppel & 0x007f_ffff | msb; | |
| // Significand bits as if using rounding to zero (truncation). | |
| short signif_bits = (short)(f_signif_bits >> (13 + expdelta)); | |
| // For round to nearest even, determining whether or not to | |
| // round up (in magnitude) is a function of the least | |
| // significant bit (LSB), the next bit position (the round | |
| // position), and the sticky bit (whether there are any | |
| // nonzero bits in the exact result to the right of the round | |
| // digit). An increment occurs in three cases: | |
| // | |
| // LSB Round Sticky | |
| // 0 1 1 | |
| // 1 1 0 | |
| // 1 1 1 | |
| // See "Computer Arithmetic Algorithms," Koren, Table 4.9 | |
| int lsb = f_signif_bits & (1 << 13 + expdelta); | |
| int round = f_signif_bits & (1 << 12 + expdelta); | |
| int sticky = f_signif_bits & ((1 << 12 + expdelta) - 1); | |
| if (round != 0 && ((lsb | sticky) != 0 )) { | |
| signif_bits++; | |
| } | |
| // No bits set in significand beyond the *first* exponent bit, | |
| // not just the significand; quantity is added to the exponent | |
| // to implement a carry out from rounding the significand. | |
| assert (0xf800 & signif_bits) == 0x0; | |
| return (short)(sign_bit | ( ((exp + 15) << 10) + signif_bits ) ); | |
| } | |
| /** | |
| * Compares two {@code Float} objects numerically. | |
| * | |
| * This method imposes a total order on {@code Float} objects | |
| * with two differences compared to the incomplete order defined by | |
| * the Java language numerical comparison operators ({@code <, <=, | |
| * ==, >=, >}) on {@code float} values. | |
| * | |
| * <ul><li> A NaN is <em>unordered</em> with respect to other | |
| * values and unequal to itself under the comparison | |
| * operators. This method chooses to define {@code | |
| * Float.NaN} to be equal to itself and greater than all | |
| * other {@code double} values (including {@code | |
| * Float.POSITIVE_INFINITY}). | |
| * | |
| * <li> Positive zero and negative zero compare equal | |
| * numerically, but are distinct and distinguishable values. | |
| * This method chooses to define positive zero ({@code +0.0f}), | |
| * to be greater than negative zero ({@code -0.0f}). | |
| * </ul> | |
| * | |
| * This ensures that the <i>natural ordering</i> of {@code Float} | |
| * objects imposed by this method is <i>consistent with | |
| * equals</i>; see {@linkplain Double##equivalenceRelation this | |
| * discussion for details of floating-point comparison and | |
| * ordering}. | |
| * | |
| * | |
| * @param anotherFloat the {@code Float} to be compared. | |
| * @return the value {@code 0} if {@code anotherFloat} is | |
| * numerically equal to this {@code Float}; a value | |
| * less than {@code 0} if this {@code Float} | |
| * is numerically less than {@code anotherFloat}; | |
| * and a value greater than {@code 0} if this | |
| * {@code Float} is numerically greater than | |
| * {@code anotherFloat}. | |
| * | |
| * @jls 15.20.1 Numerical Comparison Operators {@code <}, {@code <=}, {@code >}, and {@code >=} | |
| * @since 1.2 | |
| */ | |
| @Override | |
| public int compareTo(Float anotherFloat) { | |
| return Float.compare(value, anotherFloat.value); | |
| } | |
| /** | |
| * Compares the two specified {@code float} values. The sign | |
| * of the integer value returned is the same as that of the | |
| * integer that would be returned by the call: | |
| * <pre> | |
| * Float.valueOf(f1).compareTo(Float.valueOf(f2)) | |
| * </pre> | |
| * | |
| * @param f1 the first {@code float} to compare. | |
| * @param f2 the second {@code float} to compare. | |
| * @return the value {@code 0} if {@code f1} is | |
| * numerically equal to {@code f2}; a value less than | |
| * {@code 0} if {@code f1} is numerically less than | |
| * {@code f2}; and a value greater than {@code 0} | |
| * if {@code f1} is numerically greater than | |
| * {@code f2}. | |
| * @since 1.4 | |
| */ | |
| public static int compare(float f1, float f2) { | |
| if (f1 < f2) | |
| return -1; // Neither val is NaN, thisVal is smaller | |
| if (f1 > f2) | |
| return 1; // Neither val is NaN, thisVal is larger | |
| // Cannot use floatToRawIntBits because of possibility of NaNs. | |
| int thisBits = Float.floatToIntBits(f1); | |
| int anotherBits = Float.floatToIntBits(f2); | |
| return (thisBits == anotherBits ? 0 : // Values are equal | |
| (thisBits < anotherBits ? -1 : // (-0.0, 0.0) or (!NaN, NaN) | |
| 1)); // (0.0, -0.0) or (NaN, !NaN) | |
| } | |
| /** | |
| * Adds two {@code float} values together as per the + operator. | |
| * | |
| * @apiNote This method corresponds to the addition operation | |
| * defined in IEEE 754. | |
| * | |
| * @param a the first operand | |
| * @param b the second operand | |
| * @return the sum of {@code a} and {@code b} | |
| * @jls 4.2.4 Floating-Point Operations | |
| * @see java.util.function.BinaryOperator | |
| * @since 1.8 | |
| */ | |
| public static float sum(float a, float b) { | |
| return a + b; | |
| } | |
| /** | |
| * Returns the greater of two {@code float} values | |
| * as if by calling {@link Math#max(float, float) Math.max}. | |
| * | |
| * @apiNote | |
| * This method corresponds to the maximum operation defined in | |
| * IEEE 754. | |
| * | |
| * @param a the first operand | |
| * @param b the second operand | |
| * @return the greater of {@code a} and {@code b} | |
| * @see java.util.function.BinaryOperator | |
| * @since 1.8 | |
| */ | |
| public static float max(float a, float b) { | |
| return Math.max(a, b); | |
| } | |
| /** | |
| * Returns the smaller of two {@code float} values | |
| * as if by calling {@link Math#min(float, float) Math.min}. | |
| * | |
| * @apiNote | |
| * This method corresponds to the minimum operation defined in | |
| * IEEE 754. | |
| * | |
| * @param a the first operand | |
| * @param b the second operand | |
| * @return the smaller of {@code a} and {@code b} | |
| * @see java.util.function.BinaryOperator | |
| * @since 1.8 | |
| */ | |
| public static float min(float a, float b) { | |
| return Math.min(a, b); | |
| } | |
| /** | |
| * Returns an {@link Optional} containing the nominal descriptor for this | |
| * instance, which is the instance itself. | |
| * | |
| * @return an {@link Optional} describing the {@linkplain Float} instance | |
| * @since 12 | |
| */ | |
| @Override | |
| public Optional<Float> describeConstable() { | |
| return Optional.of(this); | |
| } | |
| /** | |
| * Resolves this instance as a {@link ConstantDesc}, the result of which is | |
| * the instance itself. | |
| * | |
| * @param lookup ignored | |
| * @return the {@linkplain Float} instance | |
| * @since 12 | |
| */ | |
| @Override | |
| public Float resolveConstantDesc(MethodHandles.Lookup lookup) { | |
| return this; | |
| } | |
| /** use serialVersionUID from JDK 1.0.2 for interoperability */ | |
| @java.io.Serial | |
| private static final long serialVersionUID = -2671257302660747028L; | |
| } |