Quelle Float.java

Sprache: JAVA

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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 wraps a value of primitive type
* {@code float} in an object. An object of type
* {@code Float} contains a single field whose type is
* {@code float}.
*
* 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}.
*
* 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 <a
* href="Double.html#equivalenceRelation">discussion of equality,
* equivalence, and comparison of floating-point values</a> that is
* equally applicable to {@code float} values.
*
* @see <a href="https://standards.ieee.org/ieee/754/6210/">
* <cite>IEEE Standard for Floating-Point Arithmetic</cite></a>
*
* @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 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}, (2-2-23)·2127.
 * 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}, 2-126. 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}, 2-149. 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.
 *
 * @since 1.5
 */
 public static final int SIZE = 32;

 /**
 * The number of bits in the significand of a {@code float} 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. 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.
 * 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.
 *
 * @since 1.8
 */
 public static final int BYTES = SIZE / Byte.SIZE;

 /**
 * The {@code Class} instance representing the primitive type
 * {@code float}.
 *
 * @since 1.1
 */
 @SuppressWarnings("unchecked")
 public static final Class<Float> TYPE = (Class<Float>) 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 m:
 * <ul>
 * <li>If m 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 m 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 m is positive and finite.
 * It is converted to a string in two stages:
 * <ul>
 * <li> Selection of a decimal:
 * A well-defined decimal dm
 * is selected to represent m.
 * This decimal is (almost always) the shortest one that
 * rounds to m according to the round to nearest
 * rounding policy of IEEE 754 floating-point arithmetic.
 * <li> Formatting as a string:
 * The decimal dm is formatted as a string,
 * either in plain or in computerized scientific notation,
 * depending on its value.
 * </ul>
 * </ul>
 * </ul>
 *
 * A decimal is a number of the form
 * s×10i
 * for some (unique) integers s > 0 and i such that
 * s is not a multiple of 10.
 * These integers are the significand and
 * the exponent, respectively, of the decimal.
 * The length of the decimal is the (unique)
 * positive integer n meeting
 * 10n-1 ≤ s < 10n.
 *
 * The decimal dm for a finite positive m
 * is defined as follows:
 * <ul>
 * <li>Let R be the set of all decimals that round to m
 * according to the usual round to nearest rounding policy of
 * IEEE 754 floating-point arithmetic.
 * <li>Let p be the minimal length over all decimals in R.
 * <li>When p ≥ 2, let T be the set of all decimals
 * in R with length p.
 * Otherwise, let T be the set of all decimals
 * in R with length 1 or 2.
 * <li>Define dm as the decimal in T
 * that is closest to m.
 * Or if there are two such decimals in T,
 * select the one with the even significand.
 * </ul>
 *
 * The (uniquely) selected decimal dm
 * is then formatted.
 * Let s, i and n be the significand, exponent and
 * length of dm, respectively.
 * Further, let e = n + i - 1 and let
 * s1…sn
 * be the usual decimal expansion of s.
 * Note that s1 ≠ 0
 * and sn ≠ 0.
 * Below, the decimal point {@code '.'} is {@code '\u005Cu002E'}
 * and the exponent indicator {@code 'E'} is {@code '\u005Cu0045'}.
 * <ul>
 * <li>Case -3 ≤ e < 0:
 * dm is formatted as
 * <code>0.0</code>…<code>0</code>s1…sn,
 * where there are exactly -(n + i) zeroes between
 * the decimal point and s1.
 * For example, 123 × 10-4 is formatted as
 * {@code 0.0123}.
 * <li>Case 0 ≤ e < 7:
 * <ul>
 * <li>Subcase i ≥ 0:
 * dm is formatted as
 * s1…sn<code>0</code>…<code>0.0</code>,
 * where there are exactly i zeroes
 * between sn and the decimal point.
 * For example, 123 × 102 is formatted as
 * {@code 12300.0}.
 * <li>Subcase i < 0:
 * dm is formatted as
 * s1…sn+i<code>.</code>sn+i+1…sn,
 * where there are exactly -i digits to the right of
 * the decimal point.
 * For example, 123 × 10-1 is formatted as
 * {@code 12.3}.
 * </ul>
 * <li>Case e < -3 or e ≥ 7:
 * computerized scientific notation is used to format
 * dm.
 * Here e is formatted as by {@link Integer#toString(int)}.
 * <ul>
 * <li>Subcase n = 1:
 * dm is formatted as
 * s1<code>.0E</code>e.
 * For example, 1 × 1023 is formatted as
 * {@code 1.0E23}.
 * <li>Subcase n > 1:
 * dm is formatted as
 * s1<code>.</code>s2…sn<code>E</code>e.
 * For example, 123 × 10-21 is formatted as
 * {@code 1.23E-19}.
 * </ul>
 * </ul>
 *
 * To create localized string representations of a floating-point
 * value, use subclasses of {@link java.text.NumberFormat}.
 *
 * @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 m:
 *
 * <ul>
 * <li>If m 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 m 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 m 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 m 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>
 * @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}.
 *
 * If {@code s} is {@code null}, then a
 * {@code NullPointerException} is thrown.
 *
 * 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 FloatValue as described by the lexical
 * syntax rules:
 *
 * <blockquote>
 * <dl>
 * <dt>FloatValue:
 * <dd>Signopt {@code NaN}
 * <dd>Signopt {@code Infinity}
 * <dd>Signopt FloatingPointLiteral
 * <dd>Signopt HexFloatingPointLiteral
 * <dd>SignedInteger
 * </dl>
 *
 * <dl>
 * <dt>HexFloatingPointLiteral:
 * <dd> HexSignificand BinaryExponent FloatTypeSuffixopt
 * </dl>
 *
 * <dl>
 * <dt>HexSignificand:
 * <dd>HexNumeral
 * <dd>HexNumeral {@code .}
 * <dd>{@code 0x} HexDigitsopt
 * {@code .} HexDigits
 * <dd>{@code 0X} HexDigitsopt
 * {@code .} HexDigits
 * </dl>
 *
 * <dl>
 * <dt>BinaryExponent:
 * <dd>BinaryExponentIndicator SignedInteger
 * </dl>
 *
 * <dl>
 * <dt>BinaryExponentIndicator:
 * <dd>{@code p}
 * <dd>{@code P}
 * </dl>
 *
 * </blockquote>
 *
 * where Sign, FloatingPointLiteral,
 * HexNumeral, HexDigits, SignedInteger and
 * FloatTypeSuffix 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 FloatValue, 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.
 *
 * To interpret localized string representations of a
 * floating-point value, use subclasses of {@link
 * java.text.NumberFormat}.
 *
 * 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
 * not 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
 * not 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 
 * {@code "1.00000017881393421514957253748434595763683319091796875001d"} 
 * results in the {@code float} value
 * {@code 1.0000002f}; if the string is converted directly to
 * {@code float}, <code>1.0000001f</code> results.
 *
 * 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.
 *
 * @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.
 */
 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)
 * @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", forRemoval = true)
 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", forRemoval = true)
 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", forRemoval = true)
 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
 */
 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
 */
 public short shortValue() {
 return (short)value;
 }

 /**
 * Returns the value of this {@code Float} as an {@code int} after
 * a narrowing primitive conversion.
 *
 * @return the {@code float} value represented by this object
 * converted to type {@code int}
 * @jls 5.1.3 Narrowing Primitive Conversion
 */
 public int intValue() {
 return (int)value;
 }

 /**
 * Returns value of this {@code Float} as a {@code long} after a
 * narrowing primitive conversion.
 *
 * @return the {@code float} value represented by this object
 * converted to type {@code long}
 * @jls 5.1.3 Narrowing Primitive Conversion
 */
 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
 */
 @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
 */
 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
 * not define an equivalence relation and to satisfy the
 * {@linkplain Object#equals equals contract} an equivalence
 * relation must be implemented; see <a
 * href="Double.html#equivalenceRelation">this discussion</a> 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)
 && (floatToIntBits(((Float)obj).value) == floatToIntBits(value));
 }

 /**
 * Returns a representation of the specified floating-point value
 * according to the IEEE 754 floating-point "single format" bit
 * layout.
 *
 * 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.
 *
 * If the argument is positive infinity, the result is
 * {@code 0x7f800000}.
 *
 * If the argument is negative infinity, the result is
 * {@code 0xff800000}.
 *
 * If the argument is NaN, the result is {@code 0x7fc00000}.
 *
 * 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.
 *
 * 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.
 *
 * If the argument is positive infinity, the result is
 * {@code 0x7f800000}.
 *
 * If the argument is negative infinity, the result is
 * {@code 0xff800000}.
 *
 * 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.
 *
 * 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.
 *
 * If the argument is {@code 0x7f800000}, the result is positive
 * infinity.
 *
 * If the argument is {@code 0xff800000}, the result is negative
 * infinity.
 *
 * 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.
 *
 * In all other cases, let s, e, and m 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 s·m·2e-150.
 *
 * 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 signaling NaNs. 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
 * not 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,
 * Emax = 15, and
 * Emin = -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 <a href="#binary16Format">binary16 format</a> 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 sigificand; 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 unordered 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 natural ordering of {@code Float}
 * objects imposed by this method is consistent with
 * equals; see <a href="Double.html#equivalenceRelation">this
 * discussion</a> 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
 */
 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;
}

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