/* * 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}. * *

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 value-based * 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. * *

Floating-point Equality, Equivalence, * and Comparison

* * 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. * *

Decimal ↔ Binary Conversion Issues

* * 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, 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}, (2-2-23)·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, * {@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 * The Java Language Specification. * * @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 TYPE = Class.getPrimitiveClass("float"); /** * Returns a string representation of the {@code float} * argument. All characters mentioned below are ASCII characters. * * *

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: *

* *

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'}. *

* *

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. * *

* * * * * * * * * * * * * * * * * * * * * * *
Examples
Floating-point ValueHexadecimal String
{@code 1.0} {@code 0x1.0p0}
{@code -1.0} {@code -0x1.0p0}
{@code 2.0} {@code 0x1.0p1}
{@code 3.0} {@code 0x1.8p1}
{@code 0.5} {@code 0x1.0p-1}
{@code 0.25} {@code 0x1.0p-2}
{@code Float.MAX_VALUE}{@code 0x1.fffffep127}
{@code Minimum Normal Value}{@code 0x1.0p-126}
{@code Maximum Subnormal Value}{@code 0x0.fffffep-126}
{@code Float.MIN_VALUE}{@code 0x0.000002p-126}
* * @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}. * *

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: * *

*
*
FloatValue: *
Signopt {@code NaN} *
Signopt {@code Infinity} *
Signopt FloatingPointLiteral *
Signopt HexFloatingPointLiteral *
SignedInteger *
* *
*
HexFloatingPointLiteral: *
HexSignificand BinaryExponent FloatTypeSuffixopt *
* *
*
HexSignificand: *
HexNumeral *
HexNumeral {@code .} *
{@code 0x} HexDigitsopt * {@code .} HexDigits *
{@code 0X} HexDigitsopt * {@code .} HexDigits *
* *
*
BinaryExponent: *
BinaryExponentIndicator SignedInteger *
* *
*
BinaryExponentIndicator: *
{@code p} *
{@code P} *
* *
* * where Sign, FloatingPointLiteral, * HexNumeral, HexDigits, SignedInteger and * FloatTypeSuffix are as defined in the lexical structure * sections of * The Java Language Specification, * 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. * *

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}, 1.0000001f 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. * * @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 * not 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. * *

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: *

* *

IEEE 754 binary16 format

* 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: * * * 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. * * * * This ensures that the natural ordering of {@code Float} * objects imposed by this method is consistent with * equals; 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: * 
     *    Float.valueOf(f1).compareTo(Float.valueOf(f2))
     *
* * @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 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; }