https://source.android.com/ 
/*
 * Copyright (C) 2016 The Android Open Source Project
 *
 * Licensed under the Apache License, Version 2.0 (the "License");
 * you may not use this file except in compliance with the License.
 * You may obtain a copy of the License at
 *
 *      http://www.apache.org/licenses/LICENSE-2.0
 *
 * Unless required by applicable law or agreed to in writing, software
 * distributed under the License is distributed on an "AS IS" BASIS,
 * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
 * See the License for the specific language governing permissions and
 * limitations under the License.
 */

package android.util;

import android.annotation.HalfFloat;
import android.annotation.NonNull;
import android.annotation.Nullable;

import sun.misc.FloatingDecimal;


The Half class is a wrapper and a utility class to manipulate half-precision 16-bit IEEE 754
floating point data types (also called fp16 or binary16). A half-precision float can be
created from or converted to single-precision floats, and is stored in a short data type.
To distinguish short values holding half-precision floats from regular short values,
it is recommended to use the @HalfFloat annotation.


The IEEE 754 standard specifies an fp16 as having the following format:


    

  • Sign bit: 1 bit
    • 

  • Exponent width: 5 bits
    • 

  • Significand: 10 bits
    • 



The format is laid out as follows:


1   11111   1111111111
^   --^--   -----^----
sign  |          |_______ significand
      |
      -- exponent



Half-precision floating points can be useful to save memory and/or
bandwidth at the expense of range and precision when compared to single-precision
floating points (fp32).


To help you decide whether fp16 is the right storage type for you need, please
refer to the table below that shows the available precision throughout the range of
possible values. The precision column indicates the step size between two
consecutive numbers in a specific part of the range.



    
Range startPrecision

    
01 ⁄ 16,777,216

    
1 ⁄ 16,3841 ⁄ 16,777,216

    
1 ⁄ 8,1921 ⁄ 8,388,608

    
1 ⁄ 4,0961 ⁄ 4,194,304

    
1 ⁄ 2,0481 ⁄ 2,097,152

    
1 ⁄ 1,0241 ⁄ 1,048,576

    
1 ⁄ 5121 ⁄ 524,288

    
1 ⁄ 2561 ⁄ 262,144

    
1 ⁄ 1281 ⁄ 131,072

    
1 ⁄ 641 ⁄ 65,536

    
1 ⁄ 321 ⁄ 32,768

    
1 ⁄ 161 ⁄ 16,384

    
1 ⁄ 81 ⁄ 8,192

    
1 ⁄ 41 ⁄ 4,096

    
1 ⁄ 21 ⁄ 2,048

    
11 ⁄ 1,024

    
21 ⁄ 512

    
41 ⁄ 256

    
81 ⁄ 128

    
161 ⁄ 64

    
321 ⁄ 32

    
641 ⁄ 16

    
1281 ⁄ 8

    
2561 ⁄ 4

    
5121 ⁄ 2

    
1,0241

    
2,0482

    
4,0964

    
8,1928

    
16,38416

    
32,76832




This table shows that numbers higher than 1024 lose all fractional precision.


/**
 * <p>The {@code Half} class is a wrapper and a utility class to manipulate half-precision 16-bit
 * <a href="https://en.wikipedia.org/wiki/Half-precision_floating-point_format">IEEE 754</a>
 * floating point data types (also called fp16 or binary16). A half-precision float can be
 * created from or converted to single-precision floats, and is stored in a short data type.
 * To distinguish short values holding half-precision floats from regular short values,
 * it is recommended to use the <code>@HalfFloat</code> annotation.</p>
 *
 * <p>The IEEE 754 standard specifies an fp16 as having the following format:</p>
 * <ul>
 * <li>Sign bit: 1 bit</li>
 * <li>Exponent width: 5 bits</li>
 * <li>Significand: 10 bits</li>
 * </ul>
 *
 * <p>The format is laid out as follows:</p>
 * <pre>
 * 1   11111   1111111111
 * ^   --^--   -----^----
 * sign  |          |_______ significand
 *       |
 *       -- exponent
 * </pre>
 *
 * <p>Half-precision floating points can be useful to save memory and/or
 * bandwidth at the expense of range and precision when compared to single-precision
 * floating points (fp32).</p>
 * <p>To help you decide whether fp16 is the right storage type for you need, please
 * refer to the table below that shows the available precision throughout the range of
 * possible values. The <em>precision</em> column indicates the step size between two
 * consecutive numbers in a specific part of the range.</p>
 *
 * <table summary="Precision of fp16 across the range">
 *     <tr><th>Range start</th><th>Precision</th></tr>
 *     <tr><td>0</td><td>1 &frasl; 16,777,216</td></tr>
 *     <tr><td>1 &frasl; 16,384</td><td>1 &frasl; 16,777,216</td></tr>
 *     <tr><td>1 &frasl; 8,192</td><td>1 &frasl; 8,388,608</td></tr>
 *     <tr><td>1 &frasl; 4,096</td><td>1 &frasl; 4,194,304</td></tr>
 *     <tr><td>1 &frasl; 2,048</td><td>1 &frasl; 2,097,152</td></tr>
 *     <tr><td>1 &frasl; 1,024</td><td>1 &frasl; 1,048,576</td></tr>
 *     <tr><td>1 &frasl; 512</td><td>1 &frasl; 524,288</td></tr>
 *     <tr><td>1 &frasl; 256</td><td>1 &frasl; 262,144</td></tr>
 *     <tr><td>1 &frasl; 128</td><td>1 &frasl; 131,072</td></tr>
 *     <tr><td>1 &frasl; 64</td><td>1 &frasl; 65,536</td></tr>
 *     <tr><td>1 &frasl; 32</td><td>1 &frasl; 32,768</td></tr>
 *     <tr><td>1 &frasl; 16</td><td>1 &frasl; 16,384</td></tr>
 *     <tr><td>1 &frasl; 8</td><td>1 &frasl; 8,192</td></tr>
 *     <tr><td>1 &frasl; 4</td><td>1 &frasl; 4,096</td></tr>
 *     <tr><td>1 &frasl; 2</td><td>1 &frasl; 2,048</td></tr>
 *     <tr><td>1</td><td>1 &frasl; 1,024</td></tr>
 *     <tr><td>2</td><td>1 &frasl; 512</td></tr>
 *     <tr><td>4</td><td>1 &frasl; 256</td></tr>
 *     <tr><td>8</td><td>1 &frasl; 128</td></tr>
 *     <tr><td>16</td><td>1 &frasl; 64</td></tr>
 *     <tr><td>32</td><td>1 &frasl; 32</td></tr>
 *     <tr><td>64</td><td>1 &frasl; 16</td></tr>
 *     <tr><td>128</td><td>1 &frasl; 8</td></tr>
 *     <tr><td>256</td><td>1 &frasl; 4</td></tr>
 *     <tr><td>512</td><td>1 &frasl; 2</td></tr>
 *     <tr><td>1,024</td><td>1</td></tr>
 *     <tr><td>2,048</td><td>2</td></tr>
 *     <tr><td>4,096</td><td>4</td></tr>
 *     <tr><td>8,192</td><td>8</td></tr>
 *     <tr><td>16,384</td><td>16</td></tr>
 *     <tr><td>32,768</td><td>32</td></tr>
 * </table>
 *
 * <p>This table shows that numbers higher than 1024 lose all fractional precision.</p>
 */
@SuppressWarnings("SimplifiableIfStatement")
public final class Half extends Number implements Comparable<Half> {
    
The number of bits used to represent a half-precision float value.

/**
     * The number of bits used to represent a half-precision float value.
     */
    public static final int SIZE = 16;

    
Epsilon is the difference between 1.0 and the next value representable
by a half-precision floating-point.

/**
     * Epsilon is the difference between 1.0 and the next value representable
     * by a half-precision floating-point.
     */
    public static final @HalfFloat short EPSILON = (short) 0x1400;

    
Maximum exponent a finite half-precision float may have.

/**
     * Maximum exponent a finite half-precision float may have.
     */
    public static final int MAX_EXPONENT = 15;
    
Minimum exponent a normalized half-precision float may have.

/**
     * Minimum exponent a normalized half-precision float may have.
     */
    public static final int MIN_EXPONENT = -14;

    
Smallest negative value a half-precision float may have.

/**
     * Smallest negative value a half-precision float may have.
     */
    public static final @HalfFloat short LOWEST_VALUE = (short) 0xfbff;
    
Maximum positive finite value a half-precision float may have.

/**
     * Maximum positive finite value a half-precision float may have.
     */
    public static final @HalfFloat short MAX_VALUE = (short) 0x7bff;
    
Smallest positive normal value a half-precision float may have.

/**
     * Smallest positive normal value a half-precision float may have.
     */
    public static final @HalfFloat short MIN_NORMAL = (short) 0x0400;
    
Smallest positive non-zero value a half-precision float may have.

/**
     * Smallest positive non-zero value a half-precision float may have.
     */
    public static final @HalfFloat short MIN_VALUE = (short) 0x0001;
    
A Not-a-Number representation of a half-precision float.

/**
     * A Not-a-Number representation of a half-precision float.
     */
    public static final @HalfFloat short NaN = (short) 0x7e00;
    
Negative infinity of type half-precision float.

/**
     * Negative infinity of type half-precision float.
     */
    public static final @HalfFloat short NEGATIVE_INFINITY = (short) 0xfc00;
    
Negative 0 of type half-precision float.

/**
     * Negative 0 of type half-precision float.
     */
    public static final @HalfFloat short NEGATIVE_ZERO = (short) 0x8000;
    
Positive infinity of type half-precision float.

/**
     * Positive infinity of type half-precision float.
     */
    public static final @HalfFloat short POSITIVE_INFINITY = (short) 0x7c00;
    
Positive 0 of type half-precision float.

/**
     * Positive 0 of type half-precision float.
     */
    public static final @HalfFloat short POSITIVE_ZERO = (short) 0x0000;

    private static final int FP16_SIGN_SHIFT        = 15;
    private static final int FP16_SIGN_MASK         = 0x8000;
    private static final int FP16_EXPONENT_SHIFT    = 10;
    private static final int FP16_EXPONENT_MASK     = 0x1f;
    private static final int FP16_SIGNIFICAND_MASK  = 0x3ff;
    private static final int FP16_EXPONENT_BIAS     = 15;
    private static final int FP16_COMBINED          = 0x7fff;
    private static final int FP16_EXPONENT_MAX      = 0x7c00;

    private static final int FP32_SIGN_SHIFT        = 31;
    private static final int FP32_EXPONENT_SHIFT    = 23;
    private static final int FP32_EXPONENT_MASK     = 0xff;
    private static final int FP32_SIGNIFICAND_MASK  = 0x7fffff;
    private static final int FP32_EXPONENT_BIAS     = 127;

    private static final int FP32_DENORMAL_MAGIC = 126 << 23;
    private static final float FP32_DENORMAL_FLOAT = Float.intBitsToFloat(FP32_DENORMAL_MAGIC);

    private final @HalfFloat short mValue;

    
Constructs a newly allocated Half object that represents the half-precision float type argument. 
Params:
  • value – The value to be represented by the Half
/**
     * Constructs a newly allocated {@code Half} object that represents the
     * half-precision float type argument.
     *
     * @param value The value to be represented by the {@code Half}
     */
    public Half(@HalfFloat short value) {
        mValue = value;
    }

    
Constructs a newly allocated Half object that represents the argument converted to a half-precision float. 
Params:
  • value – The value to be represented by the Half
See Also:
/**
     * Constructs a newly allocated {@code Half} object that represents the
     * argument converted to a half-precision float.
     *
     * @param value The value to be represented by the {@code Half}
     *
     * @see #toHalf(float)
     */
    public Half(float value) {
        mValue = toHalf(value);
    }

    
Constructs a newly allocated Half object that represents the argument converted to a half-precision float. 
Params:
  • value – The value to be represented by the Half
See Also:
/**
     * Constructs a newly allocated {@code Half} object that
     * represents the argument converted to a half-precision float.
     *
     * @param value The value to be represented by the {@code Half}
     *
     * @see #toHalf(float)
     */
    public Half(double value) {
        mValue = toHalf((float) value);
    }

    
Constructs a newly allocated Half object that represents the half-precision float value represented by the string. The string is converted to a half-precision float value as if by the valueOf(String) method.


Calling this constructor is equivalent to calling:


    new Half(Float.parseFloat(value))



Params:
  • value – A string to be converted to a Half
Throws:
See Also:
/**
     * <p>Constructs a newly allocated {@code Half} object that represents the
     * half-precision float value represented by the string.
     * The string is converted to a half-precision float value as if by the
     * {@link #valueOf(String)} method.</p>
     *
     * <p>Calling this constructor is equivalent to calling:</p>
     * <pre>
     *     new Half(Float.parseFloat(value))
     * </pre>
     *
     * @param value A string to be converted to a {@code Half}
     * @throws NumberFormatException if the string does not contain a parsable number
     *
     * @see Float#valueOf(java.lang.String)
     * @see #toHalf(float)
     */
    public Half(@NonNull String value) throws NumberFormatException {
        mValue = toHalf(Float.parseFloat(value));
    }

    
Returns the half-precision value of this Half as a short containing the bit representation described in Half. 
Returns:The half-precision float value represented by this object
/**
     * Returns the half-precision value of this {@code Half} as a {@code short}
     * containing the bit representation described in {@link Half}.
     *
     * @return The half-precision float value represented by this object
     */
    public @HalfFloat short halfValue() {
        return mValue;
    }

    
Returns the value of this Half as a byte after a narrowing primitive conversion. 
Returns:The half-precision float value represented by this object converted to type byte
/**
     * Returns the value of this {@code Half} as a {@code byte} after
     * a narrowing primitive conversion.
     *
     * @return The half-precision float value represented by this object
     *         converted to type {@code byte}
     */
    @Override
    public byte byteValue() {
        return (byte) toFloat(mValue);
    }

    
Returns the value of this Half as a short after a narrowing primitive conversion. 
Returns:The half-precision float value represented by this object converted to type short
/**
     * Returns the value of this {@code Half} as a {@code short} after
     * a narrowing primitive conversion.
     *
     * @return The half-precision float value represented by this object
     *         converted to type {@code short}
     */
    @Override
    public short shortValue() {
        return (short) toFloat(mValue);
    }

    
Returns the value of this Half as a int after a narrowing primitive conversion. 
Returns:The half-precision float value represented by this object converted to type int
/**
     * Returns the value of this {@code Half} as a {@code int} after
     * a narrowing primitive conversion.
     *
     * @return The half-precision float value represented by this object
     *         converted to type {@code int}
     */
    @Override
    public int intValue() {
        return (int) toFloat(mValue);
    }

    
Returns the value of this Half as a long after a narrowing primitive conversion. 
Returns:The half-precision float value represented by this object converted to type long
/**
     * Returns the value of this {@code Half} as a {@code long} after
     * a narrowing primitive conversion.
     *
     * @return The half-precision float value represented by this object
     *         converted to type {@code long}
     */
    @Override
    public long longValue() {
        return (long) toFloat(mValue);
    }

    
Returns the value of this Half as a float after a widening primitive conversion. 
Returns:The half-precision float value represented by this object converted to type float
/**
     * Returns the value of this {@code Half} as a {@code float} after
     * a widening primitive conversion.
     *
     * @return The half-precision float value represented by this object
     *         converted to type {@code float}
     */
    @Override
    public float floatValue() {
        return toFloat(mValue);
    }

    
Returns the value of this Half as a double after a widening primitive conversion. 
Returns:The half-precision float value represented by this object converted to type double
/**
     * Returns the value of this {@code Half} as a {@code double} after
     * a widening primitive conversion.
     *
     * @return The half-precision float value represented by this object
     *         converted to type {@code double}
     */
    @Override
    public double doubleValue() {
        return toFloat(mValue);
    }

    
Returns true if this Half value represents a Not-a-Number, false otherwise. 
Returns:True if the value is a NaN, false otherwise
/**
     * Returns true if this {@code Half} value represents a Not-a-Number,
     * false otherwise.
     *
     * @return True if the value is a NaN, false otherwise
     */
    public boolean isNaN() {
        return isNaN(mValue);
    }

    
Compares this object against the specified object. The result is true if and only if the argument is not null and is a Half object that represents the same half-precision value as the this object. Two half-precision values are considered to be the same if and only if the method halfToIntBits(short) returns an identical int value for both. 
Params:
  • o – The object to compare
See Also:
Returns:True if the objects are the same, false otherwise
/**
     * 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 Half} object
     * that represents the same half-precision value as the this object. Two
     * half-precision values are considered to be the same if and only if the method
     * {@link #halfToIntBits(short)} returns an identical {@code int} value for both.
     *
     * @param o The object to compare
     * @return True if the objects are the same, false otherwise
     *
     * @see #halfToIntBits(short)
     */
    @Override
    public boolean equals(@Nullable Object o) {
        return (o instanceof Half) &&
                (halfToIntBits(((Half) o).mValue) == halfToIntBits(mValue));
    }

    
Returns a hash code for this Half object. The result is the integer bit representation, exactly as produced by the method halfToIntBits(short), of the primitive half-precision float value represented by this Half object. 
Returns:A hash code value for this object
/**
     * Returns a hash code for this {@code Half} object. The result is the
     * integer bit representation, exactly as produced by the method
     * {@link #halfToIntBits(short)}, of the primitive half-precision float
     * value represented by this {@code Half} object.
     *
     * @return A hash code value for this object
     */
    @Override
    public int hashCode() {
        return hashCode(mValue);
    }

    
Returns a string representation of the specified half-precision float value. See toString(short) for more information. 
Returns:A string representation of this Half object
/**
     * Returns a string representation of the specified half-precision
     * float value. See {@link #toString(short)} for more information.
     *
     * @return A string representation of this {@code Half} object
     */
    @NonNull
    @Override
    public String toString() {
        return toString(mValue);
    }

    
Compares the two specified half-precision float values. The following
conditions apply during the comparison:


    

  • NaN is considered by this method to be equal to itself and greater than all other half-precision float values (including #POSITIVE_INFINITY)
    • 

  • POSITIVE_ZERO is considered by this method to be greater than NEGATIVE_ZERO.
    • 



Params:
  • h – The half-precision float value to compare to the half-precision value represented by this Half object
Returns: The value 0 if x is numerically equal to y; a value less than 0 if x is numerically less than y; and a value greater than 0 if x is numerically greater than y
/**
     * <p>Compares the two specified half-precision float values. The following
     * conditions apply during the comparison:</p>
     *
     * <ul>
     * <li>{@link #NaN} is considered by this method to be equal to itself and greater
     * than all other half-precision float values (including {@code #POSITIVE_INFINITY})</li>
     * <li>{@link #POSITIVE_ZERO} is considered by this method to be greater than
     * {@link #NEGATIVE_ZERO}.</li>
     * </ul>
     *
     * @param h The half-precision float value to compare to the half-precision value
     *          represented by this {@code Half} object
     *
     * @return  The value {@code 0} if {@code x} is numerically equal to {@code y}; a
     *          value less than {@code 0} if {@code x} is numerically less than {@code y};
     *          and a value greater than {@code 0} if {@code x} is numerically greater
     *          than {@code y}
     */
    @Override
    public int compareTo(@NonNull Half h) {
        return compare(mValue, h.mValue);
    }

    
Returns a hash code for a half-precision float value.

Params:
  • h – The value to hash
Returns:A hash code value for a half-precision float value
/**
     * Returns a hash code for a half-precision float value.
     *
     * @param h The value to hash
     *
     * @return A hash code value for a half-precision float value
     */
    public static int hashCode(@HalfFloat short h) {
        return halfToIntBits(h);
    }

    
Compares the two specified half-precision float values. The following
conditions apply during the comparison:


    

  • NaN is considered by this method to be equal to itself and greater than all other half-precision float values (including #POSITIVE_INFINITY)
    • 

  • POSITIVE_ZERO is considered by this method to be greater than NEGATIVE_ZERO.
    • 



Params:
  • x – The first half-precision float value to compare.
  • y – The second half-precision float value to compare
Returns: The value 0 if x is numerically equal to y, a value less than 0 if x is numerically less than y, and a value greater than 0 if x is numerically greater than y
/**
     * <p>Compares the two specified half-precision float values. The following
     * conditions apply during the comparison:</p>
     *
     * <ul>
     * <li>{@link #NaN} is considered by this method to be equal to itself and greater
     * than all other half-precision float values (including {@code #POSITIVE_INFINITY})</li>
     * <li>{@link #POSITIVE_ZERO} is considered by this method to be greater than
     * {@link #NEGATIVE_ZERO}.</li>
     * </ul>
     *
     * @param x The first half-precision float value to compare.
     * @param y The second half-precision float value to compare
     *
     * @return  The value {@code 0} if {@code x} is numerically equal to {@code y}, a
     *          value less than {@code 0} if {@code x} is numerically less than {@code y},
     *          and a value greater than {@code 0} if {@code x} is numerically greater
     *          than {@code y}
     */
    public static int compare(@HalfFloat short x, @HalfFloat short y) {
        if (less(x, y)) return -1;
        if (greater(x, y)) return 1;

        // Collapse NaNs, akin to halfToIntBits(), but we want to keep
        // (signed) short value types to preserve the ordering of -0.0
        // and +0.0
        short xBits = (x & FP16_COMBINED) > FP16_EXPONENT_MAX ? NaN : x;
        short yBits = (y & FP16_COMBINED) > FP16_EXPONENT_MAX ? NaN : y;

        return (xBits == yBits ? 0 : (xBits < yBits ? -1 : 1));
    }

    
Returns a representation of the specified half-precision float value according to the bit layout described in Half.


Similar to halfToIntBits(short), this method collapses all possible Not-a-Number values to a single canonical Not-a-Number value defined by NaN.


Params:
  • h – A half-precision float value
See Also:
Returns:The bits that represent the half-precision float value
/**
     * <p>Returns a representation of the specified half-precision float value
     * according to the bit layout described in {@link Half}.</p>
     *
     * <p>Similar to {@link #halfToIntBits(short)}, this method collapses all
     * possible Not-a-Number values to a single canonical Not-a-Number value
     * defined by {@link #NaN}.</p>
     *
     * @param h A half-precision float value
     * @return The bits that represent the half-precision float value
     *
     * @see #halfToIntBits(short)
     */
    public static @HalfFloat short halfToShortBits(@HalfFloat short h) {
        return (h & FP16_COMBINED) > FP16_EXPONENT_MAX ? NaN : h;
    }

    
Returns a representation of the specified half-precision float value according to the bit layout described in Half.


Unlike halfToRawIntBits(short), this method collapses all possible Not-a-Number values to a single canonical Not-a-Number value defined by NaN.


Params:
  • h – A half-precision float value
See Also:
Returns:The bits that represent the half-precision float value
/**
     * <p>Returns a representation of the specified half-precision float value
     * according to the bit layout described in {@link Half}.</p>
     *
     * <p>Unlike {@link #halfToRawIntBits(short)}, this method collapses all
     * possible Not-a-Number values to a single canonical Not-a-Number value
     * defined by {@link #NaN}.</p>
     *
     * @param h A half-precision float value
     * @return The bits that represent the half-precision float value
     *
     * @see #halfToRawIntBits(short)
     * @see #halfToShortBits(short)
     * @see #intBitsToHalf(int)
     */
    public static int halfToIntBits(@HalfFloat short h) {
        return (h & FP16_COMBINED) > FP16_EXPONENT_MAX ? NaN : h & 0xffff;
    }

    
Returns a representation of the specified half-precision float value according to the bit layout described in Half.


The argument is considered to be a representation of a half-precision float value according to the bit layout described in Half. The 16 most significant bits of the returned value are set to 0.


Params:
  • h – A half-precision float value
See Also:
Returns:The bits that represent the half-precision float value
/**
     * <p>Returns a representation of the specified half-precision float value
     * according to the bit layout described in {@link Half}.</p>
     *
     * <p>The argument is considered to be a representation of a half-precision
     * float value according to the bit layout described in {@link Half}. The 16
     * most significant bits of the returned value are set to 0.</p>
     *
     * @param h A half-precision float value
     * @return The bits that represent the half-precision float value
     *
     * @see #halfToIntBits(short)
     * @see #intBitsToHalf(int)
     */
    public static int halfToRawIntBits(@HalfFloat short h) {
        return h & 0xffff;
    }

    
Returns the half-precision float value corresponding to a given
bit representation.


The argument is considered to be a representation of a half-precision float value according to the bit layout described in Half. The 16 most significant bits of the argument are ignored.


Params:
  • bits – An integer
Returns:The half-precision float value with the same bit pattern
/**
     * <p>Returns the half-precision float value corresponding to a given
     * bit representation.</p>
     *
     * <p>The argument is considered to be a representation of a half-precision
     * float value according to the bit layout described in {@link Half}. The 16
     * most significant bits of the argument are ignored.</p>
     *
     * @param bits An integer
     * @return The half-precision float value with the same bit pattern
     */
    public static @HalfFloat short intBitsToHalf(int bits) {
        return (short) (bits & 0xffff);
    }

    
Returns the first parameter with the sign of the second parameter.
This method treats NaNs as having a sign.

Params:
  • magnitude – A half-precision float value providing the magnitude of the result
  • sign –  A half-precision float value providing the sign of the result
Returns:A value with the magnitude of the first parameter and the sign
        of the second parameter
/**
     * Returns the first parameter with the sign of the second parameter.
     * This method treats NaNs as having a sign.
     *
     * @param magnitude A half-precision float value providing the magnitude of the result
     * @param sign  A half-precision float value providing the sign of the result
     * @return A value with the magnitude of the first parameter and the sign
     *         of the second parameter
     */
    public static @HalfFloat short copySign(@HalfFloat short magnitude, @HalfFloat short sign) {
        return (short) ((sign & FP16_SIGN_MASK) | (magnitude & FP16_COMBINED));
    }

    
Returns the absolute value of the specified half-precision float.
Special values are handled in the following ways:

    

  • If the specified half-precision float is NaN, the result is NaN
    • 

  • If the specified half-precision float is zero (negative or positive), the result is positive zero (see POSITIVE_ZERO)
    • 

  • If the specified half-precision float is infinity (negative or positive), the result is positive infinity (see POSITIVE_INFINITY)
    • 



Params:
  • h – A half-precision float value
Returns:The absolute value of the specified half-precision float
/**
     * Returns the absolute value of the specified half-precision float.
     * Special values are handled in the following ways:
     * <ul>
     * <li>If the specified half-precision float is NaN, the result is NaN</li>
     * <li>If the specified half-precision float is zero (negative or positive),
     * the result is positive zero (see {@link #POSITIVE_ZERO})</li>
     * <li>If the specified half-precision float is infinity (negative or positive),
     * the result is positive infinity (see {@link #POSITIVE_INFINITY})</li>
     * </ul>
     *
     * @param h A half-precision float value
     * @return The absolute value of the specified half-precision float
     */
    public static @HalfFloat short abs(@HalfFloat short h) {
        return (short) (h & FP16_COMBINED);
    }

    
Returns the closest integral half-precision float value to the specified
half-precision float value. Special values are handled in the
following ways:

    

  • If the specified half-precision float is NaN, the result is NaN
    • 

  • If the specified half-precision float is infinity (negative or positive),
the result is infinity (with the same sign)
    • 

  • If the specified half-precision float is zero (negative or positive),
the result is zero (with the same sign)
    • 



Params:
  • h – A half-precision float value
Returns:The value of the specified half-precision float rounded to the nearest
        half-precision float value
/**
     * Returns the closest integral half-precision float value to the specified
     * half-precision float value. Special values are handled in the
     * following ways:
     * <ul>
     * <li>If the specified half-precision float is NaN, the result is NaN</li>
     * <li>If the specified half-precision float is infinity (negative or positive),
     * the result is infinity (with the same sign)</li>
     * <li>If the specified half-precision float is zero (negative or positive),
     * the result is zero (with the same sign)</li>
     * </ul>
     *
     * @param h A half-precision float value
     * @return The value of the specified half-precision float rounded to the nearest
     *         half-precision float value
     */
    public static @HalfFloat short round(@HalfFloat short h) {
        int bits = h & 0xffff;
        int e = bits & 0x7fff;
        int result = bits;

        if (e < 0x3c00) {
            result &= FP16_SIGN_MASK;
            result |= (0x3c00 & (e >= 0x3800 ? 0xffff : 0x0));
        } else if (e < 0x6400) {
            e = 25 - (e >> 10);
            int mask = (1 << e) - 1;
            result += (1 << (e - 1));
            result &= ~mask;
        }

        return (short) result;
    }

    
Returns the smallest half-precision float value toward negative infinity
greater than or equal to the specified half-precision float value.
Special values are handled in the following ways:

    

  • If the specified half-precision float is NaN, the result is NaN
    • 

  • If the specified half-precision float is infinity (negative or positive),
the result is infinity (with the same sign)
    • 

  • If the specified half-precision float is zero (negative or positive),
the result is zero (with the same sign)
    • 



Params:
  • h – A half-precision float value
Returns:The smallest half-precision float value toward negative infinity
        greater than or equal to the specified half-precision float value
/**
     * Returns the smallest half-precision float value toward negative infinity
     * greater than or equal to the specified half-precision float value.
     * Special values are handled in the following ways:
     * <ul>
     * <li>If the specified half-precision float is NaN, the result is NaN</li>
     * <li>If the specified half-precision float is infinity (negative or positive),
     * the result is infinity (with the same sign)</li>
     * <li>If the specified half-precision float is zero (negative or positive),
     * the result is zero (with the same sign)</li>
     * </ul>
     *
     * @param h A half-precision float value
     * @return The smallest half-precision float value toward negative infinity
     *         greater than or equal to the specified half-precision float value
     */
    public static @HalfFloat short ceil(@HalfFloat short h) {
        int bits = h & 0xffff;
        int e = bits & 0x7fff;
        int result = bits;

        if (e < 0x3c00) {
            result &= FP16_SIGN_MASK;
            result |= 0x3c00 & -(~(bits >> 15) & (e != 0 ? 1 : 0));
        } else if (e < 0x6400) {
            e = 25 - (e >> 10);
            int mask = (1 << e) - 1;
            result += mask & ((bits >> 15) - 1);
            result &= ~mask;
        }

        return (short) result;
    }

    
Returns the largest half-precision float value toward positive infinity
less than or equal to the specified half-precision float value.
Special values are handled in the following ways:

    

  • If the specified half-precision float is NaN, the result is NaN
    • 

  • If the specified half-precision float is infinity (negative or positive),
the result is infinity (with the same sign)
    • 

  • If the specified half-precision float is zero (negative or positive),
the result is zero (with the same sign)
    • 



Params:
  • h – A half-precision float value
Returns:The largest half-precision float value toward positive infinity
        less than or equal to the specified half-precision float value
/**
     * Returns the largest half-precision float value toward positive infinity
     * less than or equal to the specified half-precision float value.
     * Special values are handled in the following ways:
     * <ul>
     * <li>If the specified half-precision float is NaN, the result is NaN</li>
     * <li>If the specified half-precision float is infinity (negative or positive),
     * the result is infinity (with the same sign)</li>
     * <li>If the specified half-precision float is zero (negative or positive),
     * the result is zero (with the same sign)</li>
     * </ul>
     *
     * @param h A half-precision float value
     * @return The largest half-precision float value toward positive infinity
     *         less than or equal to the specified half-precision float value
     */
    public static @HalfFloat short floor(@HalfFloat short h) {
        int bits = h & 0xffff;
        int e = bits & 0x7fff;
        int result = bits;

        if (e < 0x3c00) {
            result &= FP16_SIGN_MASK;
            result |= 0x3c00 & (bits > 0x8000 ? 0xffff : 0x0);
        } else if (e < 0x6400) {
            e = 25 - (e >> 10);
            int mask = (1 << e) - 1;
            result += mask & -(bits >> 15);
            result &= ~mask;
        }

        return (short) result;
    }

    
Returns the truncated half-precision float value of the specified
half-precision float value. Special values are handled in the following ways:

    

  • If the specified half-precision float is NaN, the result is NaN
    • 

  • If the specified half-precision float is infinity (negative or positive),
the result is infinity (with the same sign)
    • 

  • If the specified half-precision float is zero (negative or positive),
the result is zero (with the same sign)
    • 



Params:
  • h – A half-precision float value
Returns:The truncated half-precision float value of the specified
        half-precision float value
/**
     * Returns the truncated half-precision float value of the specified
     * half-precision float value. Special values are handled in the following ways:
     * <ul>
     * <li>If the specified half-precision float is NaN, the result is NaN</li>
     * <li>If the specified half-precision float is infinity (negative or positive),
     * the result is infinity (with the same sign)</li>
     * <li>If the specified half-precision float is zero (negative or positive),
     * the result is zero (with the same sign)</li>
     * </ul>
     *
     * @param h A half-precision float value
     * @return The truncated half-precision float value of the specified
     *         half-precision float value
     */
    public static @HalfFloat short trunc(@HalfFloat short h) {
        int bits = h & 0xffff;
        int e = bits & 0x7fff;
        int result = bits;

        if (e < 0x3c00) {
            result &= FP16_SIGN_MASK;
        } else if (e < 0x6400) {
            e = 25 - (e >> 10);
            int mask = (1 << e) - 1;
            result &= ~mask;
        }

        return (short) result;
    }

    
Returns the smaller of two half-precision float values (the value closest
to negative infinity). Special values are handled in the following ways:


Params:
  • x – The first half-precision value
  • y – The second half-precision value
Returns:The smaller of the two specified half-precision values
/**
     * Returns the smaller of two half-precision float values (the value closest
     * to negative infinity). Special values are handled in the following ways:
     * <ul>
     * <li>If either value is NaN, the result is NaN</li>
     * <li>{@link #NEGATIVE_ZERO} is smaller than {@link #POSITIVE_ZERO}</li>
     * </ul>
     *
     * @param x The first half-precision value
     * @param y The second half-precision value
     * @return The smaller of the two specified half-precision values
     */
    public static @HalfFloat short min(@HalfFloat short x, @HalfFloat short y) {
        if ((x & FP16_COMBINED) > FP16_EXPONENT_MAX) return NaN;
        if ((y & FP16_COMBINED) > FP16_EXPONENT_MAX) return NaN;

        if ((x & FP16_COMBINED) == 0 && (y & FP16_COMBINED) == 0) {
            return (x & FP16_SIGN_MASK) != 0 ? x : y;
        }

        return ((x & FP16_SIGN_MASK) != 0 ? 0x8000 - (x & 0xffff) : x & 0xffff) <
               ((y & FP16_SIGN_MASK) != 0 ? 0x8000 - (y & 0xffff) : y & 0xffff) ? x : y;
    }

    
Returns the larger of two half-precision float values (the value closest
to positive infinity). Special values are handled in the following ways:


Params:
  • x – The first half-precision value
  • y – The second half-precision value
Returns:The larger of the two specified half-precision values
/**
     * Returns the larger of two half-precision float values (the value closest
     * to positive infinity). Special values are handled in the following ways:
     * <ul>
     * <li>If either value is NaN, the result is NaN</li>
     * <li>{@link #POSITIVE_ZERO} is greater than {@link #NEGATIVE_ZERO}</li>
     * </ul>
     *
     * @param x The first half-precision value
     * @param y The second half-precision value
     *
     * @return The larger of the two specified half-precision values
     */
    public static @HalfFloat short max(@HalfFloat short x, @HalfFloat short y) {
        if ((x & FP16_COMBINED) > FP16_EXPONENT_MAX) return NaN;
        if ((y & FP16_COMBINED) > FP16_EXPONENT_MAX) return NaN;

        if ((x & FP16_COMBINED) == 0 && (y & FP16_COMBINED) == 0) {
            return (x & FP16_SIGN_MASK) != 0 ? y : x;
        }

        return ((x & FP16_SIGN_MASK) != 0 ? 0x8000 - (x & 0xffff) : x & 0xffff) >
               ((y & FP16_SIGN_MASK) != 0 ? 0x8000 - (y & 0xffff) : y & 0xffff) ? x : y;
    }

    
Returns true if the first half-precision float value is less (smaller
toward negative infinity) than the second half-precision float value.
If either of the values is NaN, the result is false.

Params:
  • x – The first half-precision value
  • y – The second half-precision value
Returns:True if x is less than y, false otherwise
/**
     * Returns true if the first half-precision float value is less (smaller
     * toward negative infinity) than the second half-precision float value.
     * If either of the values is NaN, the result is false.
     *
     * @param x The first half-precision value
     * @param y The second half-precision value
     *
     * @return True if x is less than y, false otherwise
     */
    public static boolean less(@HalfFloat short x, @HalfFloat short y) {
        if ((x & FP16_COMBINED) > FP16_EXPONENT_MAX) return false;
        if ((y & FP16_COMBINED) > FP16_EXPONENT_MAX) return false;

        return ((x & FP16_SIGN_MASK) != 0 ? 0x8000 - (x & 0xffff) : x & 0xffff) <
               ((y & FP16_SIGN_MASK) != 0 ? 0x8000 - (y & 0xffff) : y & 0xffff);
    }

    
Returns true if the first half-precision float value is less (smaller
toward negative infinity) than or equal to the second half-precision
float value. If either of the values is NaN, the result is false.

Params:
  • x – The first half-precision value
  • y – The second half-precision value
Returns:True if x is less than or equal to y, false otherwise
/**
     * Returns true if the first half-precision float value is less (smaller
     * toward negative infinity) than or equal to the second half-precision
     * float value. If either of the values is NaN, the result is false.
     *
     * @param x The first half-precision value
     * @param y The second half-precision value
     *
     * @return True if x is less than or equal to y, false otherwise
     */
    public static boolean lessEquals(@HalfFloat short x, @HalfFloat short y) {
        if ((x & FP16_COMBINED) > FP16_EXPONENT_MAX) return false;
        if ((y & FP16_COMBINED) > FP16_EXPONENT_MAX) return false;

        return ((x & FP16_SIGN_MASK) != 0 ? 0x8000 - (x & 0xffff) : x & 0xffff) <=
               ((y & FP16_SIGN_MASK) != 0 ? 0x8000 - (y & 0xffff) : y & 0xffff);
    }

    
Returns true if the first half-precision float value is greater (larger
toward positive infinity) than the second half-precision float value.
If either of the values is NaN, the result is false.

Params:
  • x – The first half-precision value
  • y – The second half-precision value
Returns:True if x is greater than y, false otherwise
/**
     * Returns true if the first half-precision float value is greater (larger
     * toward positive infinity) than the second half-precision float value.
     * If either of the values is NaN, the result is false.
     *
     * @param x The first half-precision value
     * @param y The second half-precision value
     *
     * @return True if x is greater than y, false otherwise
     */
    public static boolean greater(@HalfFloat short x, @HalfFloat short y) {
        if ((x & FP16_COMBINED) > FP16_EXPONENT_MAX) return false;
        if ((y & FP16_COMBINED) > FP16_EXPONENT_MAX) return false;

        return ((x & FP16_SIGN_MASK) != 0 ? 0x8000 - (x & 0xffff) : x & 0xffff) >
               ((y & FP16_SIGN_MASK) != 0 ? 0x8000 - (y & 0xffff) : y & 0xffff);
    }

    
Returns true if the first half-precision float value is greater (larger
toward positive infinity) than or equal to the second half-precision float
value. If either of the values is NaN, the result is false.

Params:
  • x – The first half-precision value
  • y – The second half-precision value
Returns:True if x is greater than y, false otherwise
/**
     * Returns true if the first half-precision float value is greater (larger
     * toward positive infinity) than or equal to the second half-precision float
     * value. If either of the values is NaN, the result is false.
     *
     * @param x The first half-precision value
     * @param y The second half-precision value
     *
     * @return True if x is greater than y, false otherwise
     */
    public static boolean greaterEquals(@HalfFloat short x, @HalfFloat short y) {
        if ((x & FP16_COMBINED) > FP16_EXPONENT_MAX) return false;
        if ((y & FP16_COMBINED) > FP16_EXPONENT_MAX) return false;

        return ((x & FP16_SIGN_MASK) != 0 ? 0x8000 - (x & 0xffff) : x & 0xffff) >=
               ((y & FP16_SIGN_MASK) != 0 ? 0x8000 - (y & 0xffff) : y & 0xffff);
    }

    
Returns true if the two half-precision float values are equal. If either of the values is NaN, the result is false. POSITIVE_ZERO and NEGATIVE_ZERO are considered equal. 
Params:
  • x – The first half-precision value
  • y – The second half-precision value
Returns:True if x is equal to y, false otherwise
/**
     * Returns true if the two half-precision float values are equal.
     * If either of the values is NaN, the result is false. {@link #POSITIVE_ZERO}
     * and {@link #NEGATIVE_ZERO} are considered equal.
     *
     * @param x The first half-precision value
     * @param y The second half-precision value
     *
     * @return True if x is equal to y, false otherwise
     */
    public static boolean equals(@HalfFloat short x, @HalfFloat short y) {
        if ((x & FP16_COMBINED) > FP16_EXPONENT_MAX) return false;
        if ((y & FP16_COMBINED) > FP16_EXPONENT_MAX) return false;

        return x == y || ((x | y) & FP16_COMBINED) == 0;
    }

    
Returns the sign of the specified half-precision float.

Params:
  • h – A half-precision float value
Returns:1 if the value is positive, -1 if the value is negative
/**
     * Returns the sign of the specified half-precision float.
     *
     * @param h A half-precision float value
     * @return 1 if the value is positive, -1 if the value is negative
     */
    public static int getSign(@HalfFloat short h) {
        return (h & FP16_SIGN_MASK) == 0 ? 1 : -1;
    }

    
Returns the unbiased exponent used in the representation of the specified half-precision float value. if the value is NaN or infinite, this* method returns MAX_EXPONENT + 1. If the argument is 0 or a subnormal representation, this method returns MIN_EXPONENT - 1. 
Params:
  • h – A half-precision float value
Returns:The unbiased exponent of the specified value
/**
     * Returns the unbiased exponent used in the representation of
     * the specified  half-precision float value. if the value is NaN
     * or infinite, this* method returns {@link #MAX_EXPONENT} + 1.
     * If the argument is 0 or a subnormal representation, this method
     * returns {@link #MIN_EXPONENT} - 1.
     *
     * @param h A half-precision float value
     * @return The unbiased exponent of the specified value
     */
    public static int getExponent(@HalfFloat short h) {
        return ((h >>> FP16_EXPONENT_SHIFT) & FP16_EXPONENT_MASK) - FP16_EXPONENT_BIAS;
    }

    
Returns the significand, or mantissa, used in the representation
of the specified half-precision float value.

Params:
  • h – A half-precision float value
Returns:The significand, or significand, of the specified vlaue
/**
     * Returns the significand, or mantissa, used in the representation
     * of the specified half-precision float value.
     *
     * @param h A half-precision float value
     * @return The significand, or significand, of the specified vlaue
     */
    public static int getSignificand(@HalfFloat short h) {
        return h & FP16_SIGNIFICAND_MASK;
    }

    
Returns true if the specified half-precision float value represents
infinity, false otherwise.

Params:
  • h – A half-precision float value
Returns:True if the value is positive infinity or negative infinity,
        false otherwise
/**
     * Returns true if the specified half-precision float value represents
     * infinity, false otherwise.
     *
     * @param h A half-precision float value
     * @return True if the value is positive infinity or negative infinity,
     *         false otherwise
     */
    public static boolean isInfinite(@HalfFloat short h) {
        return (h & FP16_COMBINED) == FP16_EXPONENT_MAX;
    }

    
Returns true if the specified half-precision float value represents
a Not-a-Number, false otherwise.

Params:
  • h – A half-precision float value
Returns:True if the value is a NaN, false otherwise
/**
     * Returns true if the specified half-precision float value represents
     * a Not-a-Number, false otherwise.
     *
     * @param h A half-precision float value
     * @return True if the value is a NaN, false otherwise
     */
    public static boolean isNaN(@HalfFloat short h) {
        return (h & FP16_COMBINED) > FP16_EXPONENT_MAX;
    }

    
Returns true if the specified half-precision float value is normalized (does not have a subnormal representation). If the specified value is POSITIVE_INFINITY, NEGATIVE_INFINITY, POSITIVE_ZERO, NEGATIVE_ZERO, NaN or any subnormal number, this method returns false. 
Params:
  • h – A half-precision float value
Returns:True if the value is normalized, false otherwise
/**
     * Returns true if the specified half-precision float value is normalized
     * (does not have a subnormal representation). If the specified value is
     * {@link #POSITIVE_INFINITY}, {@link #NEGATIVE_INFINITY},
     * {@link #POSITIVE_ZERO}, {@link #NEGATIVE_ZERO}, NaN or any subnormal
     * number, this method returns false.
     *
     * @param h A half-precision float value
     * @return True if the value is normalized, false otherwise
     */
    public static boolean isNormalized(@HalfFloat short h) {
        return (h & FP16_EXPONENT_MAX) != 0 && (h & FP16_EXPONENT_MAX) != FP16_EXPONENT_MAX;
    }

    
Converts the specified half-precision float value into a
single-precision float value. The following special cases are handled:


    

  • If the input is NaN, the returned value is Float.NaN
    • 

  • If the input is POSITIVE_INFINITY or NEGATIVE_INFINITY, the returned value is respectively POSITIVE_INFINITY.POSITIVE_INFINITY or Float.NEGATIVE_INFINITY
    • 

  • If the input is 0 (positive or negative), the returned value is +/-0.0f
    • 

  • Otherwise, the returned value is a normalized single-precision float value
    • 



Params:
  • h – The half-precision float value to convert to single-precision
Returns:A normalized single-precision float value
/**
     * <p>Converts the specified half-precision float value into a
     * single-precision float value. The following special cases are handled:</p>
     * <ul>
     * <li>If the input is {@link #NaN}, the returned value is {@link Float#NaN}</li>
     * <li>If the input is {@link #POSITIVE_INFINITY} or
     * {@link #NEGATIVE_INFINITY}, the returned value is respectively
     * {@link Float#POSITIVE_INFINITY} or {@link Float#NEGATIVE_INFINITY}</li>
     * <li>If the input is 0 (positive or negative), the returned value is +/-0.0f</li>
     * <li>Otherwise, the returned value is a normalized single-precision float value</li>
     * </ul>
     *
     * @param h The half-precision float value to convert to single-precision
     * @return A normalized single-precision float value
     */
    public static float toFloat(@HalfFloat short h) {
        int bits = h & 0xffff;
        int s = bits & FP16_SIGN_MASK;
        int e = (bits >>> FP16_EXPONENT_SHIFT) & FP16_EXPONENT_MASK;
        int m = (bits                        ) & FP16_SIGNIFICAND_MASK;

        int outE = 0;
        int outM = 0;

        if (e == 0) { // Denormal or 0
            if (m != 0) {
                // Convert denorm fp16 into normalized fp32
                float o = Float.intBitsToFloat(FP32_DENORMAL_MAGIC + m);
                o -= FP32_DENORMAL_FLOAT;
                return s == 0 ? o : -o;
            }
        } else {
            outM = m << 13;
            if (e == 0x1f) { // Infinite or NaN
                outE = 0xff;
            } else {
                outE = e - FP16_EXPONENT_BIAS + FP32_EXPONENT_BIAS;
            }
        }

        int out = (s << 16) | (outE << FP32_EXPONENT_SHIFT) | outM;
        return Float.intBitsToFloat(out);
    }

    
Converts the specified single-precision float value into a
half-precision float value. The following special cases are handled:



Params:
  • f – The single-precision float value to convert to half-precision
Returns:A half-precision float value
/**
     * <p>Converts the specified single-precision float value into a
     * half-precision float value. The following special cases are handled:</p>
     * <ul>
     * <li>If the input is NaN (see {@link Float#isNaN(float)}), the returned
     * value is {@link #NaN}</li>
     * <li>If the input is {@link Float#POSITIVE_INFINITY} or
     * {@link Float#NEGATIVE_INFINITY}, the returned value is respectively
     * {@link #POSITIVE_INFINITY} or {@link #NEGATIVE_INFINITY}</li>
     * <li>If the input is 0 (positive or negative), the returned value is
     * {@link #POSITIVE_ZERO} or {@link #NEGATIVE_ZERO}</li>
     * <li>If the input is a less than {@link #MIN_VALUE}, the returned value
     * is flushed to {@link #POSITIVE_ZERO} or {@link #NEGATIVE_ZERO}</li>
     * <li>If the input is a less than {@link #MIN_NORMAL}, the returned value
     * is a denorm half-precision float</li>
     * <li>Otherwise, the returned value is rounded to the nearest
     * representable half-precision float value</li>
     * </ul>
     *
     * @param f The single-precision float value to convert to half-precision
     * @return A half-precision float value
     */
    @SuppressWarnings("StatementWithEmptyBody")
    public static @HalfFloat short toHalf(float f) {
        int bits = Float.floatToRawIntBits(f);
        int s = (bits >>> FP32_SIGN_SHIFT    );
        int e = (bits >>> FP32_EXPONENT_SHIFT) & FP32_EXPONENT_MASK;
        int m = (bits                        ) & FP32_SIGNIFICAND_MASK;

        int outE = 0;
        int outM = 0;

        if (e == 0xff) { // Infinite or NaN
            outE = 0x1f;
            outM = m != 0 ? 0x200 : 0;
        } else {
            e = e - FP32_EXPONENT_BIAS + FP16_EXPONENT_BIAS;
            if (e >= 0x1f) { // Overflow
                outE = 0x31;
            } else if (e <= 0) { // Underflow
                if (e < -10) {
                    // The absolute fp32 value is less than MIN_VALUE, flush to +/-0
                } else {
                    // The fp32 value is a normalized float less than MIN_NORMAL,
                    // we convert to a denorm fp16
                    m = (m | 0x800000) >> (1 - e);
                    if ((m & 0x1000) != 0) m += 0x2000;
                    outM = m >> 13;
                }
            } else {
                outE = e;
                outM = m >> 13;
                if ((m & 0x1000) != 0) {
                    // Round to nearest "0.5" up
                    int out = (outE << FP16_EXPONENT_SHIFT) | outM;
                    out++;
                    return (short) (out | (s << FP16_SIGN_SHIFT));
                }
            }
        }

        return (short) ((s << FP16_SIGN_SHIFT) | (outE << FP16_EXPONENT_SHIFT) | outM);
    }

    
Returns a Half instance representing the specified half-precision float value. 
Params:
  • h – A half-precision float value
Returns:a Half instance representing h
/**
     * Returns a {@code Half} instance representing the specified
     * half-precision float value.
     *
     * @param h A half-precision float value
     * @return a {@code Half} instance representing {@code h}
     */
    public static @NonNull Half valueOf(@HalfFloat short h) {
        return new Half(h);
    }

    
Returns a Half instance representing the specified float value. 
Params:
  • f – A float value
Returns:a Half instance representing f
/**
     * Returns a {@code Half} instance representing the specified float value.
     *
     * @param f A float value
     * @return a {@code Half} instance representing {@code f}
     */
    public static @NonNull Half valueOf(float f) {
        return new Half(f);
    }

    
Returns a Half instance representing the specified string value. Calling this method is equivalent to calling toHalf(Float.parseString(h)). See Float.valueOf(String) for more information on the format of the string representation. 
Params:
  • s – The string to be parsed
Throws:
Returns:a Half instance representing h
/**
     * Returns a {@code Half} instance representing the specified string value.
     * Calling this method is equivalent to calling
     * <code>toHalf(Float.parseString(h))</code>. See {@link Float#valueOf(String)}
     * for more information on the format of the string representation.
     *
     * @param s The string to be parsed
     * @return a {@code Half} instance representing {@code h}
     * @throws NumberFormatException if the string does not contain a parsable
     *         half-precision float value
     */
    public static @NonNull Half valueOf(@NonNull String s) {
        return new Half(s);
    }

    
Returns the half-precision float value represented by the specified string.
Calling this method is equivalent to calling
toHalf(Float.parseString(h)). See Float.valueOf(String) for more information on the format of the string representation. 
Params:
  • s – The string to be parsed
Throws:
Returns:A half-precision float value represented by the string
/**
     * Returns the half-precision float value represented by the specified string.
     * Calling this method is equivalent to calling
     * <code>toHalf(Float.parseString(h))</code>. See {@link Float#valueOf(String)}
     * for more information on the format of the string representation.
     *
     * @param s The string to be parsed
     * @return A half-precision float value represented by the string
     * @throws NumberFormatException if the string does not contain a parsable
     *         half-precision float value
     */
    public static @HalfFloat short parseHalf(@NonNull String s) throws NumberFormatException {
        return toHalf(FloatingDecimal.parseFloat(s));
    }

    
Returns a string representation of the specified half-precision
float value. Calling this method is equivalent to calling
Float.toString(toFloat(h)). See Float.toString(float) for more information on the format of the string representation. 
Params:
  • h – A half-precision float value
Returns:A string representation of the specified value
/**
     * Returns a string representation of the specified half-precision
     * float value. Calling this method is equivalent to calling
     * <code>Float.toString(toFloat(h))</code>. See {@link Float#toString(float)}
     * for more information on the format of the string representation.
     *
     * @param h A half-precision float value
     * @return A string representation of the specified value
     */
    @NonNull
    public static String toString(@HalfFloat short h) {
        return Float.toString(toFloat(h));
    }

    
Returns a hexadecimal string representation of the specified half-precision
float value. If the value is a NaN, the result is "NaN",
otherwise the result follows this format:


    

  • If the sign is positive, no sign character appears in the result
    • 

  • If the sign is negative, the first character is '-'
    • 

  • If the value is inifinity, the string is "Infinity"
    • 

  • If the value is 0, the string is "0x0.0p0"
    • 

  • If the value has a normalized representation, the exponent and
significand are represented in the string in two fields. The significand
starts with "0x1." followed by its lowercase hexadecimal
representation. Trailing zeroes are removed unless all digits are 0, then
a single zero is used. The significand representation is followed by the
exponent, represented by "p", itself followed by a decimal
string of the unbiased exponent
    • 

  • If the value has a subnormal representation, the significand starts
with "0x0." followed by its lowercase hexadecimal
representation. Trailing zeroes are removed unless all digits are 0, then
a single zero is used. The significand representation is followed by the
exponent, represented by "p-14"
    • 



Params:
  • h – A half-precision float value
Returns:A hexadecimal string representation of the specified value
/**
     * <p>Returns a hexadecimal string representation of the specified half-precision
     * float value. If the value is a NaN, the result is <code>"NaN"</code>,
     * otherwise the result follows this format:</p>
     * <ul>
     * <li>If the sign is positive, no sign character appears in the result</li>
     * <li>If the sign is negative, the first character is <code>'-'</code></li>
     * <li>If the value is inifinity, the string is <code>"Infinity"</code></li>
     * <li>If the value is 0, the string is <code>"0x0.0p0"</code></li>
     * <li>If the value has a normalized representation, the exponent and
     * significand are represented in the string in two fields. The significand
     * starts with <code>"0x1."</code> followed by its lowercase hexadecimal
     * representation. Trailing zeroes are removed unless all digits are 0, then
     * a single zero is used. The significand representation is followed by the
     * exponent, represented by <code>"p"</code>, itself followed by a decimal
     * string of the unbiased exponent</li>
     * <li>If the value has a subnormal representation, the significand starts
     * with <code>"0x0."</code> followed by its lowercase hexadecimal
     * representation. Trailing zeroes are removed unless all digits are 0, then
     * a single zero is used. The significand representation is followed by the
     * exponent, represented by <code>"p-14"</code></li>
     * </ul>
     *
     * @param h A half-precision float value
     * @return A hexadecimal string representation of the specified value
     */
    @NonNull
    public static String toHexString(@HalfFloat short h) {
        StringBuilder o = new StringBuilder();

        int bits = h & 0xffff;
        int s = (bits >>> FP16_SIGN_SHIFT    );
        int e = (bits >>> FP16_EXPONENT_SHIFT) & FP16_EXPONENT_MASK;
        int m = (bits                        ) & FP16_SIGNIFICAND_MASK;

        if (e == 0x1f) { // Infinite or NaN
            if (m == 0) {
                if (s != 0) o.append('-');
                o.append("Infinity");
            } else {
                o.append("NaN");
            }
        } else {
            if (s == 1) o.append('-');
            if (e == 0) {
                if (m == 0) {
                    o.append("0x0.0p0");
                } else {
                    o.append("0x0.");
                    String significand = Integer.toHexString(m);
                    o.append(significand.replaceFirst("0{2,}$", ""));
                    o.append("p-14");
                }
            } else {
                o.append("0x1.");
                String significand = Integer.toHexString(m);
                o.append(significand.replaceFirst("0{2,}$", ""));
                o.append('p');
                o.append(Integer.toString(e - FP16_EXPONENT_BIAS));
            }
        }

        return o.toString();
    }
}