| /* |
| * 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; |
| |
| /** |
| * <p>Half is 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 ⁄ 16,777,216</td></tr> |
| * <tr><td>1 ⁄ 16,384</td><td>1 ⁄ 16,777,216</td></tr> |
| * <tr><td>1 ⁄ 8,192</td><td>1 ⁄ 8,388,608</td></tr> |
| * <tr><td>1 ⁄ 4,096</td><td>1 ⁄ 4,194,304</td></tr> |
| * <tr><td>1 ⁄ 2,048</td><td>1 ⁄ 2,097,152</td></tr> |
| * <tr><td>1 ⁄ 1,024</td><td>1 ⁄ 1,048,576</td></tr> |
| * <tr><td>1 ⁄ 512</td><td>1 ⁄ 524,288</td></tr> |
| * <tr><td>1 ⁄ 256</td><td>1 ⁄ 262,144</td></tr> |
| * <tr><td>1 ⁄ 128</td><td>1 ⁄ 131,072</td></tr> |
| * <tr><td>1 ⁄ 64</td><td>1 ⁄ 65,536</td></tr> |
| * <tr><td>1 ⁄ 32</td><td>1 ⁄ 32,768</td></tr> |
| * <tr><td>1 ⁄ 16</td><td>1 ⁄ 16,384</td></tr> |
| * <tr><td>1 ⁄ 8</td><td>1 ⁄ 8,192</td></tr> |
| * <tr><td>1 ⁄ 4</td><td>1 ⁄ 4,096</td></tr> |
| * <tr><td>1 ⁄ 2</td><td>1 ⁄ 2,048</td></tr> |
| * <tr><td>1</td><td>1 ⁄ 1,024</td></tr> |
| * <tr><td>2</td><td>1 ⁄ 512</td></tr> |
| * <tr><td>4</td><td>1 ⁄ 256</td></tr> |
| * <tr><td>8</td><td>1 ⁄ 128</td></tr> |
| * <tr><td>16</td><td>1 ⁄ 64</td></tr> |
| * <tr><td>32</td><td>1 ⁄ 32</td></tr> |
| * <tr><td>64</td><td>1 ⁄ 16</td></tr> |
| * <tr><td>128</td><td>1 ⁄ 8</td></tr> |
| * <tr><td>256</td><td>1 ⁄ 4</td></tr> |
| * <tr><td>512</td><td>1 ⁄ 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 { |
| /** |
| * 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. |
| */ |
| public static final @HalfFloat short EPSILON = (short) 0x1400; |
| |
| /** |
| * 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. |
| */ |
| public static final int MIN_EXPONENT = -14; |
| |
| /** |
| * 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. |
| */ |
| public static final @HalfFloat short MAX_VALUE = (short) 0x7bff; |
| /** |
| * 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. |
| */ |
| public static final @HalfFloat short MIN_VALUE = (short) 0x0001; |
| /** |
| * 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. |
| */ |
| public static final @HalfFloat short NEGATIVE_INFINITY = (short) 0xfc00; |
| /** |
| * Negative 0 of type half-precision float. |
| */ |
| public static final @HalfFloat short NEGATIVE_ZERO = (short) 0x8000; |
| /** |
| * Positive infinity of type half-precision float. |
| */ |
| public static final @HalfFloat short POSITIVE_INFINITY = (short) 0x7c00; |
| /** |
| * 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 Half() { |
| } |
| |
| /** |
| * 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: |
| * <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: |
| * <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: |
| * <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: |
| * <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: |
| * <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: |
| * <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: |
| * <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. |
| * |
| * @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. |
| * |
| * @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. |
| * |
| * @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. |
| * |
| * @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. {@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. |
| * |
| * @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 {@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. |
| * |
| * @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. |
| * |
| * @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. |
| * |
| * @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 |
| * {@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; |
| } |
| |
| /** |
| * <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); |
| } |
| |
| /** |
| * <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 valueOf(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 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 |
| */ |
| public static String toString(@HalfFloat short h) { |
| return Float.toString(toFloat(h)); |
| } |
| |
| /** |
| * <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 |
| */ |
| 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(); |
| } |
| } |