| /* |
| * 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; |
| |
| /** |
| * <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 is stored in a short data type. A half-precision float can be |
| * created from or converted to single-precision floats.</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>Mantissa: 10 bits</li> |
| * </ul> |
| * |
| * <p>The format is laid out thusly:</p> |
| * <pre> |
| * 1 11111 1111111111 |
| * ^ --^-- -----^---- |
| * sign | |_______ mantissa |
| * | |
| * -- exponent |
| * </pre> |
| * |
| * @hide |
| */ |
| 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 short EPSILON = (short) 0x1400; |
| /** |
| * Smallest negative value a half-precision float may have. |
| */ |
| public static final short LOWEST_VALUE = (short) 0xfbff; |
| /** |
| * Maximum exponent a finite half-precision float may have. |
| */ |
| public static final short MAX_EXPONENT = 15; |
| /** |
| * Maximum positive finite value a half-precision float may have. |
| */ |
| public static final short MAX_VALUE = (short) 0x7bff; |
| /** |
| * Minimum exponent a normalized half-precision float may have. |
| */ |
| public static final short MIN_EXPONENT = -14; |
| /** |
| * Smallest positive normal value a half-precision float may have. |
| */ |
| public static final short MIN_NORMAL = (short) 0x0400; |
| /** |
| * Smallest positive non-zero value a half-precision float may have. |
| */ |
| public static final short MIN_VALUE = (short) 0x0001; |
| /** |
| * A Not-a-Number representation of a half-precision float. |
| */ |
| public static final short NaN = (short) 0x7e00; |
| /** |
| * Negative infinity of type half-precision float. |
| */ |
| public static final short NEGATIVE_INFINITY = (short) 0xfc00; |
| /** |
| * Negative 0 of type half-precision float. |
| */ |
| public static final short NEGATIVE_ZERO = (short) 0x8000; |
| /** |
| * Positive infinity of type half-precision float. |
| */ |
| public static final short POSITIVE_INFINITY = (short) 0x7c00; |
| /** |
| * Positive 0 of type half-precision float. |
| */ |
| public static final short POSITIVE_ZERO = (short) 0x0000; |
| |
| private static final int FP16_SIGN_SHIFT = 15; |
| private static final int FP16_EXPONENT_SHIFT = 10; |
| private static final int FP16_EXPONENT_MASK = 0x1f; |
| private static final int FP16_MANTISSA_MASK = 0x3ff; |
| private static final int FP16_EXPONENT_BIAS = 15; |
| |
| 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_MANTISSA_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 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(short h) { |
| return (h >>> FP16_SIGN_SHIFT) == 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 denormal, 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(short h) { |
| return ((h >>> FP16_EXPONENT_SHIFT) & FP16_EXPONENT_MASK) - FP16_EXPONENT_BIAS; |
| } |
| |
| /** |
| * Returns the mantissa, or significand, used in the representation |
| * of the specified half-precision float value. |
| * |
| * @param h A half-precision float value |
| * @return The mantissa, or significand, of the specified vlaue |
| */ |
| public static int getMantissa(short h) { |
| return h & FP16_MANTISSA_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(short h) { |
| int e = (h >>> FP16_EXPONENT_SHIFT) & FP16_EXPONENT_MASK; |
| int m = (h ) & FP16_MANTISSA_MASK; |
| return e == 0x1f && m == 0; |
| } |
| |
| /** |
| * 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(short h) { |
| int e = (h >>> FP16_EXPONENT_SHIFT) & FP16_EXPONENT_MASK; |
| int m = (h ) & FP16_MANTISSA_MASK; |
| return e == 0x1f && m != 0; |
| } |
| |
| /** |
| * <p>Converts the specified half-precision float value into a |
| * single-precision float value with the following special cases:</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(short h) { |
| int bits = h & 0xffff; |
| int s = (bits >>> FP16_SIGN_SHIFT ); |
| int e = (bits >>> FP16_EXPONENT_SHIFT) & FP16_EXPONENT_MASK; |
| int m = (bits ) & FP16_MANTISSA_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 << FP32_SIGN_SHIFT) | (outE << FP32_EXPONENT_SHIFT) | outM; |
| return Float.intBitsToFloat(out); |
| } |
| |
| /** |
| * <p>Converts the specified single-precision float value into a |
| * half-precision float value with the following special cases:</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 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_MANTISSA_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++; |
| out |= (s << FP16_SIGN_SHIFT); |
| return (short) out; |
| } |
| } |
| } |
| |
| int out = (s << FP16_SIGN_SHIFT) | (outE << FP16_EXPONENT_SHIFT) | outM; |
| return (short) out; |
| } |
| |
| /** |
| * 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(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 |
| * mantissa are represented in the string in two fields. The mantissa 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 mantissa 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 denormal representation, the mantissa 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 mantissa 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(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_MANTISSA_MASK; |
| |
| if (e == 0x1f) { // Infinite or NaN |
| if (m == 0) { |
| if (s == 1) 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 mantissa = Integer.toHexString(m); |
| o.append(mantissa.replaceFirst("0{2,}$", "")); |
| o.append("p-14"); |
| } |
| } else { |
| o.append("0x1."); |
| String mantissa = Integer.toHexString(m); |
| o.append(mantissa.replaceFirst("0{2,}$", "")); |
| o.append('p'); |
| o.append(Integer.toString(e - FP16_EXPONENT_BIAS)); |
| } |
| } |
| |
| return o.toString(); |
| } |
| } |