/**
* Copyright 2013 JogAmp Community. All rights reserved.
*
* Redistribution and use in source and binary forms, with or without modification, are
* permitted provided that the following conditions are met:
*
* 1. Redistributions of source code must retain the above copyright notice, this list of
* conditions and the following disclaimer.
*
* 2. Redistributions in binary form must reproduce the above copyright notice, this list
* of conditions and the following disclaimer in the documentation and/or other materials
* provided with the distribution.
*
* THIS SOFTWARE IS PROVIDED BY JogAmp Community ``AS IS'' AND ANY EXPRESS OR IMPLIED
* WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND
* FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL JogAmp Community OR
* CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
* CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR
* SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON
* ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
* NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF
* ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
*
* The views and conclusions contained in the software and documentation are those of the
* authors and should not be interpreted as representing official policies, either expressed
* or implied, of JogAmp Community.
*/
package com.jogamp.opengl.math;
/**
* <p>
* Functions to convert values to/from the <code>binary16</code> format
* specified in <code>IEEE 754 2008</code>.
* </p>
*/
public final class Binary16
{
/**
* The encoded form of negative infinity <code>-∞</code>.
*/
public static final char NEGATIVE_INFINITY;
/**
* The encoded form of positive infinity <code>∞</code>.
*/
public static final char POSITIVE_INFINITY;
/**
* The encoded form of positive zero <code>0</code>.
*/
public static final char POSITIVE_ZERO;
/**
* The encoded form of negative zero <code>-0</code>.
*/
public static final char NEGATIVE_ZERO;
/**
* The <i>bias</i> value used to offset the encoded exponent. A given
* exponent <code>e</code> is encoded as <code>{@link #BIAS} + e</code>.
*/
public static final int BIAS;
static {
NEGATIVE_INFINITY = 0xFC00;
POSITIVE_INFINITY = 0x7C00;
POSITIVE_ZERO = 0x0000;
NEGATIVE_ZERO = 0x8000;
BIAS = 15;
}
private static final int MASK_SIGN;
private static final int MASK_EXPONENT;
private static final int MASK_SIGNIFICAND;
static {
MASK_SIGN = 0x8000;
MASK_EXPONENT = 0x7C00;
MASK_SIGNIFICAND = 0x03FF;
}
/**
* One possible not-a-number value.
*/
public static char exampleNaN()
{
final int n =
Binary16.packSetExponentUnbiasedUnchecked(16)
| Binary16.packSetSignificandUnchecked(1);
final char c = (char) n;
return c;
}
/**
* Return <code>true</code> if the given packed <code>binary16</code> value
* is infinite.
*/
public static boolean isInfinite(
final char k)
{
if (Binary16.unpackGetExponentUnbiased(k) == 16) {
if (Binary16.unpackGetSignificand(k) == 0) {
return true;
}
}
return false;
}
/**
* Return <code>true</code> if the given packed <code>binary16</code> value
* is not a number (<code>NaN</code>).
*/
public static boolean isNaN(
final char k)
{
final int e = Binary16.unpackGetExponentUnbiased(k);
final int s = Binary16.unpackGetSignificand(k);
return (e == 16) && (s > 0);
}
/**
* <p>
* Convert a double precision floating point value to a packed
* <code>binary16</code> value.
* </p>
* <p>
* For the following specific cases, the function returns:
* </p>
* <ul>
* <li><code>NaN</code> iff <code>isNaN(k)</code></li>
* <li>{@link #POSITIVE_INFINITY} iff
* <code>k == {@link Double#POSITIVE_INFINITY}</code></li>
* <li>{@link #NEGATIVE_INFINITY} iff
* <code>k == {@link Double#NEGATIVE_INFINITY}</code></li>
* <li>{@link #NEGATIVE_ZERO} iff <code>k == -0.0</code></li>
* <li>{@link #POSITIVE_ZERO} iff <code>k == 0.0</code></li>
* </ul>
* <p>
* Otherwise, the <code>binary16</code> value that most closely represents
* <code>k</code> is returned. This may obviously be an infinite value as
* the interval of double precision values is far larger than that of the
* <code>binary16</code> type.
* </p>
*
* @see #unpackDouble(char)
*/
public static char packDouble(
final double k)
{
if (Double.isNaN(k)) {
return Binary16.exampleNaN();
}
if (k == Double.POSITIVE_INFINITY) {
return Binary16.POSITIVE_INFINITY;
}
if (k == Double.NEGATIVE_INFINITY) {
return Binary16.NEGATIVE_INFINITY;
}
if (Double.doubleToLongBits(k) == Binary64.NEGATIVE_ZERO_BITS) {
return Binary16.NEGATIVE_ZERO;
}
if (k == 0.0) {
return Binary16.POSITIVE_ZERO;
}
final long de = Binary64.unpackGetExponentUnbiased(k);
final long ds = Binary64.unpackGetSign(k);
final long dn = Binary64.unpackGetSignificand(k);
final char rsr = Binary16.packSetSignUnchecked((int) ds);
/**
* Extract the 5 least-significant bits of the exponent.
*/
final int rem = (int) (de & 0x001F);
final char rer = Binary16.packSetExponentUnbiasedUnchecked(rem);
/**
* Extract the 10 most-significant bits of the significand.
*/
final long rnm = dn & 0xFFC0000000000L;
final long rns = rnm >> 42;
final char rnr = Binary16.packSetSignificandUnchecked((int) rns);
/**
* Combine the results.
*/
return (char) (rsr | rer | rnr);
}
/**
* <p>
* Convert a single precision floating point value to a packed
* <code>binary16</code> value.
* </p>
* <p>
* For the following specific cases, the function returns:
* </p>
* <ul>
* <li><code>NaN</code> iff <code>isNaN(k)</code></li>
* <li>{@link #POSITIVE_INFINITY} iff
* <code>k == {@link Float#POSITIVE_INFINITY}</code></li>
* <li>{@link #NEGATIVE_INFINITY} iff
* <code>k == {@link Float#NEGATIVE_INFINITY}</code></li>
* <li>{@link #NEGATIVE_ZERO} iff <code>k == -0.0</code></li>
* <li>{@link #POSITIVE_ZERO} iff <code>k == 0.0</code></li>
* </ul>
* <p>
* Otherwise, the <code>binary16</code> value that most closely represents
* <code>k</code> is returned. This may obviously be an infinite value as
* the interval of single precision values is far larger than that of the
* <code>binary16</code> type.
* </p>
*
* @see #unpackFloat(char)
*/
public static char packFloat(
final float k)
{
if (Float.isNaN(k)) {
return Binary16.exampleNaN();
}
if (k == Float.POSITIVE_INFINITY) {
return Binary16.POSITIVE_INFINITY;
}
if (k == Float.NEGATIVE_INFINITY) {
return Binary16.NEGATIVE_INFINITY;
}
if (Float.floatToIntBits(k) == Binary32.NEGATIVE_ZERO_BITS) {
return Binary16.NEGATIVE_ZERO;
}
if (k == 0.0) {
return Binary16.POSITIVE_ZERO;
}
final long de = Binary32.unpackGetExponentUnbiased(k);
final long ds = Binary32.unpackGetSign(k);
final long dn = Binary32.unpackGetSignificand(k);
final char rsr = Binary16.packSetSignUnchecked((int) ds);
/**
* Extract the 5 least-significant bits of the exponent.
*/
final int rem = (int) (de & 0x001F);
final char rer = Binary16.packSetExponentUnbiasedUnchecked(rem);
/**
* Extract the 10 most-significant bits of the significand.
*/
final long rnm = dn & 0x7FE000L;
final long rns = rnm >> 13;
final char rnr = Binary16.packSetSignificandUnchecked((int) rns);
/**
* Combine the results.
*/
return (char) (rsr | rer | rnr);
}
/**
* <p>
* Encode the unbiased exponent <code>e</code>. Values should be in the
* range <code>[-15, 16]</code> - values outside of this range will be
* truncated.
* </p>
*
* @see #unpackGetExponentUnbiased(char)
*/
public static char packSetExponentUnbiasedUnchecked(
final int e)
{
final int eb = e + Binary16.BIAS;
final int es = eb << 10;
final int em = es & Binary16.MASK_EXPONENT;
return (char) em;
}
/**
* <p>
* Encode the significand <code>s</code>. Values should be in the range
* <code>[0, 1023]</code>. Values outside of this range will be truncated.
* </p>
*
* @see #unpackGetSignificand(char)
*/
public static char packSetSignificandUnchecked(
final int s)
{
final int sm = s & Binary16.MASK_SIGNIFICAND;
return (char) sm;
}
/**
* <p>
* Encode the sign bit <code>s</code>. Values should be in the range
* <code>[0, 1]</code>, with <code>0</code> ironically denoting a positive
* value. Values outside of this range will be truncated.
* </p>
*
* @see #unpackGetSign(char)
*/
public static char packSetSignUnchecked(
final int s)
{
final int ss = s << 15;
final int sm = ss & Binary16.MASK_SIGN;
return (char) sm;
}
/**
* Show the given raw packed <code>binary16</code> value as a string of
* binary digits.
*/
public static String toRawBinaryString(
final char k)
{
final StringBuilder b = new StringBuilder();
int z = k;
for (int i = 0; i < 16; ++i) {
if ((z & 1) == 1) {
b.insert(0, "1");
} else {
b.insert(0, "0");
}
z >>= 1;
}
return b.toString();
}
/**
* <p>
* Convert a packed <code>binary16</code> value <code>k</code> to a
* double-precision floating point value.
* </p>
* <p>
* The function returns:
* </p>
* <ul>
* <li><code>NaN</code> iff <code>isNaN(k)</code></li>
* <li>{@link Double#POSITIVE_INFINITY} iff
* <code>k == {@link #POSITIVE_INFINITY}</code></li>
* <li>{@link Double#NEGATIVE_INFINITY} iff
* <code>k == {@link #NEGATIVE_INFINITY}</code></li>
* <li><code>-0.0</code> iff <code>k == {@link #NEGATIVE_ZERO}</code></li>
* <li><code>0.0</code> iff <code>k == {@link #POSITIVE_ZERO}</code></li>
* <li><code>(-1.0 * n) * (2 ^ e) * 1.s</code>, for the decoded sign
* <code>n</code> of <code>k</code>, the decoded exponent <code>e</code> of
* <code>k</code>, and the decoded significand <code>s</code> of
* <code>k</code>.</li>
* </ul>
*
* @see #packDouble(double)
*/
public static double unpackDouble(
final char k)
{
if (Binary16.isNaN(k)) {
return Double.NaN;
}
if (k == Binary16.POSITIVE_INFINITY) {
return Double.POSITIVE_INFINITY;
}
if (k == Binary16.NEGATIVE_INFINITY) {
return Double.NEGATIVE_INFINITY;
}
if (k == Binary16.NEGATIVE_ZERO) {
return -0.0;
}
if (k == Binary16.POSITIVE_ZERO) {
return 0.0;
}
final long e = Binary16.unpackGetExponentUnbiased(k);
final long s = Binary16.unpackGetSign(k);
final long n = Binary16.unpackGetSignificand(k);
/**
* Shift the sign bit to the position at which it will appear in the
* resulting value.
*/
final long rsr = s << 63;
/**
* 1. Bias the exponent.
*
* 2. Shift the result left to the position at which it will appear in the
* resulting value.
*/
final long reb = (e + Binary64.BIAS);
final long rer = reb << 52;
/**
* Shift the significand left to the position at which it will appear in
* the resulting value.
*/
final long rnr = n << 42;
return Double.longBitsToDouble(rsr | rer | rnr);
}
/**
* <p>
* Convert a packed <code>binary16</code> value <code>k</code> to a
* single-precision floating point value.
* </p>
* <p>
* The function returns:
* </p>
* <ul>
* <li><code>NaN</code> iff <code>isNaN(k)</code></li>
* <li>{@link Float#POSITIVE_INFINITY} iff
* <code>k == {@link #POSITIVE_INFINITY}</code></li>
* <li>{@link Float#NEGATIVE_INFINITY} iff
* <code>k == {@link #NEGATIVE_INFINITY}</code></li>
* <li><code>-0.0</code> iff <code>k == {@link #NEGATIVE_ZERO}</code></li>
* <li><code>0.0</code> iff <code>k == {@link #POSITIVE_ZERO}</code></li>
* <li><code>(-1.0 * n) * (2 ^ e) * 1.s</code>, for the decoded sign
* <code>n</code> of <code>k</code>, the decoded exponent <code>e</code> of
* <code>k</code>, and the decoded significand <code>s</code> of
* <code>k</code>.</li>
* </ul>
*
* @see #packFloat(float)
*/
public static float unpackFloat(
final char k)
{
if (Binary16.isNaN(k)) {
return Float.NaN;
}
if (k == Binary16.POSITIVE_INFINITY) {
return Float.POSITIVE_INFINITY;
}
if (k == Binary16.NEGATIVE_INFINITY) {
return Float.NEGATIVE_INFINITY;
}
if (k == Binary16.NEGATIVE_ZERO) {
return -0.0f;
}
if (k == Binary16.POSITIVE_ZERO) {
return 0.0f;
}
final int e = Binary16.unpackGetExponentUnbiased(k);
final int s = Binary16.unpackGetSign(k);
final int n = Binary16.unpackGetSignificand(k);
/**
* Shift the sign bit to the position at which it will appear in the
* resulting value.
*/
final int rsr = s << 31;
/**
* 1. Bias the exponent.
*
* 2. Shift the result left to the position at which it will appear in the
* resulting value.
*/
final int reb = (e + Binary32.BIAS);
final int rer = reb << 23;
/**
* Shift the significand left to the position at which it will appear in
* the resulting value.
*/
final int rnr = n << 13;
return Float.intBitsToFloat(rsr | rer | rnr);
}
/**
* <p>
* Extract and unbias the exponent of the given packed <code>binary16</code>
* value.
* </p>
* <p>
* The exponent is encoded <i>biased</i> as a number in the range
* <code>[0, 31]</code>, with <code>0</code> indicating that the number is
* <i>subnormal</i> and <code>[1, 30]</code> denoting the actual exponent
* plus {@link #BIAS}. Infinite and <code>NaN</code> values always have an
* exponent of <code>31</code>.
* </p>
* <p>
* This function will therefore return:
* </p>
* <ul>
* <li>
* <code>0 - {@link #BIAS} = -15</code> iff the input is a <i>subnormal</i>
* number.</li>
* <li>An integer in the range
* <code>[1 - {@link #BIAS}, 30 - {@link #BIAS}] = [-14, 15]</code> iff the
* input is a <i>normal</i> number.</li>
* <li>
* <code>16</code> iff the input is {@link #POSITIVE_INFINITY},
* {@link #NEGATIVE_INFINITY}, or <code>NaN</code>.</li>
* </ul>
*
* @see #packSetExponentUnbiasedUnchecked(int)
*/
public static int unpackGetExponentUnbiased(
final char k)
{
final int em = k & Binary16.MASK_EXPONENT;
final int es = em >> 10;
return es - Binary16.BIAS;
}
/**
* Retrieve the sign bit of the given packed <code>binary16</code> value, as
* an integer in the range <code>[0, 1]</code>.
*
* @see Binary16#packSetSignUnchecked(int)
*/
public static int unpackGetSign(
final char k)
{
return (k & Binary16.MASK_SIGN) >> 15;
}
/**
* <p>
* Return the significand of the given packed <code>binary16</code> value as
* an integer in the range <code>[0, 1023]</code>.
* </p>
*
* @see Binary16#packSetSignificandUnchecked(int)
*/
public static int unpackGetSignificand(
final char k)
{
return k & Binary16.MASK_SIGNIFICAND;
}
private Binary16()
{
throw new AssertionError("Unreachable code, report this bug!");
}
}