com.jogamp.opengl.math.Binary16 Maven / Gradle / Ivy
/**
* 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;
/**
*
* Functions to convert values to/from the binary16 format
* specified in IEEE 754 2008.
*
*/
public final class Binary16
{
/**
* The encoded form of negative infinity -∞.
*/
public static final char NEGATIVE_INFINITY;
/**
* The encoded form of positive infinity ∞.
*/
public static final char POSITIVE_INFINITY;
/**
* The encoded form of positive zero 0.
*/
public static final char POSITIVE_ZERO;
/**
* The encoded form of negative zero -0.
*/
public static final char NEGATIVE_ZERO;
/**
* The bias value used to offset the encoded exponent. A given
* exponent e is encoded as {@link #BIAS} + e.
*/
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 true if the given packed binary16 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 true if the given packed binary16 value
* is not a number (NaN).
*/
public static boolean isNaN(
final char k)
{
final int e = Binary16.unpackGetExponentUnbiased(k);
final int s = Binary16.unpackGetSignificand(k);
return (e == 16) && (s > 0);
}
/**
*
* Convert a double precision floating point value to a packed
* binary16 value.
*
*
* For the following specific cases, the function returns:
*
*
* NaN iff isNaN(k)- {@link #POSITIVE_INFINITY} iff
*
k == {@link Double#POSITIVE_INFINITY}
* - {@link #NEGATIVE_INFINITY} iff
*
k == {@link Double#NEGATIVE_INFINITY}
* - {@link #NEGATIVE_ZERO} iff
k == -0.0
* - {@link #POSITIVE_ZERO} iff
k == 0.0
*
*
* Otherwise, the binary16 value that most closely represents
* k is returned. This may obviously be an infinite value as
* the interval of double precision values is far larger than that of the
* binary16 type.
*
*
* @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);
}
/**
*
* Convert a single precision floating point value to a packed
* binary16 value.
*
*
* For the following specific cases, the function returns:
*
*
* NaN iff isNaN(k)- {@link #POSITIVE_INFINITY} iff
*
k == {@link Float#POSITIVE_INFINITY}
* - {@link #NEGATIVE_INFINITY} iff
*
k == {@link Float#NEGATIVE_INFINITY}
* - {@link #NEGATIVE_ZERO} iff
k == -0.0
* - {@link #POSITIVE_ZERO} iff
k == 0.0
*
*
* Otherwise, the binary16 value that most closely represents
* k is returned. This may obviously be an infinite value as
* the interval of single precision values is far larger than that of the
* binary16 type.
*
*
* @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);
}
/**
*
* Encode the unbiased exponent e. Values should be in the
* range [-15, 16] - values outside of this range will be
* truncated.
*
*
* @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;
}
/**
*
* Encode the significand s. Values should be in the range
* [0, 1023]. Values outside of this range will be truncated.
*
*
* @see #unpackGetSignificand(char)
*/
public static char packSetSignificandUnchecked(
final int s)
{
final int sm = s & Binary16.MASK_SIGNIFICAND;
return (char) sm;
}
/**
*
* Encode the sign bit s. Values should be in the range
* [0, 1], with 0 ironically denoting a positive
* value. Values outside of this range will be truncated.
*
*
* @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 binary16 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();
}
/**
*
* Convert a packed binary16 value k to a
* double-precision floating point value.
*
*
* The function returns:
*
*
* NaN iff isNaN(k)- {@link Double#POSITIVE_INFINITY} iff
*
k == {@link #POSITIVE_INFINITY}
* - {@link Double#NEGATIVE_INFINITY} iff
*
k == {@link #NEGATIVE_INFINITY}
* -0.0 iff k == {@link #NEGATIVE_ZERO}0.0 iff k == {@link #POSITIVE_ZERO}(-1.0 * n) * (2 ^ e) * 1.s, for the decoded sign
* n of k, the decoded exponent e of
* k, and the decoded significand s of
* k.
*
* @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);
}
/**
*
* Convert a packed binary16 value k to a
* single-precision floating point value.
*
*
* The function returns:
*
*
* NaN iff isNaN(k)- {@link Float#POSITIVE_INFINITY} iff
*
k == {@link #POSITIVE_INFINITY}
* - {@link Float#NEGATIVE_INFINITY} iff
*
k == {@link #NEGATIVE_INFINITY}
* -0.0 iff k == {@link #NEGATIVE_ZERO}0.0 iff k == {@link #POSITIVE_ZERO}(-1.0 * n) * (2 ^ e) * 1.s, for the decoded sign
* n of k, the decoded exponent e of
* k, and the decoded significand s of
* k.
*
* @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);
}
/**
*
* Extract and unbias the exponent of the given packed binary16
* value.
*
*
* The exponent is encoded biased as a number in the range
* [0, 31], with 0 indicating that the number is
* subnormal and [1, 30] denoting the actual exponent
* plus {@link #BIAS}. Infinite and NaN values always have an
* exponent of 31.
*
*
* This function will therefore return:
*
*
* -
*
0 - {@link #BIAS} = -15 iff the input is a subnormal
* number.
* - An integer in the range
*
[1 - {@link #BIAS}, 30 - {@link #BIAS}] = [-14, 15] iff the
* input is a normal number.
* -
*
16 iff the input is {@link #POSITIVE_INFINITY},
* {@link #NEGATIVE_INFINITY}, or NaN.
*
*
* @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 binary16 value, as
* an integer in the range [0, 1].
*
* @see Binary16#packSetSignUnchecked(int)
*/
public static int unpackGetSign(
final char k)
{
return (k & Binary16.MASK_SIGN) >> 15;
}
/**
*
* Return the significand of the given packed binary16 value as
* an integer in the range [0, 1023].
*
*
* @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!");
}
}