org.monte.media.math.ExtendedReal Maven / Gradle / Ivy
/*
* @(#)ExtendedReal.java 0.1 2000-10-06
*
* Copyright (c) 1999-2000 Werner Randelshofer, Goldau, Switzerland.
* All rights reserved.
*
* You may not use, copy or modify this file, except in compliance with the
* license agreement you entered into with Werner Randelshofer.
* For details see accompanying license terms.
*/
package org.monte.media.math;
/**
* Represents an extended-real number as specified by IEEE 754.
*
* An extended-real number uses 80 bits to represent a floating point
* number. It is able to represent numbers ranging from 3.37*10^-4932
* up to 1.18*10^4932.
*
* Bit layout
*
* 79 78-64 63 62-0
* Sign Biased Exponent Integer Fraction
*
*
* For the single-real and double-real formats, only the fraction part
* of the significand is encoded. The integer is assumed to be 1 for
* all numbers except 0 and denormalized finite numbers. For the
* extended-real format, the integer is contained in bit 64, and the
* most significant fraction bit is bit 62. Here, the integer is
* explicitly set to 1 for normalized numbers, infinites, and NaNs,
* and to 0 for zero and denormalized numbers.
*
* The exponent is encoded in biased format. The biasing constant is
* 16'383 for the extended-real format.
*
* NaN Encodings for ExtendedReal:
*
* Class Sign Biased Significand
* Exponent Integer Fraction
* ------------------------------------------------------------
* Positive +Infinity 0 11..11 1 00..00
* +Normals 0 11..10 1 11..11
* . . . .
* . . . .
* 0 00..01 1 00..00
* +Denormals 0 00..00 0 11..11
* . . . .
* . . . .
* 0 00..00 0 00..01
* +Zero 0 00..00 0 00..00
* Negative -Zero 1 00..00 0 00..00
* -Denormals 1 00..00 0 00..01
* . . . .
* . . . .
* 1 00..00 0 11..11
* -Normals 1 00..01 1 00..01
* . . . .
* . . . .
* 1 11..10 1 11..11
* -Infinity 1 11..11 1 00..00
* NaNs SNaN X 11..11 1 0X..XX(2
* QNaN X 11..11 1 1X..XX
* Real Indefinite 1 11..11 1 10..00
*
*
* (2 The fraction for SNaN encodings must be non zero.
*
* @author Werner Randelshofer, Hausmatt 10, CH-6405 Goldau, Switzerland.
* @version 0.1 2000-10-06 Conversions from bit array, and to double only.
*/
public class ExtendedReal
extends Number {
/** bit 79: negSign*/
private boolean negSign;
/** bit 78 - 64: biased exponent. */
private int exponent;
/** bit 63: Integer; 62 - 0: Fraction */
private long mantissa;
public final static ExtendedReal MAX_VALUE = new ExtendedReal(
// negSign -----exponent----- int ------------------------------------------------fraction----------------------------------
// 79 78..72 71..64 63 62..54 53..48 47..40 39..32 31..24 23..16 15..8 7..0
new byte[] { (byte)0x7f, (byte)0xfe, (byte)0xff, (byte)0xff, (byte)0xff, (byte)0xff, (byte)0xff, (byte)0xff, (byte)0xff, (byte)0xff}
);
public final static ExtendedReal MIN_VALUE = new ExtendedReal(
// negSign -----exponent----- int ------------------------------------------------fraction----------------------------------
// 79 78..72 71..64 63 62..54 53..48 47..40 39..32 31..24 23..16 15..8 7..0
new byte[] { (byte)0xff, (byte)0xfe, (byte)0xff, (byte)0xff, (byte)0xff, (byte)0xff, (byte)0xff, (byte)0xff, (byte)0xff, (byte)0xff}
);
public final static ExtendedReal NaN = new ExtendedReal(
// negSign -----exponent----- int ------------------------------------------------fraction----------------------------------
// 79 78..72 71..64 63 62..54 53..48 47..40 39..32 31..24 23..16 15..8 7..0
new byte[] { (byte)0xff, (byte)0xff, (byte)0xff, (byte)0xff, (byte)0xff, (byte)0xff, (byte)0xff, (byte)0xff, (byte)0xff, (byte)0xff}
);
public final static ExtendedReal NEGATIVE_INFINITY = new ExtendedReal(
// negSign -----exponent----- int ------------------------------------------------fraction----------------------------------
// 79 78..72 71..64 63 62..54 53..48 47..40 39..32 31..24 23..16 15..8 7..0
new byte[] { (byte)0xff, (byte)0xff, (byte)0x00, (byte)0x00, (byte)0x00, (byte)0x00, (byte)0x00, (byte)0x00, (byte)0x00, (byte)0x00}
);
public final static ExtendedReal POSITIVE_INFINITY = new ExtendedReal(
// negSign -----exponent----- int ------------------------------------------------fraction----------------------------------
// 79 78..72 71..64 63 62..54 53..48 47..40 39..32 31..24 23..16 15..8 7..0
new byte[] { (byte)0x7f, (byte)0xff, (byte)0x00, (byte)0x00, (byte)0x00, (byte)0x00, (byte)0x00, (byte)0x00, (byte)0x00, (byte)0x00}
);
public ExtendedReal(byte[] bits) {
negSign = (bits[0] & 0x80) != 0;
exponent = (bits[0] & 0x7f) << 8 | (bits[1] & 0xff);
mantissa =
(bits[2] & 0xffL) << 56 |
(bits[3] & 0xffL) << 48 |
(bits[4] & 0xffL) << 40 |
(bits[5] & 0xffL) << 32 |
(bits[6] & 0xffL) << 24 |
(bits[7] & 0xffL) << 16 |
(bits[8] & 0xffL) << 8 |
(bits[9] & 0xffL) << 0;
}
public ExtendedReal(double d) {
if (Double.isNaN(d)) {
negSign = NaN.negSign;
exponent = NaN.exponent;
mantissa = NaN.mantissa;
} else if (Double.isInfinite(d)) {
if (d < 0.0) {
negSign = NEGATIVE_INFINITY.negSign;
exponent = NEGATIVE_INFINITY.exponent;
mantissa = NEGATIVE_INFINITY.mantissa;
} else {
negSign = POSITIVE_INFINITY.negSign;
exponent = POSITIVE_INFINITY.exponent;
mantissa = POSITIVE_INFINITY.mantissa;
}
} else if (d == +0.0) {
// nothing to do
} else if (d == -0.0) {
negSign = true;
} else {
long longBits = Double.doubleToLongBits(d);
negSign = (longBits & 0x8000000000000000L) != 0L;
exponent = ((int) (longBits & 0x7ff0000000000000L) >>> 52) - 1023 + 16383;
mantissa = 0x8000000000000000L | (longBits & 0x000fffffffffffffL) << 11;
}
}
public boolean isNaN() {
return exponent == 0x7ffff && (mantissa & 0x7fffffffffffffffL) != 0;
}
public boolean isInfinite() {
return exponent == 0x7ffff && mantissa == 0x7fffffffffffffffL;
}
public double doubleValue() {
if (isNaN()) {
return Double.NaN;
}
long longBits = 0;
// biased exponent
int biasedExponent = exponent - 16383 + 1023;
if (biasedExponent > 2047) {
// overflow
return (negSign) ? Double.NEGATIVE_INFINITY : Double.POSITIVE_INFINITY;
}
if (biasedExponent < 0 || (mantissa & 0x8000000000000000L) == 0L) {
// underflow
return 0.0;
}
// negSign
if (negSign) {
longBits = 0x8000000000000000L;
}
longBits = longBits | (((long) biasedExponent) << 52);
longBits = longBits | ((mantissa & 0x7fffffffffffffffL) >>> 11);
return Double.longBitsToDouble(longBits);
}
public float floatValue() {
return (float) doubleValue();
}
public int intValue() {
return (int) doubleValue();
}
public long longValue() {
return (long) doubleValue();
}
public int hashCode() {
long bits = Double.doubleToLongBits(doubleValue());
return (int)(bits ^ (bits >>> 32));
}
public boolean equals(Object obj) {
return (obj != null)
&& (obj instanceof ExtendedReal)
&& (equals((ExtendedReal) obj));
}
public boolean equals(ExtendedReal obj) {
return negSign == obj.negSign && exponent == obj.exponent && mantissa == obj.mantissa;
}
/**
* FIXME: Loss of precision, because we currently convert to double before
* we create the String.
*/
public String toString() {
return Double.toString(doubleValue());
}
}
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