Package com.io7m.ieee754b16

Class Binary16

java.lang.Object

com.io7m.ieee754b16.Binary16

public final class Binary16
extends Object

Functions to convert values to/from the binary16 format specified in IEEE 754 2008.

Field Summary

Fields

Modifier and Type	Field	Description
static final int	BIAS	The bias value used to offset the encoded exponent.
static final char	NEGATIVE_INFINITY	The encoded form of negative infinity -∞.
static final char	NEGATIVE_ZERO	The encoded form of negative zero -0.
static final char	POSITIVE_INFINITY	The encoded form of positive infinity ∞.
static final char	POSITIVE_ZERO	The encoded form of positive zero 0.

Method Summary

Modifier and Type	Method	Description
static char	exampleNaN()
static boolean	isInfinite(char k)
static boolean	isNaN(char k)
static char	packDouble(double k)	Convert a double precision floating point value to a packed binary16 value.
static char	packFloat(float k)	Convert a single precision floating point value to a packed binary16 value.
static char	packSetExponentUnbiasedUnchecked(int e)	Encode the unbiased exponent e.
static char	packSetSignificandUnchecked(int s)	Encode the significand s.
static char	packSetSignUnchecked(int s)	Encode the sign bit s.
static String	toRawBinaryString(char k)	Show the given raw packed binary16 value as a string of binary digits.
static double	unpackDouble(char k)	Convert a packed binary16 value k to a double-precision floating point value.
static float	unpackFloat(char k)	Convert a packed binary16 value k to a single-precision floating point value.
static int	unpackGetExponentUnbiased(char k)	Extract and unbias the exponent of the given packed binary16 value.
static int	unpackGetSign(char k)	Retrieve the sign bit of the given packed binary16 value, as an integer in the range [0, 1].
static int	unpackGetSignificand(char k)	Return the significand of the given packed binary16 value as an integer in the range [0, 1023].

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Field Details

NEGATIVE_INFINITY

public static final char NEGATIVE_INFINITY

The encoded form of negative infinity -∞.

POSITIVE_INFINITY

public static final char POSITIVE_INFINITY

The encoded form of positive infinity ∞.

POSITIVE_ZERO

public static final char POSITIVE_ZERO

The encoded form of positive zero 0.

NEGATIVE_ZERO

public static final char NEGATIVE_ZERO

The encoded form of negative zero -0.

BIAS

public static final int BIAS

The bias value used to offset the encoded exponent. A given exponent e is encoded as BIAS + e.

Method Details

exampleNaN

public static char exampleNaN()

Returns:

One possible not-a-number value.

isInfinite

public static boolean isInfinite(char k)

Parameters:

k - A packed binary16 value

Returns:

true if the given packed binary16 value is infinite.

isNaN

public static boolean isNaN(char k)

Parameters:

k - A packed binary16 value

Returns:

true if the given packed binary16 value is not a number (NaN).

packDouble

public static char packDouble(double k)

Convert a double precision floating point value to a packed binary16 value.

For the following specific cases, the function returns:

• NaN iff isNaN(k)
• POSITIVE_INFINITY iff k == Double.POSITIVE_INFINITY
• NEGATIVE_INFINITY iff k == Double.NEGATIVE_INFINITY
• NEGATIVE_ZERO iff k == -0.0
• 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.

Parameters:

k - A floating point value

Returns:

A packed binary16 value

See Also:

• unpackDouble(char)

unpackDouble

public static double unpackDouble(char k)

Convert a packed binary16 value k to a double-precision floating point value.

The function returns:

• NaN iff isNaN(k)
• Double.POSITIVE_INFINITY iff k == POSITIVE_INFINITY
• Double.NEGATIVE_INFINITY iff k == NEGATIVE_INFINITY
• -0.0 iff k == NEGATIVE_ZERO
• 0.0 iff k == 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.

Parameters:

k - A packed binary16 value

Returns:

A floating point value

See Also:

• packDouble(double)

unpackFloat

public static float unpackFloat(char k)

Convert a packed binary16 value k to a single-precision floating point value.

The function returns:

• NaN iff isNaN(k)
• Double.POSITIVE_INFINITY iff k == POSITIVE_INFINITY
• Double.NEGATIVE_INFINITY iff k == NEGATIVE_INFINITY
• -0.0 iff k == NEGATIVE_ZERO
• 0.0 iff k == 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.

Parameters:

k - A packed binary16 value

Returns:

A floating point value

See Also:

• packDouble(double)

packFloat

public static char packFloat(float k)

Convert a single precision floating point value to a packed binary16 value.

For the following specific cases, the function returns:

• NaN iff isNaN(k)
• POSITIVE_INFINITY iff k == Float.POSITIVE_INFINITY
• NEGATIVE_INFINITY iff k == Float.NEGATIVE_INFINITY
• NEGATIVE_ZERO iff k == -0.0
• 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.

Parameters:

k - A floating point value

Returns:

A packed binary16 value

See Also:

• unpackFloat(char)

packSetExponentUnbiasedUnchecked

public static char packSetExponentUnbiasedUnchecked(int e)

Encode the unbiased exponent e. Values should be in the range [-15, 16] - values outside of this range will be truncated.

Parameters:

e - An exponent

Returns:

A packed exponent

See Also:

• unpackGetExponentUnbiased(char)

packSetSignificandUnchecked

public static char packSetSignificandUnchecked(int s)

Encode the significand s. Values should be in the range [0, 1023]. Values outside of this range will be truncated.

Parameters:

s - A significand

Returns:

A packed significand

See Also:

• unpackGetSignificand(char)

packSetSignUnchecked

public static char packSetSignUnchecked(int s)

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.

Parameters:

s - A sign bit

Returns:

A packed sign bit

See Also:

• unpackGetSign(char)

toRawBinaryString

public static String toRawBinaryString(char k)

Show the given raw packed binary16 value as a string of binary digits.

Parameters:

k - A packed binary16 value

Returns:

A string representation

unpackGetExponentUnbiased

public static int unpackGetExponentUnbiased(char k)

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 BIAS. Infinite and NaN values always have an exponent of 31.

This function will therefore return:

• 0 - BIAS = -15 iff the input is a subnormal number.
• An integer in the range [1 - BIAS, 30 - BIAS] = [-14, 15] iff the input is a normal number.
• 16 iff the input is POSITIVE_INFINITY, NEGATIVE_INFINITY, or NaN.

Parameters:

k - A packed binary16 value

Returns:

The unbiased exponent

See Also:

• packSetExponentUnbiasedUnchecked(int)

unpackGetSign

public static int unpackGetSign(char k)

Retrieve the sign bit of the given packed binary16 value, as an integer in the range [0, 1].

Parameters:

k - A packed binary16 value

Returns:

An unpacked sign bit

See Also:

• packSetSignUnchecked(int)

unpackGetSignificand

public static int unpackGetSignificand(char k)

Return the significand of the given packed binary16 value as an integer in the range [0, 1023].

Parameters:

k - A packed binary16 value

Returns:

An unpacked significand

See Also:

• packSetSignificandUnchecked(int)