Half precision

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In computing, half precision is a computer numbering format that occupies only half of one storage location (word) in computer memory at some address. A half-precision number may be defined to be a binary or decimal integer, fixed point, or floating point. For binary integers, they are sometimes called 'short'.

Half-precision floating point is a relatively new binary floating-point format that uses 2 bytes and which is not covered by the IEEE 754 standard for encoding floating point numbers (but is included in the IEEE 754r proposed revision).

This format is used in several computer graphics environments including OpenEXR, OpenGL, and D3DX. The advantage over 8-bit or 16-bit binary integers is that the increased dynamic range allows for more detail to be preserved in highlights and shadows. The advantage over 32-bit single precision binary formats is that it requires half the storage and bandwidth. [1]

1 Half precision memory format
- 1.1 Exponent encodings
2 Half-precision examples in hexadecimal
- 2.1 Usage note
3 See also
4 External links

[edit] Half precision memory format

 Sign bit: 1
 Exponent width: 5  
 Significand precision: 10 (11 implicit)

The format is assumed to have an implicit integer bit with value 1 unless the exponent field is all zeros. Only 10 bits of the fraction appear in the memory format. In IEEE 754 parlance, there are 10 bits of significand, but there are 11 bits of significand precision (approximately 3 decimal digits, $l o g 10 (2 11)$ ).

 syyy yyxx xxxx xxxx (10 xs)

[edit] Exponent encodings

 E_min (0x01) = −14
 E_max (0x1e) = 15
 Exponent bias (0x0f) = 15

The true exponent = written exponent − exponent bias

 0x00 and 0x1f  are reserved exponents 
 0x00 is used to represent zero and denormals
 0x1f is used to represent infinity and NaNs

All bit patterns are valid encodings.

The minimum and maximum representable values are 2^-24 = 5.96E-8 (denormalized) and 65504 respectively. The minimum non-denormalized value is 2^-14 = 6.10E-5.

[edit] Half-precision examples in hexadecimal

 3c00   = 1

 c000   = -2

 7bff   = 65504  (Max Half precision)

 3555   ~ 0.33325... ~ 1/3

(1/3 rounds down like double precision, because of the odd number of bits in the significand.)

 0400   = 2^-14 ~ 6.10352E-5 (Minimum normalized)

 0001   = 2^-24 ~ 5.96046E-8 (Minimum denormalized)

 0000   = 0
 8000   = -0

 7c00   = Infinity
 fc00   = -Infinity

[edit] Usage note

When using half-precision as an adjective, as in half-precision number, hyphenate it. When using it as a noun ("Single precision differs from half precision."), do not hyphenate it. To avoid confusion with other uses, it is best to include the adjective 'binary' when describing the format.