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# Half precision

In computing, half precision is a computer numbering format that occupies only half of one storage locations in computer memory at address. A half-precision number may be defined to be an integer, fixed point, or floating point. For integers, they are typically called short.

Half-precision floating point is a relatively new format that uses 2 bytes and which is not covered by the IEEE 754 standard for encoding floating point numbers.

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

 Contents

## Half precision memory format

``` Sign bit: 1
Exponent width: 5
Significand precision: 11
```

The format is written with an implicit integer bit with value 1 unless the written exponent is all zeros. Thus only 10 bits of the fraction appear in the memory format.

``` syyy yyxx xxxx xxxx (10 xs)
```

### Exponent encodings

``` Emin (0x01) = −14
Emax (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.

``` 3c00   = 1
```
``` c000   = -2
```
``` 7dff   = 65504  (Max Half precision)
```
``` 3555   ~ 0.3325... ~ 1/3
```

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

``` 0000   = 0
8000   = -0
```
``` 7c00   = Infinity
fc00   = -Infinity
```

### Usage note

Pedantic 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.