half

Construct half-precision numeric object

Description

Use the half constructor to assign a half-precision data type to a number or variable. A half-precision data type occupies 16 bits of memory, but its floating-point representation enables it to handle wider dynamic ranges than integer or fixed-point data types of the same size.

For more information, see Floating-Point Numbers.

Creation

Syntax

a = half(v)

Description

a = half(v) converts the values in v to half-precision.

Input Arguments

v — Input array

scalar | vector | matrix | multidimensional array

Input array, specified as a scalar, vector, matrix, or multidimensional array.

Data Types: single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64 | logical
Complex Number Support: Yes

Object Functions

These functions are supported for use with half-precision inputs.

Math and Arithmetic

abs	Absolute value and complex magnitude
acos	Inverse cosine in radians
asin	Inverse sine in radians
atanh	Inverse hyperbolic tangent
ceil	Round toward positive infinity
conv	Convolution and polynomial multiplication
conv2	2-D convolution
cos	Cosine of argument in radians
cospi	Compute cos(X*pi) accurately
dot	Dot product
exp	Exponential
expm1	Compute exp(x)-1 accurately for small values of x
fix	Round toward zero
floor	Round toward negative infinity
fma	Multiply and add using fused multiply add approach
hypot	Square root of sum of squares (hypotenuse)
ldivide	Left array division
log	Natural logarithm
log1p	Compute log(1+x) accurately for small values of x
mean	Average or mean value of array
minus	Subtraction
mod	Remainder after division (modulo operation)
mtimes	Matrix multiplication
plus	Addition
pow10	Base 10 power and scale half-precision numbers
pow2	Base 2 power and scale floating-point numbers
prod	Product of array elements
rdivide	Right array division
rem	Remainder after division
round	Round to nearest decimal or integer
rsqrt	Reciprocal square root
sin	Sine of argument in radians
sinpi	Compute sin(X*pi) accurately
sqrt	Square root
sum	Sum of array elements
tanh	Hyperbolic tangent
times	Multiplication
uminus	Unary minus
uplus	Unary plus

Data Types

cast	Convert variable to different data type
cell	Cell array
double	Double-precision arrays
eps	Floating-point relative accuracy
Inf	Create array of all Inf values
int16	16-bit signed integer arrays
int32	32-bit signed integer arrays
int64	64-bit signed integer arrays
int8	8-bit signed integer arrays
isa	Determine if input has specified data type
isfloat	Determine whether input is floating-point data type
islogical	Determine if input is logical array
isnan	Determine which array elements are NaN
isnumeric	Determine whether input is numeric array
isreal	Determine whether array is real
logical	Convert numeric values to logicals
NaN	Create array of all NaN values
single	Single-precision arrays
uint16	16-bit unsigned integer arrays
uint32	32-bit unsigned integer arrays
uint64	64-bit unsigned integer arrays
uint8	8-bit unsigned integer arrays

Relational and Logical Operators

all	Determine if all array elements are nonzero or true
and	Find logical AND
any	Determine if any array elements are nonzero
eq	Determine equality
ge	Determine greater than or equal to
gt	Determine greater than
le	Determine less than or equal to
lt	Determine less than
ne	Determine inequality
not	Find logical NOT
or	Find logical OR

Array and Matrix Operations

cat	Concatenate arrays
colon	Vector creation, array subscripting, and for-loop iteration
eye	Identity matrix
full	Convert sparse matrix to full storage
horzcat	Horizontal concatenation for heterogeneous arrays
iscolumn	Determine whether input is column vector
isempty	Determine whether array is empty
isfinite	Determine which array elements are finite
isinf	Determine which array elements are infinite
ismatrix	Determine whether input is matrix
isrow	Determine whether input is row vector
isscalar	Determine whether input is scalar
isvector	Determine whether input is vector
length	Length of largest array dimension
max	Maximum elements of an array
min	Minimum elements of an array
ndims	Number of array dimensions
numel	Number of array elements
ones	Create array of all ones
repmat	Repeat copies of array
reshape	Reshape array
size	Array size
subsasgn	Redefine subscripted assignment
subsref	Subscripted reference
transpose	Transpose vector or matrix
vertcat	Vertical concatenation for heterogeneous arrays
zeros	Create array of all zeros

Language Fundamentals

display	Show information about variable or result of expression
end	Terminate block of code or indicate last array index

Graphics

bar	Bar graph
barh	Horizontal bar graph
fplot	Plot expression or function
line	Create primitive line
plot	2-D line plot
plot3	3-D point or line plot
plotmatrix	Scatter plot matrix
rgbplot	Plot colormap
scatter	Scatter plot
scatter3	3-D scatter plot
xlim	Set or query x-axis limits
ylim	Set or query y-axis limits
zlim	Set or query z-axis limits

Examples

Convert Value to Half Precision

To cast a double-precision number to half precision, use the half function.

a = half(pi)

a = 

  half

    3.1406

You can also use the half function to cast an existing variable to half-precision.

v = single(magic(3))

v = 3x3 single matrix

     8     1     6
     3     5     7
     4     9     2

a = half(v)

a = 

  3x3 half matrix

     8     1     6
     3     5     7
     4     9     2

Limitations

The following functions which support half-precision inputs, do not support complex half-precision inputs.

• rsqrt

• fma

Extended Capabilities

C/C++ Code Generation

Generate C and C++ code using MATLAB® Coder™.

All functions that support half-precision inputs, support code generation, except for the rsqrt function.

In MATLAB^®, the isobject function returns true with a half-precision input. However, in generated code, this function returns false.

If your target hardware does not have native support for half-precision, then half is used as a storage type, with arithmetic operations performed in single precision.

Some functions use half only as a storage type and the arithmetic is always performed in single-precision, regardless of the target hardware.

Code generation for 32-bit targets is not supported if your MATLAB code contains half-precision data types.

GPU Code Generation

Generate CUDA® code for NVIDIA® GPUs using GPU Coder™.

• CUDA^® compute capability of 5.3 or higher is required for generating and executing code with half-precision data types.

• CUDA toolkit version of 10.0 or higher is required for generating and executing code with half-precision data types.

• The memory allocation (malloc) mode for generating CUDA code must be set to 'Discrete'.

• Half-precision complex data types are not supported for GPU code generation.

• For GPU Code generation, half-precision matrix multiplication can only be performed with real inputs.

• In MATLAB, the isobject function returns true with a half-precision input. However, in generated code, this function returns false.

• If your target hardware does not have native support for half-precision, then half is used as a storage type, with arithmetic operations performed in single precision.

• Some functions use half only as a storage type and the arithmetic is always performed in single-precision, regardless of the target hardware.

• Code generation for 32-bit targets is not supported if your MATLAB code contains half-precision data types.