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
acosh	Inverse hyperbolic cosine
asin	Inverse sine in radians
asinh	Inverse hyperbolic sine
atan	Inverse tangent in radians
atan2	Four-quadrant inverse tangent
atanh	Inverse hyperbolic tangent
ceil	Round toward positive infinity
conj	Complex conjugate
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
fft	Fast Fourier transform
fft2	2-D fast Fourier transform
fftn	N-D fast Fourier transform
fftshift	Shift zero-frequency component to center of spectrum
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)
ifft	Inverse fast Fourier transform
ifft2	2-D inverse fast Fourier transform
ifftn	Multidimensional inverse fast Fourier transform
ifftshift	Inverse zero-frequency shift
imag	Imaginary part of complex number
ldivide	Left array division
log	Natural logarithm
log10	Common logarithm (base 10)
log1p	Compute log(1+x) accurately for small values of x
mean	Average or mean value of array
minus	Subtraction
mldivide	Solve systems of linear equations Ax = B for x
mod	Remainder after division (modulo operation)
mrdivide	Solve systems of linear equations xA = B for x
mtimes	Matrix multiplication
plus	Add numbers, append strings
pow10	Base 10 power and scale half-precision numbers
pow2	Base 2 power and scale floating-point numbers
power	Element-wise power
prod	Product of array elements
rdivide	Right array division
real	Real part of complex number
rem	Remainder after division
round	Round to nearest decimal or integer
rsqrt	Reciprocal square root
sign	Sign function (signum function)
sin	Sine of argument in radians
sinh	Hyperbolic sine
sinpi	Compute sin(X*pi) accurately
sqrt	Square root
sum	Sum of array elements
tan	Tangent of argument in radians
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 uses complex storage
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
isequal	Determine array equality
isequaln	Determine array equality, treating NaN values as equal
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
circshift	Shift array circularly
colon	Vector creation, array subscripting, and for-loop iteration
complex	Create complex array
ctranspose	Complex conjugate transpose
eye	Identity matrix
flip	Flip order of elements
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
permute	Permute array dimensions
repelem	Repeat copies of array elements
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

Graphics

area	Area of 2-D alpha shape
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

Deep Learning

activations (Deep Learning Toolbox)	Compute deep learning network layer activations
classify (Deep Learning Toolbox)	Classify data using a trained deep learning neural network
predict (Deep Learning Toolbox)	Reconstruct the inputs using trained autoencoder
predictAndUpdateState (Deep Learning Toolbox)	Predict responses using a trained recurrent neural network and update the network state

To display the complete list of supported functions, at the MATLAB^® Command Window, enter:

methods(half(1))

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. 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 performed in single-precision, regardless of the target hardware.

For deep learning code generation, half inputs are cast to single precision and computations are performed in single precision.

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 later is required for generating and executing code with half-precision data types.

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

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

• For GPU Code generation, you can perform half-precision matrix multiplication with real inputs.

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

• fft, fft2, fftn, fftshift, ifft, ifft2, ifftn,and ifftshift are not supported for GPU code generation.

• 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 performed in single-precision, regardless of the target hardware.

• For deep learning code generation, half inputs are cast to single precision and computations are performed in single precision. To perform computations in half, set the library target to 'tensorrt' and set the data type to 'FP16' in coder.DeepLearningConfig.