# numerictype

Construct an `embedded.numerictype`

object describing fixed-point
or floating-point data type

## Syntax

## Description

`T = numerictype`

creates a default `numerictype`

object.

`T = numerictype(`

creates a fixed-point
`s`

)`numerictype`

object with unspecified scaling, a signed property value of
`s`

, and a 16-bit word length.

`T = numerictype(`

creates a fixed-point `s`

,`w`

,`slopeadjustmentfactor`

,`fixedexponent`

,`bias`

)`numerictype`

object with slope and bias scaling, a
signed property value of `s`

, word length of `w`

,
`slopeadjustmentfactor`

, and `bias`

.

`T = numerictype(___,`

allows you to set properties using name-value pairs. All properties that you do not specify
a value for are assigned their default values.`Name,Value`

)

`T = numerictype(T1,`

allows you to
make a copy, `Name,Value`

)`T1`

, of an existing `numerictype`

object,
`T`

, while modifying any or all of the property values.

`T = numerictype('Double')`

creates a `numerictype`

object of data type double.

`T = numerictype('Single')`

creates a `numerictype`

object of data type single.

`T = numerictype('Half')`

creates a `numerictype`

object of data type half.

`T = numerictype('Boolean')`

creates a `numerictype`

object of data type Boolean.

## Examples

### Create a Default `numerictype`

Object

This example shows how to create a `numerictype`

object with default property settings.

T = numerictype

T = DataTypeMode: Fixed-point: binary point scaling Signedness: Signed WordLength: 16 FractionLength: 15

### Create a `numerictype`

Object with Default Word Length and Scaling

This example shows how to create a `numerictype `

object with the default word length and scaling by omitting the arguments for word length, `w`

, and fraction length, `f`

.

T = numerictype(1)

T = DataTypeMode: Fixed-point: unspecified scaling Signedness: Signed WordLength: 16

The object is signed, with a word length of 16 bits and unspecified scaling.

You can use the signedness argument, `s`

, to create an unsigned `numerictype `

object.

T = numerictype(0)

T = DataTypeMode: Fixed-point: unspecified scaling Signedness: Unsigned WordLength: 16

The object is has the default word length of 16 bits and unspecified scaling.

### Create a `numerictype`

Object with Unspecified Scaling

This example shows how to create a `numerictype`

object with unspecified scaling by omitting the fraction length argument, `f`

.

T = numerictype(1,32)

T = DataTypeMode: Fixed-point: unspecified scaling Signedness: Signed WordLength: 32

The object is signed, with a 32-bit word length.

### Create a `numerictype`

Object with Specified Word and Fraction Length

This example shows how to create a signed `numerictype`

object with binary-point scaling, a 32-bit word length, and 30-bit fraction length.

T = numerictype(1,32,30)

T = DataTypeMode: Fixed-point: binary point scaling Signedness: Signed WordLength: 32 FractionLength: 30

### Create a `numerictype`

Object with Slope and Bias Scaling

This example shows how to create a `numerictype`

object with slope and bias scaling. The real-world value of a slope and bias scaled number is represented by:

$$\mathrm{realworldvalue}=\left(\mathrm{slope}\times \mathrm{integer}\right)+\mathrm{bias}$$

Create a `numerictype`

object that describes a signed, fixed-point data type with a word length of 16 bits, a slope of 2^-2, and a bias of 4.

T = numerictype(1,16,2^-2,4)

T = DataTypeMode: Fixed-point: slope and bias scaling Signedness: Signed WordLength: 16 Slope: 0.25 Bias: 4

Alternatively, the slope can be represented by:

$$\mathrm{slope}=\mathrm{slopeadjustmentfactor}\times {2}^{\mathrm{fixedexponent}}$$

Create a `numerictype`

object that describes a signed, fixed-point data type with a word length of 16 bits, a slope adjustment factor of 1, a fixed exponent of -2, and a bias of 4.

T = numerictype(1,16,1,-2,4)

T = DataTypeMode: Fixed-point: slope and bias scaling Signedness: Signed WordLength: 16 Slope: 0.25 Bias: 4

### Create a `numerictype`

Object with Specified Property Values

This example shows how to use name-value pairs to set `numerictype`

properties at object creation.

T = numerictype('Signed',true,... 'DataTypeMode',... 'Fixed-point: slope and bias scaling', ... 'WordLength',32,... 'Slope',2^-2,... 'Bias',4)

T = DataTypeMode: Fixed-point: slope and bias scaling Signedness: Signed WordLength: 32 Slope: 0.25 Bias: 4

### Create a `numerictype`

Object with Unspecified Sign

This example shows how to create a `numerictype`

object with an unspecified sign by using name-value pairs to set the `Signedness`

property to `Auto`

.

T = numerictype('Signedness','Auto')

T = DataTypeMode: Fixed-point: binary point scaling Signedness: Auto WordLength: 16 FractionLength: 15

### Create a `numerictype`

Object with Specified Data Type

This example shows how to create a `numerictype`

object with a specific data type by using arguments and name-value pairs.

T = numerictype(0,24,12,'DataType','ScaledDouble')

T = DataTypeMode: Scaled double: binary point scaling Signedness: Unsigned WordLength: 24 FractionLength: 12

The returned `numerictype `

object, `T`

, is unsigned, and has a word length of 24 bits, a fraction length of 12 bits, and a data type set to scaled double.

### Create a Double, Single, Half, or Boolean `numerictype`

Object

This example shows how to create a `numerictype `

object with data type set to double, single, half, or Boolean at object creation.

Create a `numerictype`

object with the data type mode set to double.

`T = numerictype('Double')`

T = DataTypeMode: Double

Create a `numerictype`

object with the data type mode set to single.

`T = numerictype('Single')`

T = DataTypeMode: Single

Create a `numerictype`

object with the data type mode set to half.

`T = numerictype('Half')`

T = DataTypeMode: Half

Create a `numerictype`

object with the data type mode set to Boolean.

`T = numerictype('Boolean')`

T = DataTypeMode: Boolean

## Input Arguments

`s`

— Whether object is signed

`true`

or `1`

(default) | `false`

or `0`

Whether the object is signed, specified as a numeric or logical `1`

(`true`

) or `0`

(`false`

).

**Example: **`T = numerictype(true)`

**Data Types: **`logical`

`w`

— Word length

`16`

(default) | positive integer

Word length, in bits, of the stored integer value, specified as a positive integer.

**Example: **`T = numerictype(true,16)`

**Data Types: **`half`

| `single`

| `double`

| `int8`

| `int16`

| `int32`

| `int64`

| `uint8`

| `uint16`

| `uint32`

| `uint64`

`f`

— Fraction length

`15`

(default) | integer

Fraction length, in bits, of the stored integer value, specified as an integer.

Fraction length can be greater than word length. For more information, see Binary Point Interpretation (Fixed-Point Designer).

**Example: **`T = numerictype(true,16,15)`

**Data Types: **`half`

| `single`

| `double`

| `int8`

| `int16`

| `int32`

| `int64`

| `uint8`

| `uint16`

| `uint32`

| `uint64`

`slope`

— Slope

`3.0518e-05`

(default) | finite floating-point number greater than zero

Slope, specified as a finite floating-point number greater than zero.

The slope and the bias determine the scaling of a fixed-point number.

**Note**

$$slope=slopeadjustmentfactor\times {\text{2}}^{fixedexponent}$$

Changing one of these properties affects the others.

**Example: **`T = numerictype(true,16,2^-2,4)`

**Data Types: **`half`

| `single`

| `double`

| `int8`

| `int16`

| `int32`

| `int64`

| `uint8`

| `uint16`

| `uint32`

| `uint64`

`bias`

— Bias associated with object

`0`

(default) | floating-point number

Bias associated with the object, specified as a floating-point number.

The slope and the bias determine the scaling of a fixed-point number.

**Example: **`T = numerictype(true,16,2^-2,4)`

**Data Types: **`half`

| `single`

| `double`

| `int8`

| `int16`

| `int32`

| `int64`

| `uint8`

| `uint16`

| `uint32`

| `uint64`

`slopeadjustmentfactor`

— Slope adjustment factor

`1`

(default) | positive scalar

Slope adjustment factor, specified as a positive scalar.

The slope adjustment factor must be greater than or equal to 1 and less than 2. If
you input a `slopeadjustmentfactor`

outside this range, the
`numerictype`

object automatically applies a scaling normalization to
the values of `slopeadjustmentfactor`

and
`fixedexponent`

so that the revised slope adjustment factor is
greater than or equal to 1 and less than 2, and maintains the value of the slope.

The slope adjustment is equivalent to the fractional slope of a fixed-point number.

**Note**

$$slope=slopeadjustmentfactor\times {\text{2}}^{fixedexponent}$$

Changing one of these properties affects the others.

**Data Types: **`half`

| `single`

| `double`

| `int8`

| `int16`

| `int32`

| `int64`

| `uint8`

| `uint16`

| `uint32`

| `uint64`

`fixedexponent`

— Fixed-point exponent

`-15`

(default) | integer

Fixed-point exponent associated with the object, specified as an integer.

**Note**

The `FixedExponent`

property is the negative of the
`FractionLength`

. Changing one property changes the other.

**Data Types: **`half`

| `single`

| `double`

| `int8`

| `int16`

| `int32`

| `int64`

| `uint8`

| `uint16`

| `uint32`

| `uint64`

### Name-Value Arguments

Specify optional pairs of arguments as
`Name1=Value1,...,NameN=ValueN`

, where `Name`

is
the argument name and `Value`

is the corresponding value.
Name-value arguments must appear after other arguments, but the order of the
pairs does not matter.

*
Before R2021a, use commas to separate each name and value, and enclose*
`Name`

*in quotes.*

**Example: **```
F = numerictype('DataTypeMode','Fixed-point: binary point
scaling','DataTypeOverride','Inherit')
```

**Note**

When you create a `numerictype`

object by using name-value pairs,
Fixed-Point Designer™ creates a default `numerictype`

object, and then, for each
property name you specify in the constructor, assigns the corresponding value. This
behavior differs from the behavior that occurs when you use a syntax such as ```
T =
numerictype(s,w)
```

. See Example: Construct a numerictype Object with Property Name and Property Value Pairs.

`Bias`

— Bias

`0`

(default) | floating-point number

Bias, specified as a floating-point number.

The slope and bias determine the scaling of a fixed-point number.

**Example: **```
T = numerictype('DataTypeMode','Fixed-point: slope and bias
scaling','Bias',4)
```

**Data Types: **`half`

| `single`

| `double`

| `int8`

| `int16`

| `int32`

| `int64`

| `uint8`

| `uint16`

| `uint32`

| `uint64`

`DataType`

— Data type category

`'Fixed'`

(default) | `'Boolean'`

| `'Double'`

| `'ScaledDouble'`

| `'Single'`

| `'Half'`

Data type category, specified as one of these values:

`'Fixed'`

– Fixed-point or integer data type`'Boolean'`

– Built-in MATLAB^{®}Boolean data type`'Double'`

– Built-in MATLAB double data type`'ScaledDouble'`

– Scaled double data type`'Single'`

– Built-in MATLAB single data type`'Half'`

– MATLAB half-precision data type

**Example: **`T = numerictype('Double')`

**Data Types: **`char`

`DataTypeMode`

— Data type and scaling mode

`'Fixed-point: binary point scaling'`

(default) | `'Fixed-point: slope and bias scaling'`

| `'Fixed-point: unspecified scaling'`

| `'Scaled double: binary point scaling'`

| `'Scaled double: slope and bias scaling'`

| `'Scaled double: unspecified scaling'`

| `'Double'`

| `'Single'`

| `'Half'`

| `'Boolean'`

Data type and scaling mode associated with the object, specified as one of these values:

`'Fixed-point: binary point scaling'`

– Fixed-point data type and scaling defined by the word length and fraction length`'Fixed-point: slope and bias scaling'`

– Fixed-point data type and scaling defined by the slope and bias`'Fixed-point: unspecified scaling'`

– Fixed-point data type with unspecified scaling`'Scaled double: binary point scaling'`

– Double data type with fixed-point word length and fraction length information retained`'Scaled double: slope and bias scaling'`

– Double data type with fixed-point slope and bias information retained`'Scaled double: unspecified scaling'`

– Double data type with unspecified fixed-point scaling`'Double'`

– Built-in`double`

`'Single'`

– Built-in`single`

`'Half'`

– MATLAB half-precision data type`'Boolean'`

– Built-in`boolean`

**Example: **```
T = numerictype('DataTypeMode','Fixed-point: binary point
scaling')
```

**Data Types: **`char`

`DataTypeOverride`

— Data type override settings

'Inherit' (default) | 'Off'

Data type override settings, specified as one of these values:

`'Inherit'`

– Turn on`DataTypeOverride`

`'Off'`

– Turn off`DataTypeOverride`

**Note**

The `DataTypeOverride`

property is not visible when its value
is set to the default, `'Inherit'`

.

**Example: **```
T =
numerictype('DataTypeOverride','Off')
```

**Data Types: **`char`

`FixedExponent`

— Fixed-point exponent

`-15`

(default) | integer

Fixed-point exponent associated with the object, specified as an integer.

**Note**

The `FixedExponent`

property is the negative of the
`FractionLength`

. Changing one property changes the other.

**Example: **`T = numerictype('FixedExponent',-12)`

**Data Types: **`half`

| `single`

| `double`

| `int8`

| `int16`

| `int32`

| `int64`

| `uint8`

| `uint16`

| `uint32`

| `uint64`

`FractionLength`

— Fraction length of the stored integer value

best precision (default) | integer

Fraction length, in bits, of the stored integer value, specified as an integer.

The default value is the best precision fraction length based on the value of the object and the word length.

**Example: **`T = numerictype('FractionLength',12)`

**Data Types: **`half`

| `single`

| `double`

| `int8`

| `int16`

| `int32`

| `int64`

| `uint8`

| `uint16`

| `uint32`

| `uint64`

`Scaling`

— Fixed-point scaling mode

`'BinaryPoint'`

(default) | `'SlopeBias'`

| `'Unspecified'`

Fixed-point scaling mode of the object, specified as one of these values:

`'BinaryPoint'`

– Scaling for the`numerictype`

object is defined by the fraction length.`'SlopeBias'`

– Scaling for the`numerictype`

object is defined by the slope and bias.`'Unspecified'`

– Temporary setting that is only allowed at`numerictype`

object creation, and allows for the automatic assignment of a best-precision binary point scaling.

**Example: **`T = numerictype('Scaling','BinaryPoint')`

**Data Types: **`char`

`Signed`

— Whether the object is signed

`true`

or `1`

(default) | `false`

or `0`

Whether the object is signed, specified as a numeric or logical
`1`

(`true`

) or `0`

(`false`

).

**Note**

Although the `Signed`

property is still supported, the
`Signedness`

property always appears in the
`numerictype`

object display. If you choose to change or set the
signedness of your `numerictype`

object using the
`Signed`

property, MATLAB updates the corresponding value of the `Signedness`

property.

**Example: **`T = numerictype('Signed',true)`

**Data Types: **`logical`

`Signedness`

— Whether the object is signed

`'Signed'`

(default) | `'Unsigned'`

| `'Auto'`

Whether the object is signed, specified as one of these values:

`'Signed'`

– Signed`'Unsigned'`

– Unsigned`'Auto'`

– Unspecified sign

**Note**

Although you can create `numerictype`

objects with an
unspecified sign (`Signedness: Auto`

), all fixed-point
`numerictype`

objects must have a `Signedness`

of `Signed`

or `Unsigned`

. If you use a
`numerictype`

object with `Signedness: Auto`

to
construct a `numerictype`

object, the `Signedness`

property of the `numerictype`

object automatically defaults to
`Signed`

.

**Example: **`T = numerictype('Signedness','Signed')`

**Data Types: **`char`

`Slope`

— Slope

`3.0518e-05`

(default) | finite, positive floating-point number

Slope, specified as a finite, positive floating-point number.

The slope and bias determine the scaling of a fixed-point number.

**Note**

$$slope=slopeadjustmentfactor\times {\text{2}}^{fixedexponent}$$

Changing one of these properties affects the others.

**Example: **```
T = numerictype('DataTypeMode','Fixed-point: slope and bias
scaling','Slope',2^-2)
```

**Data Types: **`half`

| `single`

| `double`

| `int8`

| `int16`

| `int32`

| `int64`

| `uint8`

| `uint16`

| `uint32`

| `uint64`

`SlopeAdjustmentFactor`

— Slope adjustment factor

`1`

(default) | positive scalar

Slope adjustment factor, specified as a positive scalar.

The slope adjustment factor must be greater than or equal to 1 and less than 2. If
you input a `slopeadjustmentfactor`

outside this range, the
`numerictype`

object automatically applies a scaling normalization
to the values of `slopeadjustmentfactor`

and
`fixedexponent`

so that the revised slope adjustment factor is
greater than or equal to 1 and less than 2, and maintains the value of the
slope.

The slope adjustment is equivalent to the fractional slope of a fixed-point number.

**Note**

$$slope=slopeadjustmentfactor\times {\text{2}}^{fixedexponent}$$

Changing one of these properties affects the others.

**Example: **```
T = numerictype('DataTypeMode','Fixed-point: slope and bias
scaling','SlopeAdjustmentFactor',1.5)
```

**Data Types: **`half`

| `single`

| `double`

| `int8`

| `int16`

| `int32`

| `int64`

| `uint8`

| `uint16`

| `uint32`

| `uint64`

`WordLength`

— Word length of the stored integer value

`16`

(default) | positive integer

Word length, in bits, of the stored integer value, specified as a positive integer.

**Example: **`T = numerictype('WordLength',16)`

**Data Types: **`half`

| `single`

| `double`

| `int8`

| `int16`

| `int32`

| `int64`

| `uint8`

| `uint16`

| `uint32`

| `uint64`

## Extended Capabilities

### C/C++ Code Generation

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

Usage notes and limitations:

Fixed-point signals coming in to a MATLAB Function block from Simulink

^{®}are assigned a`numerictype`

object that is populated with the signal's data type and scaling information.Returns the data type when the input is a non fixed-point signal.

Use to create

`numerictype`

objects in generated code.All

`numerictype`

object properties related to the data type must be constant.

### HDL Code Generation

Generate Verilog and VHDL code for FPGA and ASIC designs using HDL Coder™.

## Version History

**Introduced before R2006a**

### R2021a: Inexact property names for `fi`

, `fimath`

, and
`numerictype`

objects not supported

In previous releases, inexact property names for `fi`

,
`fimath`

, and `numerictype`

objects would result in a
warning. In R2021a, support for inexact property names was removed. Use exact property names
instead.

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