# numerictype

Construct an `embedded.numerictype` object describing fixed-point or floating-point data type

## Syntax

``T = numerictype``
``T = numerictype(s)``
``T = numerictype(s,w)``
``T = numerictype(s,w,f)``
``T = numerictype(s,w,slope,bias)``
``T = numerictype(s,w,slopeadjustmentfactor,fixedexponent,bias)``
``T = numerictype(___,Name,Value)``
``T = numerictype(T1,Name,Value)``
``T = numerictype('Double')``
``T = numerictype('Single')``
``T = numerictype('Half')``
``T = numerictype('Boolean')``

## Description

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````T = numerictype` creates a default `numerictype` object.```

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````T = numerictype(s)` creates a fixed-point `numerictype` object with unspecified scaling, a signed property value of `s`, and a 16-bit word length.```

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````T = numerictype(s,w)` creates a fixed-point `numerictype` object with unspecified scaling, a signed property value of `s`, and word length of `w`.```

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````T = numerictype(s,w,f)` creates a fixed-point `numerictype` object with binary point scaling, a signed property value of `s`, word length of `w`, and fraction length of `f`.```

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````T = numerictype(s,w,slope,bias)` creates a fixed-point `numerictype` object with slope and bias scaling, a signed property value of `s`, word length of `w`, `slope`, and `bias`.```

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````T = numerictype(s,w,slopeadjustmentfactor,fixedexponent,bias)` creates a fixed-point `numerictype` object with slope and bias scaling, a signed property value of `s`, word length of `w`, `slopeadjustmentfactor`, and `bias`.```

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

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````T = numerictype(T1,Name,Value)` allows you to make a copy, `T1`, of an existing `numerictype` object, `T`, while modifying any or all of the property values.```

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````T = numerictype('Double')` creates a `numerictype` object of data type double.```

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````T = numerictype('Single')` creates a `numerictype` object of data type single.```

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````T = numerictype('Half')` creates a `numerictype` object of data type half.```

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````T = numerictype('Boolean')` creates a `numerictype` object of data type Boolean.```

## Examples

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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 ```

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.

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.

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 ```

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:

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

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:

`$\mathrm{slope}=\mathrm{slopeadjustmentfactor}×{2}^{\mathrm{fixedexponent}}$`

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 ```

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 ```

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 ```

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.

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

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Whether the object is signed, specified as a numeric or logical `1` (`true`) or `0` (`false`).

Example: `T = numerictype(true)`

Data Types: `logical`

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`

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

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

Note

`$slope=slopeadjustmentfactor×{\text{2}}^{fixedexponent}$`

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 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`

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

`$slope=slopeadjustmentfactor×{\text{2}}^{fixedexponent}$`

Changing one of these properties affects the others.

Data Types: `half` | `single` | `double` | `int8` | `int16` | `int32` | `int64` | `uint8` | `uint16` | `uint32` | `uint64`

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 comma-separated pairs of `Name,Value` arguments. `Name` is the argument name and `Value` is the corresponding value. `Name` must appear inside quotes. You can specify several name and value pair arguments in any order as `Name1,Value1,...,NameN,ValueN`.

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, 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`

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`

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`

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`

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`

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`

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`

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`

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

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

Note

`$slope=slopeadjustmentfactor×{\text{2}}^{fixedexponent}$`

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`

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

`$slope=slopeadjustmentfactor×{\text{2}}^{fixedexponent}$`

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`

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`

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