Configure Blocks with Fixed-Point Output

You can use fixed-point data types in your Simulink^® model to create efficient designs and perform bit-true simulations prior to hardware deployment. Fixed-Point Designer™ helps you meet the data type requirements for your desired hardware target by fine-tuning the data types for the blocks in your system.

To create a fixed-point model, configure Simulink blocks to output fixed-point signals. Simulink blocks that support fixed-point output have parameters that allow you to specify whether a block should output fixed-point signals and, if so, to set the size, scaling, and other attributes of the fixed-point output. These parameters appear on the block parameter dialog box on the Signal Attributes pane or the Data Types pane.

Specify Output Data Type and Scaling

Specify an output data type and scaling for a block using the Output data type parameter. The parameter drop-down list provides these options for specifying the block's output data type:

• Rules for inheriting data types

• Built-in data types

• An expression that evaluates to a data type

• A Simulink data type object.

The options for the Output data type parameter vary based on the supported data types for a particular block.

Use fixdt to Specify Output Data Types

You can enter a fixdt function to specify the Output data type parameter. The fixdt function allows you to specify floating point and fixed-point types, and to adjust the scaling of a fixed-point data type. For binary point scaling, use this syntax to specify a fraction length.

fixdt(Signed,WordLength,FractionLength)

For slope-bias scaling, use one of these syntaxes to specify the slope and bias.

fixdt(Signed,WordLength,Slope,Bias)
fixdt(Signed,WordLength,SlopeAdjustmentFactor,FixedExponent,Bias)

The table shows examples of binary-point scaled and unscaled data types you can specify with fixdt.

Data Type	Description	Examples
Integers	Integer values have a default binary point located to the right of all bits.	fixdt(0,16,0) specifies a 16-bit unsigned integer. fixdt(1,16,0) specifies a 16-bit signed integer.
Fractional Numbers	Fractional numbers are characterized by the position of the binary point. Unsigned fractional data types have a default binary point to the left of all bits. Signed fractional data types have a default binary point to the right of the sign bit. Both unsigned and signed fractional data types support guard bits, which guard against overflow.	fixdt(0,16,16) specifies a 16-bit unsigned fractional number. fixdt(1,16,15) specifies a 16-bit signed fractional number. fixdt(1,16,11) specifies a 16-bit signed fractional number with 4 guard bits. The guard bits lie to the left of the default binary point.
Fixed-Point Numbers with Unspecified Scaling	Fixed-point numbers with no default scaling. Note Fixed-point numbers with unspecified scaling are only supported for blocks with Output minimum and Output maximum parameters. When scaling is unspecified for these blocks, the software will select a scaling that fits the desired range.	fixdt(0,16) specifies a 16-bit unsigned generalized fixed-point number. fixdt(1,16) a 16-bit signed generalized fixed-point number.
Slope and Bias Scaled Number	Slope and bias scaled numbers use a linear transformation defined by a slope and a bias.	fixdt(0,16,0,1.5,2) specifies a 16-bit unsigned slope-bias scaled number with a slope of 1.5 and a bias of 2. The numerical value is calculated as Value = Raw Integer ×⁢⁢ 1.5 + 2 . fixdt(0,16,1.5,0,2) specifies a 16-bit unsigned slope-bias scaled number with a slope adjustment factor of 1.5, fixed exponent 0, and bias 2.The numerical value is calculated as Value = Raw Integer ×⁢⁢ (1.5 ×⁢ ⁢20)+ 2 .
Floating-Point Numbers	Single-precision and double-precision floating-point numbers as defined by the IEEE® Standard 754–1985 for Binary Floating-Point Arithmetic.	fixdt('single') specifies a single-precision floating-point number. fixdt('double') specifies a double-precision floating-point number.

Specify Fixed-Point Data Types with the Data Type Assistant

The Data Type Assistant is a graphical interactive tool that helps you specify data types for Simulink blocks and data objects. The assistant appears on block and object dialog boxes. You can access the assistant by clicking the Show data type assistant button located to the right of the Output data type parameter.

To use the Data Type Assistant to specify a fixed-point data type, set the Mode parameter to Fixed point. The assistant displays fields to specify the attributes of a fixed-point data type.

Signedness

Set the fixed-point data to Signed or Unsigned. Signed data can represent positive and negative quantities. Unsigned data represents positive values only.

Word Length

Specify the size (in bits) of the word that will hold the quantized integer. Large word sizes represent large quantities with greater precision than small word sizes. Fixed-point word sizes up to 65535 bits are supported for simulation.

Scaling

Specify the method for scaling your fixed-point data to avoid overflow conditions and minimize quantization errors.

Scaling Mode	Description
Binary point	If you select this mode, the assistant displays the Fraction length field, specifying the binary point location. Binary points can be positive or negative integers. A positive integer moves the binary point left of the rightmost bit by that amount. For example, an entry of 2 sets the binary point in front of the second bit from the right. A negative integer moves the binary point further right of the rightmost bit by that amount. See Binary-Point Scaling for more information.
Slope and bias	If you select this mode, the assistant displays fields for entering the Slope and Bias. Slope can be any positive real number. Bias can be any real number. See Slope-Bias Scaling for more information.
Best precision	If you select this mode, the block scales a constant vector or matrix such that the precision of its elements is maximized. This mode is available only for particular blocks. See Constant Scaling for Best Precision for more information.

Calculate Best-Precision Scaling

The Fixed-Point Designer software can automatically calculate best-precision values for both Binary point and Slope and bias scaling, based on the values that you specify for other parameters on the dialog box. The best-precision scaling maximizes precision within the given bit width constraints.

To calculate best-precision-scaling values automatically, enter values for the Output minimum and Output maximum parameters. Then click Calculate Best-Precision Scaling.

Rounding

Use the Integer rounding mode parameter to specify how fixed-point numbers are rounded.

The rounding mode determines how numbers are represented within a fixed-point data type when they cannot be represented exactly due to limitations on precision. These rounding modes are supported:

• Ceiling — Round toward positive infinity. This mode is equivalent to the MATLAB^® ceil function.

• Convergent — Round toward the nearest representable number, with ties rounding to the nearest even integer. Convergent rounding is equivalent to the Fixed-Point Designer convergent function.

• Floor — Round toward negative infinity. This mode is equivalent to the MATLAB floor function.

• Nearest — Round toward the nearest representable number, with the exact midpoint rounded toward positive infinity. Rounding toward nearest is equivalent to the Fixed-Point Designer nearest function.

• Round — Round to the nearest representable number, with ties for positive numbers rounding in the direction of positive infinity and ties for negative numbers rounding in the direction of negative infinity. This mode is equivalent to the Fixed-Point Designer round function.

• Simplest — Automatically choose between round toward floor and round toward zero to produce generated code that is as efficient as possible.

• Zero — Round toward zero. This mode is equivalent to the MATLAB fix function.

For more information on each of these rounding modes, see Rounding Modes.

Overflow Handling

To control how overflow conditions are handled for fixed-point operations, select Saturate on integer overflow.

If this check box is selected, overflows saturate to either the maximum or minimum value represented by the data type. For example, an overflow associated with a signed 8-bit integer can saturate to -128 or 127.

If this check box is not selected, overflows wrap to the appropriate value that is representable by the data type. For example, the number 130 does not fit in a signed 8-bit integer, and would wrap to -126.

Lock the Output Data Type Setting

To lock the output data type setting of a block, select the Lock output data type setting against changes by the fixed-point tools check box.

When locked, the Fixed-Point Tool and automatic scaling script autofixexp do not change the output data type setting. Otherwise, the Fixed-Point Tool and autofixexp script are free to adjust the output data type setting.

Real-World Values Versus Stored Integer Values

You can configure Data Type Conversion blocks to treat signals as real-world values or as stored integers with the Input and output to have equal parameter.

• Real World Value (RWV) - Signals are treated as the real-world values that they represent, accounting for scaling applied to the number. Real-world values are commonly used for high-level system modeling, testing, and validation.

• Stored Integer (SI) - Signals are treated as the raw integer value stored in memory, without accounting for scaling. Stored integer values are commonly used for modeling hardware that produces integers as output.

For more information about how integers are scaled to store real-world values, see Scaling, Range, and Precision.