To create a fixed-point model, configure Simulink^{®} blocks to output fixed-point signals. Simulink blocks that support fixed-point output provide parameters that allow you to specify whether a block should output fixed-point signals and, if so, the size, scaling, and other attributes of the fixed-point output. These parameters typically appear on the Signal Attributes pane of the block's parameter dialog box.
The following sections explain how to use these parameters to configure a block for fixed-point output.
Many Simulink blocks allow you to specify an output data type and scaling using a parameter that appears on the block dialog box. This parameter (typically named Output data type) provides a pull-down menu that lists the data types a particular block supports. In general, you can specify the output data type as a rule that inherits a data type, a built-in data type, an expression that evaluates to a data type, or a Simulink data type object. For more information, see Control Signal Data Types.
The Fixed-Point Designer™ software enables you to configure Simulink blocks with:
Fixed-point data types
Fixed-point data types are characterized by their word size in bits and by their binary point—the means by which fixed-point values are scaled. See Fixed-Point Data Types for more information.
Floating-point data types
Floating-point data types are characterized by their sign bit, fraction (mantissa) field, and exponent field. See Floating-Point Numbers for more information.
To configure blocks with Fixed-Point Designer data types, specify the data type parameter on a block dialog box as an expression that evaluates to a data type. Alternatively, you can use an assistant that simplifies the task of entering data type expressions (see Specify Fixed-Point Data Types with the Data Type Assistant). The sections that follow describe varieties of fixed-point and floating-point data types, and the corresponding functions that you use to specify them.
To specify unsigned and signed integers, use the uint
and sint
functions,
respectively.
For example, to configure a 16-bit unsigned integer via the
block dialog box, specify the Output data type parameter
as uint(16)
. To configure a 16-bit signed integer,
specify the Output data type parameter as sint(16)
.
For integer data types, the default binary point is assumed to lie to the right of all bits.
To specify unsigned and signed fractional numbers, use the ufrac
and sfrac
functions,
respectively.
For example, to configure the output as a 16-bit unsigned fractional
number via the block dialog box, specify the Output data
type parameter to be ufrac(16)
. To configure
a 16-bit signed fractional number, specify Output data type to
be sfrac(16)
.
Fractional numbers are distinguished from integers by their default scaling. Whereas signed and unsigned integer data types have a default binary point to the right of all bits, unsigned fractional data types have a default binary point to the left of all bits, while 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 act to guard against overflow. For example, sfrac(16,4)
specifies
a 16-bit signed fractional number with 4 guard bits. The guard bits
lie to the left of the default binary point.
You can specify unsigned and signed generalized fixed-point
numbers with the ufix
and sfix
functions, respectively.
For example, to configure the output as a 16-bit unsigned generalized
fixed-point number via the block dialog box, specify the Output
data type parameter to be ufix(16)
.
To configure a 16-bit signed generalized fixed-point number, specify Output
data type to be sfix(16)
.
Generalized fixed-point numbers are distinguished from integers and fractionals by the absence of a default scaling. For these data types, a block typically inherits its scaling from another block.
Note:
Alternatively, you can use the |
The Fixed-Point Designer software supports single-precision
and double-precision floating-point numbers as defined by the IEEE^{®} Standard
754-1985 for Binary Floating-Point Arithmetic. You can specify floating-point
numbers with the Simulink float
function.
For example, to configure the output as a single-precision floating-point
number via the block dialog box, specify the Output data
type parameter as float('single')
. To
configure a double-precision floating-point number, specify Output
data type as float('double')
.
The Data Type Assistant is an interactive graphical tool that simplifies the task of specifying data types for Simulink blocks and data objects. The assistant appears on block and object dialog boxes, adjacent to parameters that provide data type control, such as the Output data type parameter. For more information about accessing and interacting with the assistant, see Specify Data Types Using Data Type Assistant.
You can use the Data Type Assistant to
specify a fixed-point data type. When you select Fixed
point
in the Mode field, the assistant
displays fields for describing additional attributes of a fixed-point
data type, as shown in this example:
You can set the following fixed-point attributes:
Select whether you want the fixed-point data to be Signed
or Unsigned
.
Signed data can represent positive and negative quantities. Unsigned
data represents positive values only.
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 128 bits are supported for simulation.
Specify the method for scaling your fixed-point data to avoid overflow conditions and minimize quantization errors. You can select the following scaling modes:
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, as in this example:
See Binary-Point-Only Scaling for more information. |
Slope and bias | If you select this mode, the assistant displays fields for entering the Slope and Bias.
See Slope and 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. |
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. To calculate best-precision-scaling values automatically, enter
values for the block's Output minimum and Output
maximum parameters. Afterward, click the Calculate
Best-Precision Scaling button in the assistant.
You specify how fixed-point numbers are rounded with the Integer rounding mode parameter. The following rounding modes are supported:
Ceiling
— This mode
rounds toward positive infinity and is equivalent to the MATLAB^{®} ceil
function.
Convergent
— This
mode rounds 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
— This mode
rounds toward negative infinity and is equivalent to the MATLAB floor
function.
Nearest
— This mode
rounds 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
— This mode
rounds 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
— This
mode automatically chooses between round toward floor and round toward
zero to produce generated code that is as efficient as possible.
Zero
— This mode
rounds toward zero and is equivalent to the MATLAB fix
function.
For more information about each of these rounding modes, see Rounding.
To control how overflow conditions are handled for fixed-point operations, use the Saturate on integer overflow check box.
If this 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 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.
If the output data type is a generalized fixed-point number, you have the option of locking its output data type setting by selecting 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.
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.
The possible values are Real World Value (RWV)
and Stored
Integer (SI)
.
In terms of the variables defined in Scaling, the real-world value is given by V and the stored integer value is given by Q. You may want to treat numbers as stored integer values if you are modeling hardware that produces integers as output.