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System Toolbox blocks that have fixed-point support usually allow you to specify fixed-point characteristics through block parameters. By specifying data type and scaling information for these fixed-point parameters, you can simulate your target hardware more closely.

Floating-point inheritance takes precedence over the settings discussed in this section. When the block has floating-point input, all block data types match the input.

You can find most fixed-point parameters on the **Data
Types** pane of System Toolbox blocks. The following figure
shows a typical **Data Types** pane.

All System Toolbox blocks with fixed-point capabilities share a set of common parameters, but each block can have a different subset of these fixed-point parameters. The following table provides an overview of the most common fixed-point block parameters.

Fixed-Point Data Type Parameter | Description |
---|---|

Rounding Mode | Specifies the rounding mode for the block to use when the specified data type and scaling cannot exactly represent the result of a fixed-point calculation. See Rounding Modes for more information on the available options. |

Saturate on integer overflow | When you select this parameter, the block saturates the result of its fixed-point operation. When you clear this parameter, the block wraps the result of its fixed-point operation. For details on saturate and wrap, see Overflow Handling for fixed-point operations. |

Intermediate Product | Specifies the data type and scaling of the intermediate product for fixed-point blocks. Blocks that feed multiplication results back to the input of the multiplier use the intermediate product data type. See the reference page of a specific block to learn about the intermediate product data type for that block. |

Product Output | Specifies the data type and scaling of the product output for fixed-point blocks that must compute multiplication results. See the reference page of a specific block to learn about the product output data type for that block. For or complex-complex multiplication, the multiplication result is in the accumulator data type. See Multiplication Data Types for more information on complex fixed-point multiplication in System toolbox software. |

Accumulator | Specifies the data type and scaling of the accumulator (sum) for fixed-point blocks that must hold summation results for further calculation. Most such blocks cast to the accumulator data type before performing the add operations (summation). See the reference page of a specific block for details on the accumulator data type of that block. |

Output | Specifies the output data type and scaling for blocks. |

The **Data Type Assistant** is an interactive
graphical tool available on the **Data Types** pane
of some fixed-point System Toolbox blocks.

To learn more about using the **Data Type Assistant** to
help you specify block data type parameters, see Specify Data Types Using Data Type Assistant (Simulink).

Some fixed-point System Toolbox blocks have **Minimum** and **Maximum** parameters
on the **Data Types** pane. When a fixed-point data
type has these parameters, you can use them to specify appropriate
minimum and maximum values for range checking purposes.

To learn how to specify signal ranges and enable signal range checking, see Signal Ranges (Simulink).

You can monitor and control fixed-point settings for System
Toolbox blocks at a system or subsystem level with the Fixed-Point
Tool. For more information, see `fxptdlg`

and Fixed-Point Tool (Fixed-Point Designer).

The Fixed-Point Tool logs overflows, saturations, and simulation
minimums and maximums for fixed-point System Toolbox blocks. The Fixed-Point
Tool does not log overflows and saturations when the ```
Data
overflow
```

line in the **Diagnostics > Data
Integrity** pane of the Configuration Parameters dialog
box is set to `None`

.

You can use the Fixed-Point Tool autoscaling feature to set the scaling for System Toolbox fixed-point data types.

System Toolbox blocks obey the `Use local settings`

, `Double`

, `Single`

,
and `Off`

modes of the **Data type
override** parameter in the Fixed-Point Tool. The `Scaled double`

mode is also supported for System
Toolboxes source and byte-shuffling blocks, and for some arithmetic
blocks such as Difference and Normalization.

Selecting appropriate word lengths and scalings for the fixed-point
parameters in your model can be challenging. To aid you, an ```
Inherit
via internal rule
```

choice is often available for fixed-point
block data type parameters, such as the **Accumulator** and **Product
output** signals. The following sections describe how the
word and fraction lengths are selected for you when you choose ```
Inherit
via internal rule
```

for a fixed-point block data type
parameter in System Toolbox software:

In the equations in the following sections, *WL* =
word length and *FL* = fraction length.

The internal rule for accumulator data types first calculates
the ideal, full-precision result. Where *N* is the
number of addends:

$$W{L}_{idealaccumulator}=W{L}_{inputtoaccumulator}+\mathrm{floor}({\mathrm{log}}_{2}(N-1))+1$$

$$F{L}_{idealaccumulator}=F{L}_{inputtoaccumulator}$$

For example, consider summing all the elements of a vector of length 6 and data type sfix10_En8. The ideal, full-precision result has a word length of 13 and a fraction length of 8.

The accumulator can be real or complex. The preceding equations are used for both the real and imaginary parts of the accumulator. For any calculation, after the full-precision result is calculated, the final word and fraction lengths set by the internal rule are affected by your particular hardware. See The Effect of the Hardware Implementation Pane on the Internal Rule for more information.

The internal rule for product data types first calculates the ideal, full-precision result:

$$W{L}_{idealproduct}=W{L}_{input1}+W{L}_{input2}$$

$$F{L}_{idealproduct}=F{L}_{input1}+F{L}_{input2}$$

For example, multiplying together the elements of a real vector of length 2 and data type sfix10_En8. The ideal, full-precision result has a word length of 20 and a fraction length of 16.

For real-complex multiplication, the ideal word length and fraction length is used for both the complex and real portion of the result. For complex-complex multiplication, the ideal word length and fraction length is used for the partial products, and the internal rule for accumulator data types described above is used for the final sums. For any calculation, after the full-precision result is calculated, the final word and fraction lengths set by the internal rule are affected by your particular hardware. See The Effect of the Hardware Implementation Pane on the Internal Rule for more information.

A few System Toolbox blocks have an ```
Inherit via
internal rule
```

choice available for the block output.
The internal rule used in these cases is block-specific, and the equations
are listed in the block reference page.

As with accumulator and product data types, the final output word and fraction lengths set by the internal rule are affected by your particular hardware, as described in The Effect of the Hardware Implementation Pane on the Internal Rule.

The internal rule selects word lengths and fraction lengths
that are appropriate for your hardware. To get the best results using
the internal rule, you must specify the type of hardware you are using
on the **Hardware Implementation** pane of
the Configuration Parameters dialog box. You can open this dialog
box from the **Simulation** menu in your model.

**ASIC/FPGA. **On an ASIC/FPGA target, the ideal, full-precision word length and fraction
length calculated by the internal rule are used. If the calculated ideal word
length is larger than the largest allowed word length, you receive an
error.

**Other targets. **For all targets other than ASIC/FPGA, the ideal, full-precision
word length calculated by the internal rule is rounded up to the next
available word length of the target. The calculated ideal fraction
length is used, keeping the least-significant bits.

If the calculated ideal word length for a product data type is larger than the largest word length on the target, you receive an error. If the calculated ideal word length for an accumulator or output data type is larger than the largest word length on the target, the largest target word length is used.

The largest word length allowed for Simulink^{®} and System Toolbox software on any target is 128 bits.

The following sections show examples of how the internal rule
interacts with the **Hardware Implementation** pane
to calculate accumulator
data types and product
data types.

**Accumulator Data Types. **Consider the following model ex_internalRule_accumExp.

In the Difference blocks, the **Accumulator** parameter
is set to `Inherit: Inherit via internal rule`

,
and the **Output** parameter is set to ```
Inherit:
Same as accumulator
```

. Therefore, you can see the accumulator
data type calculated by the internal rule on the output signal in
the model.

In the preceding model, the **Device type** parameter
in the **Hardware Implementation** pane of
the Configuration Parameters dialog box is set to `ASIC/FPGA`

.
Therefore, the accumulator data type used by the internal rule is
the ideal, full-precision result.

Calculate the full-precision word length for each of the Difference blocks in the model:

$$\begin{array}{l}W{L}_{idealaccumulator}=W{L}_{inputtoaccumulator}+\mathrm{floor}({\mathrm{log}}_{2}(numberofaccumulations))+1\\ W{L}_{idealaccumulator}=9+\mathrm{floor}({\mathrm{log}}_{2}(1))+1\\ W{L}_{idealaccumulator}=9+0+1=10\\ \\ W{L}_{idealaccumulator1}=W{L}_{inputtoaccumulator1}+\mathrm{floor}({\mathrm{log}}_{2}(numberofaccumulations))+1\\ W{L}_{idealaccumulator1}=16+\mathrm{floor}({\mathrm{log}}_{2}(1))+1\\ W{L}_{idealaccumulator1}=16+0+1=17\\ \\ W{L}_{idealaccumulator2}=W{L}_{inputtoaccumulator2}+\mathrm{floor}({\mathrm{log}}_{2}(numberofaccumulations))+1\\ W{L}_{idealaccumulator2}=127+\mathrm{floor}({\mathrm{log}}_{2}(1))+1\\ W{L}_{idealaccumulator2}=127+0+1=128\end{array}$$

Calculate the full-precision fraction length, which is the same for each Matrix Sum block in this example:

$$\begin{array}{l}F{L}_{idealaccumulator}=F{L}_{inputtoaccumulator}\\ F{L}_{idealaccumulator}=4\end{array}$$

Now change the **Device type** parameter in
the **Hardware Implementation** pane of the
Configuration Parameters dialog box to ```
32–bit
Embedded Processor
```

, by changing the parameters as shown
in the following figure.

As you can see in the dialog box, this device has 8-, 16-, and 32-bit word lengths available. Therefore, the ideal word lengths of 10, 17, and 128 bits calculated by the internal rule cannot be used. Instead, the internal rule uses the next largest available word length in each case You can see this if you rerun the model, as shown in the following figure.

**Product Data Types. **Consider the following model ex_internalRule_prodExp.

In the Array-Vector Multiply blocks,
the **Product Output** parameter is set to ```
Inherit:
Inherit via internal rule
```

, and the **Output** parameter
is set to `Inherit: Same as product output`

.
Therefore, you can see the product output data type calculated by
the internal rule on the output signal in the model. The setting of
the **Accumulator** parameter does not matter because
this example uses real values.

For the preceding model, the **Device type** parameter
in the **Hardware Implementation** pane of
the Configuration Parameters dialog box is set to `ASIC/FPGA`

.
Therefore, the product data type used by the internal rule is the
ideal, full-precision result.

Calculate the full-precision word length for each of the Array-Vector Multiply blocks in the model:

$$\begin{array}{l}W{L}_{idealproduct}=W{L}_{inputa}+W{L}_{inputb}\\ W{L}_{idealproduct}=7+5=12\\ \\ W{L}_{idealproduct1}=W{L}_{inputa}+W{L}_{inputb}\\ W{L}_{idealproduct1}=16+15=31\end{array}$$

Calculate the full-precision fraction length, which is the same for each Array-Vector Multiply block in this example:

$$\begin{array}{l}F{L}_{idealaccumulator}=F{L}_{inputtoaccumulator}\\ F{L}_{idealaccumulator}=4\end{array}$$

Now change the **Device type** parameter in
the **Hardware Implementation** pane of the
Configuration Parameters dialog box to ```
32–bit
Embedded Processor
```

, as shown in the following figure.

As you can see in the dialog box, this device has 8-, 16-, and 32-bit word lengths available. Therefore, the ideal word lengths of 12 and 31 bits calculated by the internal rule cannot be used. Instead, the internal rule uses the next largest available word length in each case. You can see this if you rerun the model, as shown in the following figure.

The following sections show you how to use the Fixed-Point Tool
to select appropriate data types for fixed-point blocks in the `ex_fixedpoint_tut`

model:

Open the model by typing ex_fixedpoint_tut at the MATLAB

^{®}command line.This model uses the Cumulative Sum block to sum the input coming from the Fixed-Point Sources subsystem. The Fixed-Point Sources subsystem outputs two signals with different data types:

The Signed source has a word length of 16 bits and a fraction length of 15 bits.

The Unsigned source has a word length of 16 bits and a fraction length of 16 bits.

Run the model to check for overflow. MATLAB displays the following warnings at the command line:

Warning: Overflow occurred. This originated from 'ex_fixedpoint_tut/Signed Cumulative Sum'. Warning: Overflow occurred. This originated from 'ex_fixedpoint_tut/Unsigned Cumulative Sum'.

According to these warnings, overflow occurs in both Cumulative Sum blocks.

To investigate the overflows in this model, use the Fixed-Point Tool. You can open the Fixed-Point Tool by selecting

**Tools**>**Fixed-Point**>**Fixed-Point Tool**from the model menu. Turn on logging for all blocks in your model by setting the**Fixed-point instrumentation mode**parameter to`Minimums, maximums and overflows`

.Now that you have turned on logging, rerun the model by clicking the Simulation button.

The results of the simulation appear in a table in the central

**Contents**pane of the Fixed-Point Tool. Review the following columns:**Name**— Provides the name of each signal in the following format:`Subsystem Name/Block Name: Signal Name`

.**SimDT**— The simulation data type of each logged signal.**SpecifiedDT**— The data type specified on the block dialog for each signal.**SimMin**— The smallest representable value achieved during simulation for each logged signal.**SimMax**— The largest representable value achieved during simulation for each logged signal.**OverflowWraps**— The number of overflows that wrap during simulation.

For more information on each of the columns in this table, see the Contents Pane (Simulink) section of the Simulink

`fxptdlg`

function reference page.You can also see that the

**SimMin**and**SimMax**values for the Accumulator data types range from`0`

to`.9997`

. The logged results indicate that 8,192 overflows wrapped during simulation in the Accumulator data type of the Signed Cumulative Sum block. Similarly, the Accumulator data type of the Unsigned Cumulative Sum block had 16,383 overflows wrap during simulation.To get more information about each of these data types, highlight them in the

**Contents**pane, and click the**Show details for selected result**button ()Assume a target hardware that supports 32-bit integers, and set the Accumulator word length in both Cumulative Sum blocks to

`32`

. To do so, perform the following steps:Right-click the

`Signed Cumulative Sum: Accumulator`

row in the Fixed-Point Tool pane, and select**Highlight Block In Model**.Double-click the block in the model, and select the

**Data Types**pane of the dialog box.Open the

**Data Type Assistant for Accumulator**by clicking the Assistant button () in the Accumulator data type row.Set the

**Mode**to`Fixed Point`

. To see the representable range of the current specified data type, click the**Fixed-point details**link. The tool displays the representable maximum and representable minimum values for the current data type.Change the

**Word length**to`32`

, and click the**Refresh details**button in the**Fixed-point details**section to see the updated representable range. When you change the value of the**Word length**parameter, the**Data Type**edit box automatically updates.Click

**OK**on the block dialog box to save your changes and close the window.Set the word length of the Accumulator data type of the Unsigned Cumulative Sum block to

`32`

bits. You can do so in one of two ways:Type the data type

`fixdt([],32,0)`

directly into**Data Type**edit box for the Accumulator data type parameter.Perform the same steps you used to set the word length of the Accumulator data type of the Signed Cumulative Sum block to

`32`

bits.

To verify your changes in word length and check for overflow, rerun your model. To do so, click the

**Simulate**button in the Fixed-Point Tool.The

**Contents**pane of the Fixed-Point Tool updates, and you can see that no overflows occurred in the most recent simulation. However, you can also see that the**SimMin**and**SimMax**values range from`0`

to`0`

. This underflow happens because the fraction length of the Accumulator data type is too small. The**SpecifiedDT**cannot represent the precision of the data values. The following sections discuss how to find a floating-point benchmark and use the Fixed-Point Tool to propose fraction lengths.

The **Data type override** feature of the Fixed-Point
tool allows you to override the data types specified in your model
with floating-point types. Running your model in `Double`

override
mode gives you a reference range to help you select appropriate fraction
lengths for your fixed-point data types. To do so, perform the following
steps:

Open the Fixed-Point Tool and set

**Data type override**to`Double`

.Run your model by clicking the

**Run simulation and store active results**button.Examine the results in the

**Contents**pane of the Fixed-Point Tool. Because you ran the model in`Double`

override mode, you get an accurate, idealized representation of the simulation minimums and maximums. These values appear in the**SimMin**and**SimMax**parameters.Now that you have an accurate reference representation of the simulation minimum and maximum values, you can more easily choose appropriate fraction lengths. Before making these choices, save your active results to reference so you can use them as your floating-point benchmark. To do so, select

**Results**>**Move Active Results To Reference**from the Fixed-Point Tool menu. The status displayed in the**Run**column changes from`Active`

to`Reference`

for all signals in your model.

Now that you have your `Double`

override
results saved as a floating-point reference, you are ready to propose
fraction lengths.

To propose fraction lengths for your data types, you must have a set of

`Active`

results available in the Fixed-Point Tool. To produce an active set of results, simply rerun your model. The tool now displays both the`Active`

results and the`Reference`

results for each signal.Select the

**Use simulation min/max if design min/max is not available**check box. You did not specify any design minimums or maximums for the data types in this model. Thus, the tool uses the logged information to compute and propose fraction lengths. For information on specifying design minimums and maximums, see Signal Ranges (Simulink).Click the

**Propose fraction lengths**button (). The tool populates the proposed data types in the**ProposedDT**column of the**Contents**pane. The corresponding proposed minimums and maximums are displayed in the**ProposedMin**and**ProposedMax**columns.

Before accepting the fraction lengths proposed by the Fixed-Point Tool, it is important to look at the details of that data type. Doing so allows you to see how much of your data the suggested data type can represent. To examine the suggested data types and accept the proposed scaling, perform the following steps:

In the

**Contents**pane of the Fixed-Point Tool, you can see the proposed fraction lengths for the data types in your model.The proposed fraction length for the Accumulator data type of both the Signed and Unsigned Cumulative Sum blocks is 17 bits.

To get more details about the proposed scaling for a particular data type, highlight the data type in the

**Contents**pane of the Fixed-Point Tool.Open the Autoscale Information window for the highlighted data type by clicking the

**Show autoscale information for the selected result**button ().

When the Autoscale Information window opens, check the

**Value**and**Percent Proposed Representable**columns for the**Simulation Minimum**and**Simulation Maximum**parameters. You can see that the proposed data type can represent 100% of the range of simulation data.To accept the proposed data types, select the check box in the

**Accept**column for each data type whose proposed scaling you want to keep. Then, click the**Apply accepted fraction lengths**button (). The tool updates the specified data types on the block dialog boxes and the**SpecifiedDT**column in the**Contents**pane.To verify the newly accepted scaling, set the

**Data type override**parameter back to**Use local settings**, and run the model. Looking at**Contents**pane of the Fixed-Point Tool, you can see the following details:The

**SimMin**and**SimMax**values of the`Active`

run match the**SimMin**and**SimMax**values from the floating-point`Reference`

run.There are no longer any overflows.

The

**SimDT**does not match the**SpecifiedDT**for the Accumulator data type of either Cumulative Sum block. This difference occurs because the Cumulative Sum block always inherits its**Signedness**from the input signal and only allows you to specify a**Signedness**of`Auto`

. Therefore, the**SpecifiedDT**for both Accumulator data types is`fixdt([],32,17)`

. However, because the Signed Cumulative Sum block has a signed input signal, the**SimDT**for the Accumulator parameter of that block is also signed (`fixdt(1,32,17)`

). Similarly, the**SimDT**for the Accumulator parameter of the Unsigned Cumulative Sum block inherits its**Signedness**from its input signal and thus is unsigned (`fixdt(0,32,17)`

).