Specify Behavioral Constraints

To determine if the numerical behavior of a new fixed-point implementation is acceptable, define constraints by setting signal tolerances, by using one or more model verification blocks, or both.

In the Optimized Fixed-Point Conversion workflow of the Fixed-Point Tool, or when using fxpopt at the command line, you must specify at least one behavioral constraint. Data types are optimized to meet all specified constraints.

In the Iterative Fixed-Point Conversion workflow of the Fixed-Point Tool, or when using DataTypeWorkflow.Converter at the command line, you can specify behavioral constraints to verify the numerical behavior of the model with embedded types. After simulating with embedded types, the Workflow Browser indicates whether the embedded run meets the specified signal tolerances compared to the range collection run. For more information, see Verify New Settings.

Specify Signal Tolerances

You can specify tolerances for signals in your model that have signal logging enabled. To enable signal logging:

• In the Simulink^® Editor, select one or more signals.

• In the Signal tab of the Simulink Editor, click Log Signals.

In the Fixed-Point Tool, specify individual signal tolerances in the table under Signal Tolerances. The table contains all signals in the model with signal logging enabled. If you log additional signals after opening the Fixed-Point Tool, click Refresh Signals to update the Signal Tolerances table. At the command line, specify tolerances using the addTolerance method.

You can specify any of the following types of tolerances:

• Abs Tol — Absolute value of the maximum acceptable difference between the original signal and the signal in the converted design.

• Rel Tol — Maximum relative difference, specified as a percentage, between the original signal and the signal in the converted design. For example, a value of 1e-2 indicates a maximum relative difference of one percent.

• Time Tol (seconds) — Time interval, in which the maximum and minimum values define the upper and lower values to compare against.

Enter signal tolerances using any valid MATLAB^® expression that returns a finite, non-negative value. (since R2023a)

You can define a tolerance band using any combination of absolute, relative, and time tolerance values. When you specify the tolerance for your signal using multiple types of tolerances, the overall tolerance band is computed by selecting the most lenient tolerance result for each data point. For more information about how tolerances are computed, see Tolerance Computation.

Use Model Verification Blocks

You can use enabled Model Verification blocks to specify constraints on the behavior of your system.

The blocks in the Model Verification library maintain a true (1) assertion when a specified desired behavior is maintained by the input signals. The block halts the simulation and returns an error message by default if the true (1) assertion is not maintained. If a new fixed-point implementation is unable to maintain a true (1) assertion for a Model Verification block during simulation, that set of data types is considered infeasible for the model because it does not meet the specified constraints.

All Model Verification blocks must be able to maintain a true (1) assertion when the model is simulated with the floating-point data type selected for data type override in order to establish a baseline for the model behavior.

The following examples use Model Verification blocks for data type optimization.

• Optimize Data Types Using Multiple Simulation Scenarios contains a model that uses an Assertion block to verify that a boolean signal maintains a true (1) value during simulation.

• Image Denoising Using Fixed-Point Quantized Restricted Boltzmann Machine Algorithm contains a model that uses a Check Static Range block to verify that the mean-squared error between two signals remains within a specified threshold.