Automated Fixed-Point Conversion

Automated Fixed-Point Conversion Capabilities

You can convert floating-point MATLAB^® code to fixed-point code using the Fixed-Point Converter app or at the command line using the fiaccel function -float2fixed option. You can choose to propose data types based on simulation range data, derived (also known as static) range data, or both.

You can manually enter static ranges. These manually entered ranges take precedence over simulation ranges and the app uses them when proposing data types. In addition, you can modify and lock the proposed type so that the app cannot change it. For more information, see Locking Proposed Data Types.

For a list of supported MATLAB features and functions, see MATLAB Language Features Supported for Automated Fixed-Point Conversion.

During fixed-point conversion, you can:

Verify that your test files cover the full intended operating range of your algorithm using code coverage results.
Propose fraction lengths based on default word lengths.
Propose word lengths based on default fraction lengths.
Optimize whole numbers.
Specify safety margins for simulation min/max data.
Validate that you can build your project with the proposed data types.
Test numerics by running the test file with the fixed-point types applied.
View a histogram of bits that each variable uses.
Detect overflows.

Code Coverage

By default, the app shows code coverage results. Your test files must exercise the algorithm over its full operating range so that the simulation ranges are accurate. The quality of the proposed fixed-point data types depends on how well the test files cover the operating range of the algorithm with the accuracy that you want.

Reviewing code coverage results helps you to verify that your test files are exercising the algorithm adequately. If the code coverage is inadequate, modify the test files or add more test files to increase coverage. If you simulate multiple test files in one run, the app displays cumulative coverage. However, if you specify multiple test files, but run them one at a time, the app displays the coverage of the file that ran last.

The app displays a color-coded coverage bar to the left of the code.

Fixed-Point Converter app displaying example code with the coverage bar on the left side. The coverage bar has green, orange and red sections.

This table describes the color coding.

Coverage Bar Color	Indicates
Green	One of the following situations: The entry-point function executes multiple times and the code executes more than one time. The entry-point function executes one time and the code executes one time. Different shades of green indicate different ranges of line execution counts. The darkest shade of green indicates the highest range.
Orange	The entry-point function executes multiple times, but the code executes one time.
Red	Code does not execute.

Coverage Bar Color

Indicates

Green

One of the following situations:

The entry-point function executes multiple times and the code executes more than one time.
The entry-point function executes one time and the code executes one time.

Different shades of green indicate different ranges of line execution counts. The darkest shade of green indicates the highest range.

Orange

The entry-point function executes multiple times, but the code executes one time.

Red

Code does not execute.

When you place your cursor over the coverage bar, the color highlighting extends over the code. For each section of code, the app displays the number of times that the section executes.

Fixed-Point Converter app displaying example code with the coverage bar colors extended over the code

To verify that your test files are testing your algorithm over the intended operating range, review the code coverage results.

Coverage Bar Color	Action
Green	If you expect sections of code to execute more frequently than the coverage shows, either modify the MATLAB code or the test files.
Orange	This behavior is expected for initialization code, for example, the initialization of persistent variables. If you expect the code to execute more than one time, either modify the MATLAB code or the test files.
Red	If the code that does not execute is an error condition, this behavior is acceptable. If you expect the code to execute, either modify the MATLAB code or the test files. If the code is written conservatively and has upper and lower boundary limits, and you cannot modify the test files to reach this code, add static minimum and maximum values. See Computing Derived Ranges.

Code coverage is on by default. Turn it off only after you have verified that you have adequate test file coverage. Turning off code coverage can speed up simulation. To turn off code coverage, on the Convert to Fixed Point page:

Click the Analyze arrow .
Clear the Show code coverage check box.

Proposing Data Types

In the define input types step, you specify a test file that calls the entry-point function. The app runs the test file to analyze the code and infer the types for entry-point input arguments.

Define Input Types pane of the Fixed-Point Converter app.

The app proposes fixed-point data types based on computed ranges and the word length or fraction length setting. The computed ranges are based on simulation range data, derived range data (also known as static ranges), or both. If you run a simulation and compute derived ranges, the app merges the simulation and derived ranges.

Note

You cannot propose data types based on derived ranges for MATLAB classes.

Derived range analysis is not supported for non-scalar variables.

You can manually enter static ranges. These manually entered ranges take precedence over simulation ranges and the app uses them when proposing data types. If you analyze ranges using derived range analysis alone, you must enter static ranges.

You can modify and lock the proposed type so that the tool cannot change it. For more information, see Locking Proposed Data Types.

Running a Simulation

During fixed-point conversion, the app generates an instrumented MEX function for your entry-point MATLAB file. If the build completes without errors, the app displays compiled information (type, size, complexity) for functions and variables in your code. To navigate to local functions, click the Functions tab. If build errors occur, the app provides error messages that link to the line of code that caused the build issues. You must address these errors before running a simulation. Use the link to navigate to the offending line of code in the MATLAB editor and modify the code to fix the issue.

If your code uses functions that are not supported for fixed-point conversion, the app displays them on the Function Replacements tab. See Function Replacements. You can also use coder.float2fixed.skip to omit these functions from fixed-point conversion.

Before running a simulation, specify the test file or files that you want to run. When you run a simulation, the app runs the test file, calling the instrumented MEX function. If you modify the MATLAB design code, the app automatically generates an updated MEX function before running a test file.

If the test file runs successfully, the simulation minimum and maximum values and the proposed types are displayed on the Variables tab. If you manually enter static ranges for a variable, the manually entered ranges take precedence over the simulation ranges. If you manually modify the proposed types by typing or using the histogram, the data types are locked so that the app cannot modify them.

If the test file fails, the errors are displayed on the Output tab.

Test files must exercise your algorithm over its full operating range. The quality of the proposed fixed-point data types depends on how well the test file covers the operating range of the algorithm with the accuracy that you want. You can add test files and select to run more than one test file during the simulation. If you run multiple test files, the app merges the simulation results.

Optionally, you can select to log data for histograms. After running a simulation, you can view the histogram for each variable. For more information, see Log Data for Histogram.

Computing Derived Ranges

The advantage of proposing data types based on derived ranges is that you do not have to provide test files that exercise your algorithm over its full operating range. Running such test files often takes a very long time. The app can compute derived ranges for scalar variables only.

To compute derived ranges and propose data types based on these ranges, provide static minimum and maximum values or proposed data types for all input variables. To improve the analysis, enter as much static range information as possible for other variables. You can manually enter ranges or promote simulation ranges to use as static ranges. Manually entered static ranges always take precedence over simulation ranges.

If you know what data type your hardware target uses, set the proposed data types to match this type. Manually entered data types are locked so that the app cannot modify them. The app uses these data types to calculate the input minimum and maximum values and to derive ranges for other variables. For more information, see Locking Proposed Data Types.

When you select Compute Derived Ranges, the app runs a derived range analysis to compute static ranges for variables in your MATLAB algorithm. When the analysis is complete, the static ranges are displayed on the Variables tab. If the run produces +/-Inf derived ranges, consider defining ranges for all persistent variables.

Optionally, you can select Quick derived range analysis. With this option, the app performs faster static analysis. The computed ranges might be larger than necessary. Select this option in cases where the static analysis takes more time than you can afford.

If the derived range analysis for your project is taking a long time, you can optionally set a timeout. When the timeout is reached, the app aborts the analysis.

Locking Proposed Data Types

You can lock proposed data types against changes by the app using one of the following methods:

Manually setting a proposed data type in the app.
Right-clicking a type proposed by the tool and selecting Lock computed value.

The app displays locked data types in bold so that they are easy to identify. You can unlock a type using one of the following methods:

Manually overwriting it.
Right-clicking it and selecting Undo changes. This action unlocks only the selected type.
Right-clicking and selecting Undo changes for all variables. This action unlocks all locked proposed types.

Viewing Functions

During the Convert to Fixed Point step of the fixed-point conversion process, you can view a list of functions in your project in the left pane. This list also includes function specializations and class methods. When you select a function from the list, the MATLAB code for that function or class method is displayed in the code window and the variables that they use are displayed on the Variables tab.

After conversion, the left pane also displays a list of output files including the fixed-point version of the original algorithm. If your function is not specialized, the app retains the original function name in the fixed-point file name and appends the fixed-point suffix. For example, here the fixed-point version of ex_2ndOrder_filter.m is ex_2ndOrder_filter_fixpt.m.

Fixed-Point Converter app displaying fixed-point file

Classes

The app displays information for the class and each of its methods. For example, consider a class, Counter, that has a static method, MAX_VALUE, and a method, next.

If you select the class, the app displays the class and its properties on the Variables tab.

Fixed-Point Converter app with a class selected in the left side column. The Variables tab displays the variables associated with the selected class.

If you select a method, the app displays only the variables that the method uses.

Fixed-Point Converter app with a method selected in the left side column. The Variables tab displays the variables associated with the selected method.

Specializations

If a function is specialized, the app lists each specialization and numbers them sequentially. For example, consider a function, dut, that calls subfunctions, foo and bar, multiple times with different input types.

function y = dut(u, v)
 
tt1 = foo(u);
tt2 = foo([u v]);
tt3 = foo(complex(u,v));
 
ss1 = bar(u);
ss2 = bar([u v]); 
ss3 = bar(complex(u,v));
 
y = (tt1 + ss1) + sum(tt2 + ss2) + real(tt3) + real(ss3);
 
end
 
function y = foo(u)
  y = u * 2;
end
 
function y = bar(u)
  y = u * 4;
end

If you select the top-level function, the app displays all the variables on the Variables tab.

Fixed-Point Converter app with the top-level function selected in the left side column

If you select the tree view, the app also displays the line numbers for the call to each specialization.

Fixed-Point Converter app displaying the tree view of the specialized functions in the left side column

If you select a specialization, the app displays only the variables that the specialization uses on the Variables tab.

Fixed-Point Converter app with a function specialization selected in the left side column

In the generated fixed-point code, the number of each fixed-point specialization matches the number in the Source Code list, which makes it easy to trace between the floating-point and fixed-point versions of your code. For example, the generated fixed-point function for foo > 1 is named foo_s1.

Fixed Point Converter app displaying generated fixed-point code with specialized function names

Viewing Variables

The Variables tab provides the following information for each variable in the function selected in the Navigation pane:

Type — The original data type of the variable in the MATLAB algorithm.
Sim Min and Sim Max — The minimum and maximum values assigned to the variable during simulation.
You can edit the simulation minimum and maximum values. Edited fields are shown in bold. Editing these fields does not trigger static range analysis, but the tool uses the edited values in subsequent analyses. You can revert to the types proposed by the app.
Static Min and Static Max — The static minimum and maximum values.
To compute derived ranges and propose data types based on these ranges, provide static minimum and maximum values for all input variables. To improve the analysis, enter as much static range information as possible for other variables.
When you compute derived ranges, the app runs a static analysis to compute static ranges for variables in your code. When the analysis is complete, the static ranges are displayed. You can edit the computed results. Edited fields are shown in bold. Editing these fields does not trigger static range analysis, but the tool uses the edited values in subsequent analyses. You can revert to the types proposed by the app.
Whole Number — Whether all values assigned to the variable during simulation are integers.
The app determines whether a variable is always a whole number. You can modify this field. Edited fields are shown in bold. Editing these fields does not trigger static range analysis, but the app uses the edited values in subsequent analyses. You can revert to the types proposed by the app.
The proposed fixed-point data type for the specified word (or fraction) length. Proposed data types use the numerictype notation. For example, numerictype(1,16,12) denotes a signed fixed-point type with a word length of 16 and a fraction length of 12. numerictype(0,16,12) denotes an unsigned fixed-point type with a word length of 16 and a fraction length of 12.
Because the app does not apply data types to expressions, it does not display proposed types for them. Instead, it displays their original data types.

You can also view and edit variable information in the code pane by placing your cursor over a variable name.

You can use Ctrl+F to search for variables in the MATLAB code and on the Variables tab. The app highlights occurrences in the code and displays only the variable with the specified name on the Variables tab.

Viewing Information for MATLAB Classes

The app displays:

Code for MATLAB classes and code coverage for class methods in the code window. Use the Source Code list on the Convert to Fixed Point page to select which class or class method to view. If you select a class method, the app highlights the method in the code window.
Information about MATLAB classes on the Variables tab.

Log Data for Histogram

To log data for histograms:

On the Convert to Fixed Point page, click the Analyze arrow .
Select Log data for histogram.
Click Analyze Ranges.

After simulation, to view the histogram for a variable, on the Variables tab, click the Proposed Type field for that variable.

The histogram provides the range of the proposed data type and the percentage of simulation values that the proposed data type covers. The bit weights are displayed along the X-axis, and the percentage of occurrences along the Y-axis. Each bin in the histogram corresponds to a bit in the binary word. For example, this histogram displays the range for a variable of type numerictype(1,16,14).

Histogram with proposed data type

You can view the effect of changing the proposed data types by:

Dragging the edges of the bounding box in the histogram window to change the proposed data type.
Selecting or clearing Signed.

To revert to the types proposed by the automatic conversion, in the histogram window, click .

Function Replacements

If your MATLAB code uses functions that do not have fixed-point support, the app lists these functions on the Function Replacements tab. You can choose to replace unsupported functions with a custom function replacement or with a lookup table.

You can add and remove function replacements from this list. If you enter a function replacement for a function, the replacement function is used when you build the project. If you do not enter a replacement, the app uses the type specified in the original MATLAB code for the function.

Note

Using this table, you can replace the names of the functions but you cannot replace argument patterns.

If code generation readiness screening is disabled, the list of unsupported functions on the Function Replacements tab can be incomplete or incorrect. In this case, add the functions manually. See Code Generation Readiness Screening in the MATLAB Coder App (MATLAB Coder).

Alternatively, you can exclude functions from fixed-point conversion using coder.float2fixed.skip. For example, you may want to exclude a function from fixed-point conversion if you are using a custom function that already uses fixed-point data types, or if you wish to take advantage of native floating point support for HDL Code generation. For more information, see coder.float2fixed.skip.

Validating Types

Converting the code to fixed point validates the build using the proposed fixed-point data types. If the validation is successful, you are ready to test the numerical behavior of the fixed-point MATLAB algorithm.

If the errors or warnings occur during validation, they are displayed on the Output tab. If errors or warning occur:

On the Variables tab, inspect the proposed types and manually modified types to verify that they are valid.
On the Function Replacements tab, verify that you have provided function replacements for unsupported functions.

Testing Numerics

After converting code to fixed point and validating the proposed fixed-point data types, click Test to verify the behavior of the fixed-point MATLAB algorithm. By default, if you added a test file to define inputs or run a simulation, the app uses this test file to test numerics. Optionally, you can add test files and select to run more than one test file. The app compares the numerical behavior of the generated fixed-point MATLAB code with the original floating-point MATLAB code. If you select to log inputs and outputs for comparison plots, the app generates an additional plot for each scalar output. This plot shows the floating-point and fixed-point results and the difference between them. For nonscalar outputs, only the error information is shown.

After fixed-point simulation, if the numerical results do not meet the accuracy that you want, modify fixed-point data type settings and repeat the type validation and numerical testing steps. You might have to iterate through these steps multiple times to achieve the results that you want.

Detecting Overflows

When testing numerics, selecting Use scaled doubles to detect overflows enables overflow detection. When this option is selected, the conversion app runs the simulation using scaled double versions of the proposed fixed-point types. Because scaled doubles store their data in double-precision floating-point, they carry out arithmetic in full range. They also retain their fixed-point settings, so they are able to report when a computation goes out of the range of the fixed-point type. For more information, see Scaled Doubles.

If the app detects overflows, on its Overflow tab, it provides:

A list of variables and expressions that overflowed
Information on how much each variable overflowed
A link to the variables or expressions in the code window

Overflows tab of the Fixed-Point Converter app

If your original algorithm uses scaled doubles, the app also provides overflow information for these expressions.