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Detect Overflows

This example shows how to detect overflows using the MATLAB® Coder™ app. At the numerical testing stage in the conversion process, you choose to simulate the fixed-point code using scaled doubles. The app then reports which expressions in the generated code produce values that overflow the fixed-point data type.

Prerequisites

This example requires the following products:

Create a New Folder and Copy Relevant Files

  1. In a local, writable folder, create a function overflow.m.

    function y = overflow(b,x,reset)
    if nargin<3, reset = true; end
    persistent z p
    if isempty(z) || reset
        p = 0;
        z = zeros(size(b));
    end
    [y,z,p] = fir_filter(b,x,z,p);
end
function [y,z,p] = fir_filter(b,x,z,p)
    y = zeros(size(x));
    nx = length(x);
    nb = length(b);
    for n = 1:nx
        p=p+1; if p>nb, p=1; end
        z(p) = x(n);        
        acc = 0;
        k = p;
        for j=1:nb
            acc = acc + b(j)*z(k);
            k=k-1; if k<1, k=nb; end
        end        
        y(n) = acc;
    end
end

  2. Create a test file, overflow_test.m, to exercise the overflow algorithm. You use this test file to define input types for b, x, and reset, and, later, to verify the fixed-point version of the algorithm.

    function overflow_test
    % The filter coefficients were computed 
    % using the FIR1 function from
    % Signal Processing Toolbox.
    %   b = fir1(11,0.25);
    b = [-0.004465461051254
         -0.004324228005260
         +0.012676739550326
         +0.074351188907780
         +0.172173206073645
         +0.249588554524763
         +0.249588554524763
         +0.172173206073645
         +0.074351188907780
         +0.012676739550326
         -0.004324228005260
         -0.004465461051254]';
    
    % Input signal
    nx = 256;
    t = linspace(0,10*pi,nx)';

    % Impulse
    x_impulse = zeros(nx,1); x_impulse(1) = 1;

    % Max Gain
    % The maximum gain of a filter will occur when the 
    % inputs line up with the signs of the filter's 
    % impulse response.
    x_max_gain = sign(b)';
    x_max_gain = repmat(x_max_gain,ceil(nx/length(b)),1);
    x_max_gain = x_max_gain(1:nx);

    % Sums of sines
    f0=0.1; f1=2;
    x_sines = sin(2*pi*t*f0) + 0.1*sin(2*pi*t*f1);

    % Chirp
    f_chirp = 1/16;                  % Target frequency
    x_chirp = sin(pi*f_chirp*t.^2);  % Linear chirp

    x = [x_impulse,x_max_gain,x_sines,x_chirp];
    titles = {'Impulse','Max gain','Sum of sines','Chirp'};
    y = zeros(size(x));

    for i=1:size(x,2)
        reset = true;
        y(:,i) = overflow(b,x(:,i),reset);
    end

    test_plot(1,titles,t,x,y)

end
function test_plot(fig,titles,t,x,y1)
    figure(fig)
    clf
    sub_plot = 1;
    font_size = 10;
    for i=1:size(x,2)
        subplot(4,1,sub_plot)
        sub_plot = sub_plot+1;
        plot(t,x(:,i),'c',t,y1(:,i),'k')
        axis('tight')
        xlabel('t','FontSize',font_size);
        title(titles{i},'FontSize',font_size);
        ax = gca;
        ax.FontSize = 10;
    end
    figure(gcf)
end
TypeNameDescription
Function codeoverflow.mEntry-point MATLAB function
Test fileoverflow_test.mMATLAB script that tests overflow.m

Open the MATLAB Coder App

  1. Navigate to the work folder that contains the file for this example.

  2. On the MATLAB Toolstrip Apps tab, under Code Generation, click the app icon.

Select Source Files

To add the entry-point function overflow to the project, browse to the file overflow.m, and then click Open. By default, the app saves information and settings for this project in the current folder in a file named overflow.prj.

Enable Fixed-Point Conversion

  1. Set Numeric Conversion to Convert to fixed point.

  2. Click Next to go to the Define Input Types step.

    The app screens overflow.m for code violations and code generation readiness issues. The app does not find issues in overflow.m.

Define Input Types

  1. On the Define Input Types page, to add overflow_test as a test file, browse to overflow_test.m, and then click Open.

  2. Click Autodefine Input Types.

    The test file runs. The app determines from the test file that the input type of b is double(1x12), x is double(256x1), and reset is logical(1x1).

  3. Click Next to go to the Check for Run-Time Issues step.

Check for Run-Time Issues

The Check for Run-Time Issues step generates instrumented MEX. It runs the test file overflow_test replacing calls to overflow with calls to the generated MEX function. If the app finds issues, it provides warning and error messages. You can click a message to highlight the problematic code in a pane where you can edit the code.

  1. On the Check for Run-Time Issues page, the app populates the test file field with overflow_test, the test file that you used to define the input types.

  2. Click Check for Issues.

    The app does not detect issues.

  3. Click Next to go to the Convert to Fixed Point step.

Convert to Fixed Point

  1. The app displays compiled information — type, size, and complexity — for variables in your code. For more information, see View and Modify Variable Information.

    On the Function Replacements tab the app displays functions that are not supported for fixed-point conversion. See Running a Simulation.

  2. To view the fimath settings, click the Settings arrow . Set the fimath Product mode and Sum mode to KeepLSB. These settings model the behavior of integer operations in the C language.

  3. Click Analyze.

    The test file, overflow_test, runs. The app displays simulation minimum and maximum ranges on the Variables tab. Using the simulation range data, the software proposes fixed-point types for each variable based on the default type proposal settings, and displays them in the Proposed Type column.

  4. To convert the floating-point algorithm to fixed point, click Convert.

    The software validates the proposed types and generates a fixed-point version of the entry-point function.

    If errors and warnings occur during validation, the app displays them on the Output tab. See Validating Types.

Test Numerics and Check for Overflows

  1. Click the Test arrow . Verify that the test file is overflow_test.m. Select Use scaled doubles to detect overflows, and then click Test.

    The app runs the test file that you used to define input types to test the fixed-point MATLAB code. Because you selected to detect overflows, it also runs the simulation using scaled double versions of the proposed fixed-point types. Scaled doubles store their data in double-precision floating-point, so they carry out arithmetic in full range. Because they retain their fixed-point settings, they can report when a computation goes out of the range of the fixed-point type.

    The simulation runs. The app detects an overflow. The app reports the overflow on the Overflow tab. To highlight the expression that overflowed, click the overflow.

  2. Determine whether it was the sum or the multiplication that overflowed.

    In the fimath settings, set Product mode to FullPrecision, and then repeat the conversion and test the fixed-point code again.

    The overflow still occurs, indicating that it is the addition in the expression that is overflowing.