Propose Data Types Based on Simulation Ranges

This example shows how to propose fixed-point data types based on simulation range data using the fiaccel function.

• Prerequisites

• Create a New Folder and Copy Relevant Files

• Set Up the Fixed-Point Configuration Object

• Collect Simulation Ranges and Generate Fixed-Point Code

• View Range Information

• View Generated Fixed-Point MATLAB Code

Prerequisites

To complete this example, you must install the following products:

• MATLAB^®

• Fixed-Point Designer™

• C compiler

  See Supported Compilers.

  You can use mex -setup to change the default compiler. See Change Default Compiler.

Create a New Folder and Copy Relevant Files

1. Create a local working folder, for example, c:\ex_2ndOrder_filter.

2. Change to the docroot\toolbox\fixpoint\examples folder. At the MATLAB command line, enter:

   cd(fullfile(docroot, 'toolbox', 'fixpoint', 'examples')) 

3. Copy the ex_2ndOrder_filter.m and ex_2ndOrder_filter_test.m files to your local working folder.

   It is best practice to create a separate test script to do all the pre- and post-processing such as loading inputs, setting up input values, calling the function under test, and outputting test results.

   Type	Name	Description
   Function code	ex_2ndOrder_filter.m	Entry-point MATLAB function
   Test file	ex_2ndOrder_filter_test.m	MATLAB script that tests ex_2ndOrder_filter.m

 The ex_2ndOrder_filter Function

function y = ex_2ndOrder_filter(x) %#codegen
  persistent z
  if isempty(z)
      z = zeros(2,1);
  end
  % [b,a] = butter(2, 0.25)
  b = [0.0976310729378175,  0.195262145875635,  0.0976310729378175];
  a = [1, -0.942809041582063,  0.3333333333333333];

 
  y = zeros(size(x));
  for i = 1:length(x)
      y(i) = b(1)*x(i) + z(1);
      z(1) = b(2)*x(i) + z(2) - a(2) * y(i);
      z(2) = b(3)*x(i)        - a(3) * y(i);
  end
end

 The ex_2ndOrder_filter_test Script

The test script runs the ex_2ndOrder_filter function with three input signals: chirp, step, and impulse to cover the full intended operating range of the system. The script then plots the outputs.

% ex_2ndOrder_filter_test
%
% Define representative inputs
N = 256;                   % Number of points
t = linspace(0,1,N);       % Time vector from 0 to 1 second
f1 = N/2;                  % Target frequency of chirp set to Nyquist
x_chirp = sin(pi*f1*t.^2); % Linear chirp from 0 to Fs/2 Hz in 1 second
x_step = ones(1,N);        % Step
x_impulse = zeros(1,N);    % Impulse
x_impulse(1) = 1;

% Run the function under test
x = [x_chirp;x_step;x_impulse];
y = zeros(size(x));
for i = 1:size(x,1)
  y(i,:) = ex_2ndOrder_filter(x(i,:));
end

% Plot the results
titles = {'Chirp','Step','Impulse'}
clf
for i = 1:size(x,1)
  subplot(size(x,1),1,i)
  plot(t,x(i,:),t,y(i,:))
  title(titles{i})
  legend('Input','Output')
end
xlabel('Time (s)')
figure(gcf)

disp('Test complete.')

Set Up the Fixed-Point Configuration Object

Create a fixed-point configuration object and configure the test file name.

cfg = coder.config('fixpt');
cfg.TestBenchName = 'ex_2ndOrder_filter_test';

Collect Simulation Ranges and Generate Fixed-Point Code

Use the fiaccel function to convert the floating-point MATLAB function, ex_2ndOrder_filter, to fixed-point MATLAB code. Set the default word length for the fixed-point data types to 16.

cfg.ComputeSimulationRanges = true;
cfg.DefaultWordLength = 16;

% Derive ranges  and generate fixed-point code
fiaccel -float2fixed cfg ex_2ndOrder_filter

fiaccel analyzes the floating-point code. Because you did not specify the input types for the ex_2ndOrder_filter function, the conversion process infers types by simulating the test file. The conversion process then derives ranges for variables in the algorithm. It uses these derived ranges to propose fixed-point types for these variables. When the conversion is complete, it generates a type proposal report.

View Range Information

Click the link to the type proposal report for the ex_2ndOrder_filter function, ex_2ndOrder_filter_report.html.

The report opens in a web browser.

View Generated Fixed-Point MATLAB Code

fiaccel generates a fixed-point version of the ex_2ndOrder_filter.m function, ex_2ndOrder_filter_fixpt.m, and a wrapper function that calls ex_2ndOrder_filter_fixpt. These files are generated in the codegen\ex_2ndOrder_filter\fixpt folder in your local working folder.

function y = ex_2ndOrder_filter_fixpt(x) %#codegen
  fm = get_fimath();

  persistent z
  if isempty(z)
      z = fi(zeros(2,1), 1, 16, 15, fm);
  end
  % [b,a] = butter(2, 0.25)
  b = fi([0.0976310729378175,  0.195262145875635,  0.0976310729378175], 0, 16, 18, fm);
  a = fi([                 1, -0.942809041582063,  0.3333333333333333], 1, 16, 14, fm);

 
  y = fi(zeros(size(x)), 1, 16, 14, fm);
  for i=1:length(x)
      y(i) = b(1)*x(i) + z(1);
      z(1) = fi_signed(b(2)*x(i) + z(2)) - a(2) * y(i);
      z(2) = fi_signed(b(3)*x(i))        - a(3) * y(i);
  end
end



function y = fi_signed(a)
    coder.inline( 'always' );
    if isfi( a ) && ~(issigned( a ))
        nt = numerictype( a );
        new_nt = numerictype( 1, nt.WordLength + 1, nt.FractionLength );
        y = fi( a, new_nt, fimath( a ) );
    else
        y = a;
    end
end

function fm = get_fimath()
	fm = fimath('RoundingMethod', 'Floor', 'OverflowAction', 'Wrap', 'ProductMode', 'FullPrecision', 'MaxProductWordLength', 128, 'SumMode', 'FullPrecision', 'MaxSumWordLength', 128);
end