Visualize Differences Between Floating-Point and Fixed-Point Results

This example shows how to configure the codegen function to use a custom plot function to compare the behavior of the generated fixed-point code against the behavior of the original floating-point MATLAB^® code.

By default, when the LogIOForComparisonPlotting option is enabled, the conversion process uses a time series based plotting function to show the floating-point and fixed-point results and the difference between them. However, during fixed-point conversion you might want to visualize the numerical differences in a view that is more suitable for your application domain. This example shows how to customize plotting and produce scatter plots at the test numerics step of the fixed-point conversion.

• Prerequisites

• Create a New Folder and Copy Relevant Files

• Set Up Configuration Object

• Convert to Fixed Point

Prerequisites

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

• MATLAB

• MATLAB Coder™

• 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:\custom_plot.

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

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

3. Copy the myFilter.m, myFilterTest.m, plotDiff.m, and filterData.mat files to your local working folder.

   Type	Name	Description
   Function code	myFilter.m	Entry-point MATLAB function
   Test file	myFilterTest.m	MATLAB script that tests myFilter.m
   Plotting function	plotDiff.m	Custom plot function
   MAT-file	filterData.mat	Data to filter.

 The myFilter Function

function [y, ho] = myFilter(in)

persistent b h;
if isempty(b)
  b = complex(zeros(1,16));
  h = complex(zeros(1,16));
  h(8) = 1;
end

b = [in, b(1:end-1)];
y = b*h.';

errf = 1-sqrt(real(y)*real(y) + imag(y)*imag(y));
update = 0.001*conj(b)*y*errf;

h = h + update;
h(8) = 1;
ho = h;

end

 The myFilterTest File

% load data
data = load('filterData.mat');
d = data.symbols;

for idx = 1:4000
    y = myFilter(d(idx));
end

 The plotDiff Function

% varInfo - structure with information about the variable. It has the following fields
%            i) name
%            ii) functionName
% floatVals - cell array of logged original values for the 'varInfo.name' variable
% fixedVals - cell array of logged values for the 'varInfo.name' variable after Fixed-Point conversion.
function plotDiff(varInfo, floatVals, fixedVals)
    varName = varInfo.name;
    fcnName = varInfo.functionName;

    % escape the '_'s because plot titles treat these as subscripts
    escapedVarName = regexprep(varName,'_','\\_');
    escapedFcnName = regexprep(fcnName,'_','\\_');
    
    % flatten the values
    flatFloatVals = floatVals(1:end);
    flatFixedVals = fixedVals(1:end);

    % build Titles
    floatTitle = [ escapedFcnName ' > ' 'float : ' escapedVarName ];
    fixedTitle = [ escapedFcnName ' > ' 'fixed : ' escapedVarName ];
    
    data = load('filterData.mat');
    
    switch varName
        case 'y'
            x_vec = data.symbols;
            
            figure('Name', 'Comparison plot', 'NumberTitle', 'off');
            
            % plot floating point values
            y_vec = flatFloatVals;
            subplot(1, 2, 1);
            plotScatter(x_vec, y_vec, 100, floatTitle);
            
            % plot fixed point values
            y_vec = flatFixedVals;
            subplot(1, 2, 2);
            plotScatter(x_vec, y_vec, 100, fixedTitle);

        otherwise
            % Plot only output 'y' for this example, skip the rest
    end

end

function plotScatter(x_vec, y_vec, n, figTitle)
    % plot the last n samples
    x_plot = x_vec(end-n+1:end);
    y_plot = y_vec(end-n+1:end);
    
    hold on
    scatter(real(x_plot),imag(x_plot), 'bo');    

    hold on
    scatter(real(y_plot),imag(y_plot), 'rx');
    
    title(figTitle);
end

Set Up Configuration Object

1. Create a coder.FixptConfig object.

   fxptcfg = coder.config('fixpt');

2. Specify the test file name and custom plot function name. Enable logging and numerics testing.

   fxptcfg.TestBenchName = 'myFilterTest';
   fxptcfg.PlotFunction = 'plotDiff';
   fxptcfg.TestNumerics = true; 
   fxptcfg.LogIOForComparisonPlotting = true;
   fxptcfg.DefaultWordLength = 16;
   

Convert to Fixed Point

Convert the floating-point MATLAB function, myFilter, to fixed-point MATLAB code. You do not need to specify input types for the codegen command because it infers the types from the test file.

codegen -args {complex(0, 0)} -float2fixed fxptcfg myFilter

The conversion process generates fixed-point code using a default word length of 16 and then runs a fixed-point simulation by running the myFilterTest.m function and calling the fixed-point version of myFilter.m.

Because you selected to log inputs and outputs for comparison plots and to use the custom plotting function, plotDiff.m, for these plots, the conversion process uses this function to generate the comparison plot.

The plot shows that the fixed-point results do not closely match the floating-point results.

Increase the word length to 24 and then convert to fixed point again.

fxptcfg.DefaultWordLength = 24;
codegen -args {complex(0, 0)} -float2fixed fxptcfg myFilter

The increased word length improved the results. This time, the plot shows that the fixed-point results match the floating-point results.