Replace the exp Function with a Lookup Table

This example shows how to replace the exp function with a lookup table approximation in fixed-point code generated using the MATLAB® Coder™ app.

Prerequisites

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

• MATLAB

• MATLAB Coder

• Fixed-Point Designer™

• C compiler

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

Create Algorithm and Test Files

1. Create a MATLAB function, my_fcn.m, that calls the exp function.

function y = my_fcn(x)
y = exp(x);
end
2. Create a test file, my_fcn_test.m, that uses my_fcn.m.

close all

x = linspace(-10,10,1e3);
for itr = 1e3:-1:1
y(itr) = my_fcn( x(itr) );
end
plot( x, y );

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 my_fcn to the project, browse to the file my_fcn.m, and then click . By default, the app saves information and settings for this project in the current folder in a file named my_fcn.prj.

Enable Fixed-Point Conversion

1. Set Numeric Conversion to Convert to fixed point. 2. Click to go to the Define Input Types step.

The app screens my_fcn.m for code violations and code generation readiness issues. The app opens the Review Code Generation Readiness page.

1. Click . The app indicates that the exp function is not supported for fixed-point conversion. In a later step, you specify a lookup table replacement for this function. 2. Click to go to the Define Input Types step.

Define Input Types

1. Add my_fcn_test as a test file and then click .

The test file runs. The app determines from the test file that x is a scalar double.

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

Check for Run-Time Issues

The Check for Run-Time Issues step generates an instrumented MEX function. It runs the test file my_fcn_test replacing calls to my_fcn 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 my_fcn_test, the test file that you used to define the input types.

2. Click .

The app does not detect issues.

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

Replace exp Function with Lookup Table

1. Select the Function Replacements tab.

The app indicates that you must replace the exp function. 2. On the Function Replacements tab, right-click the exp function and select Lookup Table. The app moves the exp function to the list of functions that it will replace with a Lookup Table. By default, the lookup table uses linear interpolation and 1000 points. Design Min and Design Max are set to Auto which means that the app uses the design minimum and maximum values that it detects by either running a simulation or computing derived ranges. 3. Click the Analyze arrow , select Log data for histogram, and verify that the test file is my_fcn_test. 4. Click Analyze.

The simulation runs. On the Variables tab, the app displays simulation minimum and maximum ranges. 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. The app enables the Convert option.

5. Examine the proposed types and verify that they cover the full simulation range. To view logged histogram data for a variable, click its Proposed Type field. The histogram provides range information and the percentage of simulation range covered by the proposed data type. Convert to Fixed Point

1. Click .

The app validates the proposed types, and generates a fixed-point version of the entry-point function, my_fcn_fixpt.m.

2. In the Output Files list, select my_fcn_fixpt.m.

The conversion process generates a lookup table approximation, replacement_exp, for the exp function. The generated fixed-point function, my_fcn_fixpt.m, calls this approximation instead of calling exp. The fixed-point conversion process infers the ranges for the function and then uses an interpolated lookup table to replace the function. By default, the lookup table uses linear interpolation, 1000 points, and the minimum and maximum values detected by running the test file.

function y = my_fcn_fixpt(x)
fm = get_fimath();

y = fi(replacement_exp(x), 0, 16, 1, fm);
end

You can now test the generated fixed-point code and compare the results against the original MATLAB function. If the behavior of the generated fixed-point code does not match the behavior of the original code closely enough, modify the interpolation method or number of points used in the lookup table. Then, regenerate the code.

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