Replace the exp Function with a Lookup Table

With HDL Coder™, you can handle functions that are not supported for fixed point and replace your own functions. To replace a custom function with a Lookup Table, use the HDL Coder App, or the fiaccel codegen function.

From the UI
From the Command Line

From the UI

This example shows how to replace a custom function with a Lookup Table using the HDL Coder app.

Create Algorithm and Test Files
Create and Set up a HDL Coder Project
Define Input Types
Replace custom_fcn with Lookup Table
Validate Fixed-Point Types

Create Algorithm and Test Files

In a local, writable folder:

Create a MATLAB^® function, custom_fcn, which is the function that you want to replace.
```
function y = custom_fcn(x)
  y = 1./(1+exp(-x));
end
```

Create a wrapper function that calls custom_fcn.

function y = call_custom_fcn(x)
  y = custom_fcn(x);
end

Create a test file, custom_test, which uses call_custom_fcn.

close all

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

Create and Set up a HDL Coder Project

Navigate to the work folder that contains the file for this example.
To open the HDL Coder app, in the MATLAB command prompt, enter hdlcoder. Set Name to custom_project.prj and click OK. The project opens in the MATLAB workspace.
In the project window, on the MATLAB Function tab, click the Add MATLAB function link. Browse to the file call_custom_fcn.m, and then click OK to add the file to the project.

Define Input Types

To define input types for call_custom_fcn.m, on the MATLAB Function tab, click Autodefine types.
Add custom_test as a test file, and then click Run.
From the test file, HDL Coder determines that x is a scalar double.
Click Use These Types.

Replace custom_fcn with Lookup Table

To open the HDL Workflow Advisor, click Workflow Advisor, and in the Workflow Advisor window, click Fixed-Point Conversion.
To replace custom_fcn with a Lookup Table, on the Function Replacements tab, enter custom_fcn, select Lookup Table, and then click +.
By default, the lookup table uses linear interpolation, 1000 points, and design minimum and maximum values that the app detects by running a simulation or computing derived ranges.
Under Run Simulation, select Log data for histogram, and then click Run Simulation. Verify that custom_test file is selected as the test file.
The simulation runs and the tool displays simulation minimum and maximum ranges on the Variables tab. HDL Coder plots the simulation results in the MATLAB Editor.

Validate Fixed-Point Types

In the Proposed Type column, verify that the fixed-point types proposed by software 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 that the proposed data type covers.
To validate the build by using the proposed types, click Validate Types.
The software validates the proposed types and generates a fixed-point code, call_custom_fcn_fixpt.

To view the generated fixed-point code, click the call_custom_fcn_fixpt link.

The generated fixed-point function, call_custom_fcn_fixpt.m, calls this approximation instead of calling custom_fcn.

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

  y = fi(replacement_custom_fcn(x), 0, 14, 14, fm);
end

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

From the Command Line

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

Prerequisites
Create Algorithm and Test Files
Configure Approximation
Set Up Configuration Object
Convert to Fixed Point
View Generated Fixed-Point 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 Algorithm and Test Files

Create a MATLAB function, my_fcn.m, that calls the exp function.
```
function y = my_fcn(x)
  y = exp(x);
end
```

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 );

Configure Approximation

Create a function replacement configuration object to approximate the exp function, using the default settings of linear interpolation and 1000 points in the lookup table.

q = coder.approximation('exp');

Set Up Configuration Object

Create a coder.FixptConfig object, fixptcfg. Specify the test file name and enable numerics testing. Associate the function replacement configuration object with the fixed-point configuration object.

fixptcfg = coder.config('fixpt');
fixptcfg.TestBenchName = 'my_fcn_test';
fixptcfg.TestNumerics = true;
fixptcfg.DefaultWordLength = 16;
fixptcfg.addApproximation(q);

Convert to Fixed Point

Generate fixed-point MATLAB code.

codegen -float2fixed fixptcfg my_fcn

View Generated Fixed-Point Code

To view the generated fixed-point code, click the link to my_fcn_fixpt.

The generated code contains a lookup table approximation, replacement_exp, for the exp function. 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.

The generated fixed-point function, my_fcn_fixpt, calls this approximation instead of calling exp.

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 and then regenerate code.

Documentation