This example shows how to convert a neural network regression model in Simulink to fixed point using the `fxpopt`

function and Lookup Table Optimizer.

Fixed-Point Designer provides workflows via the Fixed Point Tool that can convert a design from floating-point data types to fixed-point data types. The `fxpopt`

function optimizes data types in a model based on specified system behavioral constraints. For additional information, refer to the documentation link https://www.mathworks.com/help/fixedpoint/ref/fxpopt.html The Lookup Table Optimizer generates memory-efficient lookup table replacements for unbounded functions such as `exp`

and `log2`

. Using these tools, this example showcases how to convert a trained floating-point neural network regression model to use embedded-efficient fixed-point data types.

Neural Network Toolbox ships with `engine_dataset`

which contains data representing the relationship between the fuel rate and speed of the engine, and its torque and gas emissions.

% Use the function fitting tool (nftool) from Neural Network Toolbox(TM) to % train a neural network to estimate torque and gas emissions of an engine % given the fuel rate and speed. Use the following commands to train % the neural network. load engine_dataset; x = engineInputs; t = engineTargets; net = fitnet(10); net = train(net,x,t); view(net)

Close all windows of training tool and view of the network.

```
nnet.guis.closeAllViews();
nntraintool('close');
```

Once the network is trained, use the `gensim`

function from the Neural Network Toolbox™ to generate a Simulink model.

[sysName, netName] = gensim(net, 'Name', 'mTrainedNN'); %#ok

The model generated by the `gensim`

function contains the neural network with trained weights and biases. To prepare this generated model for fixed-point conversion, follow the preparation steps in the best practices guidelines. https://www.mathworks.com/help/fixedpoint/ug/best-practices-for-using-the-fixed-point-tool-to-propose-data-types-for-your-simulink-model.html

After applying these principles, the trained neural network is further modified to enable signal logging at the output of the network, add input stimuli and verification blocks. The modified model is saved as fxpdemo_neuralnet_regression.

Copy the model to a temporary writable directory.

model = 'fxpdemo_neuralnet_regression'; current_dir = pwd; fxpnn_demo_dir = fullfile(matlabroot, 'toolbox', 'simulink', 'fixedandfloat', 'fxpdemos'); fxpnn_temp_dir = [tempdir 'fxpnn_dir']; cd(tempdir); [~, ~, ~] = rmdir(fxpnn_temp_dir, 's'); mkdir(fxpnn_temp_dir); cd(fxpnn_temp_dir); copyfile(fullfile(fxpnn_demo_dir, [model,'.slx']), fullfile(fxpnn_temp_dir, [model '_toconvert.slx']));

Open and inspect the model.

model = [model '_toconvert']; system_under_design = [model '/Function Fitting Neural Network']; baseline_output = [model '/yarr']; open_system(model); % Set up model for HDL code generation hdlsetup(model);

### <a href="matlab:configset.internal.open('fxpdemo_neuralnet_regression_toconvert','SingleTaskRateTransMsg')">SingleTaskRateTransMsg</a> value is set from 'none' to 'error' (<a href="matlab:set_param('fxpdemo_neuralnet_regression_toconvert','SingleTaskRateTransMsg', 'none')">revert</a>). ### <a href="matlab:configset.internal.open('fxpdemo_neuralnet_regression_toconvert','Solver')">Solver</a> value is set from 'FixedStepAuto' to 'FixedStepDiscrete' (<a href="matlab:set_param('fxpdemo_neuralnet_regression_toconvert','Solver', 'FixedStepAuto')">revert</a>). ### <a href="matlab:configset.internal.open('fxpdemo_neuralnet_regression_toconvert','AlgebraicLoopMsg')">AlgebraicLoopMsg</a> value is set from 'warning' to 'error' (<a href="matlab:set_param('fxpdemo_neuralnet_regression_toconvert','AlgebraicLoopMsg', 'warning')">revert</a>). ### <a href="matlab:configset.internal.open('fxpdemo_neuralnet_regression_toconvert','BlockReduction')">BlockReduction</a> value is set from 'on' to 'off' (<a href="matlab:set_param('fxpdemo_neuralnet_regression_toconvert','BlockReduction', 'on')">revert</a>). ### <a href="matlab:configset.internal.open('fxpdemo_neuralnet_regression_toconvert','ConditionallyExecuteInputs')">ConditionallyExecuteInputs</a> value is set from 'on' to 'off' (<a href="matlab:set_param('fxpdemo_neuralnet_regression_toconvert','ConditionallyExecuteInputs', 'on')">revert</a>). ### <a href="matlab:configset.internal.open('fxpdemo_neuralnet_regression_toconvert','DefaultParameterBehavior')">DefaultParameterBehavior</a> value is set from 'Tunable' to 'Inlined' (<a href="matlab:set_param('fxpdemo_neuralnet_regression_toconvert','DefaultParameterBehavior', 'Tunable')">revert</a>). ### <a href="matlab:configset.internal.open('fxpdemo_neuralnet_regression_toconvert','ProdHWDeviceType')">ProdHWDeviceType</a> value is set from 'Intel->x86-64 (Windows64)' to 'ASIC/FPGA->ASIC/FPGA' (<a href="matlab:set_param('fxpdemo_neuralnet_regression_toconvert','ProdHWDeviceType', 'Intel->x86-64 (Windows64)')">revert</a>). ### The listed configuration parameter values are modified as a part of hdlsetup. Please refer to <a href="matlab:helpview(fullfile(docroot, 'hdlcoder', 'helptargets.map'), 'msg_hdlsetup_function')">hdlsetup</a> document for best practices on model settings.

Simulate the model to observe model performance when using double-precision floating-point data types.

sim_out = sim(model, 'SaveFormat', 'Dataset'); plotRegression(sim_out, baseline_output, system_under_design, 'Regression before conversion');

opts = fxpOptimizationOptions(); opts.addTolerance(system_under_design, 1, 'RelTol', 0.05); opts.addTolerance(system_under_design, 1, 'AbsTol', 50) opts.AllowableWordLengths = 8:32;

Use the `fxpopt`

function to optimize the data types in the system under design and explore the solution. The software analyzes the range of objects in `system_under_design`

and wordlength and tolerance constraints specified in `opts`

to apply heterogeneous data types to the model while minimizing total bit width.

```
solution = fxpopt(model, system_under_design, opts);
best_solution = solution.explore; %#ok
```

+ Preprocessing + Modeling the optimization problem - Constructing decision variables + Running the optimization solver - Evaluating new solution: cost 483, does not meet the tolerances. - Evaluating new solution: cost 541, does not meet the tolerances. - Evaluating new solution: cost 599, does not meet the tolerances. - Evaluating new solution: cost 657, does not meet the tolerances. - Evaluating new solution: cost 715, does not meet the tolerances. - Evaluating new solution: cost 773, does not meet the tolerances. - Evaluating new solution: cost 831, does not meet the tolerances. - Evaluating new solution: cost 889, meets the tolerances. - Updated best found solution, cost: 889 - Evaluating new solution: cost 885, meets the tolerances. - Updated best found solution, cost: 885 - Evaluating new solution: cost 875, meets the tolerances. - Updated best found solution, cost: 875 - Evaluating new solution: cost 874, meets the tolerances. - Updated best found solution, cost: 874 - Evaluating new solution: cost 873, meets the tolerances. - Updated best found solution, cost: 873 - Evaluating new solution: cost 872, meets the tolerances. - Updated best found solution, cost: 872 - Evaluating new solution: cost 871, meets the tolerances. - Updated best found solution, cost: 871 - Evaluating new solution: cost 870, meets the tolerances. - Updated best found solution, cost: 870 - Evaluating new solution: cost 869, meets the tolerances. - Updated best found solution, cost: 869 - Evaluating new solution: cost 868, meets the tolerances. - Updated best found solution, cost: 868 - Evaluating new solution: cost 867, meets the tolerances. - Updated best found solution, cost: 867 - Evaluating new solution: cost 857, meets the tolerances. - Updated best found solution, cost: 857 - Evaluating new solution: cost 856, meets the tolerances. - Updated best found solution, cost: 856 - Evaluating new solution: cost 855, meets the tolerances. - Updated best found solution, cost: 855 - Evaluating new solution: cost 854, meets the tolerances. - Updated best found solution, cost: 854 - Evaluating new solution: cost 853, meets the tolerances. - Updated best found solution, cost: 853 - Evaluating new solution: cost 852, meets the tolerances. - Updated best found solution, cost: 852 - Evaluating new solution: cost 847, meets the tolerances. - Updated best found solution, cost: 847 - Evaluating new solution: cost 846, meets the tolerances. - Updated best found solution, cost: 846 - Evaluating new solution: cost 841, does not meet the tolerances. - Evaluating new solution: cost 845, meets the tolerances. - Updated best found solution, cost: 845 - Evaluating new solution: cost 837, meets the tolerances. - Updated best found solution, cost: 837 - Evaluating new solution: cost 836, meets the tolerances. - Updated best found solution, cost: 836 - Evaluating new solution: cost 832, does not meet the tolerances. - Evaluating new solution: cost 826, meets the tolerances. - Updated best found solution, cost: 826 - Evaluating new solution: cost 825, meets the tolerances. - Updated best found solution, cost: 825 - Evaluating new solution: cost 824, meets the tolerances. - Updated best found solution, cost: 824 - Evaluating new solution: cost 823, meets the tolerances. - Updated best found solution, cost: 823 - Evaluating new solution: cost 822, meets the tolerances. - Updated best found solution, cost: 822 - Evaluating new solution: cost 821, meets the tolerances. - Updated best found solution, cost: 821 - Evaluating new solution: cost 820, meets the tolerances. - Updated best found solution, cost: 820 - Evaluating new solution: cost 819, meets the tolerances. - Updated best found solution, cost: 819 - Evaluating new solution: cost 818, meets the tolerances. - Updated best found solution, cost: 818 - Evaluating new solution: cost 808, meets the tolerances. - Updated best found solution, cost: 808 - Evaluating new solution: cost 807, meets the tolerances. - Updated best found solution, cost: 807 - Evaluating new solution: cost 806, meets the tolerances. - Updated best found solution, cost: 806 - Evaluating new solution: cost 805, meets the tolerances. - Updated best found solution, cost: 805 - Evaluating new solution: cost 804, meets the tolerances. - Updated best found solution, cost: 804 - Evaluating new solution: cost 803, meets the tolerances. - Updated best found solution, cost: 803 - Evaluating new solution: cost 798, meets the tolerances. - Updated best found solution, cost: 798 - Evaluating new solution: cost 797, meets the tolerances. - Updated best found solution, cost: 797 - Evaluating new solution: cost 792, does not meet the tolerances. - Evaluating new solution: cost 796, does not meet the tolerances. - Evaluating new solution: cost 789, meets the tolerances. - Updated best found solution, cost: 789 - Evaluating new solution: cost 788, meets the tolerances. - Updated best found solution, cost: 788 - Evaluating new solution: cost 784, meets the tolerances. - Updated best found solution, cost: 784 - Evaluating new solution: cost 774, does not meet the tolerances. + Optimization has finished. - Neighborhood search complete. - Maximum number of iterations completed. + Fixed-point implementation that met the tolerances found. - Total cost: 784 - Maximum absolute difference: 53.582715 - Use the explore method of the result to explore the implementation.

Verify model accuracy after conversion by simulating the model.

sim_out = sim(model, 'SaveFormat', 'Dataset');

Plot the regression accuracy of the fixed-point model.

```
plotRegression(sim_out, baseline_output, system_under_design, 'Regression after conversion');
```

The Tanh Activation function in Layer 1 can be replaced with either a lookup table or a CORDIC implementation for more efficient fixed-point code generation. In this example, we will be using the Lookup Table Optimizer to get a lookup table as a replacement for `tanh`

. We will be using `EvenPow2Spacing`

for faster execution speed. For more information, see https://www.mathworks.com/help/fixedpoint/ref/functionapproximation.options-class.html.

block_path = [system_under_design '/Layer 1/tansig']; p = FunctionApproximation.Problem(block_path); p.Options.WordLengths = 8:32; p.Options.BreakpointSpecification = 'EvenPow2Spacing'; solution = p.solve; solution.replaceWithApproximate;

| ID | Memory (bits) | Feasible | Table Size | Breakpoints WLs | TableData WL | BreakpointSpecification | Error(Max,Current) | | 0 | 46 | 0 | 2 | 15 | 8 | EvenPow2Spacing | 7.812500e-03, 1.000000e+00 | | 1 | 8222 | 1 | 1024 | 15 | 8 | EvenPow2Spacing | 7.812500e-03, 7.812500e-03 | | 2 | 8212 | 1 | 1024 | 10 | 8 | EvenPow2Spacing | 7.812500e-03, 7.812500e-03 | | 3 | 4126 | 1 | 512 | 15 | 8 | EvenPow2Spacing | 7.812500e-03, 7.812500e-03 | | 4 | 4114 | 1 | 512 | 9 | 8 | EvenPow2Spacing | 7.812500e-03, 7.812500e-03 | | 5 | 48 | 0 | 2 | 15 | 9 | EvenPow2Spacing | 7.812500e-03, 1.000000e+00 | | 6 | 50 | 0 | 2 | 15 | 10 | EvenPow2Spacing | 7.812500e-03, 1.000000e+00 | | 7 | 52 | 0 | 2 | 15 | 11 | EvenPow2Spacing | 7.812500e-03, 1.000000e+00 | | 8 | 54 | 0 | 2 | 15 | 12 | EvenPow2Spacing | 7.812500e-03, 1.000000e+00 | | 9 | 56 | 0 | 2 | 15 | 13 | EvenPow2Spacing | 7.812500e-03, 1.000000e+00 | Best Solution | ID | Memory (bits) | Feasible | Table Size | Breakpoints WLs | TableData WL | BreakpointSpecification | Error(Max,Current) | | 4 | 4114 | 1 | 512 | 9 | 8 | EvenPow2Spacing | 7.812500e-03, 7.812500e-03 |

Verify model accuracy after function replacement

sim_out = sim(model, 'SaveFormat', 'Dataset');

Plot regression accuracy after function replacement.

```
plotRegression(sim_out, baseline_output, system_under_design, 'Regression after function replacement');
```

Generating HDL code requires an HDL Coder™ license.

Choose the model for which to generate HDL code and a test bench.

`systemname = 'fxpdemo_neuralnet_regression_toconvert/Function Fitting Neural Network';`

Use a temporary directory for the generated files.

`workingdir = tempname;`

You can run the following command to check for HDL code generation compatibility.

`checkhdl(systemname,'TargetDirectory',workingdir);`

Run the following command to generate HDL code.

`makehdl(systemname,'TargetDirectory',workingdir);`

Run the following command to generate the test bench.

`makehdltb(systemname,'TargetDirectory',workingdir);`

close all; Simulink.sdi.close; clear engineInputs engineTargets net x t clear h1 h2 h3 clear sim_out logsout nn_out yarr_out ypred actual clear solution opts p close_system(model, 0); close_system(sysName, 0); clear system_under_design model block_path clear netName sysName clear best_solution baseline_output cd(current_dir); status = rmdir(fxpnn_temp_dir, 's'); %#ok clear fxpnn_demo_dir fxpnn_temp_dir current_dir status

Create a function to plot regression data.

function plotRegression(sim_out, baseline_path, neural_network_output_path, plotTitle) nn_out = find(sim_out.logsout, 'BlockPath', neural_network_output_path); yarr_out = find(sim_out.logsout, 'BlockPath', baseline_path); ypred = nn_out{1}.Values.Data; actual = yarr_out{1}.Values.Data; figure; plotregression(double(ypred), actual, plotTitle); end