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Optimize Code for Reduction Operations by Using SIMD

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This example shows how to generate optimized single instruction, multiple data (SIMD) code that performs reduction operations. A reduction is an operation that reduces a set of elements, such as an array, to a single value using an associative binary operator. For example, calculating the sum of the elements in an array is a reduction operation that uses the addition operator. For processors that support SIMD instructions, you can optimize reduction operations by generating parallel code that uses the SIMD instructions for the operation.

Example Model

Open the example model ex_rowmajor_algorithm. The model calculates the sum of the elements in a 4 by 3 by 2 array.

model = 'ex_rowmajor_algorithm';
open_system(model)

rowmajor_algorithm_model.png

Generate SIMD Code Without Reduction Optimization

Open the configuration parameters for the model. On the Modeling tab, click Settings. On the Code Generation pane, set System target file to grt.tlc. On the Optimization pane, set the Leverage target hardware instruction set extensions to SSE2. Alternatively, use the command-line.

set_param(model, 'SystemTargetFile', 'grt.tlc');
set_param(model, 'SaveOutput', 'off');
set_param(model, 'RTWVerbose', 'off');
set_param(model, 'InstructionSetExtensions', 'SSE2');

De-select the parameter Optimize reductions.

set_param(model, 'OptimizeReductions', 'off');

Build the model.

slbuild(model);
### Starting build procedure for: ex_rowmajor_algorithm
### Successful completion of build procedure for: ex_rowmajor_algorithm

Build Summary

Top model targets built:

Model                  Action                        Rebuild Reason                                    
=======================================================================================================
ex_rowmajor_algorithm  Code generated and compiled.  Code generation information file does not exist.  

1 of 1 models built (0 models already up to date)
Build duration: 0h 0m 9.5185s

Inspect the generated ex_rowmajor_algorithm_step function.

file = fullfile('ex_rowmajor_algorithm_grt_rtw','ex_rowmajor_algorithm.c');
coder.example.extractLines(file,'/* Model step function */','/* End of Sum',1,1);
/* Model step function */
void ex_rowmajor_algorithm_step(void)
{
  int32_T i;

  /* Sum: '<Root>/Sum of Elements Dim1' incorporates:
   *  Constant: '<Root>/Constant1'
   */
  ex_rowmajor_algorithm_Y.Out2 = -0.0F;
  for (i = 0; i < 24; i++) {
    ex_rowmajor_algorithm_Y.Out2 +=
      ex_rowmajor_algorithm_ConstP.Constant1_Value[i];
  }

The generated code contains a non-vectorized loop that adds each array element individually.

Generate SIMD Code With Reduction Optimization

Open the configuration parameters for the model. On the Modeling tab, click Settings. On the Optimization pane, set the Leverage target hardware instruction set extensions to SSE2. Alternatively, use the command-line.

set_param(model, 'InstructionSetExtensions', 'SSE2');

Select the parameter Optimize reductions. If you want to optimize reduction operations that operate on floating-point values, set Support: Non-finite numbers to Off. Reduction optimization does not support operations on floating-point values when non-finite numbers are supported.

set_param(model, 'OptimizeReductions', 'on');
set_param(model, 'SupportNonFinite', 'off');
set_param(model, 'MatFileLogging', 'off');

Build the model.

slbuild(model);
### Starting build procedure for: ex_rowmajor_algorithm
### Successful completion of build procedure for: ex_rowmajor_algorithm

Build Summary

Top model targets built:

Model                  Action                        Rebuild Reason                   
======================================================================================
ex_rowmajor_algorithm  Code generated and compiled.  Generated code was out of date.  

1 of 1 models built (0 models already up to date)
Build duration: 0h 0m 6.5175s

Inspect the generated ex_rowmajor_algorithm_step function.

file = fullfile('ex_rowmajor_algorithm_grt_rtw','ex_rowmajor_algorithm.c');
coder.example.extractLines(file,'/* Model step function */','/* Matfile',1,1);
/* Model step function */
void ex_rowmajor_algorithm_step(void)
{
  __m128 tmp;
  __m128 tmp_0;
  int32_T i;
  real32_T tmp_1[4];
  tmp = _mm_set1_ps(0.0F);
  for (i = 0; i <= 20; i += 4) {
    /* Sum: '<Root>/Sum of Elements Dim1' incorporates:
     *  Constant: '<Root>/Constant1'
     */
    tmp_0 = _mm_loadu_ps(&ex_rowmajor_algorithm_ConstP.Constant1_Value[i]);
    tmp = _mm_add_ps(tmp, tmp_0);
  }

  _mm_storeu_ps(&tmp_1[0], tmp);

  /* Sum: '<Root>/Sum of Elements Dim1' */
  ex_rowmajor_algorithm_Y.Out2 = (tmp_1[0] + tmp_1[1]) + (tmp_1[2] + tmp_1[3]);
}

/* Model initialize function */
void ex_rowmajor_algorithm_initialize(void)
{
  /* Registration code */

  /* initialize error status */
  rtmSetErrorStatus(ex_rowmajor_algorithm_M, (NULL));

  /* external outputs */
  ex_rowmajor_algorithm_Y.Out2 = 0.0F;
}

/* Model terminate function */
void ex_rowmajor_algorithm_terminate(void)
{
  /* (no terminate code required) */
}

The vectorized loop uses the SSE2 function mm_add_ps, which adds four elements of the array to the sum in one step. This optimization improves the execution speed of the generated code.

Open the code generation report. On the C Code tab, click Open Report.

reduction_optimization_report.png

On the report summary, in the Additional Information section, the report indicates that reduction operations are optimized using the SSE2 instruction set.

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