CODEWITHSUNDEEP
optimizationparallel-processingarmvectorizationneon
Wolfrum
Wolfrum

Reputation: 73

Vectorizing Code for efficient implementation

The following is an IIR code. I need to vectorize the code so that I can write NEON code efficiently.

Example of vectorization Non vectorized code

for(i=0;i<100;i++)
a[i] =a[i]*b[i];     //only one independent multiplication cannot take
                     //advantage of multiple multiplication units

Vectorized code

for(i=0;i<25;i++)
{
a[i*4] =a[i*4]*b[i*4];                //four  independent multiplications can use
a[(i+1)*4] =a[(i+1)*4]*b[(i+1)*4];    // multiple multiplication units to perform the 
a[(i+2)*4] =a[(i+2)*4]*b[(i+2)*4];    //operation in parallel
a[(i+3)*4] =a[(i+3)*4]*b[(i+3)*4];
}

Please help me in vectorizing the for loop below so as to implement the code efficiently by using the vector capability of hardware (my hardware can perform 4 multiplications simultaneously).

 main()
    {
        for(j=0;j<NUMBQUAD;j++)
    {
        for(i=2;i<SAMPLES+2 ;i++)
        {
            w[i] = x[i-2] + a1[j]* w[i-1] + a2[j]*w[i-2];
            y[i-2] = w[i] + b1[j]* w[i-1] + b2[j]*w[i-2];

        }
        w[0]=0;
        w[1] =0;
    }
    }

Upvotes: 2

Views: 437

Answers (1)

Aki Suihkonen
Aki Suihkonen

Reputation: 20037

Once you have fixed (or verified) the equations, you should notice that there are 4 independent multiplications in each round of the equation. The task becomes in finding the proper and least number of instructions to permute input vectors x[...], y[...], w[...] to some register 

   q0 = | w[i-1] | w[i-2] | w[i-1] | w[i-2]|
   q1 = | a1[j]  | a2[j]  | b1[j]  | b2[j] |   // vld1.32 {d0,d1}, [r1]!
   q2 =   q0 .* q1

A potentially much more effective method of wavefront parallelism can be achieved by inverting the for loops.

   x0 = *x++;

   w0 =  x0 + a*w1 + b*w2;  // pipeline warming stage
   y0 =  w0 + c*w1 + d*w2;  // 

   [REPEAT THIS]
     // W2 = W1; W1 = W0;
     W0 = y0 + A*W1 + B*W2;
     Y0 = W0 + C*W1 + D*W2;
     // w2 = w1; w1 = w0;

     x0 = *x++;
     *output++= Y0;

     w0 = x0 + a*w1 + b*w2;
     y0 = w0 + c*w1 + d*w2;
   [REPEAT ENDS]

   W0 = y0 + A*W1 + B*W2;   // pipeline cooling stage
   Y0 = W0 + C*W1 + D*W2;
   *output++= Y0;

While there are still dependencies between x0->w0->y0->W0->Y0, there's an opportunity of full 2-way parallelism in between lower-case and upper-case expressions. Also one can try to get rid of shifting the values w2=w1; w1=w0; by unrolling the loop and doing manual register renaming.

Upvotes: 2

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