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POZGEMM using SSE, not giving speedup
 

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  1. POZGEMM using SSE, not giving speedup
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    <p>I'm performing a matrix matrix multiplication of complex doubles (ZGEMM) and thought using SSE will help, but its not, in fact its slowing the code down. I wanted to know if, maybe, its because its memory bound?</p> <p>Heres the pseudocode:</p> <p>For multiplying two complex doubles I use the following, as proposed by intel (assuming real and complex are stored contiguously):</p> <p>If M=(a+ib) and IN= (c+id):</p> <pre><code>M1 = _mm_loaddup_pd(&amp;M[0]);//M1-&gt;|a|a| I1 = _mm_load_pd(&amp;IN);//I1-&gt;|d|c| T1 = _mm_mul_pd(M1,I1);//T1-&gt;|a*d|a*c| M1 = _mm_loaddup_pd(&amp;M[1]);//M1-&gt;|b|b| I1 = _mm_shuffle_pd(I1,I1,1);//I1-&gt;|c|d| I1 = _mm_mul_pd(M1,I1);//I1-&gt;|b*c|b*d| T1 = _mm_addsub_pd(T1,I1); //T1-&gt; |ad+bc|ac-bd| </code></pre> <p>Thus T1 stores the result of the complex multiplication.</p> <p>This is the matrix multiplication(<code>C[i][j] += A[i][k]*B[k][j]</code>):</p> <pre><code>/*Assumes real and imaginary elements are stored contiguously*/ /*Used loop order: ikj for better cache locality and used 2*2 block matrix mult*/ for(i=0;i&lt;N;i+=2){ for(k=0;k&lt;N;k+=2){ /*Perform the _mm_loaddup() part here for A[i][k],A[i][k+1],A[i+1][k],A[i+1][k+1] since im blocking for 2*2 matrix mult i.e will load duplicates of 8 double values into 8 SIMD registers here*/ A00r = _mm_loaddup_pd(&amp;A[(i*N+k)*2+0]); A00i = _mm_loaddup_pd(&amp;A[(i*N+k)*2+1]); A01r = _mm_loaddup_pd(&amp;A[(i*N+k)*2+2]); A01i = _mm_loaddup_pd(&amp;A[(i*N+k)*2+3]); A10r = _mm_loaddup_pd(&amp;A[((i+1)*N+k)*2+0]); A10i = _mm_loaddup_pd(&amp;A[((i+1)*N+k)*2+1); A11r = _mm_loaddup_pd(&amp;A[((i+1)*N+k)*2+2); A11i = _mm_loaddup_pd(&amp;A[((i+1)*N+k)*2+2); for(j=0;j&lt;N;j+=2){ double out[8] = {0,0,0,0,0,0,0,0}; op00=op01=op10=op11=_mm_setzero_pd(); B00 = _mm_loadu_pd(&amp;B[(k*N+j)*2]); B00_r = _mm_shuffle_pd(B00,B00,1); B01 = _mm_loadu_pd(&amp;B[(k*N+j+1)*2]); B01_r = _mm_shuffle_pd(B01,B01,1); /*Perform A[i][k]*B[k][j], A[i][k]*B[k][j+1], A[i+1][k]*B[k][j], A[i+1][k]*B[k][j+1] and assign it to op00,op01,op10,op11 respectively -&gt; takes 8 _mm_mul_pd() and 4 _mm_addsub_pd()*/ T1 = _mm_mul_pd(A00r,B00); T2 = _mm_mul_pd(A00i,B00_r); op00 = _mm_addsub_pd(T1,T2); T1 = _mm_mul_pd(A00r,B01); T2 = _mm_mul_pd(A00i,B01_r); op01 = _mm_addsub_pd(T1,T2); T1 = _mm_mul_pd(A10r,B00); T2 = _mm_mul_pd(A10i,B00_r); op10 = _mm_addsub_pd(T1,T2); T1 = _mm_mul_pd(A10r,B01); T2 = _mm_mul_pd(A10i,B01_r); op11 = _mm_addsub_pd(T1,T2); B00 = _mm_loadu_pd(&amp;B[((k+1)*N+j)*2]); B00_r = _mm_shuffle_pd(B00,B00,1); B01 = _mm_loadu_pd(&amp;B[((k+1)*N+j+1)*2]); B00_r = _mm_shuffle_pd(B01,B01,1); /*Perform A[i][k+1]*B[k+1][j],A[i][k+1]*B[k+1][j+1],A[i+1][k+1]*B[k+1][j],A[i+1][k+1]*B[k+1][j+1] and add it to op00,op01,op10,op11 respectively-&gt; takes 8 _mm_mul_pd(), 4 _mm_add_pd(), 4 _mm_addsub_pd()*/ T1 = _mm_mul_pd(A01r,B10); T2 = _mm_mul_pd(A01i,B10_r); op00 = _mm_add_pd(op00,_mm_addsub_pd(T1,T2)); T1 = _mm_mul_pd(A01r,B11); T2 = _mm_mul_pd(A01i,B11_r); op01 = _mm_add_pd(op01,_mm_addsub_pd(T1,T2)); T1 = _mm_mul_pd(A11r,B10); T2 = _mm_mul_pd(A11i,B10_r); op10 = _mm_add_pd(op10,_mm_addsub_pd(T1,T2)); T1 = _mm_mul_pd(A11r,B11); T2 = _mm_mul_pd(A11i,B11_r); op11 = _mm_add_pd(op11,_mm_addsub_pd(T1,T2)); /*Store op00,op01,op10,op11 into out[0],out[2],out[4] and out[6] -&gt; 4 stores*/ _mm_storeu_pd(&amp;out[0],op00); _mm_storeu_pd(&amp;out[2],op01); _mm_storeu_pd(&amp;out[4],op10); _mm_storeu_pd(&amp;out[6],op11); /*Perform the following 8 operations*/ C[(i*N+j)*2+0] += out[0]; C[(i*N+j)*2+1] += out[1]; . . . C[((i+1)*N+j)*2+3] += out[7]; } } } </code></pre> <p>The L1 cache is of 32KB, so I used cache blocking too (tile size of 16*16 which makes the working set size to be 12KB(3*2^4*2^4*2^3*2)) but it didn't help much. I'm only getting about 50% of the theoretical peak performance. Any pointers on how I could improve this?</p>
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    1. PTQuestion
    1. USuser1715122
    1. USuser1715122
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      1. VTUpMod
    1. COWhere's the actual SSE computation? I see almost none.
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      1. USMysticial
    2. CO@Mysticial: It is when I perform the multiplications. For example, if I perform A[i][k]*B[k][j], and I have stored the real and imaginary parts of A[i][k] in A_r and A_i, B_ri stores real and imaginary parts of B[k][j] contiguously and B_ri_r stores them in reverse order, I'll have to do: T1 = _mm_mul_pd(A_r,B_ri);T2 = _mm_mul_pd(A_i,B_ri_r);op00 = _mm_addsub_pd(T1,T2);
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      1. USuser1715122
    3. COI guess that's the "almost none". Yeah, you simply have too little computation with respect to the amount of shuffling and data movement.
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      1. POZGEMM using SSE, not giving speedup
      1. USMysticial
 

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