Notes on Homework 1

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# Notes on Homework 1 - PowerPoint PPT Presentation

Notes on Homework 1. 2x2 Matrix Multiply. C 00 += A 00 B 00 + A 01 B 10 C 10 += A 10 B 00 + A 11 B 10 C 01 += A 00 B 01 + A 01 B 11 C 11 += A 10 B 01 + A 11 B 11 Rewrite as SIMD algebra C00_C10 += A00_A10 * B00_B00 C01_C11 += A00_A10 * B01_B01 C00_C10 += A01_A11 * B10_B10

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Presentation Transcript
CS267 Lecture 72x2 Matrix Multiply
• C00 += A00B00 + A01B10
• C10 += A10B00 + A11B10
• C01 += A00B01 + A01B11
• C11 += A10B01 + A11B11
• Rewrite as SIMD algebra
• C00_C10 += A00_A10 * B00_B00
• C01_C11 += A00_A10 * B01_B01
• C00_C10 += A01_A11 * B10_B10
• C01_C11 += A01_A11 * B11_B11

Summary of SSE intrinsics

• #include <emmintrin.h>
• Vector data type:
• __m128d

• _mm_store_pd
• _mm_storeu_pd

Arithmetic:

• _mm_mul_pd

Example: multiplying 2x2 matrices

#include <emmintrin.h>

for( inti = 0; i < 2; i++ )

{

c1=_mm_add_pd( c1, _mm_mul_pd( a, b1 ) ); //rank-1 update

c2=_mm_add_pd( c2, _mm_mul_pd( a, b2 ) );

}

_mm_storeu_pd( C+0*lda, c1 ); //store unaligned block in C

_mm_storeu_pd( C+1*lda, c2 );

General suggestions for optimizations

• Changing the order of the loops (i, j, k)
• changes which matrix stays in memory and the type of product
• Blocking for multiple levels (registers or SIMD, L1, L2)
• L3 is not important as most matrices will fit and optimizations not likely to bring more benefits
• Unrolling the loops
• Copy optimizations
• will be a large benefit if done for sub-matrix that is kept in memory
• careful not to overdo (overhead is high for every level)
• can help with SIMD performance
• eliminating special cases and bad performance
• cannot get over 50% without explicit intrinsics or auto-vectorization
• Tuning parameters
• various block sizes, register sizes (perhaps automate)

Other issues

• Checking compilers
• options available PGI, PathScale, GNU, Cray
• Cray compiler seems to have an issue with explicit intrinsics
• Using compiler flags
• remember not allowed to use MM specific flags (-matmul)
• Checking assembly code for SSE instructions
• use the –S flag to see assembly
• should have mainly ADDPD & MULPD ops, ADDSD & MULSD are scalar computations
• Remember the write-up
• want to know what optimizations you tried and what worked and failed
• try and have an incremental design and show the performance of multiple iterations
• DUE DATE changed, now due Monday Feb 17th at 11:59pm