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AN INTEGER PROGRAMMING FRAMEWORK FOR OPTIMIZING SHARED MEMORY USE ON GPUS

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AN INTEGER PROGRAMMING FRAMEWORK FOR OPTIMIZING SHARED MEMORY USE ON GPUS. Wenjing Ma Gagan Agrawal The Ohio State University. GPGPU. General Purpose Programming on GPUs (accelerators) ‏ High performance/price ratio High language support CUDA Performance vs Productivity

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AN INTEGER PROGRAMMING FRAMEWORK FOR OPTIMIZING SHARED MEMORY USE ON GPUS

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  1. AN INTEGER PROGRAMMING FRAMEWORK FOR OPTIMIZING SHARED MEMORY USE ON GPUS Wenjing Ma Gagan Agrawal The Ohio State University

  2. GPGPU • General Purpose Programming on GPUs (accelerators)‏ • High performance/price ratio • High language support • CUDA • Performance vs Productivity • Hard to program • Memory hierarchy to manage • ...

  3. And Make the Programming Simple! Get High Performance from GPU • Automatic code generation • Device memory access is expensive • Using shared memory • Texture and constant memory • Coalescing device memory access • ...

  4. FEATURES OF SHARED MEMORY • Small, fast, like a cache • 16KB on each multiprocessor (no more than 48KB even on the latest GPU) • Read-write • Software controlled • __shared__ float data[n][n]; • Allocating shared memory: • Similar to register allocation

  5. Problem Formulation for Shared Memory Arrangement • Consider variables and basic blocks in a function • Element of array, array, section of array • Each variable can have several live ranges in the function • Access feature of live range: read, write, read-write, temp • Determine in which basic block a variable is allocated to shared memory • Assign_point[i][k]: variable i, basic block k

  6. Integer Programming Problem • Integer Linear Programming • Objective function • Maximize z = CT x • Constraints • Solution • Values of x • Special case of linear programming • All the unknown variables are integers (1-0 in our case)‏ • Solvable for reasonable size of problems

  7. Integer Programming for Shared Memory Arrangement • Objective Function • Maximize shared memory usage • Minimize data transfer between memory hierarchies

  8. Integer Programming for Shared Memory Arrangement (cnt’d)‏ • Objective Function

  9. An Example to Show size_alloc for (int i=0; i<n; i++)‏ for (int j=0; j<m; j++)‏ for (int k = 0; k<r; k++)‏ C[k] += A[i][k]- B[j][k]; ......

  10. Integer Programming for Shared Memory Arrangement (cnt’d)‏ • Constraints • Total allocation does not exceed the limit of shared memory at any time • Only at most one assign_point is 1 in each live range

  11. Integer Programming for Shared Memory Arrangement (cnt’d)‏ • Obtaining parameters • Using LLVM compiler framework • Pass 1: get access features • Read, write, read-write, temp • Pass 2: get live ranges, loop information, indices, and all other parameters

  12. Code Generation • According to the shared memory arrangement obtained from the integer programming model • Under the framework in previous work • Move data to cover gap caused by data evicted from shared memory

  13. An Example for (int i=0; i<n; i++)‏ for (int j=0; j<m; j++)‏ for (int k = 0; k<r; k++)‏ C[k] += A[i][k]- B[j][k]; ...... Integer Programming Solver A: n*r B: m*r C: r n: 2048 m: 3 r: 3 NUM_THREADS: 256 assign_point[0][1]=1; assign_point[1][0]=1; assign_point[2][0]=1; /* all other elements of assign_point are 0 */

  14. An Example (cnt’d)‏ Generated Code: __shared__ float s_B[m][r]; __shared__ float s_C[r*NUM_THREADS]; __shared__ float s_A[r*NUM_THREADS]; for(int i=0;i<m*r;i++) s_B[i]=B[i]; for(int i=0;i<n;i+=NUM_THREADS) { for(int j=0;j<r;j++)‏ s_A[tid*r+j]=A[tid+i][j]; for(int j=0;j<m;j++)‏ for(int k=0;k<r;k++)‏ s_C[k*tid]+=s_A[tid*r+k]-s_B[j][k]; ...... } /* Synchronize and combination of C */

  15. Suggesting Loop Transformation for (int rc = 0; rc < nRowCl; rc++) { tempDis = 0; for(int c = 0;c<numCol;c++)‏ tempDis = tempDis + data[r][c] * Acomp[rc][colCL[c]]; } for (int rc = 0; rc < nRowCl; rc++) tempDis[rc] = 0; for(int c = 0;c<numCol;c++)‏ { /* load into shared memory */ for (int rc = 0; rc < nRowCl; rc++)‏ { tempDis[rc] += data[r][c] * Acomp[rc][colCL[c]]; } }

  16. Experiments • Effectiveness of using shared memory • Compare with intuitive approach in previous work • Greedy sorting: sort all the variables in increasing order of size, and allocation them on shared memory until to the limit of shared memory • Effectiveness of loop transformation suggested by the integer programming model

  17. Experiment Results

  18. Experiment Results • K-means EM

  19. Experiment Results (cnt’d)‏ • PCA Co-clustering

  20. Effect of Loop Transformation • PCA Co-clustering

  21. Conclusion and Future Work • Proposed an integer programming model for shared memory arrangement on GPU • Consider numeric variable, array, and section of array • Suggested loop transformation for optimization • Got better results than the intuitive method • Will automate the code generation and loop transformation selection in future

  22. THANK YOU! Questions?

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