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Using Machine Learning to Auto-tune a Stencil Code on a Multicore Architecture Archana Ganapathi, Kaushik Datta, Armando Fox, David Patterson {archanag, kdatta, fox, pattrsn } @eecs.berkeley.edu RESULTS 2. Define kernel function (similarity metric between datapoints) ,[object Object],[object Object],[object Object],[object Object],KX KY MACHINE LEARNING METHODOLOGY Y 1. Convert raw data into multi-dimensional vectors Configuration parameters: Performance metrics: X Feature Vector Y Feature Vector = Poor Performance! Performance Comparison Energy Efficiency Comparison Summary ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],B ERKELEY P AR L AB KX*A KY*B X Y KCCA Raw Data Space KCCA Data Space ??? Nearest Neighbors Inverse Image Problem ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Configuration features Performance Metrics 4. Finding an optimal configuration Threads Blks_X Blks_Y Blks_Z Pad_sz Pref type Pref dist Stmt 4 32 128 256 32 Plane 64 ind Cycle L1_DCM L2_DCM TLB_DM CA_SHR CA_CLN CA_ITV Energy 1.9E7 2.4E5 1.5E5 1.2E4 1.2E5 1.4E4 1.2E3 2.3E4 MOTIVATION ,[object Object],[object Object],[object Object],[object Object],[object Object],Auto-tuning: Identify motif-specific optimizations Choose parameter Range for each optimization Automatically search parameter space for best configuration ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Machine Learning: Structured Grids Dense Linear Algebra Sparse Linear Algebra Motifs Intel/AMD x86 Sun Niagara2 IBM Blue Gene Diverse Multicore Architectures gcc icc xlc Compilers alone (No code tuning) + + Optimization Parameters Total Configs Thread Count 1 4 Domain Decomposition 4 36 Software Prefetching 2 18 Padding 1 32 Inner Loop 8 480 Total 16 4x10 7 3. Kernel Canonical Correlation Analysis 0 KXKY KYKX 0 KXKX 0 0 KYKY A B A B = Configuration Features: KX*A Solve the generalized eigenvalue equation: = eigenvalues A = basis vector for workload subspace B = basis vector for performance metrics subspace How it works: 1. Project each of two datasets onto infinitely many directions 2. Select basis vectors representing the top N directions of maximal correlation Performance Features: KY*B EXPERIMENTAL TESTBED Chosen Motif: Structured Grids (Stencil Codes) ,[object Object],[object Object],Prefetching distance Software prefetching Low memory bandwidth Register block dimensions/Inner loop reordering Register blocking/Inner loop optimizations Poor functional unit usage Core block dimensions Core blocking Capacity misses Padding amount Array padding Conflict misses NUMA-aware on/off NUMA-aware allocation Poor data placement Associated Parameters Solutions Code Bottlenecks Next[x,y,z]= C0 * Current[x,y,z]+ C1 *(Current[x-1,y,z]+ Current[x+1,y,z]+ Current[x,y-1,z]+ Current[x,y+1,z]+ Current[x,y,z-1]+ Current[x,y,z+1]); Inner Loop Pseudocode: 667MHz FBDIMMs Chipset (4x64b controllers) 10.66 GB/s(write) 21.33 GB/s(read) 10.66 GB/s Core FSB Core Core Core 10.66 GB/s Core FSB Core Core Core 4MB shared L2 4MB shared L2 4MB shared L2 4MB shared L2 2.66 GHz Intel Xeon (Clovertown) Chosen Architecture ,[object Object],[object Object],[object Object],[object Object],[object Object],Adaptive Mesh Refinement (AMR) x y z (unit-stride) 3D 7-point stencil y-1 (x,y,z) x+1 x-1 y+1 z-1 z+1 256 3 regular grid 3D 27-point stencil Training Time Performance Energy Efficiency

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