Data Partitioning for Reconfigurable Architectures with Distributed Block RAM Wenrui Gong Gang Wang Ryan Kastner Department of Electrical and Computer Engineering University of California, Santa Barbara {gong, wanggang, June 10, 2005

3/22/2005GONG et al: Data Partitioning for Reconfigurable Architectures with Distributed Block RAM2 What are we dealing with?  Mapping high-level programs into FPGA-based reconfigurable computing architectures with distributed block RAM modules  Objective: Improve utilizations of available storage resources, optimize system performance, and meet design goals

3/22/2005GONG et al: Data Partitioning for Reconfigurable Architectures with Distributed Block RAM3 Outline  Target architectures  Data partitioning problem  Memory optimizations  Experimental results  Concluding remarks

3/22/2005GONG et al: Data Partitioning for Reconfigurable Architectures with Distributed Block RAM4 Outline  Target architectures  Data partitioning problem  Memory optimizations  Experimental results  Concluding remarks

3/22/2005GONG et al: Data Partitioning for Reconfigurable Architectures with Distributed Block RAM5 Target Architecture  FPGA-based fine-grained reconfigurable computing architecture with distributed block RAM modules

3/22/2005GONG et al: Data Partitioning for Reconfigurable Architectures with Distributed Block RAM6 Memory Access Latencies  Memory access delay including access delay and propagation delays. Propagation delays are variables.  One clock cycle to access near data, or two or even more to access data far away from the CLB.  Difficult to distinguish which ones are near and which ones are remote before physical synthesis  More difficult than traditional data partitioning in parallelizing compilation for NUMA machines

3/22/2005GONG et al: Data Partitioning for Reconfigurable Architectures with Distributed Block RAM7 Outline  Target architectures  Data partitioning problem  Problem formulation  Data partitioning algorithm  Memory optimizations  Experimental results  Concluding remarks

3/22/2005GONG et al: Data Partitioning for Reconfigurable Architectures with Distributed Block RAM8 Problem Formulation  Inputs:  An l-level nested loop L  A set of n data arrays N  An architecture with m BRAM modules M.  Assumptions:  Index expressions of array references are affine functions of loop indices;  No indirect array references, or other similar pointer operations;  All data arrays are assigned to block RAM modules  No duplicate data.

3/22/2005GONG et al: Data Partitioning for Reconfigurable Architectures with Distributed Block RAM9 Problem Formulation (cont’d)  Partitioning problem: partition data arrays N into a set of data portions P, and seek an assignment from P to block RAM modules M.  Constraints:  1) hardware resource constraint  2) capacity constraint of each block RAM module  3) all data arrays are assigned to block RAM and each data element is assigned to one and only one block RAM module.  Objective: minimize the total execution time (or maximize the system throughput) under the above constraints.

3/22/2005GONG et al: Data Partitioning for Reconfigurable Architectures with Distributed Block RAM10 Overview of Data Partitioning Algorithm  Code analysis to determine possible partitioning directions  Architectural-level synthesis discover the design properties  Resource allocation, scheduling and binding  Granularity adjustment  Use experiential cost function to estimate performances

3/22/2005GONG et al: Data Partitioning for Reconfigurable Architectures with Distributed Block RAM11 Code Analysis  Calculate the iteration space IS(L)  Calculate the data space DS(Ni)  Obtain data access footprint F using the affine functions of loop indices  Analyze F and IS(L) to obtain a set of possible partitioning directions.

3/22/2005GONG et al: Data Partitioning for Reconfigurable Architectures with Distributed Block RAM12 Architectural-level Synthesis  Synthesize and pipeline the innermost iteration body, and collect execution time T, initial intervals II, and resource utilization um, ur, and ua

3/22/2005GONG et al: Data Partitioning for Reconfigurable Architectures with Distributed Block RAM13 Granularity Adjustment  For each possible partitioning direction, check different granularity to obtain the best performance  Calculate the finest and coarsest grain for a homogeneous partitioning  Finest: as less iterations as possible in one block RAM module, use all block RAM modules  Coarsest: use as less block RAM modules as possible  Estimate global memory accesses m r and total memory accesses m t, and their ratio  Use cost function to estimate the execution time

3/22/2005GONG et al: Data Partitioning for Reconfigurable Architectures with Distributed Block RAM14 Cost Function  An experiential formulation based our architectural- level synthesis results.  Estimate initial intervals for pipelined designs  Benefit memory accesses to nearby block RAM modules  Different resource utilizations and granularities affect the initial intervals

3/22/2005GONG et al: Data Partitioning for Reconfigurable Architectures with Distributed Block RAM15 Outline  Target architectures  Data partitioning problem  Memory optimizations  Scalar replacement  Data prefetching  Experimental results  Concluding remarks

3/22/2005GONG et al: Data Partitioning for Reconfigurable Architectures with Distributed Block RAM16 Scalar Replacement  Scalar replacement increases data reuses and reduces memory access  Memory are accessed in the previous iteration  Use contents already in registers rather than access it again

3/22/2005GONG et al: Data Partitioning for Reconfigurable Architectures with Distributed Block RAM17 Data Prefetching and Buffer Insertion  Buffer insertion reduces critical paths, and optimizes clock frequencies.  Schedule the global memory access one cycle earlier  Reduce the length of critical paths

3/22/2005GONG et al: Data Partitioning for Reconfigurable Architectures with Distributed Block RAM18 Outline  Target architectures  Data partitioning problem  Memory optimizations  Experimental results  Concluding remarks

3/22/2005GONG et al: Data Partitioning for Reconfigurable Architectures with Distributed Block RAM19 Experimental Setup  Target architecture: Xilinx Virtex II FPGA.  Target frequency: 150 MHz.  Benchmarks: image processing applications and DSP  SOBEL edge detection  Bilinear filtering  2D Gauss blurring  1D Gauss filter  SUSAN principle.

3/22/2005GONG et al: Data Partitioning for Reconfigurable Architectures with Distributed Block RAM20 Results: Architectural Exploration  Correlation bank:  Different partitions of the array S deliver a wide variety of candidate solutions  With quite different overall performance after synthesis and physical design.

3/22/2005GONG et al: Data Partitioning for Reconfigurable Architectures with Distributed Block RAM21 Results: Execution Time  The average speedup: 2.75 times, and after further optimizations, the average speedup is 4.80 times faster.

3/22/2005GONG et al: Data Partitioning for Reconfigurable Architectures with Distributed Block RAM22 Results: Achievable Clock Frequencies  About 10 percent slower than the original ones. After optimizations, about 7 percent faster than those of partitioned ones.

3/22/2005GONG et al: Data Partitioning for Reconfigurable Architectures with Distributed Block RAM23 Outline  Target architectures  Data partitioning problem  Memory optimizations  Experimental results  Concluding remarks

3/22/2005GONG et al: Data Partitioning for Reconfigurable Architectures with Distributed Block RAM24 Concluding Remarks  A data and iteration space partitioning approach for homogeneous block RAM modules  integrated with existing architectural-level synthesis techniques  parallelize input designs  dramatically improve system performance  Future work  Irregular memory access  Heterogeneous block RAM modules

3/22/2005GONG et al: Data Partitioning for Reconfigurable Architectures with Distributed Block RAM25 Thank You  Prof Ryan Kastner and Gang Wang  Reviewers  All audiences

3/22/2005GONG et al: Data Partitioning for Reconfigurable Architectures with Distributed Block RAM26 Questions