SOAP: Structural optimization of arithmetic expressions for high-level synthesis

Gao, Xitong; Bayliss, Samuel; Constantinides, George A.

doi:10.1109/fpt.2013.6718340

Cited by 14 publications

(12 citation statements)

References 14 publications

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“…Despite the simplicity of NumImp, it includes all the features of a full programming language rather than an expression language used in prior work [4]. Additional language features, for example, array and matrix types, and also power, exponentiation and logarithm operators, can be added with few changes to our method.…”

Section: Language Definitionmentioning

confidence: 97%

“…In the high-level synthesis (HLS) community, a technique is developed in [2] to automatically trade-off the data path wordlengths of algorithms that contain loops. However, these methods changes datapath size by varying precisions of arithmetic operators, whereas there is currently little work on performing structural improvements to datapaths in HLS, except for SOAP's arithmetic expression optimization [4].…”

Section: Related Workmentioning

confidence: 99%

“…By comparison, not only do we propagate the values, but we use the static analysis approach of [4] to propagate the round-off errors associated with the numerical computations. For instance, if we know that floating point values a and b are respectively bounded by [0, 1] and [1,2], and they have no round-off errors associated with them, then evaluating a + b would result in a floating-point value that is bounded by [1,3], and we can compute the operation would result in a round-off error in the range of [−1.19209304 × 10 −7 , 1.19209304 × 10 −7 ].…”

Section: Performance Analysesmentioning

confidence: 99%

“…A naïve strategy to search for the Pareto optimal implementations is to discover all possible equivalent expressions. However, this would result in combinatorial explosion and become intractable even for very small expressions [4,6,10]. To remedy this, Gao et al [4] proposed a novel approach, known as SOAP, to significantly reduce the space and time complexity to produce a subset of the Pareto frontier.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Numerical Program Optimization for High-Level Synthesis

Gao

Constantinides

2015

Proceedings of the 2015 ACM/SIGDA International Symposium on Field-Programmable Gate Arrays

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This paper introduces a new technique, and its associated open source tool, SOAP2, to automatically perform sourceto-source optimization of numerical programs, specifically targeting the trade-off between numerical accuracy and resource usage as a high-level synthesis flow for FPGA implementations. We introduce a new intermediate representation, which we call metasemantic intermediate representation (MIR), to enable the abstraction and optimization of numerical programs. We efficiently discover equivalent structures in MIRs by exploiting the rules of real arithmetic, such as associativity and distributivity, and rules that allow control flow restructuring, and produce Pareto frontiers of equivalent programs that trades off LUTs, DSPs and accuracy. Additionally, we further broaden the Pareto frontier in our optimization flow to automatically explore the numerical implications of partial loop unrolling and loop splitting. In real applications, our tool discovers a wide range of Pareto optimal options, and the most accurate one improves the accuracy of numerical programs by up to 65%.

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Section: Language Definitionmentioning

confidence: 97%

Section: Related Workmentioning

confidence: 99%

Section: Performance Analysesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Numerical Program Optimization for High-Level Synthesis

Gao

Constantinides

2015

Proceedings of the 2015 ACM/SIGDA International Symposium on Field-Programmable Gate Arrays

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“…1 equivalent expressions [6,7]. We therefore base our optimizer on the open-source SOAP2 framework [6,8], which specifically tackles the efficient discovery of equivalent structures in numerical programs, by intelligently pruning the set of candidates as it progresses up the input program's abstract syntax tree. We also exploit SOAP2's ability to analyze the numerical accuracy of a given program.…”

Section: −24mentioning

confidence: 99%

Automatically Optimizing the Latency, Area, and Accuracy of C Programs for High-Level Synthesis

Gao

Wickerson

Constantinides

2016

Proceedings of the 2016 ACM/SIGDA International Symposium on Field-Programmable Gate Arrays

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Loops are pervasive in numerical programs, so high-level synthesis (HLS) tools use state-of-the-art scheduling techniques to pipeline them efficiently. Still, the run time performance of the resultant FPGA implementation is limited by data dependences between loop iterations. Some of these dependence constraints can be alleviated by rewriting the program according to arithmetic identities (e.g. associativity and distributivity), memory access reductions, and control flow optimizations (e.g. partial loop unrolling). HLS tools cannot safely enable such rewrites by default because they may impact the accuracy of floating-point computations and increase area usage. In this paper, we introduce the first open-source program optimizer for automatically rewriting a given program to optimize latency while controlling for accuracy and area. Our tool, SOAP3, reports a multi-dimensional Pareto frontier that the programmer can use to resolve the trade-off according to their needs. When applied to a suite of PolyBench and Livermore Loops benchmarks, our tool has generated programs that enjoy up to a 12× speedup, with a simultaneous 7× increase in accuracy, at a cost of up to 4× more LUTs.

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Neural Network Precision Tuning

Ioualalen¹,

Martel²

2019

Lecture Notes in Computer Science

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SOAP: Structural optimization of arithmetic expressions for high-level synthesis

Cited by 14 publications

References 14 publications

Numerical Program Optimization for High-Level Synthesis

Numerical Program Optimization for High-Level Synthesis

Automatically Optimizing the Latency, Area, and Accuracy of C Programs for High-Level Synthesis

Neural Network Precision Tuning

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