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Register allocation for programs in ssaform
 In Compiler Construction 2006, volume 3923 of LNCS
, 2006
"... In this technical report, we present an architecture for register allocation on the SSAform. We show, how the properties of SSAform programs and their interference graphs can be exploited to develop new methods for spilling, coloring and coalescing. We present heuristic and optimal solution method ..."
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Cited by 26 (3 self)
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In this technical report, we present an architecture for register allocation on the SSAform. We show, how the properties of SSAform programs and their interference graphs can be exploited to develop new methods for spilling, coloring and coalescing. We present heuristic and optimal solution methods for these three subtasks. 1
Register allocation via coloring of chordal graphs
 In Proceedings of APLAS’05, Asian Symposium on Programming Languages and Systems
, 2005
"... Abstract. We present a simple algorithm for register allocation which is competitive with the iterated register coalescing algorithm of George and Appel. We base our algorithm on the observation that 95 % of the methods in the Java 1.5 library have chordal interference graphs when compiled with the ..."
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Cited by 20 (2 self)
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Abstract. We present a simple algorithm for register allocation which is competitive with the iterated register coalescing algorithm of George and Appel. We base our algorithm on the observation that 95 % of the methods in the Java 1.5 library have chordal interference graphs when compiled with the JoeQ compiler. A greedy algorithm can optimally color a chordal graph in time linear in the number of edges, and we can easily add powerful heuristics for spilling and coalescing. Our experiments show that the new algorithm produces better results than iterated register coalescing for settings with few registers and comparable results for settings with many registers. 1
Extended Linear Scan: an Alternate Foundation for Global Register Allocation
"... Abstract. In this paper, we extend past work on Linear Scan register allocation, and propose two Extended Linear Scan (ELS) algorithms that retain the compiletime efficiency of past Linear Scan algorithms while delivering performance that can match or surpass that of Graph Coloring. Specifically, th ..."
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Cited by 11 (1 self)
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Abstract. In this paper, we extend past work on Linear Scan register allocation, and propose two Extended Linear Scan (ELS) algorithms that retain the compiletime efficiency of past Linear Scan algorithms while delivering performance that can match or surpass that of Graph Coloring. Specifically, this paper makes the following contributions: – We highlight three fundamental theoretical limitations in using Graph Coloring as a foundation for global register allocation, and introduce a basic Extended Linear Scan algorithm, ELS0, which addresses all three limitations for the problem of SpillFree Register Allocation. – We introduce the ELS1 algorithm which extends ELS0 to obtain a greedy algorithm for the problem of Register Allocation with Total Spills. – Finally, we present experimental results to compare the Graph Coloring and Extended Linear Scan algorithms. Our results show that the compiletime speedups for ELS1 relative to GC were significant, and varied from 15 × to 68×. In addition, the resulting execution time improved by up to 5.8%, with an average improvement of 2.3%. Together, these results show that Extended Linear Scan is promising as an alternate foundation for global register allocation, compared to Graph Coloring, due to its compiletime scalability without loss of execution time performance. 1
Register allocation : what does the NPCompleteness proof of Chaitin et al. really prove? Or revisting register allocation: why and how
 In Proc. of the 19 th International Workshop on Languages and Compilers for Parallel Computing (LCPC ’06
, 2006
"... Register allocation is one of the most studied problems in compilation. It is considered as an NPcomplete problem since Chaitin et al., in 1981, modeled the problem of assigning temporary variables to k machine registers as the problem of coloring, with k colors, the interference graph associated t ..."
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Cited by 10 (4 self)
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Register allocation is one of the most studied problems in compilation. It is considered as an NPcomplete problem since Chaitin et al., in 1981, modeled the problem of assigning temporary variables to k machine registers as the problem of coloring, with k colors, the interference graph associated to the variables. The fact that the interference graph can be arbitrary proves the NPcompleteness of this formulation. However, this original proof does not really show where the complexity of register allocation comes from. Recently, the rediscovery that interference graphs of SSA programs can be colored in polynomial time raised the question: Can we exploit SSA form to perform register allocation in polynomial time, without contradicting Chaitin et al’s NPcompleteness result? To address such a question and, more generally, the complexity of register allocation, we revisit Chaitin et al’s proof to better identify the interactions between spilling (load/store insertion), coalescing/splitting (removal/insertion of moves between registers), critical edges (a property of the controlflow graph), and coloring (assignment to registers). In particular, we show that, in general (we will make clear when), it is easy to decide if temporary variables can be assigned to k registers or if some spilling is necessary. In other words, the real complexity does not come from the coloring itself (as a wrong interpretation of the proof of Chaitin et al. may suggest) but comes from the presence of critical edges and from the optimizations of spilling and coalescing.
On the complexity of register coalescing
 In Proc. of the International Symposium on Code Generation and Optimization (CGO ’07
, 2006
"... Memory transfers are becoming more important to optimize, for both performance and power consumption. With this goal in mind, new register allocation schemes are developed, which revisit not only the spilling problem but also the coalescing problem. Indeed, a more aggressive strategy to avoid load/s ..."
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Cited by 9 (3 self)
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Memory transfers are becoming more important to optimize, for both performance and power consumption. With this goal in mind, new register allocation schemes are developed, which revisit not only the spilling problem but also the coalescing problem. Indeed, a more aggressive strategy to avoid load/store instructions may increase the constraints to suppress (coalesce) move instructions. This paper is devoted to the complexity of the coalescing phase, in particular in the light of recent developments on the SSA form. We distinguish several optimizations that occur in coalescing heuristics: a) aggressive coalescing removes as many moves as possible, regardless of the colorability of the resulting interference graph; b) conservative coalescing removes as many moves as possible while keeping the colorability of the graph; c) incremental conservative coalescing removes one particular move while keeping the colorability of the graph; d) optimistic coalescing coalesces moves aggressively, then gives up about as few moves as possible so that the graph becomes colorable again. We almost completely classify the NPcompleteness of these problems, discussing also on the structure of the interference graph: arbitrary, chordal, or kcolorable in a greedy fashion. We believe that such a study is a necessary step for designing new coalescing strategies. 1
Optimal Register Sharing for HighLevel Synthesis Of SSA . . .
 IEEE TRANS. COMPUTER AIDED DESIGN
, 2006
"... Register sharing for highlevel synthesis of programs represented in static single assignment (SSA) form is proven to have a polynomialtime solution. Register sharing is modeled as a graphcoloring problem. Although graph coloring is NPComplete in the general case, an interference graph constructe ..."
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Cited by 8 (3 self)
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Register sharing for highlevel synthesis of programs represented in static single assignment (SSA) form is proven to have a polynomialtime solution. Register sharing is modeled as a graphcoloring problem. Although graph coloring is NPComplete in the general case, an interference graph constructed for a program in SSA form probably belongs to the class of chordal graphs that have an optimal O(V time algorithm. Chordal graph coloring reduces the number of registers allocated to the program by as much as 86% and 64.93% on average compared to linear scan register allocation.
Fast Liveness Checking for SSAForm Programs
"... Liveness analysis is an important analysis in optimizing compilers. Liveness information is used in several optimizations and is mandatory during the codegeneration phase. Two drawbacks of conventional liveness analyses are that their computations are fairly expensive and their results are easily i ..."
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Cited by 6 (2 self)
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Liveness analysis is an important analysis in optimizing compilers. Liveness information is used in several optimizations and is mandatory during the codegeneration phase. Two drawbacks of conventional liveness analyses are that their computations are fairly expensive and their results are easily invalidated by program transformations. We present a method to check liveness of variables that overcomes both obstacles. The major advantage of the proposed method is that the analysis result survives all program transformations except for changes in the controlflow graph. For common program sizes our technique is faster and consumes less memory than conventional dataflow approaches. Thereby, we heavily make use of SSAform properties, which allow us to completely circumvent dataflow equation solving. We evaluate the competitiveness of our approach in an industrial strength compiler. Our measurements use the integer part of the SPEC2000 benchmarks and investigate the liveness analysis used by the SSA destruction pass. We compare the net time spent in liveness computations of our implementation against the one provided by that compiler. The results show that in the vast majority of cases our algorithm, while providing the same quality of information, needs less time: an average speedup of 16%.
Revisiting OutofSSA Translation for Correctness, Code Quality, and Efficiency
"... Static single assignment (SSA) form is an intermediate program representation in which many code optimizations can be performed with fast and easytoimplement algorithms. However, some of these optimizations create situations where the SSA variables arising from the same original variable now have ..."
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Cited by 6 (3 self)
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Static single assignment (SSA) form is an intermediate program representation in which many code optimizations can be performed with fast and easytoimplement algorithms. However, some of these optimizations create situations where the SSA variables arising from the same original variable now have overlapping live ranges. This complicates the translation out of SSA code into standard code. There are three issues to consider: correctness, code quality (elimination of copies), and algorithm efficiency (speed and memory footprint). Briggs et al. proposed patches to correct the initial approach of Cytron et al. A cleaner and more general approach was proposed by Sreedhar et al., along with techniques to reduce the number of generated copies. We propose a new approach based on coalescing and a precise view of interferences, in which correctness and optimizations are separated. Our approach is provably correct and simpler to implement, with no patches or particular cases as in previous solutions, while reducing the number of generated copies. Also, experiments with SPEC CINT2000 show that it is 2x faster and 10x less memoryconsuming than the Method III of Sreedhar et al., which makes it suitable for justintime compilation.
Register Allocation after Classical SSA Elimination is NPcomplete
"... Abstract. Chaitin proved that register allocation is equivalent to graph coloring and hence NPcomplete. Recently, Bouchez, Brisk, and Hack have proved independently that the interference graph of a program in static single assignment (SSA) form is chordal and therefore colorable in linear time. Can ..."
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Cited by 5 (0 self)
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Abstract. Chaitin proved that register allocation is equivalent to graph coloring and hence NPcomplete. Recently, Bouchez, Brisk, and Hack have proved independently that the interference graph of a program in static single assignment (SSA) form is chordal and therefore colorable in linear time. Can we use the result of Bouchez et al. to do register allocation in polynomial time by first transforming the program to SSA form, then performing register allocation, and finally doing the classical SSA elimination that replaces φfunctions with copy instructions? In this paper we show that the answer is no, unless P = NP: register allocation after classical SSA elimination is NPcomplete. Chaitin’s proof technique does not work for programs after classical SSA elimination; instead we use a reduction from the graph coloring problem for circular arc graphs. 1