Linear scan to assign physical registers. SSA liveness must have been computed already. It also spills registers that are live during gc calls.
References
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Linear Scan Register Allocation by Massimiliano Poletto and Vivek Sarkar http://www.cs.ucla.edu/~palsberg/course/cs132/linearscan.pdf
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Linear Scan Register Allocation for the Java HotSpot Client Compiler by Christian Wimmer and http://www.ssw.uni-linz.ac.at/Research/Papers/Wimmer04Master/
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Quality and Speed in Linear-scan Register Allocation by Omri Traub, Glenn Holloway, Michael D. Smith http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.34.8435