source: Papers/sttt/main.tex @ 3471

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\title{On the correctness of a branch displacement algorithm
\thanks{Research supported by the CerCo project, within the Future and Emerging Technologies (FET) programme of the Seventh Framework Programme for Research of the European Commission, under FET-Open grant number 243881}}
\author{Jaap Boender \and Dominic P. Mulligan \and Claudio Sacerdoti Coen}

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\begin{abstract}
Optimising assemblers face the `branch displacement problem', i.e. how best to choose between concrete machine code jump instructions---typically of differing instruction and offset sizes---when expanding pseudo-instructions.
Ideally, a well-implemented optimising assembler would choose the set of jump expansions that minimises the size of the resulting machine code program, a task that is provably \textsc{np}-hard.

As part of CerCo (`Certified Complexity')---an \textsc{eu}-funded project to develop a verified concrete complexity preserving compiler for a large subset of the C programming language---we have implemented and proved correct an assembler within an interactive theorem prover.
Our assembler targets the instruction set of a typical micro-controller, the \textsc{mcs}-51.
As is common in embedded systems, this micro-controller has a paucity of available code memory and therefore we face additional pressure in reducing the size of any assembled machine code program.
Out of necessity, then, our assembler must implement an algorithm for solving the branch displacement problem, and we must prove that this algorithm is correct.

We discuss wider problems associated with proving an optimising assembler correct, discuss possible solutions to those problems, and detail our chosen solutions and their proofs of correctness.

\keywords{formal verification, interactive theorem proving, assembler, branch displacement optimisation}
\end{abstract}

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