For a Few Dollars More: Verified Fine-Grained Algorithm Analysis Down to LLVM

We present a framework to verify both, functional correctness and (amortized) worst-case complexity of practically efficient algorithms. implemented stepwise refinement approach, using the novel concept resource currencies naturally structure analysis along chain, allow fine-grained operation counts. Our targets LLVM intermediate representation. extend its semantics from earlier work with cost model. As case studies, we amortized constant time push on dynamic arrays O ( n log ) introsort algorithm, refine them down implementations. sorting algorithm performs par state-of-the-art implementation found in GNU C++ Library, provably satisfies required by standard.