Scaling up Superoptimization

Abstract

Developing a code optimizer is challenging, especially for new, idiosyncratic ISAs. Superoptimization can, in principle, discover machine-specific optimizations automatically by searching the space of all instruction sequences. If we can increase the size of code fragments a superoptimizer can optimize, we will be able to discover more optimizations.We develop LENS, a search algorithm that increases the size of code a superoptimizer can synthesize by rapidly pruning away invalid candidate programs. Pruning is achieved by selectively refining the abstraction under which candidates are considered equivalent, only in the promising part of the candidate space. LENS also uses a bidirectional search strategy to prune the candidate space from both forward and backward directions. These pruning strategies allow LENS to solve twice as many benchmarks as existing enumerative search algorithms, while LENS is about 11-times faster.Additionally, we increase the effective size of the superoptimized fragments by relaxing the correctness condition using contexts (surrounding code). Finally, we combine LENS with complementary search techniques into a cooperative superoptimizer, which exploits the stochastic search to make random jumps in a large candidate space, and a symbolic (SAT-solver-based) search to synthesize arbitrary constants. While existing superoptimizers consistently solve 9-16 out of 32 benchmarks, the cooperative superoptimizer solves 29 benchmarks. It can synthesize code fragments that are up to 82% faster than code generated by gcc -O3 from WiBench and MiBench.

Optimization space pruning without regrets

“…Super-optimization is a class of algorithms to find the optimal instruction sequence for a given computation. However, these algorithms are limited to straight-line code (or assimilated to it) (Phothilimthana et al 2016). Our search space is structurally very different and too large even for plain enumeration.…”

Synthesizing highly expressive SQL queries from input-output examples

“…Results showed that SCYTHE quickly and precisely solved more than 74% of the benchmarks and 80% out of these solved benchmarks were solved within a few seconds. Our algorithm solved 51 more cases within 600 seconds compared to the enumerative search algorithm [25,37] and outperformed SQLSynthesizer [40] on their project benchmarks with 4 more cases solved.…”

“…Such algorithms enumerate all programs in the program space of a given depth limit and retain only those consistent with the provided I/O examples. Previous enumerative synthesizers [2,25,37] adopt the concept of equivalence classes to optimize the search process: they group programs into equivalence classes based on their behaviors on the input example to compress the search space. The search then proceeds iteratively: within each stage, the algorithms enumerate all programs in the current search space, group them based on an equivalence metric, and proceed to the next stage.…”

Speeding up machine-code synthesis

“…5. Given a formula ϕ, the slave enumerates templatized instruction-sequences of increasing length, and uses CEGIS to check if there exists an instantiation of a candidate instruction-sequence that implements ϕ (Lines [16][17][18][19][20][21]. Before the CEGIS loop, the slave tries to prune away candidates via abstract semanticfootprints: if the abstract semantic-footprints of the candi- for each prefix p ∈ prefixes do 5: prefixes ← prefixes − {p} 6: for each templatized instruction i ∈ instrPool do 7:…”

“…Superoptimization. Superoptimization aims to find an optimal instruction-sequence for a target instruction-sequence [4,5,13,16,18,19,23]. Peephole superoptimization [4] uses "peepholes" to harvest target instruction-sequences, and replace them with equivalent instruction sequences that have a lower cost.…”