This article presents the first optimal algorithm for trace scheduling. The trace is a global scheduling region used by compilers to exploit instruction-level parallelism across basic block boundaries. Several heuristic techniques have been proposed for trace scheduling, but the precision of these techniques has not been studied relative to optimality. This article describes a technique for finding provably optimal trace schedules, where optimality is defined in terms of a weighted sum of schedule lengths across all code paths in a trace. The optimal algorithm uses branch-and-bound enumeration to efficiently explore the entire solution space. Experimental evaluation of the algorithm shows that, with a time limit of 1 s per problem, 91% of the hard trace scheduling problems in the SPEC CPU 2006 Integer Benchmarks are solved optimally. For 58% of these hard problems, the optimal schedule is improved compared to that produced by a heuristic scheduler with a geometric mean improvement of 3.2% in weighted schedule length and 18% in compensation code size.

Graphics Processing Units have emerged as powerful accelerators for massively parallel, numerically intensive workloads. The two dominant software models for these devices are NVIDIA's CUDA and the cross-platform OpenCL standard. Until now, there has not been a fully open-source compiler targeting the CUDA environment, hampering general compiler and architecture research and making deployment difficult in datacenter or supercomputer environments. In this paper, we present gpucc, an LLVM-based, fully open-source, CUDA compatible compiler for high performance computing. It performs various general and CUDAspecific optimizations to generate high performance code. The Clang-based frontend supports modern language features such as those in C++11 and C++14. Compile time is 8% faster than NVIDIA's toolchain (nvcc) and it reduces compile time by up to 2.4x for pathological compilations (>100 secs), which tend to dominate build times in parallel build environments. Compared to nvcc, gpucc's runtime performance is on par for several open-source benchmarks, such as Rodinia (0.8% faster), SHOC (0.5% slower), or Tensor (3.7% faster). It outperforms nvcc on internal large-scale end-to-end benchmarks by up to 51.0%, with a geometric mean of 22.9%.

{ This paper presents a new approach to local instruction scheduling based on integer programming that produces optimal instruction schedules in a reasonable time, even for very large basic blocks. The new approach rst uses a set of graph transformations to simplify the datadependency graph while preserving the optimality of the nal schedule. The simpli ed g r aph results in a simpli ed integer program which can be solved much faster. A new integerprogramming formulation is then applied to the simpli ed graph. Various techniques are used to simplify the formulation, resulting in fewer integer-program variables, fewer integer-program constraints and fewer terms in some of the remaining constraints, thus reducing integer-program solution time. The new formulation also uses certain adaptively added c onstraints (cuts) to reduce solution time. The proposed optimal instruction scheduler is built within the Gnu Compiler Collection (GCC) and is evaluated experimentally using the SPEC95 oating point benchmarks. Although optimal scheduling for the target processor is considered i n t r actable, all of the benchmarks' basic blocks are o ptimally scheduled, including blocks with up to 1000 instructions, while total compile time increases by only 14%.

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