Survey on Combinatorial Register Allocation and Instruction Scheduling

Register allocation (mapping variables to processor registers or memory) and instruction scheduling (reordering instructions to increase instruction-level parallelism) are essential tasks for generating efficient assembly code in a compiler. In the last three decades, combinatorial optimization has emerged as an alternative to traditional, heuristic algorithms for these two tasks. Combinatorial optimization approaches can deliver optimal solutions according to a model, can precisely capture trade-offs between conflicting decisions, and are more flexible at the expense of increased compilation time. This paper provides an exhaustive literature review and a classification of combinatorial optimization approaches to register allocation and instruction scheduling, with a focus on the techniques that are most applied in this context: integer programming, constraint programming, partitioned Boolean quadratic programming, and enumeration. Researchers in compilers and combinatorial optimization can benefit from identifying developments, trends, and challenges in the area; compiler practitioners may discern opportunities and grasp the potential benefit of applying combinatorial optimization

Processor Models For Instruction Scheduling using Constraint Programming

Instruction scheduling is one of the most important optimisations performed when producing code in a compiler. The problem consists of finding a minimum length schedule subject to latency and different resource constraints. This is a hard problem, classically approached by heuristic algorithms. In the last decade, research interest has shifted from heuristic to potentially optimal methods. When using optimal methods, a lot of compilation time is spent searching for an optimal solution. This makes it important that the problem definition reflects the reality of the processor. In this work, a constraint programming approach was used to study the impact that the model detail has on performance. Several models of a superscalar processor were embedded in LLVM and evaluated using SPEC CPU2000. The result shows that there is substantial performance to be gained, over 5% for some programs. The stability of the improvement is heavily dependent on the accuracy of the model

Reproducibility, accuracy and performance of the Feltor code and library on parallel computer architectures

Feltor is a modular and free scientific software package. It allows developing platform independent code that runs on a variety of parallel computer architectures ranging from laptop CPUs to multi-GPU distributed memory systems. Feltor consists of both a numerical library and a collection of application codes built on top of the library. Its main target are two- and three-dimensional drift- and gyro-fluid simulations with discontinuous Galerkin methods as the main numerical discretization technique. We observe that numerical simulations of a recently developed gyro-fluid model produce non-deterministic results in parallel computations. First, we show how we restore accuracy and bitwise reproducibility algorithmically and programmatically. In particular, we adopt an implementation of the exactly rounded dot product based on long accumulators, which avoids accuracy losses especially in parallel applications. However, reproducibility and accuracy alone fail to indicate correct simulation behaviour. In fact, in the physical model slightly different initial conditions lead to vastly different end states. This behaviour translates to its numerical representation. Pointwise convergence, even in principle, becomes impossible for long simulation times. In a second part, we explore important performance tuning considerations. We identify latency and memory bandwidth as the main performance indicators of our routines. Based on these, we propose a parallel performance model that predicts the execution time of algorithms implemented in Feltor and test our model on a selection of parallel hardware architectures. We are able to predict the execution time with a relative error of less than 25% for problem sizes between 0.1 and 1000 MB. Finally, we find that the product of latency and bandwidth gives a minimum array size per compute node to achieve a scaling efficiency above 50% (both strong and weak)

An Integer Programming Approach to Optimal Basic Block Instruction Scheduling for Single-Issue Processors

We present a novel integer programming formulation for basic block instruction scheduling on single-issue processors. The problem can be considered as a very general sequential task scheduling problem with delayed precedence-constraints. Our model is based on the linear ordering problem and has, in contrast to the last IP model proposed, numbers of variables and constraints that are strongly polynomial in the instance size. Combined with improved preprocessing techniques and given a time limit of ten minutes of CPU and system time, our branch-and-cut implementation is capable to solve all but eleven of the 369,861 basic blocks of the SPEC 2000 integer and floating point benchmarks to proven optimality. This is competitive to the current state-of-the art constraint programming approach that has also been evaluated on this test suite

Modeling Algorithm Performance on Highly-threaded Many-core Architectures

The rapid growth of data processing required in various arenas of computation over the past decades necessitates extensive use of parallel computing engines. Among those, highly-threaded many-core machines, such as GPUs have become increasingly popular for accelerating a diverse range of data-intensive applications. They feature a large number of hardware threads with low-overhead context switches to hide the memory access latencies and therefore provide high computational throughput. However, understanding and harnessing such machines places great challenges on algorithm designers and performance tuners due to the complex interaction of threads and hierarchical memory subsystems of these machines. The achieved performance jointly depends on the parallelism exploited by the algorithm, the effectiveness of latency hiding, and the utilization of multiprocessors (occupancy). Contemporary work tries to model the performance of GPUs from various aspects with different emphasis and granularity. However, no model considers all of these factors together at the same time. This dissertation presents an analytical framework that jointly addresses parallelism, latency-hiding, and occupancy for both theoretical and empirical performance analysis of algorithms on highly-threaded many-core machines so that it can guide both algorithm design and performance tuning. In particular, this framework not only helps to explore and reduce the runtime configuration space for tuning kernel execution on GPUs, but also reflects performance bottlenecks and predicts how the runtime will trend as the problem and other parameters scale. The framework consists of a pair of analytical models with one focusing on higher-level asymptotic algorithm performance on GPUs and the other one emphasizing lower-level details about scheduling and runtime configuration. Based on the two models, we have conducted extensive analysis of a large set of algorithms. Two analysis provides interesting results and explains previously unexplained data. In addition, the two models are further bridged and combined as a consistent framework. The framework is able to provide an end-to-end methodology for algorithm design, evaluation, comparison, implementation, and prediction of real runtime on GPUs fairly accurately. To demonstrate the viability of our methods, the models are validated through data from implementations of a variety of classic algorithms, including hashing, Bloom filters, all-pairs shortest path, matrix multiplication, FFT, merge sort, list ranking, string matching via suffix tree/array, etc. We evaluate the models\u27 performance across a wide spectrum of parameters, data values, and machines. The results indicate that the models can be effectively used for algorithm performance analysis and runtime prediction on highly-threaded many-core machines

Mechanistic analytical modeling of superscalar in-order processor performance

Superscalar in-order processors form an interesting alternative to out-of-order processors because of their energy efficiency and lower design complexity. However, despite the reduced design complexity, it is nontrivial to get performance estimates or insight in the application--microarchitecture interaction without running slow, detailed cycle-level simulations, because performance highly depends on the order of instructions within the application’s dynamic instruction stream, as in-order processors stall on interinstruction dependences and functional unit contention. To limit the number of detailed cycle-level simulations needed during design space exploration, we propose a mechanistic analytical performance model that is built from understanding the internal mechanisms of the processor. The mechanistic performance model for superscalar in-order processors is shown to be accurate with an average performance prediction error of 3.2% compared to detailed cycle-accurate simulation using gem5. We also validate the model against hardware, using the ARM Cortex-A8 processor and show that it is accurate within 10% on average. We further demonstrate the usefulness of the model through three case studies: (1) design space exploration, identifying the optimum number of functional units for achieving a given performance target; (2) program--machine interactions, providing insight into microarchitecture bottlenecks; and (3) compiler--architecture interactions, visualizing the impact of compiler optimizations on performance

Pipeline Task Scheduling on Network Processors

Chip Multi-Processors (CMPs) are now available in a variety of systems and provide the opportunity for achieving high computational performance by exploiting application-level parallelism. In the communications environment, network processors (NPs), designed around CMP architectures, are generally usable in a pipelined manner. This leads to the issue of scheduling tasks on processor pipelines. This paper considers problems associated with determining optimal schedules for such pipelines. A system and algorithm called Greedy Pipe is presented. The algorithm employs a greedy heuristic to schedule tasks derived from multiple application flows on pipelines with an arbitrary number of stages. Tasks may be shared, and different bandwidths may be associated with each of the application flows. Experimental results indicate that, 95% of the time Greedy Pipe obtains schedules within 10% of optimal. Examples are given to show the use of Greedy Pipe for general pipeline/algorithm design, and for use in the NP environment with typical networking applications