A mathematical formulation of the loop pipelining problem

This paper presents a mathematical model for the loop pipelining problem that considers several parameters for optimization and supports any combination of resource and timing constraints. The unrolling degree of the loop is one of the variables explored by the model. By using Farey’s series, an optimal exploration of the unrolling degree is performed and optimal solutions not considered by other methods are obtained. Finding an optimal schedule that minimizes resource and register requirements is solved by using an Integer linear programming (ILP) model. A novel paradigm called branch and prune is proposed to eficiently converge towards the optimal schedule and prune the search tree for integer solutions, thus drastically reducing the running time. This is the first formulation that combines the unrolling degree of the loop with timing and resource constraints in a mathematical model that guarantees optimal solutions.Peer ReviewedPostprint (author's final draft

SIRA: Schedule Independent Register Allocation for Software Pipelining

International audienceThe register allocation in loops is generally carried out after or during the software pipelining process. This is because doing the register allocation at first step without assuming a schedule lacks the information of interferences between values live ranges. The register allocator introduces extra false dependencies which reduces dramatically the original ILP (Instruction Level Parallelism). In this paper, we give a new formulation to carry out the register allocation before the scheduling process, directly on the data dependence graph by inserting some anti dependencies arcs (reuse edges). This graph extension is first constrained by minimizing the critical cycle and hence minimizing the ILP loss due to the register pressure. The second constraint is to ensure that there is always a cyclic register allocation with the set of available registers, and this for any software pipelining of the new graph. We give the exact formulation of this problem with linear integer programming

Minimizing Register Requirements under Resource-Constrained Rate-Optimal Software Pipelining

The rapid advances in high-performance computer architecture and compilation techniques provide both challenges and opportunities to exploit the rich solution space of software pipelined loop schedules. In this paper, we develop a framework to construct a software pipelined loop schedule which runs on the given architecture (with a fixed number of processor resources) at the maximum possible iteration rate (`a la rate-optimal) while minimizing the number of buffers --- a close approximation to minimizing the number of registers. The main contributions of this paper are: ffl First, we demonstrate that such problem can be described by a simple mathematical formulation with precise optimization objectives under a periodic linear scheduling framework. The mathematical formulation provides a clear picture which permits one to visualize the overall solution space (for rate-optimal schedules) under different sets of constraints. ffl Secondly, we show that a precise mathematical formulation..

Predicate-aware, makespan-preserving software pipelining of scheduling tables

International audienceWe propose a software pipelining technique adapted to specific hard real-time scheduling problems. Our technique optimizes both computation throughput and execution cycle makespan, with makespan being prioritary. It also takes advantage of the predicated execution mechanisms of our embedded execution plat-form. To do so, it uses a reservation table formalism allowing the manipulation of the execution conditions of operations. Our reservation tables allow the double reservation of a resource at the same dates by two different operations, if the operations have exclusive execution conditions. Our analyses can determine when double reservation is possible even for operations belonging to different iterations

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

Clustered VLIW architecture based on queue register files

Institute for Computing Systems ArchitectureInstruction-level parallelism (ILP) is a set of hardware and software techniques that allow parallel execution of machine operations. Superscalar architectures rely most heavily upon hardware schemes to identify parallelism among operations. Although successful in terms of performance, the hardware complexity involved might limit the scalability of this model. VLIW architectures use a different approach to exploit ILP. In this case all data dependence analyses and scheduling of operations are performed at compile time, resulting in a simpler hardware organization. This allows the inclusion of a larger number of functional units (FUs) into a single chip. IN spite of this relative simplification, the scalability of VLIW architectures can be constrained by the size and number of ports of the register file. VLIW machines often use software pipelining techniques to improve the execution of loop structures, which can increase the register pressure. Furthermore, the access time of a register file can be compromised by the number of ports, causing a negative impact on the machine cycle time. For these reasons we understand that the benefits of having parallel FUs, which have motivated the investigation of alternative machine designs. This thesis presents a scalar VLIW architecture comprising clusters of FUs and private register files. Register files organised as queue structures are used as a mechanism for inter-cluster communication, allowing the enforcement of fixed latency in the process. This scheme presents better possibilities in terms of scalability as the size of the individual register files is not determined by the total number of FUs, suggesting that the silicon area may grow only linearly with respect to the total number of FUs. However, the effectiveness of such an organization depends on the efficiency of the code partitioning strategy. We have developed an algorithm for a clustered VLIW architecture integrating both software pipelining and code partitioning in a a single procedure. Experimental results show it may allow performance levels close to an unclustered machine without communication restraints. Finally, we have developed silicon area and cycle time models to quantify the scalability of performance and cost for this class of architecture