Heuristics for offset assignment in embedded processors

This thesis deals with the optimization of program size and performance in current generation embedded digital signal processors (DSPs) by the design of optimal memory layouts for data. Given the tight constraints on the size, power consumption, cost and performance of these processors, the minimization of code size in terms of the number of instructions required and the associated reduction in execution time are important. Several DSPs provide limited addressing modes and the layout of data, known as offset assignment, plays a critical role in determining the code size and performance. Even the simplest variant of the offset assignment problem is NP-complete. Research effort in this area has focused on the design, implementation and evaluation of effective heuristics for several variants of the offset assignment problem. One of the most important factors in the determination of the size, and hence, execution time of a code is the number of instructions required to access the variables stored in the processor memory. The indirect addressing mode common in DSPs requires memory accesses to be realized through address registers that hold the address of the memory location to be accessed. The architecture provides instructions for adding to and subtracting from the values of the address registers to compute the addresses of subsequent data that need to be accessed. In addition, some DSP processors include multiple memory banks that allow increased parallelism in memory access. Proper partitioning of variables across memory banks is critical to effectively using the increased parallelism. The work reported in this thesis aims to evolve efficient methods for designing memory layouts under the conditions of availability of one address register (SOA) or of multiple address registers (GOA). It also proposes a novel technique for choosing the assignment of variables to the memory banks. This thesis motivates, proposes and evaluates heuristics for all these three problems. For the SOA and GOA problems, the heuristics are implemented and tested on different random sample inputs, and the results obtained are compared to those obtained by prior heuristics. In addition, this thesis provides some insight into the SOA, GOA and the variable partitioning problems

Compilation and Scheduling Techniques for Embedded Systems

Embedded applications are constantly increasing in size, which has resulted in increasing demand on designers of digital signal processors (DSPs) to meet the tight memory, size and cost constraints. With this trend, memory requirement reduction through code compaction and variable coalescing techniques are gaining more ground. Also, as the current trend in complex embedded systems of using multiprocessor system-on-chip (MPSoC) grows, problems like mapping, memory management and scheduling are gaining more attention. The first part of the dissertation deals with problems related to digital signal processors. Most modern DSPs provide multiple address registers and a dedicated address generation unit (AGU) which performs address generation in parallel to instruction execution. A careful placement of variables in memory is important in decreasing the number of address arithmetic instructions leading to compact and efficient code. Chapters 2 and 3 present effective heuristics for the simple and the general offset assignment problems with variable coalescing. A solution based on simulated annealing is also presented. Chapter 4 presents an optimal integer linear programming (ILP) solution to the offset assignment problem with variable coalescing and operand permutation. A new approach to the general offset assignment problem is introduced. Chapter 5 presents an optimal ILP formulation and a genetic algorithm solution to the address register allocation problem (ARA) with code transformation techniques. The ARA problem is used to generate compact codes for array-intensive embedded applications. In the second part of the dissertation, we study problems related to MPSoCs. MPSoCs provide the flexibility to meet the performance requirements of multimedia applications while respecting the tight embedded system constraints. MPSoC-based embedded systems often employ software-managed memories called scratch-pad memories (SPM). Scheduling the tasks of an application on the processors and partitioning the available SPM budget among those processors are two critical issues in reducing the overall computation time. Traditionally, the step of task scheduling is applied separately from the memory partitioning step. Such a decoupled approach may miss better quality schedules. Chapters 6 and 7 present effective heuristics that integrate task allocation and SPM partitioning to further reduce the execution time of embedded applications for single and multi-application scenarios

Address optimizations for embedded processors

Embedded processors that are common in electronic devices perform a limited set of tasks compared to general-purpose processor systems. They have limited resources which have to be efficiently used. Optimal utilization of program memory needs a reduction in code size which can be achieved by eliminating unnecessary address computations i.e., generate optimal offset assignment that utilizes built-in addressing modes. Single offset assignment (SOA) solutions, used for processors with one address register; start with the access sequence of variables to determine the optimal assignment. This research uses the basic block to commutatively transform statements to alter the access sequence. Edges in the access graphs are classified into breakable and unbreakable edges. Unbreakable edges are preferred when selecting edges for the assignment. Breakable edges are used to commutatively transform statements such that the assignment cost is reduced. The use of a modify register in some processors allows the address to be modified by a value in MR in addition to post-increment/decrement modes. Though finding the most beneficial value of MR is a common practice, this research shows that modifying the access sequence using edge fold, node swap, and path interleave techniques for an MR value of two has significant benefit. General offset assignment requires variables in the access sequence to be partitioned to various address registers. Use of the node degree in the access graph demonstrates greater benefit than using edge weights and frequency of variables. The Static Single Assignment (SSA) form of the basic block introduces new variables to an access graph, making it sparser. Sparser access graphs usually have lower assignment costs. The SSA form allows reuse of variable space based on variable lifetimes. Offset assignment solutions may be improved by incrementally assignment based on uncovered edges, providing the best cost improvement. This heuristic considers improvements due to all uncovered edges. Optimization techniques have primarily been edge-based. Node-based SOA technique has been tested for use with commutative transformations and shown to be better than edge-based heuristics. Heuristics developed in this research perform address optimizations for embedded processors, employing new techniques that lower address computation costs

Memory optimization techniques for embedded systems

Embedded systems have become ubiquitous and as a result optimization of the design and performance of programs that run on these systems have continued to remain as significant challenges to the computer systems research community. This dissertation addresses several key problems in the optimization of programs for embedded systems which include digital signal processors as the core processor. Chapter 2 develops an efficient and effective algorithm to construct a worm partition graph by finding a longest worm at the moment and maintaining the legality of scheduling. Proper assignment of offsets to variables in embedded DSPs plays a key role in determining the execution time and amount of program memory needed. Chapter 3 proposes a new approach of introducing a weight adjustment function and showed that its experimental results are slightly better and at least as well as the results of the previous works. Our solutions address several problems such as handling fragmented paths resulting from graph-based solutions, dealing with modify registers, and the effective utilization of multiple address registers. In addition to offset assignment, address register allocation is important for embedded DSPs. Chapter 4 develops a lower bound and an algorithm that can eliminate the explicit use of address register instructions in loops with array references. Scheduling of computations and the associated memory requirement are closely inter-related for loop computations. In Chapter 5, we develop a general framework for studying the trade-off between scheduling and storage requirements in nested loops that access multi-dimensional arrays. Tiling has long been used to improve the memory performance of loops. Only a sufficient condition for the legality of tiling was known previously. While it was conjectured that the sufficient condition would also become necessary for large enough tiles, there had been no precise characterization of what is large enough. Chapter 6 develops a new framework for characterizing tiling by viewing tiles as points on a lattice. This also leads to the development of conditions under the legality condition for tiling is both necessary and sufficient

Heuristics for memory access optimization in embedded processors

Digital signal processors (DSPs) such as the Motorola 56k are equipped with two memory banks that are accessible in parallel in order to offer high memory bandwidth, which is required for high-performance applications. In order to make efficient use of the memory bandwidth offered by two or more memory banks, compilers for such DSPs should be capable of appropriately partitioning the program variables between the two memory banks and scheduling accesses. If two variables can be accessed simultaneously, then it is essential to have these two variables assigned to two different memory banks. Also if these two variables are in different banks, then instead of using two separate instructions for accessing the variables, both the accesses can be encoded into a single instruction, thereby reducing the code size as well. An efficient heuristic for maximizing the parallel accesses in DSPs with dual memory banks is proposed and evaluated. The heuristic is shown to be very effective on several examples. Architectures like the M3 DSP have a group memory for the single-instruction multiple-data (SIMD) architecture, for which addressing an element of the group means to access all the elements of that group in parallel, so there is no need for separately addressing each element of the group. Given a variable access sequence for a particular code, instead of separately accessing each one of the variables, if the variables are grouped then the number of memory accesses can be reduced as per SIMD paradigm. An efficient way of forming groups can significantly reduce the memory accesses. Two solutions for this problem are presented in this thesis. First, a novel integer linear programming formulation for forming the groups, thereby reducing the number of memory accesses in DSPs with SIMD architecture is presented. Second, a heuristic based on the solution for optimizing multiple memory bank accesses is presented and evaluated for this problem. Results on several graphs show the effectiveness of the heuristic

Solving the Simple Offset Assignment Problem as a Traveling Salesman

In this paper, we present an exact approach to the Simple Offset Assignment problem arising in the domain of address code generation for digital signal processors. It is based on transformations to weighted Hamiltonian cycle problems and integer linear programming. To the best of our knowledge, it is the first approach capable to solve all instances of the established OffsetStone benchmark set to optimality within reasonable time. Therefore, it enables to evaluate the quality of several heuristics relative to the optimum solutions for the first time. Further, using the same transformations, we present a simple and effective improvement heuristic. In addition, we include an existing heuristic into our experiments that has so far not been evaluated with OffsetStone

Solving the Simple Offset Assignment Problem as a Traveling Salesman

In this paper, we present an exact approach to the Simple Offset Assignment problem arising in the domain of address code generation for digital signal processors. It is based on transformations to weighted Hamiltonian cycle problems and integer linear programming. To the best of our knowledge, it is the first approach capable to solve all instances of the established OffsetStone benchmark set to optimality within reasonable time. Therefore, it enables to evaluate the quality of several heuristics relative to the optimum solutions for the first time. Further, using the same transformations, we present a simple and effective improvement heuristic. In addition, we include an existing heuristic into our experiments that has so far not been evaluated with OffsetStone

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

State of the art baseband DSP platforms for Software Defined Radio: A survey

Software Defined Radio (SDR) is an innovative approach which is becoming a more and more promising technology for future mobile handsets. Several proposals in the field of embedded systems have been introduced by different universities and industries to support SDR applications. This article presents an overview of current platforms and analyzes the related architectural choices, the current issues in SDR, as well as potential future trends.Peer reviewe