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

AmiGo: Computational Design of Amigurumi Crochet Patterns

We propose an approach for generating crochet instructions (patterns) from an input 3D model. We focus on Amigurumi, which are knitted stuffed toys. Given a closed triangle mesh, and a single point specified by the user, we generate crochet instructions, which when knitted and stuffed result in a toy similar to the input geometry. Our approach relies on constructing the geometry and connectivity of a Crochet Graph, which is then translated into a crochet pattern. We segment the shape automatically into chrochetable components, which are connected using the join-as-you-go method, requiring no additional sewing. We demonstrate that our method is applicable to a large variety of shapes and geometries, and yields easily crochetable patterns.Comment: 11 pages, 10 figures, SCF 202

USING HOMING, SYNCHRONIZING AND DISTINGUISHING INPUT SEQUENCES FOR THE ANALYSIS OF REVERSIBLE FINITE STATE MACHINES

A digital device is called reversible if it realizes a reversible mapping, i.e., the one for which there exist a unique inverse. The field of reversible computing is devoted to studying all aspects of using and designing reversible devices. During last 15 years this field has been developing very intensively due to its applications in quantumcomputing, nanotechnology and reducing power consumption of digital devices. We present an analysis of the Reversible Finite State Machines (RFSM) with respect to three well known sequences used in the testability analysis of the classical Finite State Machines (FSM). The homing, distinguishing and synchronizing sequences areapplied to two types of reversible FSMs: the converging FSM (CRFSM) and the nonconverging FSM (NCRFSM) and the effect is studied and analyzed. We show that while only certain classical FSMs possess all three sequences, CRFSMs and NCRFSMs have properties allowing to directly determine what type of sequences these machines possess

A transformation-based method for loop folding

[[abstract]]We propose a transformation-based scheduling algorithm for the problem - given a loop construct, a target initiation interval and a set of resource constraints, schedule the loop in a pipelined fashion such that the iteration time of executing an iteration of the loop is minimized. The iteration time is an important quality measure of a data path design because it affects both storage and control costs. Our algorithm first performs an As Soon As Possible Pipelined (ASAPP) scheduling regardless the resource constraint. It then resolves resource constraint violations by rescheduling some operations. The software system implementing the proposed algorithm, called Theda.Fold, can deal with behavioral loop descriptions that contain chained, multicycle and/or structural pipelined operations as well as those having data dependencies across iteration boundaries. Experiment on a number of benchmarks is reported.[[fileno]]2030214010003[[department]]資訊工程學