Trace-level reuse

Trace-level reuse is based on the observation that some traces (dynamic sequences of instructions) are frequently repeated during the execution of a program, and in many cases, the instructions that make up such traces have the same source operand values. The execution of such traces will obviously produce the same outcome and thus, their execution can be skipped if the processor records the outcome of previous executions. This paper presents an analysis of the performance potential of trace-level reuse and discusses a preliminary realistic implementation. Like instruction-level reuse, trace-level reuse can improve performance by decreasing resource contention and the latency of some instructions. However, we show that trace-level reuse is more effective than instruction-level reuse because the former can avoid fetching the instructions of reused traces. This has two important benefits: it reduces the fetch bandwidth requirements, and it increases the effective instruction window size since these instructions do not occupy window entries. Moreover, trace-level reuse can compute all at once the result of a chain of dependent instructions, which may allow the processor to avoid the serialization caused by data dependences and thus, to potentially exceed the dataflow limit.Peer ReviewedPostprint (published version

Trace-level speculative multithreaded architecture

This paper presents a novel microarchitecture to exploit trace-level speculation by means of two threads working cooperatively in a speculative and non-speculative way respectively. The architecture presents two main benefits: (a) no significant penalties are introduced in the presence of a misspeculation and (b) any type of trace predictor can work together with this proposal. In this way, aggressive trace predictors can be incorporated since misspeculations do not introduce significant penalties. We describe in detail TSMA (trace-level speculative multithreaded architecture) and present initial results to show the benefits of this proposal. We show how simple trace predictors achieve significant speed-up in the majority of cases. Results of a simple trace speculation mechanism show an average speed-up of 16%.Peer ReviewedPostprint (published version

The relevance of the evolution of experimental studies for the interpretation and evaluation of some trace physical evidence

In order for trace evidence to have a high evidential value, experimental studies which mimic the forensic reality are of fundamental importance. Such primary level experimentation is crucial to establish a coherent body of theory concerning the generation, transfer and persistence of different forms of trace physical evidence. We contend that the forensic context, at whatever scale, will be specific to each individual forensic case and this context in which a crime takes place will influence the properties of trace evidence. it will, therefore, be necessary in many forensic cases to undertake secondary level experimental studies that incorporate specific variables pertinent to a particular case and supplement the established theory presented in the published literature. Such studies enable a better understanding of the specific forensic context and thus allow More accurate collection, analysis and interpretation of the trace physical evidence to be achieved. This paper presents two cases where the findings of secondary level experimental studies undertaken to address specific issues particular to two forensic investigations proved to be important. Specific pre-, syn- and post-forensic event factors were incorporated into the experimental design and proved to be invaluable in the recovery, analysis and in achieving accurate interpretations of both soil evidence from footwear and glass trace evidence from a broken window.These Studies demonstrate that a fuller understanding of the specific context within which trace physical evidence is generated and subsequently collected, as well as an understanding of the behaviour of certain forms of trace physical evidence under specific conditions, can add evidentiary weight to the analysis and interpretation of that evidence and thus help a court with greater certainty where resources (time and cost) permit

Analysis of a high order Trace Finite Element Method for PDEs on level set surfaces

We present a new high order finite element method for the discretization of partial differential equations on stationary smooth surfaces which are implicitly described as the zero level of a level set function. The discretization is based on a trace finite element technique. The higher discretization accuracy is obtained by using an isoparametric mapping of the volume mesh, based on the level set function, as introduced in [C. Lehrenfeld, \emph{High order unfitted finite element methods on level set domains using isoparametric mappings}, Comp. Meth. Appl. Mech. Engrg. 2016]. The resulting trace finite element method is easy to implement. We present an error analysis of this method and derive optimal order $H^1(\Gamma)$-norm error bounds. A second topic of this paper is a unified analysis of several stabilization methods for trace finite element methods. Only a stabilization method which is based on adding an anisotropic diffusion in the volume mesh is able to control the condition number of the stiffness matrix also for the case of higher order discretizations. Results of numerical experiments are included which confirm the theoretical findings on optimal order discretization errors and uniformly bounded condition numbers.Comment: 28 pages, 5 figures, 1 tabl

On the trace formula for Hecke operators on congruence subgroups, II

In a previous paper, we obtained a general trace formula for double coset operators acting on modular forms for congruence subgroups, expressed as a sum over conjugacy classes. Here we specialize it to the congruence subgroups $\Gamma_0(N)$ and $\Gamma_1(N)$, obtaining explicit formulas in terms of class numbers for the trace of a composition of Hecke and Atkin-Lehner operators. The formulas are among the simplest in the literature, and hold without any restriction on the index of the operators. We give two applications of the trace formula for $\Gamma_1(N)$: we determine explicit trace forms for $\Gamma_0(4)$ with Nebentypus, and we compute the limit of the trace of a fixed Hecke operator as the level $N$ tends to infinity

Multi-Trace Superpotentials vs. Matrix Models

We consider N = 1 supersymmetric U(N) field theories in four dimensions with adjoint chiral matter and a multi-trace tree-level superpotential. We show that the computation of the effective action as a function of the glueball superfield localizes to computing matrix integrals. Unlike the single-trace case, holomorphy and symmetries do not forbid non-planar contributions. Nevertheless, only a special subset of the planar diagrams contributes to the exact result. Some of the data of this subset can be computed from the large-N limit of an associated multi-trace Matrix model. However, the prescription differs in important respects from that of Dijkgraaf and Vafa for single-trace superpotentials in that the field theory effective action is not the derivative of a multi-trace matrix model free energy. The basic subtlety involves the correct identification of the field theory glueball as a variable in the Matrix model, as we show via an auxiliary construction involving a single-trace matrix model with additional singlet fields which are integrated out to compute the multi-trace results. Along the way we also describe a general technique for computing the large-N limits of multi-trace Matrix models and raise the challenge of finding the field theories whose effective actions they may compute. Since our models can be treated as N = 1 deformations of pure N =2 gauge theory, we show that the effective superpotential that we compute also follows from the N = 2 Seiberg-Witten solution. Finally, we observe an interesting connection between multi-trace local theories and non-local field theory.Comment: 35 pages, LaTeX, 6 EPS figures. v2: typos fixed, v3: typos fixed, references added, Sec. 5 added explaining how multi-trace theories can be linearized in traces by addition of singlet fields and the relation of this approach to matrix model

Towards a Generic Trace for Rule Based Constraint Reasoning

CHR is a very versatile programming language that allows programmers to declaratively specify constraint solvers. An important part of the development of such solvers is in their testing and debugging phases. Current CHR implementations support those phases by offering tracing facilities with limited information. In this report, we propose a new trace for CHR which contains enough information to analyze any aspects of \CHRv\ execution at some useful abstract level, common to several implementations. %a large family of rule based solvers. This approach is based on the idea of generic trace. Such a trace is formally defined as an extension of the $\omega_r^\lor$ semantics of CHR. We show that it can be derived form the SWI Prolog CHR trace