An efficient reduction algorithm for computation of interconnect delay variability for statistical timing analysis in clock tree planning

In this paper, we propose a novel and efficient algorithm for modelling sub-65 nm clock interconnect-networks in the presence of process variation. We develop a method for delay analysis of interconnects considering the impact of Gaussian metal process variations. The resistance and capacitance of a distributed RC line are expressed as correlated Gaussian random variables which are then used to compute the standard deviation of delay Probability Distribution Function (PDF) at all nodes in the interconnect network. Main objective is to find delay PDF at a cheaper cost. Convergence of this approach is in probability distribution but not in mean of delay. We validate our approach against SPICE based Monte Carlo simulations while the current method entails significantly lower computational cost.

Implications of program phase behavior on timing analysis

Knowledge about program worst case execution time (WCET) is essential in validating real-time systems and helps in effective scheduling. One popular approach used in industry is to measure execution time of program components on the target architecture and combine them using static analysis of the program. Measurements need to be taken in the least intrusive way in order to avoid affecting accuracy of estimated WCET. Several programs exhibit phase behavior, wherein program dynamic execution is observed to be composed of phases. Each phase being distinct from the other, exhibits homogeneous behavior with respect to cycles per instruction (CPI), data cache misses etc. In this paper, we show that phase behavior has important implications on timing analysis. We make use of the homogeneity of a phase to reduce instrumentation overhead at the same time ensuring that accuracy of WCET is not largely affected. We propose a model for estimating WCET using static worst case instruction counts of individual phases and a function of measured average CPI. We describe a WCET analyzer built on this model which targets two different architectures. The WCET analyzer is observed to give safe estimates for most benchmarks considered in this paper. The tightness of the WCET estimates are observed to be improved for most benchmarks compared to Chronos, a well known static WCET analyzer.

A Transit Timing Analysis of Mine RISE Light Curves of the Exoplanet System TrES-3

We present nine newly observed transits of TrES-3, taken as part of a transit timing program using the RISE instrument on the Liverpool Telescope. A Markov-Chain Monte Carlo analysis was used to determine the planet star radius ratio and inclination of the system, which were found to be R-p/R-star = 0.1664(-0.0018)(+0.0011) and i = 81.73(-0.04)(+0.13), respectively, consistent with previous results. The central transit times and uncertainties were also calculated, using a residual-permutation algorithm as an independent check on the errors. A re-analysis of eight previously published TrES-3 light curves was conducted to determine the transit times and uncertainties using consistent techniques. Whilst the transit times were not found to be in agreement with a linear ephemeris, giving chi(2) = 35.07 for 15 degrees of freedom, we interpret this to be the result of systematics in the light curves rather than a real transit timing variation. This is because the light curves that show the largest deviation from a constant period either have relatively little out-of-transit coverage or have clear systematics. A new ephemeris was calculated using the transit times and was found to be T-c(0) = 2454632.62610 +/- 0.00006 HJD and P = 1.3061864 +/- 0.0000005 days. The transit times were then used to place upper mass limits as a function of the period ratio of a potential perturbing planet, showing that our data are sufficiently sensitive to have probed sub-Earth mass planets in both interior and exterior 2:1 resonances, assuming that the additional planet is in an initially circular orbit.

A transit timing analysis of seven RISE light curves of the exoplanet system HAT-P-3

We present seven light curves of the exoplanet system HAT-P-3, taken as part of a transit timing programme using the rapid imager to search for exoplanets instrument on the Liverpool Telescope. The light curves are analysed using a Markov chain Monte Carlo algorithm to update the parameters of the system. The inclination is found to be i = 86.75+0.22-0.21°, the planet-star radius ratio to be Rp/R* = 0.1098+0.0010-0.0012 and the stellar radius to be R* = 0.834+0.018-0.026Rsolar, consistent with previous results but with a significant improvement in the precision. Central transit times and uncertainties for each light curve are also determined, and a residual permutation algorithm is used as an independent check on the errors. The transit times are found to be consistent with a linear ephemeris, and a new ephemeris is calculated as Tc(0) = 2454856.70118 +/- 0.00018 HJD and P = 2.899738 +/- 0.000007 d. Model timing residuals are fitted to the measured timing residuals to place upper mass limits for a hypothetical perturbing planet as a function of the period ratio. These show that we have probed for planets with masses as low as 0.33 and 1.81 M? in the interior and exterior 2:1 resonances, respectively, assuming the planets are initially in circular orbits.

Functional timing analysis of VLSI circuits containing complex gates

The recent advances in CMOS technology have allowed for the fabrication of transistors with submicronic dimensions, making possible the integration of tens of millions devices in a single chip that can be used to build very complex electronic systems. Such increase in complexity of designs has originated a need for more efficient verification tools that could incorporate more appropriate physical and computational models. Timing verification targets at determining whether the timing constraints imposed to the design may be satisfied or not. It can be performed by using circuit simulation or by timing analysis. Although simulation tends to furnish the most accurate estimates, it presents the drawback of being stimuli dependent. Hence, in order to ensure that the critical situation is taken into account, one must exercise all possible input patterns. Obviously, this is not possible to accomplish due to the high complexity of current designs. To circumvent this problem, designers must rely on timing analysis. Timing analysis is an input-independent verification approach that models each combinational block of a circuit as a direct acyclic graph, which is used to estimate the critical delay. First timing analysis tools used only the circuit topology information to estimate circuit delay, thus being referred to as topological timing analyzers. However, such method may result in too pessimistic delay estimates, since the longest paths in the graph may not be able to propagate a transition, that is, may be false. Functional timing analysis, in turn, considers not only circuit topology, but also the temporal and functional relations between circuit elements. Functional timing analysis tools may differ by three aspects: the set of sensitization conditions necessary to declare a path as sensitizable (i.e., the so-called path sensitization criterion), the number of paths simultaneously handled and the method used to determine whether sensitization conditions are satisfiable or not. Currently, the two most efficient approaches test the sensitizability of entire sets of paths at a time: one is based on automatic test pattern generation (ATPG) techniques and the other translates the timing analysis problem into a satisfiability (SAT) problem. Although timing analysis has been exhaustively studied in the last fifteen years, some specific topics have not received the required attention yet. One such topic is the applicability of functional timing analysis to circuits containing complex gates. This is the basic concern of this thesis. In addition, and as a necessary step to settle the scenario, a detailed and systematic study on functional timing analysis is also presented.

Timing analysis of assembler code control-flow paths

Timinganalysis of assembler code is essential to achieve the strongest possible guarantee of correctness for safety-critical, real-time software. Previous work has shown how timingconstrain ts on controlflow paths through high-level language programs can be formalised using the semantics of the statements comprisingthe path. We extend these results to assembler-level code where it becomes possible to not only determine timingconstrain ts, but also to verify them against the known execution times for each instruction. A minimal formal model is developed with both a weakest liberal precondition and a strongest postcondition semantics. However, despite the formalism’s simplicity, it is shown that complex timingb ehaviour associated with instruction pipeliningand iterative code can be modelled accurately.

Programs as paths: An approach to timing constraint analysis

A program can be decomposed into a set of possible execution paths. These can be described in terms of primitives such as assignments, assumptions and coercions, and composition operators such as sequential composition and nondeterministic choice as well as finitely or infinitely iterated sequential composition. Some of these paths cannot possibly be followed (they are dead or infeasible), and they may or may not terminate. Decomposing programs into paths provides a foundation for analyzing properties of programs. Our motivation is timing constraint analysis of real-time programs, but the same techniques can be applied in other areas such as program testing. In general the set of execution paths for a program is infinite. For timing analysis we would like to decompose a program into a finite set of subpaths that covers all possible execution paths, in the sense that we only have to analyze the subpaths in order to determine suitable timing constraints that cover all execution paths.

Exploiting dynamic timing margins in microprocessors for frequency-over-scaling with instruction-based clock adjustment

Static timing analysis provides the basis for setting the clock period of a microprocessor core, based on its worst-case critical path. However, depending on the design, this critical path is not always excited and therefore dynamic timing margins exist that can theoretically be exploited for the benefit of better speed or lower power consumption (through voltage scaling). This paper introduces predictive instruction-based dynamic clock adjustment as a technique to trim dynamic timing margins in pipelined microprocessors. To this end, we exploit the different timing requirements for individual instructions during the dynamically varying program execution flow without the need for complex circuit-level measures to detect and correct timing violations. We provide a design flow to extract the dynamic timing information for the design using post-layout dynamic timing analysis and we integrate the results into a custom cycle-accurate simulator. This simulator allows annotation of individual instructions with their impact on timing (in each pipeline stage) and rapidly derives the overall code execution time for complex benchmarks. The design methodology is illustrated at the microarchitecture level, demonstrating the performance and power gains possible on a 6-stage OpenRISC in-order general purpose processor core in a 28nm CMOS technology. We show that employing instruction-dependent dynamic clock adjustment leads on average to an increase in operating speed by 38% or to a reduction in power consumption by 24%, compared to traditional synchronous clocking, which at all times has to respect the worst-case timing identified through static timing analysis.

A framework for memory contention analysis in multi-core platforms

The last decade has witnessed a major shift towards the deployment of embedded applications on multi-core platforms. However, real-time applications have not been able to fully benefit from this transition, as the computational gains offered by multi-cores are often offset by performance degradation due to shared resources, such as main memory. To efficiently use multi-core platforms for real-time systems, it is hence essential to tightly bound the interference when accessing shared resources. Although there has been much recent work in this area, a remaining key problem is to address the diversity of memory arbiters in the analysis to make it applicable to a wide range of systems. This work handles diverse arbiters by proposing a general framework to compute the maximum interference caused by the shared memory bus and its impact on the execution time of the tasks running on the cores, considering different bus arbiters. Our novel approach clearly demarcates the arbiter-dependent and independent stages in the analysis of these upper bounds. The arbiter-dependent phase takes the arbiter and the task memory-traffic pattern as inputs and produces a model of the availability of the bus to a given task. Then, based on the availability of the bus, the arbiter-independent phase determines the worst-case request-release scenario that maximizes the interference experienced by the tasks due to the contention for the bus. We show that the framework addresses the diversity problem by applying it to a memory bus shared by a fixed-priority arbiter, a time-division multiplexing (TDM) arbiter, and an unspecified work-conserving arbiter using applications from the MediaBench test suite. We also experimentally evaluate the quality of the analysis by comparison with a state-of-the-art TDM analysis approach and consistently showing a considerable reduction in maximum interference.

Holistic Analysis for Fork-Join Distributed Tasks supported by the FTT-SE Protocol

11th IEEE World Conference on Factory Communication Systems (WFCS 2015). 27 to 29, May, 2015, TII-SS-2: Scheduling and Performance Analysis. Palma de Mallorca, Spain.

Um Estudo de técnicas de aceleração para algoritmos de análise de timing funcional baseados em geração automática de teste

Este trabalho tem como objetivo estudar e avaliar técnicas para a aceleração de algoritmos de análise de timing funcional (FTA - Functional Timing Analysis) baseados em geração automática de testes (ATPG – Automatic Test Generation). Para tanto, são abordados três algoritmos conhecidos : algoritmo-D, o PODEM e o FAN. Após a análise dos algoritmos e o estudo de algumas técnicas de aceleração, é proposto o algoritmo DETA (Delay Enumeration-Based Timing Analysis) que determina o atraso crítico de circuitos que contêm portas complexas. O DETA está definido como um algoritmo baseado em ATPG com sensibilização concorrente de caminhos. Na implementação do algoritmo, foi possível validar o modelo de computação de atrasos para circuitos que contêm portas complexas utilizando a abordagem de macro-expansão implícita. Além disso, alguns resultados parciais demonstram que, para alguns circuitos, o DETA apresenta uma pequena dependência do número de entradas quando comparado com a dependência no procedimento de simulação. Desta forma, é possível evitar uma pesquisa extensa antes de se encontrar o teste e assim, obter sucesso na aplicação de métodos para aceleração do algoritmo.

Pulse phase-coherent timing and spectroscopy of CXOU J164710.2−45521 outbursts

We present a long-term phase-coherent timing analysis and pulse-phase resolved spectroscopy for the two outbursts observed from the transient anomalous X-ray pulsar CXOU J164710.2−455216. For the first outburst we used 11 Chandra and XMM–Newton observations between 2006 September and 2009 August, the longest baseline yet for this source. We obtain a coherent timing solution with P = 10.61065583(4) s, Ṗ = 9.72(1) × 10−13 s s−1 and P̈ = –1.05(5) × 10−20 s s−2. Under the standard assumptions this implies a surface dipolar magnetic field of ∼1014 G, confirming this source as a standard B magnetar. We also study the evolution of the pulse profile (shape, intensity and pulsed fraction) as a function of time and energy. Using the phase-coherent timing solution we perform a phase-resolved spectroscopy analysis, following the spectral evolution of pulse-phase features, which hints at the physical processes taking place on the star. The results are discussed from the perspective of magnetothermal evolution models and the untwisting magnetosphere model. Finally, we present similar analysis for the second, less intense, 2011 outburst. For the timing analysis we used Swift data together with 2 XMM–Newton and Chandra pointings. The results inferred for both outbursts are compared and briefly discussed in a more general framework.

Orbital evolution studies of two HMXB pulsars

High mass X-ray binary (HMXB) pulsars are of two types, persistent and transient. 4U1538-52 is a persistent HMXB whose orbit was previously measured to be circular but the RXTE observations revealed an eccentric orbit. We observed this system with RXTE-PCA in August 2003 and our timing analysis supports the eccentric orbit of the system. However, we do not find any evidence for orbital evolution. Rotational and tidal interactions between the stars of a closed binary system result in apsidal motion which can be measured in systems with eccentric orbit. 4U0115+63 is a Be-transient HMXB whose eccentric orbit was well-determined during its 1978 outburst. We report preliminary results from analysis of data obtained during the 1999 outburst of this source with the RXTE-PCA.

Orbital evolution and orbital phase resolved spectroscopy of the HMXB pulsar 4U 1538-52 with RXTE-PCA and BeppoSAX

We report here results from detailed timing and spectral studies of the high mass X-ray binary pulsar 4U 1538-52 over several binary periods using observations made with the Rossi X-ray Timing Explorer (RXTE) and BeppoSAX satellites. Pulse timing analysis with the 2003 RXTE data over two binary orbits confirms an eccentric orbit of the system. Combining the orbitial parameters determined from this observation with the earlier measurements we did not find any evidence of orbital decay in this X-ray binary. We have carried out orbital phase resolved spectroscopy to measure changes in the spectral parameters with orbital phase, particularly the absorption column density and the iron line flux. The RXTE-PCA spectra in the 3-20 keV energy range were fitted with a power law and a high energy cut-off along with a Gaussian line at similar to 6.4 keV, whereas the BeppoSAX spectra needed only a power law and Gaussian emission line at similar to 6.4keV in the restricted energy range of 0.3-10.0 keV. An absorption along the line of sight was included for both the RXTE and BeppoSAX data. The variation of the free spectral parameters over the binary orbit was investigated and we found that the variation of the column density of absorbing material in the line of sight with orbital phase is in reasonable agreement with a simple model of a spherically symmetric stellar wind from the companion star.

Orbital evolution studies of two HMXB pulsars

High mass X-ray binary (H M X B) pulsars are of two types, persistent and transient. 4U 1538-52 is a persistent HMXB whose orbit was previously measured to be circular but the RXTE observations revealed an eccentric orbit. We observed this system with RXTE-PCA in August 2003 and our timing analysis supports the eccentric orbit of the system. However, we do not find any evidence for orbital evolution. Rotational and tidal interactions between the stars of a closed binary system result in apsidal motion which can be measured in systems with eccentric orbit. 4U0115+63 is a Be-transient HMXB whose eccentric orbit was well-determined during its 1978 outburst. We report preliminary results from analysis of data obtained during the 1999 outburst of this source with the RXTE-PCA.