139 research outputs found
Unfaithful Glitch Propagation in Existing Binary Circuit Models
We show that no existing continuous-time, binary value-domain model for
digital circuits is able to correctly capture glitch propagation. Prominent
examples of such models are based on pure delay channels (P), inertial delay
channels (I), or the elaborate PID channels proposed by Bellido-D\'iaz et al.
We accomplish our goal by considering the solvability/non-solvability border of
a simple problem called Short-Pulse Filtration (SPF), which is closely related
to arbitration and synchronization. On one hand, we prove that SPF is solvable
in bounded time in any such model that provides channels with non-constant
delay, like I and PID. This is in opposition to the impossibility of solving
bounded SPF in real (physical) circuit models. On the other hand, for binary
circuit models with constant-delay channels, we prove that SPF cannot be solved
even in unbounded time; again in opposition to physical circuit models.
Consequently, indeed none of the binary value-domain models proposed so far
(and that we are aware of) faithfully captures glitch propagation of real
circuits. We finally show that these modeling mismatches do not hold for the
weaker eventual SPF problem.Comment: 23 pages, 15 figure
A Digital Delay Model Supporting Large Adversarial Delay Variations
Dynamic digital timing analysis is a promising alternative to analog
simulations for verifying particularly timing-critical parts of a circuit. A
necessary prerequisite is a digital delay model, which allows to accurately
predict the input-to-output delay of a given transition in the input signal(s)
of a gate. Since all existing digital delay models for dynamic digital timing
analysis are deterministic, however, they cannot cover delay fluctuations
caused by PVT variations, aging and analog signal noise. The only exception
known to us is the -IDM introduced by F\"ugger et al. at DATE'18, which
allows to add (very) small adversarially chosen delay variations to the
deterministic involution delay model, without endangering its faithfulness. In
this paper, we show that it is possible to extend the range of allowed delay
variations so significantly that realistic PVT variations and aging are covered
by the resulting extended -IDM
Experimental Validation of a Faithful Binary Circuit Model
International audienceFast digital timing simulations based on continuous-time, digital-value circuit models are an attractive and heavily used alternative to analog simulations. Models based on analytic delay formulas are particularly interesting here, as they also facilitate formal verification and delay bound synthesis of complex circuits. Recently, FĂĽgger et al. (arXiv:1406.2544 [cs.OH]) proposed a circuit model based on so-called involution channels. It is the first binary circuit model that realistically captures solvability of short-pulse filtration, a non-trivial glitch propagation problem related to building one-shot inertial delays. In this work, we address the question of whether involu-tion channels also accurately model the delay of real circuits. Using both Spice simulations and physical measurements, we confirm that modeling an inverter chain by involution channels accurately describes reality. We also demonstrate that transitions in vanishing pulse trains are accurately predicted by the involution model. For our Spice simulations, we used both UMC-90 and UMC-65 technology, with varying supply voltages from nominal down to near sub-threshold range. The measurements were performed on a special-purpose UMC-90 ASIC that combines an inverter chain with low-intrusive high-speed on-chip analog amplifiers
Towards the Multiple Constant Multiplication at Minimal Hardware Cost
Multiple Constant Multiplication (MCM) over integers is a frequent operation
arising in embedded systems that require highly optimized hardware. An
efficient way is to replace costly generic multiplication by bit-shifts and
additions, i.e. a multiplierless circuit. In this work, we improve the
state-of-the-art optimal approach for MCM, based on Integer Linear Programming
(ILP). We introduce a new lower-level hardware cost, based on counting the
number of one-bit adders and demonstrate that it is strongly correlated with
the LUT count. This new model for the multiplierless MCM circuits permitted us
to consider intermediate truncations that permit to significantly save
resources when a full output precision is not required. We incorporate the
error propagation rules into our ILP model to guarantee a user-given error
bound on the MCM results. The proposed ILP models for multiple flavors of MCM
are implemented as an open-source tool and, combined with the FloPoCo code
generator, provide a complete coefficient-to-VHDL flow. We evaluate our models
in extensive experiments, and propose an in-depth analysis of the impact that
design metrics have on actually synthesized hardware.Comment: 10 pages, 3 tables, 6 figures, journal submissio
An Accurate Hybrid Delay Model for Multi-Input Gates
Accurately modeling the delay of multi-input gates is challenging due to
variations caused by switching different inputs in close temporal proximity.
This paper introduces a hybrid model for a CMOS NOR gate, which is based on
replacing transistors with time-variant resistors. We analytically solve the
resulting non-constant coefficient differential equations and derive
expressions for the gate delays, which also paved the way to an empirical
parametrization procedure. By comparison with Spice simulation data, we show
that our model indeed faithfully represents all relevant multi-input switching
effects. Using an implementation in the Involution Tool, we also demonstrate
that it surpasses the few alternative models known so far in terms of accuracy
On digit-recurrence division algorithms for self-timed circuits
The optimization of algorithms for self-timed or asynchronous circuits requires specific solutions. Due to the variable-time capabilities of asynchronous circuits, the average computation time should be optimized and not only the worst case of the signal propagation. If efficient algorithms and implementations are known for asynchronous addition and multiplication, only straightforward algorithms have been studied for division. This paper compares several digit-recurrence division algorithms (speed, area and circuit activity for estimating the power consumption). The comparison is based on simulations of the different operators described at the gate level. This work shows that the best solutions for asynchronous circuits are quite different from those used in synchronous circuits
Design for soft error tolerance in FPGA-implemented asynchronous circuits
This research in its present form is the result of experimentation on effect of soft error in FPGA-implemented asynchronous circuit. The conclusion are drawn that asynchronous circuit are much easier to detect soft error than synchronous circuits. The asynchronous circuit is implemented in FPGA with software fault injection method to analyze the behavior of soft error generation in FPGA implementation asynchronous circuits. The proposed detection circuit can detect all soft errors that generated in FPGA-implemented asynchronous circuit. The contributions include: investigation of FPGA structure, investigation of soft error model in FPGA, mechanism of FPGA implemented asynchronous circuit, behavior of soft error injection in FPGA look up table that implemented asynchronous circuit, and proposed detection scheme. The research on soft error injection in FPGA routing system and soft error rate estimation will be done in the future
Propagation Networks: A Flexible and Expressive Substrate for Computation
PhD thesisI propose a shift in the foundations of computation. Practically all ideas of general-purpose computation today are founded either on execution of sequences of atomic instructions, i.e., assembly languages, or on evaluation of tree-structured expressions, i.e., most higher level programming languages. Both have served us well in the past, but it is increasingly clear that we need something more. I suggest that we can build general-purpose computation on propagation of information through networks of stateful cells interconnected with stateless autonomous asynchronous computing elements. Various forms of this general idea have been used with great success for various special purposes; perhaps the most immediate example is constraint propagation in constraint satisfaction systems. These special-purpose systems, however, are all complex and all different, and neither compose well, nor interoperate well, nor generalize well. A foundational layer is missing. The key insight in this work is that a cell should not be seen as storing a value, but as accumulating information about a value. The cells should never forget information -- such monotonicity prevents race conditions in the behavior of the network. Monotonicity of information need not be a severe restriction: for example, carrying reasons for believing each thing makes it possible to explore but thenpossibly reject tentative hypotheses, thus appearing to undo something, while maintaining monotonicity. Accumulating information is a broad enough design principle to encompass arbitrary computation. The object of this dissertation is therefore to architect a general-purpose computing system based on propagation networks; to subsume expression evaluation under propagation just as instruction execution is subsumed under expression evaluation; to demonstrate that a general-purpose propagation system can recover all the benefits that have been derived from special-purpose propagation systems, allow them to compose andinteroperate, and offer further expressive power beyond what we have known in the past; and finally to contemplate the lessons that such a fundamental shift can teach us about the deep nature of computation.My graduate career in general, and this work in particular, have been sponsored in part by a National Science Foundation Graduate Research Fellowship, by the Disruptive Technology Office as part of the AQUAINT Phase 3 research program, by the Massachusetts Institute of Technology, by Google, Inc., and by the National Science Foundation Cybertrust (05-518) program.Doctor of Philosoph
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