Rajeev R. Rao

Razor: a low-power pipeline based on circuit-level timing speculation

With increasing clock frequencies and silicon integration, power aware computing has become a critical concern in the design of embedded processors and systems-on-chip. One of the more effective and widely used methods for power-aware computing is dynamic voltage scaling (DVS). In order to obtain the maximum power savings from DVS, it is essential to scale the supply voltage as low as possible while ensuring correct operation of the processor. The critical voltage is chosen such that under a worst-case scenario of process and environmental variations, the processor always operates correctly. However, this approach leads to a very conservative supply voltage since such a worst-case combination of different variabilities is very rare. In this paper, we propose a new approach to DVS, called Razor, based on dynamic detection and correction of circuit timing errors. The key idea of Razor is to tune the supply voltage by monitoring the error rate during circuit operation, thereby eliminating the need for voltage margins and exploiting the data dependence of circuit delay. A Razor flip-flop is introduced that double-samples pipeline stage values, once with a fast clock and again with a time-borrowing delayed clock. A metastability-tolerant comparator then validates latch values sampled with the fast clock. In the event of timing error, a modified pipeline mispeculation recovery mechanism restores correct program state. A prototype Razor pipeline was designed in a 0.18 /spl mu/m technology and was analyzed. Razor energy overhead during normal operation is limited to 3.1%. Analyses of a full-custom multiplier and a SPICE-level Kogge-Stone adder model reveal that substantial energy savings are possible for these devices (up to 64.2%) with little impact on performance due to error recovery (less than 3%).

Statistical analysis of subthreshold leakage current for VLSI circuits

We develop a method to estimate the variation of leakage current due to both intra-die and inter-die gate length process variability. We derive an analytical expression to estimate the probability density function (PDF) of the leakage current for stacked devices found in CMOS gates. These distributions of individual gate leakage currents are then combined to obtain the mean and variance of the leakage current for an entire circuit. We also present an approach to account for both the inter- and intra-die gate length variations to ensure that the circuit leakage PDF correctly models both types of variation. The proposed methods were implemented and tested on a number of benchmark circuits. Comparison to Monte Carlo simulation validates the accuracy of the proposed method and demonstrates the efficiency of the proposed analysis method. Comparison with traditional deterministic leakage current analysis demonstrates the need for statistical methods for leakage current analysis.

Computing the Soft Error Rate of a Combinational Logic Circuit Using Parameterized Descriptors

Soft errors have emerged as an important reliability challenge for nanoscale very large scale integration designs. In this paper, we present a fast and efficient soft error rate (SER) analysis methodology for combinational circuits. We first present a novel parametric waveform model based on the Weibull function to represent particle strikes at individual nodes in the circuit. We then describe the construction of the descriptor object that efficiently captures the correlation between the transient waveforms and their associated rate distribution functions. The proposed algorithm consists of operations to inject, propagate, and merge these descriptors while traversing forward along the gates in a circuit. The parameterized waveforms enable an efficient static approach to calculate the SER of a circuit. We exercise the proposed approach on a wide variety of combinational circuits and observe that our algorithm has linear runtime with the size of the circuit. The runtimes for soft error estimation were observed to be in the order of about 1 s, compared to several minutes or even hours for previously proposed methods

Soft error reduction in combinational logic using gate resizing and flipflop selection

Soft errors in logic are emerging as a significant reliability problem for VLSI designs. This paper presents novel circuit optimization techniques to mitigate soft error rates (SER) of combinational logic circuits. First, we propose a gate sizing algorithm that trades off SER reduction and area overhead. This approach first computes bounds on the maximum achievable SER reduction by resizing a gate. This bound is then used to prune the circuit graph, arriving at a smaller set of candidate gates on which we perform incremental sensitivity computations to determine the gates that are the largest contributors to circuit SER. Second, we propose a flipflop selection method that uses slack information at each primary output node to determine the flipflop configuration that produces maximum SER savings. This approach uses an enhanced flipflop library that contains flipflops of varying temporal masking ability. Third, we propose a unified, co-optimization approach combining flipflop selection with the gate sizing algorithm. The joint optimization algorithm produces larger SER reductions while incurring smaller circuit overhead than either technique taken in isolation. Experimental results on a variety of benchmarks show SER reductions of 7.9times with gate sizing, 6.6times with flipflop assignment, and 28.2times for the combined optimization approach, with no delay penalties and area overheads within 5-6%. The runtimes for the optimization algorithms are on the order of 1-3 minutes

An Efficient Static Algorithm for Computing the Soft Error Rates of Combinational Circuits

Soft errors have emerged as an important reliability challenge for nanoscale VLSI designs. In this paper, we present a fast and efficient soft error rate (SER) computation algorithm for combinational circuits. We first present a novel parametric waveform model based on the Weibull function to represent particle strikes at individual nodes in the circuit. We then describe the construction of the SET descriptor that efficiently captures the correlation between the transient waveforms and their associated rate distribution functions. The proposed algorithm consists of operations to inject, propagate and merge SET descriptors while traversing forward along the gates in a circuit. The parameterized waveforms enable an efficient static approach to calculate the SER of a circuit. We exercise the proposed approach on a wide variety of combinational circuits and observe that our algorithm has linear runtime with the size of the circuit. The runtimes for soft error estimation were observed to be in the order of about one second, compared to several minutes or even hours for previously proposed methods

Logic SER reduction through flip flop redesign

In this paper, we present a new flip flop sizing scheme that efficiently immunizes combinational logic circuits from the effects of radiation induced single event transients (SET). The proposed technique leverages the effect of temporal masking by selectively increasing the length of the latching windows associated with the flip flops thereby preventing faulty transients from being registered. We propose an effective flip flop sizing scheme and construct a variety of flip flop variants that function as low-pass filters for SETs and reduce the soft error rates (SER) of combinational circuits. In contrast to previously proposed flip flop designs that rely on logic duplication and complicated circuit design styles, our method provides a simple yet highly effective mechanism for logic SER reduction while incurring very small overheads in both delay (about 5 FO4) and power (about 5%). Experimental results at the circuit level on a wide range of benchmarks show 1000times reductions in SER for small increases in circuit delay and power

Leakage-and crosstalk-aware bus encoding for total power reduction

Power consumption, particularly runtime leakage, in long on-chip buses has grown to an unacceptable portion of the total power budget due to heavy buffer insertion to combat RC delays. In this paper, we propose a new bus encoding algorithm and circuit scheme for on-chip buses that eliminates capacitive crosstalk while simultaneously reducing total power. We introduce a new buffer design approach with selective use of high threshold voltage transistors and couple this buffer design with a novel bus encoding scheme. The proposed encoding scheme significantly reduces total power by 26% and runtime leakage power by 42% while also eliminating capacitive crosstalk. In addition, the proposed encoding is specifically optimized to reduce the complexity of the encoding logic, allowing for a significant reduction in overhead which has not been considered in previous bus encoding work.

Analytical yield prediction considering leakage/performance correlation

In addition to traditional constraints on frequency, leakage current has emerged as a stringent constraint in modern processor designs. Since leakage current exhibits a strong inverse correlation with circuit delay, effective parametric yield prediction must consider the dependence of leakage current on frequency. In this paper, a new chip-level statistical method to estimate the total leakage current in the presence of within-die and die-to-die variability is presented. A closed-form equation for total chip leakage that models the dependence of the leakage current distribution on different process parameters is developed. The proposed analytical expression is obtained directly from pertinent design information and includes both subthreshold and gate leakage currents. Using this model, an integrated approach to accurately estimate the yield loss when both frequency and power limits are imposed on a design is then presented. The proposed method demonstrates the importance of considering both these limiting factors while calculating the yield of a lot

Modeling and analysis of parametric yield under power and performance constraints

Leakage current is a stringent constraint in todays ASIC designs. Effective parametric yield prediction must consider leakage currents dependence on chip frequency. The authors propose an analytical expression that includes both subthreshold and gate leakage currents. This model underlies an integrated approach to accurately estimating yield loss for a design with both frequency and power limits.

Bus encoding for total power reduction using a leakage-aware buffer configuration

Power consumption, particularly runtime leakage, in long on-chip buses has grown to be an unacceptable portion of the total power budget due to heavy buffer insertion used to combat RC delays. In this paper, we propose a new bus encoding algorithm and circuit scheme for on-chip buses that eliminates capacitive crosstalk while simultaneously reducing total power. We utilize a buffer design approach with a selective use of high-threshold voltage transistors and couple this buffer design with a novel bus encoding scheme. The proposed encoding scheme significantly reduces total power by 26% and runtime leakage power by 42% while also eliminating capacitive crosstalk. In addition, the proposed encoding is specifically optimized to reduce the complexity of the encoding logic, allowing for a significant reduction in overhead which has not been considered in previous bus encoding work.