Energy is increasingly a first-order concern in computer systems. Exploiting energy-accuracy trade-offs is an attractive choice in applications that can tolerate inaccuracies. Recent work has explored exposing this trade-off in programming models. A key challenge, though, is how to isolate parts of the program that must be precise from those that can be approximated so that a program functions correctly even as quality of service degrades. We propose using type qualifiers to declare data that may be subject to approximate computation. Using these types, the system automatically maps approximate variables to low-power storage, uses low-power operations, and even applies more energy-efficient algorithms provided by the programmer. In addition, the system can statically guarantee isolation of the precise program component from the approximate component. This allows a programmer to control explicitly how information flows from approximate data to precise data. Importantly, employing static analysis eliminates the need for dynamic checks, further improving energy savings. As a proof of concept, we develop EnerJ, an extension to Java that adds approximate data types. We also propose a hardware architecture that offers explicit approximate storage and computation. We port several applications to EnerJ and show that our extensions are expressive and effective; a small number of annotations lead to significant potential energy savings (10%–50%) at very little accuracy cost.

We present a program analysis for verifying quantitative robustness properties of programs, stated generally as: “If the inputs of a program are perturbed by an arbitrary amount ɛ, then its outputs change at most by Kɛ, where K can depend on the size of the input but not its value. ” Robustness properties generalize the analytic notion of continuity—e.g., while the function e x is continuous, it is not robust. Our problem is to verify the robustness of a function P that is coded as an imperative program, and can use diverse data types and features such as branches and loops. Our approach to the problem soundly decomposes it into two subproblems: (a) verifying that the smallest possible perturbations to the inputs of P do not change the corresponding outputs significantly, even if control now flows

We present PowerDial, a system for dynamically adapting application behavior to execute successfully in the face of load and power fluctuations. PowerDial transforms static configuration parameters into dynamic knobs that the PowerDial control system can manipulate to dynamically trade off the accuracy of the computation in return for reductions in the computational resources that the application requires to produce its results. These reductions translate directly into performance improvements and power savings. Our experimental results show that PowerDial can enable our benchmark applications to execute responsively in the face of power caps that would otherwise significantly impair responsiveness. They also show that PowerDial can significantly reduce the number of machines required to service intermittent load spikes, enabling reductions in power and capital costs.

Applications that process complex inputs often react in different ways to changes in different regions of the input. Small changes to forgiving regions induce correspondingly small changes in the behavior and output. Small changes to critical regions, on the other hand, can induce disproportionally large changes in the behavior or output. Identifying the critical and forgiving regions in the input and the corresponding critical and forgiving regions of code is directly relevant to many software engineering tasks. We present a system, Snap, for automatically grouping related input bytes into fields and classifying each field and corresponding regions of code as critical or forgiving. Given an application and one or more inputs, Snap uses targeted input fuzzing in combination with dynamic execution and influence tracing to classify regions of input fields and code as critical or forgiving. Our experimental evaluation shows that Snap makes classifications with close to perfect precision (99%) and very good recall (between 99 % and 73%, depending on the application).

This work analyzes the stochastic behavior of writing to embedded flash memory at voltages lower than recommended by a microcontroller’s specifications to reduce energy consumption. Flash memory integrated within a microcontroller typically requires the entire chip to operate on common supply voltage almost double what the CPU portion requires. Our approach tolerates a lower supply voltage so that the CPU may operate in a more energy efficient manner. Energy efficient coding algorithms then cope with flash memory that behaves unpredictably. Our software-only coding algorithms (in-place writes, multiple-place writes, RS-Berger codes) enable reliable storage at low voltages on unmodified hardware by exploiting the electrically cumulative nature of half-written data in write-once bits. For a sensor monitoring application using the MSP430, coding with in-place writes reduces the overall energy consumption by 34%. In-place writes are competitive when the time spent on computation is at least four times greater than the time spent on writes to flash memory. Our evaluation shows that tightly maintaining the digital abstraction for storage in embedded flash memory comes at a significant cost to energy consumption with minimal gain in reliability. 1

Abstract—Approximating ideal program outputs is a common technique for solving computationally difficult problems, for adhering to processing or timing constraints, and for performance optimization in situations where perfect precision is not necessary. To this end, programmers often use approximation algorithms, iterative methods, data resampling, and other heuristics. However, programming such variable accuracy algorithms presents difficult challenges since the optimal algorithms and parameters may change with different accuracy requirements and usage environments. This problem is further compounded when multiple variable accuracy algorithms are nested together due to the complex way that accuracy requirements can propagate across algorithms and because of the size of the set of allowable compositions. As a result, programmers often deal with this issue in an ad-hoc manner that can sometimes violate sound programming practices such as maintaining library abstractions. In this paper, we propose language extensions that expose trade-offs between time and accuracy to the compiler. The compiler performs fully automatic compile-time and installtime autotuning and analyses in order to construct optimized algorithms to achieve any given target accuracy. We present novel compiler techniques and a structured genetic tuning algorithm to search the space of candidate algorithms and accuracies in the presence of recursion and sub-calls to other variable accuracy code. These techniques benefit both the library writer, by providing an easy way to describe and search the parameter and algorithmic choice space, and the library user, by allowing high level specification of accuracy requirements which are then met automatically without the need for the user to understand any algorithm-specific parameters. Additionally, we present a new suite of benchmarks, written in our language, to examine the efficacy of our techniques. Our experimental results show that by relaxing accuracy requirements, we can easily obtain performance improvements ranging from 1.1x to orders of magnitude of speedup.

We present several general, broadly applicable mechanisms that enable computations to execute with reduced resources, typically at the cost of some loss in the accuracy of the result they produce. We identify several general computational patterns that interact well with these resource reduction mechanisms, present a concrete manifestation of these patterns in the form of simple model programs, perform simulationbased explorations of the quantitative consequences of applying these mechanisms to our model programs, and relate the model computations (and their interaction with the resource reduction mechanisms) to more complex benchmark applications drawn from a variety of fields.

Approximating ideal program outputs is a common technique for solving computationally difficult problems, for adhering to processing or timing constraints, and for performance optimization in situations where perfect precision is not necessary. To this end, programmers often use approximation algorithms, iterative methods, data resampling, and other heuristics. However, programming such variable accuracy algorithms presents difficult challenges since the optimal algorithms and parameters may change with different accuracy requirements and usage environments. This problem is further compounded when multiple variable accuracy algorithms are nested together due to the complex way that accuracy requirements can propagate across algorithms and because of the resulting size of the set of allowable compositions.

This paper describes a learning-based approach to the acceleration of approximate programs. We describe the Parrot transformation, a program transformation that selects and trains a neural network to mimic a region of imperative code. After the learning phase, the compiler replaces the original code with an invocation of a low-power accelerator called a neural processing unit (NPU). The NPU is tightly coupled to the processor pipeline to accelerate small code regions. Since neural networks produce inherently approximate results, we define a programming model that allows programmers to identify approximable code regions—code that can produce imprecise but acceptable results. Offloading approximable code regions to NPUs is faster and more energy efficient than executing the original code. For a set of diverse applications, NPU acceleration provides wholeapplication speedup of 2.3 × and energy savings of 3.0 × on average with quality loss of at most 9.6%. 1.

Approximate program transformations such as skipping tasks [29, 30], loop perforation [21, 22, 35], reduction sampling [38], multiple selectable implementations [3, 4, 16, 38], dynamic knobs [16], synchronization elimination [20, 32], approximate function memoization [11], and approximate data types [34] produce programs that can execute at a variety of points in an underlying performance versus accuracy tradeoff space. These transformed programs have the ability to trade accuracy of their results for increased performance by dynamically and nondeterministically modifying variables that control their execution. We call such transformed programs relaxed programs because they have been extended with additional nondeterminism to relax their semantics and enable greater flexibility in their execution. We present language constructs for developing and specifying relaxed programs. We also present proof rules for reasoning about acceptability properties [28], which the program must satisfy to be acceptable. Our proof rules work with two kinds of acceptability properties: relational acceptability properties, which characterize desired relationships between the values of variables in the original and relaxed programs, and unary acceptability properties, which involve values only from a single (original or relaxed) program. The proof rules support a staged reasoning approach in which the majority of the reasoning effort works with the original program. Exploiting the common structure that the original and relaxed programs share, relational reasoning transfers reasoning effort from the original program to prove properties of the relaxed program. We have formalized the dynamic semantics of our target programming language and the proof rules in Coq and verified that the proof rules are sound with respect to the dynamic semantics. Our Coq implementation enables developers to obtain fully machinechecked verifications of their relaxed programs.