In this paper, we present a framework for analytically estimating the output quality of common digital signal processing (DSP) blocks that utilize approximate adders. The framework is based on considering the error of approximate adders as an additive noise (approximation noise) that disturbs the output of the DSP block in question. A signal processing theoretical modeling approach for describing the power of the approximation noise which is the integral of error spectral density over the bandwidth, is developed. The output qualities of DSP blocks, such as finite impulse response filter, discrete cosine transform, and fast Fourier transform, which utilize approximate adders, are thus estimated. The accuracy of the proposed framework is evaluated by comparing mathematical model predictions to simulation results by using the signal-to-noise ratio (SNR) metric. The inaccuracy of the SNRs predicted by the framework was, on average, less than 2.5dB compared with that obtained from simulations. Therefore, a mathematical optimization approach based on Lagrange Multipliers for optimizing design parameters is also presented. The optimization is realized by choosing a proper configuration of the target block, such as determining the data width of the inexact computation part for each approximate adder in the design.

A Theoretical Framework for Quality Estimation and Optimization of DSP Applications Using Low-Power Approximate Adders

High performance compact energy efficient error tolerant adders and multipliers for 16-bit image processing applications

In this paper, we proposed High Performance Error Tolerant Adders (HPETA) which have an efficient design and quality metrics for inexact computing applications. To achieve high performance, Multipl...

High Performance Error Tolerant Adders for Image Processing Applications

Low power and area efficient error tolerant adder for image processing application

Approximate Computing offers enhanced energy efficiency by exploring quality relaxation on applications. Application-agnostic hardware-level techniques can provide high benefits under certain scenarios, but their integration on a general-purpose architecture presents novel control challenges. We present Risk-5, an extension of the RISC-V architecture that implements control mechanisms to orchestrate multiple coexisting approximation techniques within an architecture. In Risk-5, approximate hardware capabilities are exposed to software through identification registers, data structures, and drivers that describe the nature and configuration parameters for each approximate design. This allows the software stack to control what and how much is approximated in an application. Control options range from activating or deactivating a certain approximation (e.g., approximating ALU operations), to configuring allowable error levels (e.g., for a configurable FPU), and configuring operation parameters that may lead to probabilistic errors (e.g., setting the refresh rate for an approximate SDRAM). Approximations may be dynamically configured and combined at runtime, allowing for simplified design space exploration. Finally, supervisor- and machine-level control allows for the use of certain approximations without requiring changes to applications. In this article, we discuss the implementation of different classes of approximation techniques, detailing and evaluating how they interact with each other. Risk-5 and the selected approximations are demonstrated in the functional level in a RISC-V ISA simulator augmented with an approximate computing framework. Our experiments evaluate how six applications from different computing domains behave when subjected to a combination of approximation techniques. Our results show how Risk-5 can bridge the gap between software and hardware approximations, allowing designers to easily evaluate energy-quality tradeoffs.

Risk-5: Controlled Approximations for RISC-V

In this paper, a 1-bit modified full adder (MFA) cell is proposed. This eliminates the carry propagation during the addition by allowing errors in the carry bit. Using the proposed MFA, a 16-bit high speed error tolerant adder (HSETA) circuit is designed with conventional carry select adder (CSLA) structure for higher order bits and MFA based structure for lower order bits. The performance of HSETA is compared with existing adders in terms of accuracy, gate count, delay and power dissipation. The gate count of the HSETA is reduced by 23% and speed is improved by 43% compared to a conventional 16-bit adder structure. Further, implementation on FPGA Spartan 6 shows that HSETA uses 53% fewer LUT and 63% fewer slices compared to the conventional adder. Image blending application is used to evaluate the performance of the HSETA. In addition, to perform extensive error analysis, an analytical model is developed for HSETA and tested for varying bit widths and input probabilities. The analytical model is validated through simulation.

High Speed Error Tolerant Adder for Multimedia Applications

This paper presents possible designs for high speed error tolerant adder using Gate Diffusion Input (GDI) technique. The 1-bit modified full adder (MFA) proposed in [1] is implemented using GDI technique (GDI-MFA). The GDI-MFA is extended to implement a 16-bit high speed error tolerant adder (GDI-HSETA). The performance of various configurations is studied based on metrics such as delay, area and power dissipation. The circuits have been simulated using pSPICE software. From the results it is observed that the proposed GDI-MFA has 52% less transistor count and consumes 33% less power compared to conventional adders. Results of simulation of GDI-HSETA and other adders in pSpice indicate that the proposed adder has 21.6% power reduction and 13% less transistor count. Also, based on the implementation of GDI-HSETA and existing 16-bit adders on FPGA Spartan 6 platform, it is observed that GDI-HSETA achieved power reduction compared to 16-bit adders using conventional design.

P. Amritvalli

Papers

High Speed Error Tolerant Adder for Multimedia Applications

Design of High Speed Error Tolerant Adder Using Gate Diffusion Input Technique