Accelerated Image Processing Through IMPLY-Based NoCarry Approximated Adders
Fabian Seiler, Nima TaheriNejad
Abstract
As the demand for computational power increases drastically, traditional solutions to address those needs struggle to keep up. Consequently, there has been a proliferation of alternative computing paradigms aimed at tackling this disparity. Approximate Computing (AxC) has emerged as a modern way of improving speed, area efficiency, and energy consumption in error-resilient applications such as image processing or machine learning. The trade-off for these enhancements is the loss in accuracy. From a technology point of view, memristors have garnered significant attention due to their low power consumption and inherent non-volatility that makes them suitable for In-Memory Computation (IMC). Another computing paradigm that has risen to tackle the aforementioned disparity between the demand growth and performance improvement. In this work, we leverage a memristive stateful in-memory logic, namely Material Implication (IMPLY). We investigate advanced adder topologies within the context of AxC, aiming to combine the strengths of both of these novel computing paradigms. We present two approximated algorithms for each IMPLY based adder topology. When embedded in an Ripple Carry Adder (RCA), they reduce the number of steps by <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$6\%-54\%$</tex-math> </inline-formula> and the energy consumption by <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$7\%-54\%$</tex-math> </inline-formula> compared to the corresponding exact full adders. We compare our work to State-of-the-Art (SoA) approximations at circuit-level, which improves the speed and energy efficiency by up to <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$72\%$</tex-math> </inline-formula> and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$34\%$</tex-math> </inline-formula> , while lowering the Normalized Median Error Distance (NMED) by up to <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$81\%$</tex-math> </inline-formula> . We evaluate our adders in four common image processing applications, for which we introduce two new test datasets as well. When applied to image processing, our proposed adders can reduce the number of steps by up to <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$60\%$</tex-math> </inline-formula> and the energy consumption by up to <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$57\%$</tex-math> </inline-formula> , while also improving the quality metrics over the SoA in most cases.