Assessing Approximate Arithmetic Designs in the presence of Process Variations and Voltage Scaling

As environmental concerns and portability of electronic devices move to the forefront of priorities, innovative approaches which reduce processor energy consumption are sought. Approximate arithmetic units are one of the avenues whereby significant energy savings can be achieved. Approximation of fundamental arithmetic units is achieved by judiciously reducing the number of transistors in the circuit. A satisfactory tradeoff of energy vs. accuracy of the circuit can be determined by trial-and-error methods of each functional approximation. Although the accuracy of the output is compromised, it is only decreased to an acceptable extent that can still fulfill processing requirements. A number of scenarios are evaluated with approximate arithmetic units to thoroughly cross-check them with their accurate counterparts. Some of the attributes evaluated are energy consumption, delay and process variation. Additionally, novel methods to create such approximate units are developed. One such method developed uses a Genetic Algorithm (GA), which mimics the biologically-inspired evolutionary techniques to obtain an optimal solution. A GA employs genetic operators such as crossover and mutation to mix and match several different types of approximate adders to find the best possible combination of such units for a given input set. As the GA usually consumes a significant amount of time as the size of the input set increases, we tackled this problem by using various methods to parallelize the fitness computation process of the GA, which is the most compute intensive task. The parallelization improved the computation time from 2,250 seconds to 1,370 seconds for up to 8 threads, using both OpenMP and Intel TBB. Apart from using the GA with seeded multiple approximate units, other seeds such as basic logic gates with limited logic space were used to develop completely new multi-bit approximate adders with good fitness levels. iii The effect of process variation was also calculated. As the number of transistors is reduced, the distribution of the transistor widths and gate oxide may shift away from a Gaussian Curve. This result was demonstrated in different types of single-bit adders with the delay sigma increasing from 6psec to 12psec, and when the voltage is scaled to Near-Threshold-Voltage (NTV) levels sigma increases by up to 5psec. Approximate Arithmetic Units were not affected greatly by the change in distribution of the thickness of the gate oxide. Even when considering the 3-sigma value, the delay of an approximate adder remains below that of a precise adder with additional transistors. Additionally, it is demonstrated that the GA obtains innovative solutions to the appropriate combination of approximate arithmetic units, to achieve a good balance between energy savings and accuracy

Designing Energy-Efficient Approximate Adders Using Parallel Genetic Algorithms

Approximate computing involves selectively reducing the number of transistors in a circuit to improve energy savings. Energy savings may be achieved at the cost of reduced accuracy for signal processing applications whereby constituent adder and multiplier circuits need not generate a precise output. Since the performance versus energy savings landscape is complex, we investigate the acceleration of the design of approximate adders using parallelized Genetic Algorithms (GAs). The fitness evaluation of each approximate adder is explored by the GA in a non-sequential fashion to automatically generate novel approximate designs within specified performance thresholds. This paper advances methods of parallelizing GAs and implements a new parallel GA approach for approximate multi-bit adder design. A speedup of approximately 16-fold is achieved using a quad-core Intel processor and results indicate that the proposed GA is able to find adders which consume 63:8% less energy than accurate adders