Fixed-width multiplier for DSP application

A Survey on Approximate Multiplier Designs for Energy Efficiency: From Algorithms to Circuits

“…Comparing APP2 and AW, the altered partial products obviously help the efficiency of the reduction procedure but at the cost of area and power. Among all the BAM multipliers, BAM (8,16) provides the best trade-off between accuracy and circuit cost. OPACT, configured with automatically optimized compressor allocation and order connection, provides negligible error with moderate hardware savings.…”

“…Thus, the designs that are closer to the lower right corner are preferred. It can be observed that, while OPACT, BAM (8,16), SSM, ALM_SOA, AW, APP2, BAM (4,8), DRUM, and LM can achieve good improvements in energy efficiency with a limited or almost negligible accuracy loss on the MNIST (MLP), only OPCAT, DRUM, and BAM(4,8) can keep good accuracy with large improvements in energy efficiency on the CIFRA10 (AlexNet). This simply indicates that the potential approximation design space actually changes for different algorithms and demands more in-depth understanding of the approximation error propagation when executing the algorithm.…”

“…In addition, some multipliers, like ALM_SOA and LM, introduce one-sided errors that can become more difficult to be cancelled out during the approximation error propagation within the AlexNet. Finally, the multipliers such as BAM (8,16), AW, and APP2 tend to introduce larger relative errors for small inputs with their aggressive approximations in the least-significant bits. Thus, when deploying an approximate multiplier, instead of simply selecting the one based on its MRED, we should choose one with balance among error bias, approximation aggressiveness, and its fitness to a particular algorithm.…”

“…Since then, the approximation technique of truncation and its variants, such as the fixed-width multiplier that enforces the same bit-width for both inputs and outputs, have been proposed for achieving area efficiency [12,13]. To reduce the truncation induced inaccuracy, around 2000, a few compensation techniques were suggested at the cost of additional complexity [14][15][16][17][18]. Recently, with the popularity of IoT devices and their stringent resource constraints, researchers from both academia and industry have devoted significant efforts to approximate multiplier design and optimization, which resulted in many effective and interesting approximation techniques [8,[19][20][21][22][23][24][25][26][27][28][29][30][31][32][33][34][35][36][37][38].…”