ML-PLAC: Multiplierless Piecewise Linear Approximation for Nonlinear Function Evaluation

QPA: A Quantization-Aware Piecewise Polynomial Approximation Methodology for Hardware-Efficient Implementations

“…For example, QPA-Gn can be configured as QPA-G1 which is a PWL method; or QPA-G2, which is a PWQ method. The QPA-Mn means the multiplier corresponding to the highest power is replaced with a shiftadder like [18], and the QPA-Sn-m means replace 𝑚 multipliers in the polynomial calculation circuit with 𝑚 barrel shifters. As these three methods are all QPA-based, designers can make some simple modifications to change from one approximation method to another, such as changing from QPA-G1 to QPA-G2, or from QPA-M1 to QPA-S2-1, to adapt to more ASIC design requirements while consistently ensuring that each specific method they used is currently the most advanced.…”

“…When the bit width of the multiplier is small enough, the universal multiplier can be replaced by a specially designed shift-adder to achieve a higher calculation speed. The PWL version of this idea is first proposed in [18] and named ML-SQ. However, the ML-SQ method cannot be used in arbitrary-order approximation, so we improve the fitting part of the ML-SQ method and propose the QPA-Mn fitting algorithm.…”

“…For example, when 𝑛 1, the resulting array 𝐴 could be 𝑎 , 𝑡 / 2 or 𝑎 , 𝑡 1 /2 , depending on which combination results in a smaller 𝑟𝑀𝐴𝐸. By using a small 𝑤 , we can also limit the value of 𝑎 to a small range, the techniques of shiftadder designing proposed in [18] can be used for higher-order approximation, with a better fitting effect. We configure our QPA-Mn method as the QPA-M1 method, which is equivalent to an optimization of the ML-SQ method, and compare the fitting performance of the two methods in Table VI.…”

“…Dong et al [17] optimized it and proposed a more advanced PWL method named piecewise linear approximation N 2 > REPLACE THIS LINE WITH YOUR MANUSCRIPT ID NUMBER (DOUBLE-CLICK HERE TO EDIT) < computation (PLAC), which can achieve the theoretical best segmentation performance for logarithmic function. Lyu et al [18] further optimized the PLAC method, they combine the segmentation operation and quantization operation into one and propose the SQ method, which is the state-of-the-art of universal PWL method. They also use a shift-adder to replace the multiplier, which can achieve better performance when the number of segments is small enough.…”

“…They also use a shift-adder to replace the multiplier, which can achieve better performance when the number of segments is small enough. Ref [16]- [18] makes the PWL method more and more complete and efficient, but the fitting algorithm they use cannot achieve the best fitting performance when fitting the non-convex functions, and these methods cannot be used on higher-order approximation scenarios.…”