Function evaluation is an important arithmetic computation in many signal processing applications, such as special function units in modern graphics processing units (GPUs). Hardware implementations of function evaluation usually consists of lookup tables (LUT) and some simple arithmetic units of multipliers and/or adders. LUT usually takes a significant portion of total area cost, especially when function evaluators are allowed to compute several different arithmetic functions with shared arithmetic units where evaluation of each function needs separate LUT. In this paper, we focus on the category of table-addition (TA) function evaluators that are composed of two types of LUT, table of initial values (TI) and table of offset values (TO), followed by a multi-operand adder. It has been shown that multipartite table method (MP) has significant improvement over prior similar designs such as symmetric bipartite table methods (SBTM) and symmetric table addition methods (STAM) for applications with low-to-medium precision requirements. This paper presents an extension of MP, called hierarchical multipartite (HMP), which further reduces total table size by applying several levels of table decompositions. Furthermore, we perform the bit-width optimization by jointly considering the impacts of all error sources during the search of best table decompositions, leading to more efficient hardware design. Besides, a new lossless decomposition of TI is presented, resulting in additional saving of table size without incurring any extra errors. Experimental results show that the proposed design can efficiently reduce the total area cost in ASIC and FPGA implementations.

Function evaluation is an important arithmetic computation in many signal processing applications, such as the special function unit in modern graphics processing units (GPUs). Lookup table (LUT) usually takes a significant portion of total area in function evaluation using piecewise polynomial approximation. Many papers have proposed various approaches to reduce table size without sacrificing precision requirement. This paper presents new LUT compression methods that do not introduce extra errors but can effectively further reduce the table size in the piecewise polynomial approximation with uniform or non-uniform segmentations.

In the piecewise function evaluation with polynomial approximation, nonuniform segmentation can effectively reduce the size of lookup tables for some arithmetic functions compared to uniform segmentation approaches, at the cost of the extra segment address (index) encoder that results in area and delay overhead. Also, it is observed that the nonuniform segmentation reflects a design tradeoff between the ROM size and the area cost of the subsequent arithmetic computation hardware. In this paper, we propose a new nonuniform segmentation method that searches for the optimal segmentation scheme with the goal of minimized ROM, total area, or delay. For some high-variation arithmetic functions, the proposed segmentation method achieves significant area reduction compared to the uniform segmentation method. We also demonstrate the design tradeoff among uniform and nonuniform segmentation, and degree-one and degree-two polynomial approximations, with respect to precision ranging from 12 to 32 bits for the elementary function of reciprocal.

This paper presents a cell-based AISC design flow where the traditional CMOS cell library is replaced by pass-transistor logic (PTL) cell library. In particular, we develop an automatic PTL logic synthesizer to perform area-oriented synthesis by exploiting the characteristics of the PTL cell circuits. Two methods are used to reduce the area cost. The first method, called buffer elimination, for the pre-layout area minimization is to reduce the redundant inverters in the gate-level netlist during the logic mapping stage and results in an area saving of more than 50%. The second method, called layout compaction, is to reduce the layout area in the physical level by considering the design rules imposed on the PTL cell circuits, and lead to an additional 30% area saving.