In this article, we propose a multiplierless piecewise linear (PWL) approximation computation (ML-PLAC) method for nonlinear unary functions. ML-PLAC seeks the minimum number of segments with the predefined fractional bit width and number of adders to satisfy the restriction on the maximum absolute error ( MAE ). Compared with the previous universal PWL approximation method, multiplication operations in the segmentor are replaced by a simulation of shift-and-add operations by reducing the fractional bit width of the slope of linear functions. Various numbers of segments are obtained by different predefined numbers of adders to balance the two numbers. In addition, adders are used to replace the multiplier in hardware architecture. The synthesized results prove that ML-PLAC has increased performance without any compromises. Compared with state-of-the-art methods, ML-PLAC saves 58.82% area, 38.16% delay, 60.31% power and 6.10% MAE when computing logarithmic functions; 51.51% area, 46.49% delay, and 46.95% power while maintaining the comparable MAE when computing antilogarithmic functions; 55.21% area, 25% delay, 61.21% power, and 37.30% MAE when computing hyperbolic tangent functions; 82.47% area, 60% delay, 77.51% power and 12.74% MAE when computing sigmoid functions; and 46.43% area, 31.43% delay, and 61.16% power while maintaining the same MAE when computing softsign functions.

State-of-the-art approaches that perform root computations based on the COordinate Rotation Digital Computer (CORDIC) algorithm suffer from high latency in performing multiple iterations. Therefore, root computations based on the CORDIC algorithm cannot meet the strict latency requirements of some applications. In this paper, we propose a methodology for performing Nth root computations on floating-point numbers based on the piecewise linear (PWL) approximation method. The proposed method divides an Nth root computation into several subtasks approximated by the PWL algorithm. It determines the widest segments of the subtasks and the smallest fractional width needed to satisfy the predefined maximum relative error Max_Err _r . Our design is coded in Verilog HDL and synthesized under TSMC 40 nm CMOS technology. The synthesized results show that our design can reach the highest frequency of 2.703 GHz with an area consumption of 2608.84 μ m ² and a power consumption of 2.4476 mW. Compared with one stateof-the-art architecture, our design saves 91.60%, 89.84%, and 63.33% of the area, power, and latency @1.89GHz frequency, respectively, while reducing Max_Err _r by 57.30%. In addition, it saves 94.52%, 92.68%, and 73.17% of the area, power, and delay @1.89GHz frequency, respectively, and reduces Max_Err _r by 1.65% when compared with the other state-of-the-art design.

In this brief, we propose a logarithmic converter for floating-point numbers based on the piecewise linear (PWL) approximation method. The proposed method is applicable to any customized floating-point format with a mantissa length of 16-23 bits and a maximum absolute error (MAE) larger than 10 ^-6 . The logarithmic function is automatically segmented into several maximal subsections by a software-based segmentation scheme with the restriction of a predefined MAE and a fractional word length for the computing units. Then, we make a tradeoff between the piecewise number and the fractional word length. Based on the results of the segmentor, our design is coded in the Verilog hardware description language. The synthesized results show that our design consumes less area, time, and power without compromising accuracy compared to existing techniques based on the COordinate Rotation Digital Computer (CORDIC) and PWL methods.

In this brief, we propose a fully pipelined divider for single-precision floating-point numbers based on a universal piecewise linear (PWL) approximation method and a modified Goldschmidt algorithm. The state-of-the-art universal PWL method uses a suitable number of segments and fractional bit widths to meet the requirement of the predefined maximum absolute error. Small multipliers are employed in the modified Goldschmidt algorithm. In the hardware implementation, the multipliers are optimized with the radix-4 and radix-8 booth encoding methods to reduce the number of partial products. In addition, the sum of the partial products and other data are calculated by a compressor and an adder to shorten the critical path. Synthesized results show that the maximum achievable frequency of our design is better than those of the existing methods. In addition, our design shows overwhelming superiority in terms of latency and throughput compared with existing methods.

In recent years, researchers have placed great importance on the use of silicon (Si)-related materials as efficient light sources for the purpose of realizing Si-based monolithic optoelectronic integration. Previous works were mostly focused on Si nanostructured materials, and, so far, exciting results from Si-based compounds are still lacking. In this paper, we have systematically demonstrated the high photoluminescence external quantum efficiency (PL EQE) and internal quantum efficiency (PL IQE) of amorphous silicon oxynitride (a-SiN_xO_y) systems. Within an integration sphere, we directly measured the PL EQE values of a-SiN_xO_y, which ranged from approximately 2% to 10% in the visible range at room temperature. Then, we calculated the related PL IQE through temperature-dependent PL measurements. The obtained PL IQE values (~84% at 480 nm emission peak wavelength) were very high compared with those of reported Si-based luminescent thin films. We also calculated the temperature-dependent PL EQE values of a-SiN_xO_y systems, and discussed the related PL mechanisms.

In this paper, we propose a methodology for computing the square root of a complex number based on a piecewise linear (PWL) approximation method. The proposed method relies on a software-based segmentor that automatically divides the three real square root functions used in complex square root computation into the fewest segments with a predefined fractional bit width and maximum absolute error (MAE). The coefficients, including the start point, end point, slope and y-intercept of each segment, are stored for use in the implementation of the hardware design. The proposed fully pipelined circuit is coded in the Verilog hardware description language (HDL). The results of synthesis in TSMC (Taiwan Semiconductor Manufacturing Company) 65-nm CMOS technology show that our design achieves savings of 64.21% in area, 16.67% in delay and 65.08% in power compared to the existing methods. Moreover, implementation results on an FPGA (Field-Programmable Gate Array) platform (XC7Z020-CLG400) show that the proposed design reduces the number of LUTs by 29.38%, delay by 28.57% and power consumption by 53.47%.