Posit number system has been used as an alternative to IEEE floating-point number system in many applications, especially the recent popular deep learning. Its non-uniformed number distribution fits well with the data distribution of deep learning and thus can speedup the training process of deep learning. Among all the related arithmetic operations, multiplication is one of the most frequent operations used in applications. However, due to the bit-width flexibility nature of posit numbers, the hardware multiplier is usually designed with the maximum possible mantissa bit-width. As the mantissa bit-width is not always the maximum value, such multiplier design leads to a high power consumption especially when the mantissa bit-width is small. In this brief, a power efficient posit multiplier architecture is proposed. The mantissa multiplier is still designed for the maximum possible bit-width, however, the whole multiplier is divided into multiple smaller multipliers. Only the required small multipliers are enabled at run-time. Those smaller multipliers are controlled by the regime bit-width which can be used to determine the mantissa bit-width. This design technique is applied to 8-bit, 16-bit, and 32-bit posit formats in this brief and an average of 16% power reduction can be achieved with negligible area and timing overhead.

The recently proposed posit number system is more accurate and can provide a wider dynamic range than the conventional IEEE754-2008 floating-point numbers. Its nonuniform data representation makes it suitable in deep learning applications. Posit adder and posit multiplier have been well developed recently in the literature. However, the use of posit in fused arithmetic unit has not been investigated yet. In order to facilitate the use of posit number format in deep learning applications, in this paper, an efficient architecture of posit multiply-accumulate (MAC) unit is proposed. Unlike IEEE754-2008 where four standard binary number formats are presented, the posit format is more flexible where the total bitwidth and exponent bitwidth can be any number. Therefore, in this proposed design, bitwidths of all datapath are parameterized and a posit MAC unit generator written in C language is proposed. The proposed generator can generate Verilog HDL code of posit MAC unit for any given total bitwidth and exponent bitwidth. The code generated by the generator is a combinational design, however a 5-stage pipeline strategy is also presented and analyzed in this paper. The worst case delay, area, and power consumption of the generated MAC unit under STM-28nm library with different bitwidth choices are provided and analyzed.

In this paper, a new flexible multiple-precision multiply-accumulate unit is proposed for deep neural network training and inference. The proposed unit supports both fixed-point and floating-point operations. For floating-point format, the proposed unit supports one 16-bit MAC operation or sum of two 8-bit multiplications plus a 16-bit addend. To make the proposed MAC unit more versatile, the bit-width of exponent and mantissa can be flexibly exchanged. By setting the bit-width of exponent to zero, the proposed MAC unit also supports fixed-point operations. For fixed-point format, the proposed unit supports one 16-bit MAC or sum of two 8-bit multiplications plus a 16-bit addend. Moreover, the proposed unit can be further divided to support sum of four 4-bit multiplications plus a 16-bit addend. At the lowest precision, the proposed MAC unit supports accumulating of eight 1-bit logic AND operations to enable the support of binary neural networks. Compared to the standard 16-bit half-precision MAC unit, the proposed MAC unit provides more flexibility with only 21.8% area overhead. Compared to a standard 32-bit single-precision MAC unit, the proposed MAC unit requires much less hardware cost but still provides 8-bit exponent in the numerical format to maintain large dynamic range for deep learning computing.

Deep learning is getting more and more attentions in recent years. Many hardware architectures have been proposed for efficient implementation of deep neural network. The arithmetic unit, as a core processing part of the hardware architecture, can determine the functionality of the whole architecture. In this paper, an efficient fixed/floating-point merged multiply-accumulate unit for deep learning processor is proposed. The proposed architecture supports 16-bit half-precision floating-point multiplication with 32-bit single-precision accumulation for training operations of deep learning algorithm. In addition, within the same hardware, the proposed architecture also supports two parallel 8-bit fixed-point multiplications and accumulating the products to 32-bit fixed-point number. This will enable higher throughput for inference operations of deep learning algorithms. Compared to a half-precision multiply-accumulate unit (accumulating to single-precision), the proposed architecture has only 4.6% area overhead. With the proposed multiply-accumulate unit, the deep learning processor can support both training and high-throughput inference.