In this paper, we introduce a novel implementation of a square root algorithm specifically tailored for posit arithmetic. Unlike traditional methods, the proposed approach capitalizes on the inherent flexibility of posits, which lack fixed-length fields, to optimize square root computations. By accurately estimating the minimum number of required fraction bits, our algorithm substantially reduces the recurrence iterations without sacrificing accuracy. Implemented across standard 16-bit, 32-bit, and 64-bit posit formats, our units showcase a significant latency reduction in different applications with only a marginal increase in resource utilization. Comparative analysis against previous pipelined designs underscores the area efficiency of our proposed solutions. This research significantly contributes to the advancement of posit-based arithmetic units, presenting promising opportunities for improving computational system efficiency.

Posit ™ arithmetic is a promising alternative to IEEE 754 floating-point arithmetic due to its higher accuracy, larger dynamic range, and bitwise compatibility. While posit arithmetic has been well studied for basic arithmetic operations, division has received little attention. This paper proposes multiple divider designs for posit arithmetic based on digit recurrence and iterative approximation, and evaluates their performance. ASIC synthesis results show that the proposed designs significantly reduce hardware requirements for 32-bit division units compared to previous works by 1.14 × in area, 1.11× in power, and 1.04×in datapath delay. Moreover, the paper introduces an approximate logarithmic posit division that achieves an 8.8×reduction in area and 29×reduction in energy consumption with negligible degradation of the final results, making it suitable for error-tolerant applications.

Representing and operating on real numbers in a microprocessor presents unique challenges not encountered with the set of integers. Working with real numbers introduces additional concepts such as precision, that is, the error made between the number with which we want to operate and the approximation that we can represent in a finite number of bits. Currently, the universally extended way of representing the set of real numbers is using floating-point numbers defined by the IEEE 754 standard. This format presents a series of difficulties, such as the different rounding schemes, reproducibility problems depending on the implementation, a multitude of ways to represent Not a Numbers (NaNs) or the existence of plus and minus zero.

Recently, the posit number system has demonstrated a higher accuracy over standard floating-point arithmetic for many scientific applications. However, when it comes to implementing accelerators for these applications, the tool support for this arithmetic format is still missing, especially during the step. In this paper, we incorporate the posit data type into the high-level synthesis (HLS) design process, so that we can generate the implementation directly from a given behavioral specification, but using posit numbers instead of the classical floating-point notations. Our evaluations show that, even if posit-based circuits require more area than their floating-point counterparts, they offer higher accuracy when using the same bitwidth. For example, using posit arithmetic can reduce computation errors by about two orders of magnitude when compared to using standard floating-point numbers. Our approach also includes an alternative to mitigate the high overheads of the posits and broadening the potential use of this format. We also propose a hybrid scheme that uses posit numbers only in the private local memory, while the accelerator operates in the classic floating-point notation. This solution is useful when the designers want to optimize local memories and data transfers, but still use legacy high-level synthesis (HLS) tools that only support traditional floating-point notations.

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Posit arithmetic is an alternative format to the standard IEEE 754 for floating-point numbers that claims to provide compelling advantages over floats, including higher accuracy, larger dynamic range, or bitwise compatibility across systems. The interest in the design of arithmetic units for this novel format has increased in the last few years. However, while multiple designs for posit adder and multiplier have been developed recently in the literature, fused units for posit arithmetic are still in the early stages of research. Moreover, due to the large size of accumulators needed in fused operations, the few fused posit units proposed so far still require many hardware resources. In order to contribute to the development of the posit number format, and facilitate its use in applications such as deep learning, this paper presents several designs of energy-efficient posit multiply- accumulate (MAC) units with support for standard quire format. Concretely, the proposed designs are capable of computing fused dot products of large vectors without accuracy drop, while consuming less energy than previous implementations. Experiments show that, compared to previous implementations, the proposed designs consume up to 75.49%, 88.45% and 83.43% less energy and are 73.18%, 87.36% and 83.00% faster for 8, 16 and 32 bitwidths, with an additional area of only 4.97%, 7.44% and 4.24%, respectively.

The posit number system, which is proposed as a replacement of IEEE floating-point numbers, is in the spotlight of Arithmetic research due to the recent breakthroughs. This format claims to provide more accurate results with the same bitwidth than standard floating point, but the run-time variability during the detection of the posit fields involves a hardware design challenge. In this work, we propose parameterized designs for multiple posit functional units, including addition and multiplication, and integrate them as templates of the FloPoCo framework. The integration of the proposed algorithms within FloPoCo can provide synthesizable VHDL code for posit arithmetic of any possible configuration 〈n, es〉. Experiments show an improvement in terms of area and energy with respect to state-of-the-art works up to 35.9% and 30.8%, respectively.