PERI

Owing to the failure of Dennard’s scaling, the past decade has seen a steep growth of prominent new paradigms leveraging opportunities in computer architecture. Two technologies of interest are Posit and RISC-V. Posit was introduced in mid-2017 as a viable alternative to IEEE-754, and RISC-V provides a commercial-grade open source Instruction Set Architecture (ISA). In this article, we bring these two technologies together and propose a Configurable Posit Enabled RISC-V Core called PERI. The article provides insights on how the Single-Precision Floating Point (“F”) extension of RISC-V can be leveraged to support posit arithmetic. We also present the implementation details of a parameterized and feature-complete posit Floating Point Unit (FPU). The configurability and the parameterization features of this unit generate optimal hardware, which caters to the accuracy and energy/area tradeoffs imposed by the applications, a feature not possible with IEEE-754 implementation. The posit FPU has been integrated with the RISC-V compliant SHAKTI C-class core as an execution unit. To further leverage the potential of posit , we enhance our posit FPU to support two different exponent sizes (with posit-size being 32-bits), thereby enabling multiple-precision at runtime. To enable the compilation and execution of C programs on PERI, we have made minimal modifications to the GNU C Compiler (GCC), targeting the “F” extension of the RISC-V. We compare posit with IEEE-754 in terms of hardware area, application accuracy, and runtime. We also present an alternate methodology of integrating the posit FPU with the RISC-V core as an accelerator using the custom opcode space of RISC-V.

High-Performance Computation in Residue Number System Using Floating-Point Arithmetic

Residue number system (RNS) is known for its parallel arithmetic and has been used in recent decades in various important applications, from digital signal processing and deep neural networks to cryptography and high-precision computation. However, comparison, sign identification, overflow detection, and division are still hard to implement in RNS. For such operations, most of the methods proposed in the literature only support small dynamic ranges (up to several tens of bits), so they are only suitable for low-precision applications. We recently proposed a method that supports arbitrary moduli sets with cryptographically sized dynamic ranges, up to several thousands of bits. The practical interest of our method compared to existing methods is that it relies only on very fast standard floating-point operations, so it is suitable for multiple-precision applications and can be efficiently implemented on many general-purpose platforms that support IEEE 754 arithmetic. In this paper, we make further improvements to this method and demonstrate that it can successfully be applied to implement efficient data-parallel primitives operating in the RNS domain, namely finding the maximum element of an array of RNS numbers on graphics processing units. Our experimental results on an NVIDIA RTX 2080 GPU show that for random residues and a 128-moduli set with 2048-bit dynamic range, the proposed implementation reduces the running time by a factor of 39 and the memory consumption by a factor of 13 compared to an implementation based on mixed-radix conversion.