Arbitrary Reduced Precision for Fine-grained Accuracy and Energy Trade-offs

Abstract

Full-precision Floating-Point Units (FPUs) can be a source of extensive hardware overhead (power consumption, area, memory footprint, etc.). As several modern applications feature an inherent tolerance to precision loss, a new computing paradigm has emerged: Transprecision Computing (TC). TC proposes several tools and techniques that trade precision for energy efficiency. However, most of these tools require developers to rewrite part or all of their existing software stacks, which is often infeasible, complex, or requires extensive development efforts. In addition to their intrusiveness, TC tools can only simulate the impact of precision loss, and they do not provide corresponding hardware designs that take advantage of the simulations.This work proposes a non-intrusive hardware-oriented approach, requiring no modification of source code that applies approximations at the low-level in assembly. The approach can be used to approximate virtually all types of executable binaries (bare-metal applications, single−/multi-threaded user applications, OS/RTOS, etc.). We introduce AxQEMU: a software based on the well known QEMU dynamic binary translator. We demonstrate how our approach can determine the effects of FP approximations on application-level Quality of Result (QoR), and how it interfaces with other tools from the literature. A hardware-level case study on a 28-nm FD-SOI implementation is presented, demonstrating how fine-grained energy/accuracy trade-offs can be made thanks to floating-point arbitrary reduced precision (ARP). For instance, considering the well-known arclength FP application, FPU computation energy savings of up to 19.4% were achieved with an accuracy threshold of 10 significant digits, and up to 60.7% with a 4-digit accuracy when using ARP. These savings compared favorably to the limited 7.7% saving afforded by using standard variable type optimization tools.