Fixed-Posit：一种用于容错应用的浮点表示
Fixed-Posit: A Floating-Point Representation for Error-Resilient Applications
摘要：
今天，几乎所有的计算机系统都使用IEEE-754浮点数来表示实数。最近，IEEE-754浮点数的替代方案被提出，因为它具有更好的精度和更大的动态范围。可配置的性质，具有不同数量的制度和指数位，已成为其采用的一个障碍。为了克服这一缺点，我们提出了固定位数表示，其中的制度和指数位的数量是固定的，并提出了一个固定位数乘法器的设计。我们评估了固定的乘法器上的错误弹性应用程序的AxBench和OpenBLAS基准以及神经网络。所提出的固定位数乘法器的功耗，面积和延迟分别节省47%，38.5%，22%相比，与32位IEEE-754乘法器相比，功耗，面积和延迟分别节省高达70%，66%，26%。这些节省伴随着OpenBLAS和AxBench工作负载的最小输出质量损失（1.2%的平均相对误差）。此外，对于像ImageNet上的ResNet-18这样的神经网络，我们观察到使用固定乘数的准确性损失可以忽略不计（0.12%）。
英文摘要：
Today, almost all computer systems use IEEE-754 floating point to represent real numbers. Recently, posit was proposed as an alternative to IEEE-754 floating point as it has better accuracy and a larger dynamic range. The configurable nature of posit, with varying number of regime and exponent bits, has acted as a deterrent to its adoption. To overcome this shortcoming, we propose fixed-posit representation where the number of regime and exponent bits are fixed, and present the design of a fixed-posit multiplier. We evaluate the fixed-posit multiplier on error-resilient applications of AxBench and OpenBLAS benchmarks as well as neural networks. The proposed fixed-posit multiplier has 47%, 38.5%, 22% savings for power, area and delay respectively when compared to posit multipliers and up to 70%, 66%, 26% savings in power, area and delay respectively when compared to 32-bit IEEE-754 multiplier. These savings are accompanied with minimal output quality loss (1.2% average relative error) across OpenBLAS and AxBench workloads. Further, for neural networks like ResNet-18 on ImageNet we observe a negligible accuracy loss (0.12%) on using the fixed-posit multiplier.
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