We propose ReFloat, a principled approach for low-cost floating-point processing in ReRAM. The exponent offsets based on a base are stored by a flexible and fine-grained floating-point number representation. The key motivation is that, while the number of exponent bits must be reduced due to the exponential relation to the computation latency and hardware cost, the convergence still requires sufficient accuracy for exponents. Our design reconciles the conflicting goals by storing the exponent offsets from a common base among matrix values in a block, which is the granularity of computation in ReRAM. Due to the value locality, the differences among the exponents in a block are small, thus the offsets require much less number of bits to represent exponents. In essence, ReFloat enables the principled local fine-tuning of floating-point representation. Based on the idea, we define a flexible ReFloat format that specifies matrix block size, and the number of bits for exponent and fraction. To determine the base for each block, we propose an optimization method that minimizes the difference between the exponents of the original matrix block and the converted block. We develop the conversion scheme from default double-precision floating-point format to ReFloat format, the computation procedure, and the low-cost floating-point processing architecture in ReRAM.

中文翻译：

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ReFloat：ReRAM 中的低成本浮点处理

我们提出了 ReFloat，这是一种在 ReRAM 中进行低成本浮点处理的原则性方法。基于基数的指数偏移量由灵活且细粒度的浮点数表示存储。关键动机是，虽然由于与计算延迟和硬件成本的指数关系，必须减少指数位数，但收敛仍然需要指数足够的精度。我们的设计通过在块中的矩阵值之间存储来自公共基的指数偏移量来协调相互冲突的目标，这是 ReRAM 中的计算粒度。由于值的局部性，块中指数之间的差异很小，因此偏移量需要更少的位数来表示指数。在本质上，ReFloat 实现了浮点表示的原则性局部微调。基于这个想法，我们定义了一种灵活的 ReFloat 格式，该格式指定矩阵块大小以及指数和分数的位数。为了确定每个块的基数，我们提出了一种优化方法，以最小化原始矩阵块和转换块的指数之间的差异。我们在 ReRAM 中开发了从默认双精度浮点格式到 ReFloat 格式的转换方案、计算过程和低成本浮点处理架构。我们提出了一种优化方法，可以最小化原始矩阵块和转换块的指数之间的差异。我们在 ReRAM 中开发了从默认双精度浮点格式到 ReFloat 格式的转换方案、计算过程和低成本浮点处理架构。我们提出了一种优化方法，可以最小化原始矩阵块和转换块的指数之间的差异。我们在 ReRAM 中开发了从默认双精度浮点格式到 ReFloat 格式的转换方案、计算过程和低成本浮点处理架构。