Approximate computing techniques have been successful in reducing computation and power costs in several domains. However, error sensitive applications in high-performance computing are unable to benefit from existing approximate computing strategies that are not developed with guaranteed error bounds. While approximate computing techniques can be developed for individual high-performance computing applications by domain specialists, this often requires additional theoretical analysis and potentially extensive software modification. Hence, the development of low-level error-bounded approximate computing strategies that can be introduced into any high-performance computing application without requiring additional analysis or significant software alterations is desirable. In this paper, we provide a contribution in this direction by proposing a general framework for designing error-bounded approximate computing strategies and apply it to the dot product kernel to develop qdot -- an error-bounded approximate dot product kernel. Following the introduction of qdot, we perform a theoretical analysis that yields a deterministic bound on the relative approximation error introduced by qdot. Empirical tests are performed to illustrate the tightness of the derived error bound and to demonstrate the effectiveness of qdot on a synthetic dataset, as well as two scientific benchmarks -- Conjugate Gradient (CG) and the Power method. In particular, using qdot for the dot products in CG can result in a majority of components being perforated or quantized to half precision without increasing the iteration count required for convergence to the same solution as CG using a double precision dot product.

中文翻译：

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QDOT：用于近似高性能计算的量化点积内核

近似计算技术已成功地减少了多个领域的计算和功耗成本。但是，高性能计算中对错误敏感的应用程序无法从没有以保证的错误范围开发的现有近似计算策略中受益。虽然领域专家可以为各个高性能计算应用程序开发近似的计算技术，但这通常需要进行额外的理论分析并可能需要大量的软件修改。因此，需要开发可以引入到任何高性能计算应用程序中而无需进行额外分析或进行重大软件更改的低级错误边界近似计算策略。在本文中，我们为此提出了一个通用框架，以设计误差有界的近似计算策略，并将其应用于点积内核以开发qdot（误差有界的近似点积内核），从而为这一方向做出了贡献。引入qdot之后，我们进行了理论分析，得出了由qdot引入的相对逼近误差的确定性界限。进行了经验测试，以说明导出的误差范围的紧密度，并证明qdot在合成数据集以及两个科学基准（共轭梯度（CG）和幂方法）上的有效性。特别是，