The typical processors used for scientific computing have fixed-width data-paths. This implies that mathematical libraries were specifically developed to target each of these fixed precisions (binary16, binary32, binary64). However, to address the increasing energy consumption and throughput requirements of scientific applications, library and hardware designers are moving beyond this one-size-fits-all approach. In this article we propose to study the effects and benefits of using user-defined floating-point formats and target accuracies in calculations involving mathematical functions. Our tool collects input-data profiles and iteratively explores lower precisions for each call-site of a mathematical function in user applications. This profiling data will be a valuable asset for specializing and fine-tuning mathematical function implementations for a given application. We demonstrate the tool's capabilities on SGP4, a satellite tracking application. The profile data shows the potential for specialization and provides insight into answering where it is useful to provide variable-precision designs for elementary function evaluation.

中文翻译：

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用于代码分析和优化的自定义精度数学库探索

用于科学计算的典型处理器具有固定宽度的数据路径。这意味着数学库是专门针对这些固定精度（binary16、binary32、binary64）中的每一个而开发的。然而，为了解决科学应用日益增长的能耗和吞吐量要求，图书馆和硬件设计人员正在超越这种一刀切的方法。在本文中，我们建议研究在涉及数学函数的计算中使用用户定义的浮点格式和目标精度的影响和好处。我们的工具收集输入数据配置文件，并迭代地探索用户应用程序中数学函数的每个调用点的较低精度。对于特定应用程序的专业化和微调数学函数实现，此分析数据将是宝贵的资产。我们在卫星跟踪应用程序 SGP4 上演示了该工具的功能。配置文件数据显示了专业化的潜力，并提供了深入了解为基本函数评估提供可变精度设计的有用之处。