Recently some scientific computing users have discovered that they can replace 64-bit with 32-bit operations for carefully selected portions of the computation, and still retain acceptable accuracy in the final results. In addition, developers of some emerging applications such as machine learning have discovered that they can achieve acceptable results with only 16-bit precision in certain portions of the code. At the other end of the precision spectrum, some users have explored using 128-bit arithmetic in some particularly demanding applications, while others have done computations using much higher precision—hundreds or even thousands of digits. Such work has underscored the need to develop new mathematical and software frameworks to support a dynamically variable level of precision, and, more generally, to rethink what “reproducibility” means in a variable precision environment. This article summarizes some of the work being done in this arena, and lists research problems that need to be solved.

中文翻译：

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再现性和可变精度计算

最近，一些科学计算用户发现，他们可以用 32 位运算替换 64 位运算，用于精心选择的计算部分，并且在最终结果中仍保持可接受的准确性。此外，一些新兴应用程序（例如机器学习）的开发人员发现，他们可以在代码的某些部分仅以 16 位精度获得可接受的结果。在精度范围的另一端，一些用户已经探索在一些特别苛刻的应用程序中使用 128 位算法，而其他用户则使用更高的精度进行计算——数百甚至数千位数字。此类工作强调需要开发新的数学和软件框架，以支持动态可变的精度水平，更一般地说，重新思考“再现性”在可变精度环境中的含义。本文总结了该领域的一些工作，并列出了需要解决的研究问题。