CSR: SMALL: Design Validation Methods for Reliable and Efficient Floating-Point

浮点运算使计算机能够顺利而有效地处理诸如原子直径或恒星直径等变化很大的数值，并将这些数值装入标准宽度的计算机文字中。不幸的是，当对浮点数执行计算时，会引入舍入错误，这通常会导致现实世界的灾难，例如错误的导弹发射。虽然使用较大的计算机字宽可以最大限度地减少这些错误，但它也减慢了计算速度，增加了内存和能源需求。这个项目可能会产生广泛的影响，为科学程序员开发更可靠的浮点程序提供急需的调试支持。该项目开发了估算舍入误差的新方法，从而帮助程序员获得高效的浮点计算机代码。特别强调的是处理棘手的情况，如平方数和取他们的三角值，以前的研究没有足够先进。通过开发强大且自动化的精确估计工具，它允许程序员调整他们的代码并在不失去准确性的情况下吝啬地选择单词宽度。研究人员利用这些工具开发教学材料和基于实践经验的最佳实践，帮助那些通常没有教过浮点运算陷阱的学生。

Floating-point arithmetic enables computers to smoothly andefficiently handle widely varying magnitudes such as the diameter ofan atom or that of a star, and fit these measures within computerwords that come in standard widths. Unfortunately,when calculations are performed on floating numbers, round-off errorsare introduced, often causing real-world disasters, such as errantmissile launches. While employing large computer word widths canminimize these errors, it also slows down computations, increasestheir memory, and energy needs. This project could have a broad impactby providing much needed debug support for scientific programmers to develop more reliable floating point programs.This project develops novel ways to estimate round-off errors, thushelping programmers arrive at efficient floating-point computer codes.Special emphasis is placed on handling tricky cases such as squaringnumbers and taking their trigonometric values where prior research hadnot sufficiently advanced. By developing powerful and automated toolsfor precision estimation, it allows programmers to tune their codesand pick word widths parsimoniously while not losing accuracy. The investigators use these tools to develop pedagogical material and bestpractices based on hands-on experience that helps inform students whotypically are not taught the pitfalls of floating-point arithmetic.