Floating point numbers are real numbers
arXiv:1605.092027 citationsh-index: 12
Originality Synthesis-oriented
AI Analysis
For numerical analysts and computer scientists, this work offers theoretically grounded error bounds for fundamental floating point operations.
The authors use continuous mathematics to derive new, sharp results for evaluating sums, square roots, and dot products in floating point arithmetic, providing simple error bounds.
Floating point arithmetic allows us to use a finite machine, the digital computer, to reach conclusions about models based on continuous mathematics. In this article we work in the other direction, that is, we present examples in which continuous mathematics leads to sharp, simple and new results about the evaluation of sums, square roots and dot products in floating point arithmetic.