This paper discusses both the theoretical and statistical errors obtained by various well-known dot products, from the canonical to pairwise algorithms, and introduces a new and mo...
Anthony M. Castaldo, R. Clint Whaley, Anthony T. C...
The IEEE Standard 754-1985 for Binary Floating-Point Arithmetic [1] was revised [2], and an important addition is the definition of decimal floating-point arithmetic. This is inte...
Marius Cornea, Cristina Anderson, John Harrison, P...
Studying floating point arithmetic, authors have shown that the implemented operations (addition, subtraction, multiplication, division and square root) can compute a result and a...
Decreasing feature sizes allow additional functionality to be added to future microprocessors to improve the performance of important application domains. As a result of rapid gro...
Given a vector of floating-point numbers with exact sum s, we present an algorithm for calculating a faithful rounding of s, i.e. the result is one of the immediate floating-point ...