:<i>Nicolas Chuquet, Renaissance Mathematician: A Study with Extensive Translation of Chuquet's Mathematical Manuscript Completed in 1484</i>

Keen, Ralph; Flegg, Graham; Hay, Cynthia; Moss, Barbara

doi:10.2307/2540328

Cited by 2 publications

(1 citation statement)

References 0 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…A kind of exponential notation for representing huge numbers was described by in his treatise The Sand Reckoner (Hirshfeld 2009). It seems that the first person to consider zero or negative exponents was Nicolas Chuquet (c. 1450-1488) (Flegg, Hay and Moss 1985). Some of the first computers, designed from the 1940s on, provided a floating-point arithmetic.…”

Section: Introductionmentioning

confidence: 99%

Floating-point arithmetic

Boldo¹,

Jeannerod²,

Melquiond³

et al. 2023

Acta Numerica

View full text Add to dashboard Cite

Floating-point numbers have an intuitive meaning when it comes to physics-based numerical computations, and they have thus become the most common way of approximating real numbers in computers. The IEEE-754 Standard has played a large part in making floating-point arithmetic ubiquitous today, by specifying its semantics in a strict yet useful way as early as 1985. In particular, floating-point operations should be performed as if their results were first computed with an infinite precision and then rounded to the target format. A consequence is that floating-point arithmetic satisfies the ‘standard model’ that is often used for analysing the accuracy of floating-point algorithms. But that is only scraping the surface, and floating-point arithmetic offers much more.In this survey we recall the history of floating-point arithmetic as well as its specification mandated by the IEEE-754 Standard. We also recall what properties it entails and what every programmer should know when designing a floating-point algorithm. We provide various basic blocks that can be implemented with floating-point arithmetic. In particular, one can actually compute the rounding error caused by some floating-point operations, which paves the way to designing more accurate algorithms. More generally, properties of floating-point arithmetic make it possible to extend the accuracy of computations beyond working precision.

show abstract

Section: Introductionmentioning

confidence: 99%