Topic
Real data type
About: Real data type is a research topic. Over the lifetime, 70 publications have been published within this topic receiving 991 citations.
Papers published on a yearly basis
Papers
TL;DR: In this article, a set of algorithms which given a univariate polynomial with integer coefficients (with possible multiple zeros) and a positive rational error bound, uses infinite-precision integer arithmetic and Sturm's Theorem to compute intervals containing the real zeros of the poynomial and whose lengths are less than the given error bound are discussed.
Abstract: This paper discusses a set of algorithms which given a univariate polynomial with integer coefficients (with possible multiple zeros) and a positive rational error bound, uses infinite-precision integer arithmetic and Sturm's Theorem to compute intervals containing the real zeros of the polynomial and whose lengths are less than the given error bound. The algorithms also provide a simple means of determining the number of real zeros in any interval. Theoretical computing time bounds are developed for the algorithms and some empirical results are reported.
86 citations
TL;DR: In this article, the authors discuss the real numbers as a wreath product and discuss the construction of real numbers by algorithmically describing the operations of binary addition, multiplication, and division on infinite strings of zeros and ones.
38 citations
TL;DR: This article explains the standards evolved by The Institute of Electrical and Electronic Engineers in 1985 and augmented in 2008 to represent floating point numbers and process them, now used by all computer manufacturers while designing floating point arithmetic units so that programs are portable among computers.
Abstract: Floating point numbers are an important data type in computation which is used extensively. Yet, many users do not know the standard which is used in almost all computer hardware to store and process these. In this article, we explain the standards evolved by The Institute of Electrical and Electronic Engineers in 1985 and augmented in 2008 to represent floating point numbers and process them. This standard is now used by all computer manufacturers while designing floating point arithmetic units so that programs are portable among computers.
32 citations
TL;DR: For each algorithm, the resulting sequence is a valid representation of the exact real result of therational, algebraic or transcendental function according to the sequences representing these arguments.
31 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2021 | 1 |
| 2019 | 1 |
| 2017 | 1 |
| 2016 | 2 |
| 2015 | 2 |
| 2013 | 2 |