DocumentCode
261985
Title
New Arithmetic Algorithms for Hereditarily Binary Natural Numbers
Author
Tarau, Paul
Author_Institution
Deptartment of Comput. Sci. & Eng., Univ. of North Texas, Denton, TX, USA
fYear
2014
fDate
22-25 Sept. 2014
Firstpage
109
Lastpage
116
Abstract
Hereditarily binary numbers are a tree-based number representation derived from a bijection between natural numbers and iterated applications of two simple functions corresponding to bijective base 2 numbers. This paper describes several new arithmetic algorithms on hereditarily binary numbers that, while within constant factors from their traditional counterparts for their average case behavior, make tractable important computations that are impossible with traditional number representations.
Keywords
digital arithmetic; number theory; trees (mathematics); arithmetic algorithms; bijective base 2 numbers; hereditarily binary natural numbers; iterated applications; tree-based number representation; Benchmark testing; Complexity theory; Equations; Libraries; Newton method; Performance evaluation; Poles and towers; arithmetic computations with giant numbers; compact representation of large prime numbers; compressed number representations; hereditary numbering systems;
fLanguage
English
Publisher
ieee
Conference_Titel
Symbolic and Numeric Algorithms for Scientific Computing (SYNASC), 2014 16th International Symposium on
Conference_Location
Timisoara
Print_ISBN
978-1-4799-8447-3
Type
conf
DOI
10.1109/SYNASC.2014.23
Filename
7034673
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