Title :
New Arithmetic Algorithms for Hereditarily Binary Natural Numbers
Author_Institution :
Deptartment of Comput. Sci. & Eng., Univ. of North Texas, Denton, TX, USA
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;
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
DOI :
10.1109/SYNASC.2014.23
