Converting to and from Dilated Integers

Dilated integers form an ordered group of the Cartesian indices into a d-dimensional array represented in the Morton order. Efficient implementations of its operations can be found elsewhere. This paper offers efficient casting (type)conversions to and from an ordinary integer representation. As the...

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Vydáno v:IEEE transactions on computers Ročník 57; číslo 4; s. 567 - 573
Hlavní autoři: Raman, R., Wise, D.S.
Médium: Journal Article
Jazyk:angličtina
Vydáno: New York IEEE 01.04.2008
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Témata:
Algorithm design and analysis
Analysis of Algorithms
and Problem Complexity: Numerical algorithms
Arrays
Blocking
Cartesian
Casting
Computer architecture
Conversion
Data Structures: Arrays
Indexes
Integers
Memory Structures: Design Styles
problems: computations on matrices
Program processors
Programming
Programming Techniques: General
Representations
Studies
Table lookup
Tables (data)
Three dimensional
Three dimensional displays
problems: computations on matrices
Programming Techniques: General
Data Structures: Arrays
Analysis of Algorithms
Memory Structures: Design Styles
and Problem Complexity: Numerical algorithms
ISSN:0018-9340, 1557-9956
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Popis
Shrnutí:Dilated integers form an ordered group of the Cartesian indices into a d-dimensional array represented in the Morton order. Efficient implementations of its operations can be found elsewhere. This paper offers efficient casting (type)conversions to and from an ordinary integer representation. As the Morton order representation for 2D and 3D arrays attracts more users because of its excellent block locality, the efficiency of these conversions becomes important. They are essential for programmers who would use Cartesian indexing there. Two algorithms for each casting conversion are presented here, including to-and-from dilated integers for both d = 2 and d = 3. They fall into two families. One family uses newly compact table lookup, so the cache capacity is better preserved. The other generalizes better to all d, using processor-local arithmetic that is newly presented as abstract d-ary and (d - 1)-ary recurrences. Test results for two and three dimensions generally favor the former.
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ISSN:0018-9340
1557-9956
DOI:10.1109/TC.2007.70814