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Speculatively Redundant Continued Logarithm Representation
November 2010 (vol. 59 no. 11)
pp. 1441-1454
ASCII Text
x 
 
Tomáš Brabec, "Speculatively Redundant Continued Logarithm Representation," IEEE Transactions on Computers, vol. 59, no. 11, pp. 1441-1454, November, 2010.
 
 
BibTex
x
 
@article{ 10.1109/TC.2010.110,
author = {Tomáš Brabec},
title = {Speculatively Redundant Continued Logarithm Representation},
journal ={IEEE Transactions on Computers},
volume = {59},
number = {11},
issn = {0018-9340},
year = {2010},
pages = {1441-1454},
doi = {http://doi.ieeecomputersociety.org/10.1109/TC.2010.110},
publisher = {IEEE Computer Society},
address = {Los Alamitos, CA, USA},
}
 
 
RefWorks Procite/RefMan/Endnote
x 
 
TY - JOUR
JO - IEEE Transactions on Computers
TI - Speculatively Redundant Continued Logarithm Representation
IS - 11
SN - 0018-9340
SP1441
EP1454
EPD - 1441-1454
A1 - Tomáš Brabec,
PY - 2010
KW - Computer arithmetic
KW - representation of numbers
KW - continued fraction
KW - redundancy
KW - computable real numbers
KW - exact arithmetic.
VL - 59
JA - IEEE Transactions on Computers
ER -
 
Tomáš Brabec, Czech Technical University in Prague, Prague
Continued logarithms, as originally introduced by Gosper, represent a means for exact rational arithmetic, but their application to exact real arithmetic is limited by the uniqueness of their representation. This is quite unfortunate, as this representation seems promising for efficient hardware implementation. We propose an idea of making the representation redundant using speculative recognition of noncomputable cases. This approach solves the problem of real number computability, preserves most of the beneficial properties of continued logarithms, and only moderately affects complexity of arithmetic algorithms, thus, keeping the prospect of efficient implementation.

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Index Terms:
Computer arithmetic, representation of numbers, continued fraction, redundancy, computable real numbers, exact arithmetic.
Citation:
Tomáš Brabec, "Speculatively Redundant Continued Logarithm Representation," IEEE Transactions on Computers, vol. 59, no. 11, pp. 1441-1454, Nov. 2010, doi:10.1109/TC.2010.110
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