On the number of iterations required by Von Neumann addition

Rudolf Grübel; Anke Reimers

RAIRO - Theoretical Informatics and Applications (2010)

  • Volume: 35, Issue: 2, page 187-206
  • ISSN: 0988-3754

Abstract

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We investigate the number of iterations needed by an addition algorithm due to Burks et al. if the input is random. Several authors have obtained results on the average case behaviour, mainly using analytic techniques based on generating functions. Here we take a more probabilistic view which leads to a limit theorem for the distribution of the random number of steps required by the algorithm and also helps to explain the limiting logarithmic periodicity as a simple discretization phenomenon.

How to cite

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Grübel, Rudolf, and Reimers, Anke. "On the number of iterations required by Von Neumann addition." RAIRO - Theoretical Informatics and Applications 35.2 (2010): 187-206. <http://eudml.org/doc/221982>.

@article{Grübel2010,
abstract = { We investigate the number of iterations needed by an addition algorithm due to Burks et al. if the input is random. Several authors have obtained results on the average case behaviour, mainly using analytic techniques based on generating functions. Here we take a more probabilistic view which leads to a limit theorem for the distribution of the random number of steps required by the algorithm and also helps to explain the limiting logarithmic periodicity as a simple discretization phenomenon. },
author = {Grübel, Rudolf, Reimers, Anke},
journal = {RAIRO - Theoretical Informatics and Applications},
keywords = {Carry propagation; limit distributions; total variation distance; logarithmic periodicity; Gumbel distributions; discretization; large deviations.; multiprecision arithmetic},
language = {eng},
month = {3},
number = {2},
pages = {187-206},
publisher = {EDP Sciences},
title = {On the number of iterations required by Von Neumann addition},
url = {http://eudml.org/doc/221982},
volume = {35},
year = {2010},
}

TY - JOUR
AU - Grübel, Rudolf
AU - Reimers, Anke
TI - On the number of iterations required by Von Neumann addition
JO - RAIRO - Theoretical Informatics and Applications
DA - 2010/3//
PB - EDP Sciences
VL - 35
IS - 2
SP - 187
EP - 206
AB - We investigate the number of iterations needed by an addition algorithm due to Burks et al. if the input is random. Several authors have obtained results on the average case behaviour, mainly using analytic techniques based on generating functions. Here we take a more probabilistic view which leads to a limit theorem for the distribution of the random number of steps required by the algorithm and also helps to explain the limiting logarithmic periodicity as a simple discretization phenomenon.
LA - eng
KW - Carry propagation; limit distributions; total variation distance; logarithmic periodicity; Gumbel distributions; discretization; large deviations.; multiprecision arithmetic
UR - http://eudml.org/doc/221982
ER -

References

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