# On the number of iterations required by Von Neumann addition

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications (2001)

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

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topGrübel, Rudolf, and Reimers, Anke. "On the number of iterations required by Von Neumann addition." RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications 35.2 (2001): 187-206. <http://eudml.org/doc/92661>.

@article{Grübel2001,

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 - Informatique Théorique et Applications},

keywords = {carry propagation; limit distributions; total variation distance; logarithmic periodicity; Gumbel distributions; discretization; large deviations; multiprecision arithmetic},

language = {eng},

number = {2},

pages = {187-206},

publisher = {EDP-Sciences},

title = {On the number of iterations required by Von Neumann addition},

url = {http://eudml.org/doc/92661},

volume = {35},

year = {2001},

}

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 - Informatique Théorique et Applications

PY - 2001

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/92661

ER -

## References

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