### Abstract

We describe NC algorithms for doing exact arithmetic with real algebraic numbers in the signcoded representation introduced by Coste and Roy [CoR 1988]. We present polynomial sized circuits of depth O(log^{3} N) for the monadic operations -α, 1/α, as well as α + r, α · r, and sgn (α - r), where r is rational and α is real algebraic. We also present polynomial sized circuits of depth O(log^{7} N) for the dyadic operations α+β, α·β, and sgn(α-β), where α and β are both real algebraic. Our algorithms employ a strengthened form of the NC polynomial-consistency algorithm of Ben-Or, Kozen, and Reif [BKR 1986].

Original language | English (US) |
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Title of host publication | ISSAC '90 Proceedings of International Symposium on Symbolic and Algebraic Computation |

Editors | Shunro Watanabe, Morio Nagata |

Publisher | Publ by ACM |

Pages | 120-126 |

Number of pages | 7 |

ISBN (Print) | 0201548925 |

State | Published - 1990 |

Event | ISSAC '90 Proceedings of International Symposium on Symbolic and Algebraic Computation - Tokyo, Jpn Duration: Aug 20 1990 → Aug 24 1990 |

### Other

Other | ISSAC '90 Proceedings of International Symposium on Symbolic and Algebraic Computation |
---|---|

City | Tokyo, Jpn |

Period | 8/20/90 → 8/24/90 |

### Fingerprint

### ASJC Scopus subject areas

- Engineering(all)

### Cite this

*ISSAC '90 Proceedings of International Symposium on Symbolic and Algebraic Computation*(pp. 120-126). Publ by ACM.

**Arithmetic with real algebraic numbers is in NC.** / Mishra, Bhubaneswar; Pedersen, Paul.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*ISSAC '90 Proceedings of International Symposium on Symbolic and Algebraic Computation.*Publ by ACM, pp. 120-126, ISSAC '90 Proceedings of International Symposium on Symbolic and Algebraic Computation, Tokyo, Jpn, 8/20/90.

}

TY - GEN

T1 - Arithmetic with real algebraic numbers is in NC

AU - Mishra, Bhubaneswar

AU - Pedersen, Paul

PY - 1990

Y1 - 1990

N2 - We describe NC algorithms for doing exact arithmetic with real algebraic numbers in the signcoded representation introduced by Coste and Roy [CoR 1988]. We present polynomial sized circuits of depth O(log3 N) for the monadic operations -α, 1/α, as well as α + r, α · r, and sgn (α - r), where r is rational and α is real algebraic. We also present polynomial sized circuits of depth O(log7 N) for the dyadic operations α+β, α·β, and sgn(α-β), where α and β are both real algebraic. Our algorithms employ a strengthened form of the NC polynomial-consistency algorithm of Ben-Or, Kozen, and Reif [BKR 1986].

AB - We describe NC algorithms for doing exact arithmetic with real algebraic numbers in the signcoded representation introduced by Coste and Roy [CoR 1988]. We present polynomial sized circuits of depth O(log3 N) for the monadic operations -α, 1/α, as well as α + r, α · r, and sgn (α - r), where r is rational and α is real algebraic. We also present polynomial sized circuits of depth O(log7 N) for the dyadic operations α+β, α·β, and sgn(α-β), where α and β are both real algebraic. Our algorithms employ a strengthened form of the NC polynomial-consistency algorithm of Ben-Or, Kozen, and Reif [BKR 1986].

UR - http://www.scopus.com/inward/record.url?scp=0025559994&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0025559994&partnerID=8YFLogxK

M3 - Conference contribution

SN - 0201548925

SP - 120

EP - 126

BT - ISSAC '90 Proceedings of International Symposium on Symbolic and Algebraic Computation

A2 - Watanabe, Shunro

A2 - Nagata, Morio

PB - Publ by ACM

ER -