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TAPSOFT

1995

Springer

1995

Springer

The Pentium computer chip’s division algorithm relies on a table from which ﬁve entries were inadvertently omitted, with the result that 1738 single precision dividenddivisor pairs yield relative errors whose most signiﬁcant bit is uniformly distributed from the 14th to the 23rd (least signiﬁcant) bit. This corresponds to a rate of one error every 40 billion random single precision divisions. The same general pattern appears at double precision, with an error rate of one in every 9 billion divisions or 75 minutes of division time. These rates assume randomly distributed data. The distribution of the faulty pairs themselves however is far from random, with the eﬀect that if the data is so nonrandom as to be just the constant 1, then random calculations started from that constant produce a division error once every few minutes, and these errors will sometimes propagate many more steps. A much higher rate yet is obtained when dividing small (< 100) integers “bruised” by ...

Added |
26 Aug 2010 |

Updated |
26 Aug 2010 |

Type |
Conference |

Year |
1995 |

Where |
TAPSOFT |

Authors |
Vaughan R. Pratt |

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