10 Oct 1998 01:05:26 -0400

Related articles |
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Re: inlining + optimization = nuisance bugs luddy@concmp.com (Luddy Harrison) (1998-09-29) |

Re: floating point, was inlining + optimization = nuisance bugs chase@world.std.com (David Chase) (1998-10-04) |

Re: floating point will@ccs.neu.edu (William D Clinger) (1998-10-05) |

Re: floating point comments@cygnus-software.com (Bruce Dawson) (1998-10-07) |

Re: floating point will@ccs.neu.edu (William D Clinger) (1998-10-10) |

Re: floating point dmcq@fano.demon.co.uk (David McQuillan) (1998-10-13) |

Re: floating point darcy@CS.Berkeley.EDU (Joseph D. Darcy) (1998-10-19) |

Re: floating point darcy@usul.CS.Berkeley.EDU (1998-10-24) |

Re: floating point comments@cygnus-software.com (Bruce Dawson) (1998-11-01) |

Re: floating point comments@cygnus-software.com (Bruce Dawson) (1998-11-01) |

Re: floating point darcy@usul.CS.Berkeley.EDU (1998-11-06) |

[6 later articles] |

From: | William D Clinger <will@ccs.neu.edu> |

Newsgroups: | comp.compilers |

Date: | 10 Oct 1998 01:05:26 -0400 |

Organization: | Northeastern University |

References: | 98-09-164 98-10-018 98-10-040 98-10-056 |

Keywords: | arithmetic |

Concerning the frequency of incorrect results caused by double

rounding to IEEE extended precision and then again to IEEE double

precision, Bruce Dawson wrote:

*> Although, with rounding set to double precision they probably do get*

*> them 99.999% of the time - any other guesses?*

About 99.9755859375 % = 1 - 2^12. The result of double rounding won't

be wrong unless the low-order 11 bits of the 64-bit significand are

10000000000. When that bit pattern occurs, then the result of

rounding a second time to double precision's 53-bit significand will

be wrong about half the time.

Will

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