Re: floating point

William D Clinger <>
10 Oct 1998 01:05:26 -0400

          From comp.compilers

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[6 later articles]
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From: William D Clinger <>
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.


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