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Re: Re: Odd behavior?

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  • Subject: [mg101897] Re: [mg101886] Re: Odd behavior?
  • From: Mark McClure <mcmcclur at>
  • Date: Tue, 21 Jul 2009 03:52:32 -0400 (EDT)
  • References: <> <h41f90$rmb$>

On Mon, Jul 20, 2009 at 7:21 PM, Richard Fateman <fateman at>wrote:

> I agree with DrMajorBob that 0 is the wrong answer, in the context of
> double-float machine-precision arithmetic.  The answer is
> -2^(-53)-2^(-52), or -3.33... d-16 approximately.

Certainly, (5.1 - 4.5) - 0.6 = -3.3307e-16 in IEEE double-float arithmetic.
But, 5.1 + (-4.5 - 0.6) = 0.0.  Now, IEEE specifies a lot (like the addition
two floating point numbers) but also leaves a lot unspecified.  Is the sum
a list of numbers specified in the IEEE standard?  I honestly don't know.
Certainly, Kahan summation yields -3.3307e-16 and this is what I would
expect from any good tool in numerical analysis.

> That is not the question posted, however.  The question was, what
> changed between version 6 and version 7. (see below)
> since I do not currently have a copy of version 7 to play with, I can
> only speculate that (finally!) access to machine-precision arithmetic
> has been improved.  And that the user of Mathematica can view,
> unimpeded, the actual machine arithmetic results, for the first time.

Actually, V5.2 returns the expected -3.3307e-16!

Mark McClure

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