Re: Re: Odd behavior?
- To: mathgroup at smc.vnet.net
- Subject: [mg101897] Re: [mg101886] Re: Odd behavior?
- From: Mark McClure <mcmcclur at unca.edu>
- Date: Tue, 21 Jul 2009 03:52:32 -0400 (EDT)
- References: <200907191115.HAA20885@smc.vnet.net> <h41f90$rmb$1@smc.vnet.net>
On Mon, Jul 20, 2009 at 7:21 PM, Richard Fateman <fateman at cs.berkeley.edu>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 of two floating point numbers) but also leaves a lot unspecified. Is the sum of 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
- References:
- Odd behavior?
- From: elliot <esadlon@stevens.edu>
- Odd behavior?