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Re: Round-off error?

  • To: mathgroup at smc.vnet.net
  • Subject: [mg131957] Re: Round-off error?
  • From: Bill Rowe <readnews at sbcglobal.net>
  • Date: Wed, 6 Nov 2013 00:36:03 -0500 (EST)
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  • Delivered-to: l-mathgroup@wolfram.com
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On 11/4/13 at 11:17 PM, fateman at cs.berkeley.edu (Richard Fateman)
wrote:

>On 11/1/2013 11:21 PM, Bill Rowe wrote:

>>shows the two machine precision numbers differ by 1 bit and
>>consequently are considered equal by Equal as documented.

>>This type of issue is inherent in floating point arithmetic done on
>>any modern computer.

>This is not at all true.  Mathematica chooses to implement a fuzzy
>version of equality that does not correspond to any hardware
>floating-point operation on any modern computer that I am aware of.

Just to clarify my comment. My intended meaning was (n+1)*dt
will differ from n*dt+dt for some values of n and dt, a
characteristic of any modern computer and a fundamental
characteristic of floating point arithmetic. I had not intended
to imply Mathematica's design for Equal is universal.




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