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Re: Mathematica Weirdness

  • To: mathgroup at smc.vnet.net
  • Subject: [mg116750] Re: Mathematica Weirdness
  • From: Bill Rowe <readnews at sbcglobal.net>
  • Date: Sat, 26 Feb 2011 06:06:34 -0500 (EST)

On 2/25/11 at 6:32 AM, sebhofer at gmail.com (Sebastian) wrote:

>On Feb 24, 12:26 pm, Daniel Lichtblau <d... at wolfram.com> wrote:
>
>>If instead you numerically evaluate using precision tracking you
>>will get a positive result.

>I'm curious: why does N[#,MachinePrecisison] evaluate to the wrong
>result while N[#,n], where n is any number (also smaller than 16),
>evaluates to the correct result? What is so special about
>MachinePrecision?

When using MachinePrecision, floating point operations are done
by your FPU and are dependent on the specifics of your platform.
Using anything other than MachinePrecision invokes Mathematica's
arbitrary precision algorithms and it is Mathematica that
controls the floating point operations rather than simply
handing things over to the FPU.

The advantage of Mathematica algorithms over hardware (FPU) can
be a better result. The cost is slower execution.



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