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Re: Re: SetPrecision causes logical comparisons to fail in Mathematica 5.1 on Mac OS X?

• To: mathgroup at smc.vnet.net
• Subject: [mg64182] Re: [mg64173] Re: SetPrecision causes logical comparisons to fail in Mathematica 5.1 on Mac OS X?
• From: Pratik Desai <pdesai1 at umbc.edu>
• Date: Sat, 4 Feb 2006 04:13:35 -0500 (EST)
• References: <200601251345.IAA25867@smc.vnet.net> <dra3g3$m55$1@smc.vnet.net> <200602030658.BAA17085@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

Paul Abbott wrote:

>In article <dra3g3$m55$1 at smc.vnet.net>,
> Andrzej Kozlowski <akoz at mimuw.edu.pl> wrote:
>
>  
>
>>A partial explanation is given in the documentation for Equal:
>>
>>"Approximate numbers are considered equal if they differ in at most  
>>their last eight binary digits (roughly their last two decimal digits)."
>>    
>>
>
>There is a subtlety here: clearly
>
>  RealDigits[1.101`2, 2]
>
>and
>
>  RealDigits[1`2, 2]
>
>do differ in their "last eight" binary digits (actually, in both cases 
>there are only seven binary digits). The sublety is that all following 
>(suppressed) binary digits are 0.
>
>  
>
One can check this out using, NumericalMath`ComputerArithmetic`
In[10]:=
<<NumericalMath`ComputerArithmetic`
ComputerNumber[1.101`2]
ComputerNumber[1.2`2]

Out[11]=
0

Out[12]=
0

>>The workaround is never to set anything to have so few digits of  
>>precision; there is no reason at all to do so. Mathematica's  
>>"significance" arithmetic is an approximation to true interval  
>>arithmetic that works well only at high precision.
>>    
>>
>
>But if the application is fixed precision arithmetic then one could use 
>RealDigits (in base 2 or 10). For example,
>
>  RealDigits[1.101`2, 2] == RealDigits[1`2, 2]
>
>  RealDigits[1.101`2] == RealDigits[1`2]
>
>  
>
>>If you only wanted to reduce the number of digits displayed you  
>>should use
>>
>>NumberForm[1.101, 2]
>>    
>>
>
>Or set the PrintPrecision options using the Option Inspector.
>
>Cheers,
>Paul
>
>_______________________________________________________________________
>Paul Abbott                                      Phone:  61 8 6488 2734
>School of Physics, M013                            Fax: +61 8 6488 1014
>The University of Western Australia         (CRICOS Provider No 00126G)    
>AUSTRALIA                               http://physics.uwa.edu.au/~paul
>
>  
>

• References:
  • Re: SetPrecision causes logical comparisons to fail in Mathematica 5.1 on Mac OS X?
    • From: Paul Abbott <paul@physics.uwa.edu.au>