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Re: Beware of adding 0.0


On 8/20/04 at 4:58 AM, paul_tan at aoI.com (paul) wrote:

>In Mathematica 5.0, I get a very strange result when I add 0.0 to a
>number, why is this?  See below:

>p = SetPrecision[314159265358979323, 25]
>q = SetPrecision[314159265358979323., 25]
>r = SetPrecision[314159265358979323.00000000000000000000, 25]
>s = SetPrecision[p + 0.0, 25]

>\!\(3.14159265358979323`25.*^17\)
>Out[47]=
>\!\(3.14159265358979323`25.*^17\)
>Out[48]=
>\!\(3.14159265358979323`25.*^17\)
>Out[49]=
>\!\(3.14159265358979328`25.*^17\)   *****NOTICE the 28 instead of 23 at the
>end, why does this happen? *******

Look closely at what you are doing, particularly the sequence. You are adding a machine precision number (0.0) to a higher precision number. The precision of this sum will be machine precision. Then you are asking Mathematica to raise the precision of a machine precision number. Once you lose precision by performing the addition you cannot gain it back by using SetPrecision.
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