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Re: Beware of adding 0.0

• To: mathgroup at smc.vnet.net
• Subject: [mg50232] Re: Beware of adding 0.0
• From: Bill Rowe <readnewsciv at earthlink.net>
• Date: Sun, 22 Aug 2004 00:19:41 -0400 (EDT)
• Sender: owner-wri-mathgroup at wolfram.com

On 8/21/04 at 3:04 AM, gruszkiewicz at ornl.gov (Mirek Gruszkiewicz)
wrote:

>This is normal:

>o=SetPrecision[1/9, 25] 
>oo=SetPrecision[1./9, 25]

>0.1111111111111111111111111
>0.1111111111111111049432054

>Here is the magic:

>ox = SetPrecision[o + 0.0, 25] 
>ooxx = SetPrecision[oo + 0.0, 25]

>0.1111111111111111049432054 
>0.1111111111111111049432054

If you consider the first example as "normal" why do you see the second as "magic"?

SetPrecision[1./9, 25] is exactly equivalent to 
SetPrecision[SetPrecision[1/9, MachinePrecision], 25]

So not surprisingly SetPrecision[1/9 , 25] doesn't give the same result

Now, 0.0 is a MachinePrecision number. So, you should expect adding 0.0 to any number with higher precision should result in a MachinePrecision number

That is:

SetPrecision[o + 0.0, 25] is equivalent to
SetPrecision[SetPrecision[o, MachinePrecision], 25] which is equivalent to
SetPrecision[SetPrecision[1/9, MachinePrecision], 25]

And

SetPrecision[oo + 0.0, 25] is equivalent to
SetPrecision[SetPrecision[oo, MachinePrecision], 25] which has already been shown to be equivalent to

SetPrecision[SetPrecision[1/9, MachinePrecision], 25] that is the same result is obtained for both ox and ooxx
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