Re: {Precision@N[2^1024],N[2^1024]===\$MaxMachineNumber}

• To: mathgroup at smc.vnet.net
• Subject: [mg80721] Re: {Precision@N[2^1024],N[2^1024]===\$MaxMachineNumber}
• From: Bill Rowe <readnewsciv at sbcglobal.net>
• Date: Thu, 30 Aug 2007 02:31:20 -0400 (EDT)

```On 8/29/07 at 4:10 AM, chris at chiasson.name (Chris Chiasson) wrote:

>on my computer, this command gives {15.9546,False}

>However, I think the result is supposed to be
>{MachinePrecision,True}

>Is there something wrong with N?

I don't think so. On my machine there is a slight difference
between \$MaxMachineNumber and N[2^1024] that can be seen using RealDigits

In[1]:= RealDigits[2^1024 // N]

Out[1]= {{1,7,9,7,6,9,3,1,3,4,8,6,2,3,1,6},309}

In[2]:= RealDigits[\$MaxMachineNumber]

Out[2]= {{1,7,9,7,6,9,3,1,3,4,8,6,2,3,1,5},309}

In[3]:= \$Version

Out[3]= 6.0 for Mac OS X PowerPC (32-bit) (June 19, 2007)

Hence, the false result returned when testing if these two
numbers are identical

>My computer is an Athlon XP running Windows XP SP2.

>Also, why does ByteCount@\$MaxMachineNumber give 16 ? I'm sure I am
>missing something, but I thought a double precision floating point
>number would only take up 8 bytes.

ByteCount returns the amount of memory Mathematica uses
internally to store an object. This will be the number of bytes
the object takes plus any additional information or tags
Mathematica associates with the object. The point is the value
returned by ByteCount cannot be assumed to be just the amount of
memory needed store a number.
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```

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