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Re: Re: floor problems

  • To: mathgroup at
  • Subject: [mg8266] Re: [mg8176] Re: floor problems
  • From: ross at (Ross Moore)
  • Date: Sat, 23 Aug 1997 01:59:04 -0400
  • Sender: owner-wri-mathgroup at

>Tom (toad at wrote:
>: Hello Mathematica users.
>Mathematica is NOT making a mistake, even though if you simply ask for
>the products .7 67 10 and 67 10 .7 you get the same output 469.  This
>is an inherent problem with approximate machine arithmetic -- it is
>NOT associative! And .7 does not have an exact binary representation
>(no matter how many bits of precision you might want).
>To see what's happening, you can look at the actual binary
>representation of the two products.  Do
>$NumberBits[.7 67 10]
>$NumberBits[67 10 .7]
>and you will get different results.  Evidently, when Mathematica takes
>the floor (of the binary representation), it therefore gets different

I beg to differ on the *will* here.
I think *may* is more apt.  :-)

What kind of Macintosh were you using, Tom ?

I tried this on a PowerMac (604) with Mathematica 2.2
and also on a PowerBook 540c with Mathematica 3.0

Both gave the same correct answer of  469
and both gave identical results from $NumberBits ...

...though the PowerMac and PowerBook actually produced
different output with  $NumberBits :

Each claimed 9-bit precision, but differed from the 9th bit onwards:

PowerMac:  11101010100000....            ( 64 bits in all )
PowerBook: 11101010011111...  ...1100    ( 53 consecutive 1s )

Nice example of ...

>Welcome to the world of numerical analysis where, as one wit put it,
>no number that anyone really cares about has ever been calculated exactly.

I like it.


        Ross Moore

Ross Moore                             email: ross at
Mathematics Department                 phone:      +612 9850 8955
Macquarie University                     fax:      +612 9850 8114
Sydney, NSW 2109                    Internet:


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